From 997c91fcf0aacc288a3934418bbc3c6a0b4ed103 Mon Sep 17 00:00:00 2001 From: williamfreigang <40257048+williamfreigang@users.noreply.github.com> Date: Fri, 24 Aug 2018 16:22:27 -0600 Subject: [PATCH 01/32] WIP v5 Ischemia Tutorial Major WIP --- IschemiaTutorial.md | 1 + 1 file changed, 1 insertion(+) create mode 100644 IschemiaTutorial.md diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md new file mode 100644 index 0000000..1f54199 --- /dev/null +++ b/IschemiaTutorial.md @@ -0,0 +1 @@ +# Ischemia Model tutorial #### SCIRun 4.7 Documentation ``` Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah ``` ``` SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc ``` This project was supported by grants from the National Center for Research Resources **(5P41RR012553-14)** and the National Institute of General Medical Sciences **(8 P41 GM103545-14)** from the National Institutes of Health. ``` Author(s): Jeroen Stinstra, Darrell Swenson ``` ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. ``` CHAPTER 1. OVERVIEW 3 ``` ``` In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ``` ``` ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: ``` ``` φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ``` ``` ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. ``` #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility ``` The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. ``` **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. ``` CHAPTER 1. OVERVIEW 5 ``` #### Chapter 2 # Reading and Visualization of Image # Data ``` Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets ``` #### 2.1 Loading The Dataset ``` We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in theBasicTutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main ``` ``` Figure 2.1. The main SCIRun window (File #1) ``` **6 Chapter 2** Figure 2.2. Finding a module and opening its GUI (File #2) SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. ``` CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 ``` ``` Figure 2.3. Select a file name and a file type (File #3) ``` ``` By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type ``` **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which ``` CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 ``` ``` Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) ``` ``` will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modulesConvertFieldsToTexture,ShowTextureS- lices,CreateStandardColorMaps,ShowSceneand connect the modules as depicted in figure 2.5. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figure 2.5 has been entered in the Network Editor, open up theUI of theShowTextureSlicesmodule and select to show the X, Y, and Z plane as indicated in the figure. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoviewin the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.6. By pressingShiftand clicking with the left mouse button on the light blue widget in the center of the viewer, the currently visible plane of the of 3D dataset can be altered. By clicking on theUIofGenerateStandardColorMapsmodule, the colormap of the current visualization can be altered (illustrated in figure 2.7). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In ``` **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. ``` CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 ``` ``` Figure 2.7. Network for checking contents of the file ``` **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets ``` CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 ``` ``` Figure 3.2. Reading in two datasets ``` #### 3.1 Volume Renderer and Clipping Planes ``` In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use theShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as theShowTextureSlicesmodule, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use theHeartMRI.nrrdand HeartMRI-Perfusionbed.nrrdas the two datasets for the two ReadFieldmodules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left ``` **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrdand a diffusion tensor image (DTI)HeartMRI-FiberOrientation.nrrd. Using theSeg3Dprogram the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrdandHeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up theViewScenemodule and pressConfigure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select theObjectstab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try theClippingtab, which will allow to clip the visualization. Open up the Clippingtab and switch on theClipping Plane Visiblebutton, next drag theXslider to 1.0. Now use theDslider to slide the clipping plane along the X-axis. The clipping widget has been configured, so thatDcorresponds to the full range of X that is spanned ``` CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 ``` ``` Figure 3.4. Slicing the dataset ``` ``` by the two images that are displayed in the viewer window. By draggingDfrom -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, pressPlane 2and then activate this plane by selecting theClipping Plane Visibleonce more. To make it easier to generate a thin slice, select the theReverse Clipping Plane Normaloption for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up theUIof theShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. ``` #### 3.2 Isosurfacing and Mesh Fairing ``` In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding theExtractIsosurface,FairMeshandShowFieldmodules to the network, as depicted in figure 3.5. TheExtractIsosurfaceshould get its input from the module that reads the perfusion bed field. Make sure to select theQuantitytab in the UIof the ExtractIsosurfacemodule as depicted in figure 3.5. TheExtractIsosurfacemodule extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the ``` **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. TheFairMesh module takes the output from theExtractIsosurfacemodule and smoothes out the surface. Because the data is discretized the isosurface will bestair-stepped. TheFairMeshmodule takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use theShowTextureVolumeto display the surface. Instead we use ``` CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 ``` ``` Figure 3.6. Coupling Two ViewScene Windows ``` ``` theShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into theViewScenemodule, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, theViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from theViewScenemodule. Press theNewWindowbutton to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the VolumeRendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press theLockViewbutton to unlock the window. When pressing the button theLockViewbutton changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the ``` **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select theViewsmenu at the top of the window and select theOther Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressingLon the keyboard when the window is selected. Likewise a view from an other window can be copied by pressingctrl 1to copy the view from the first window,ctrl 2for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Autoview also has a keyboard shortcut and is activated by pressing 0. ``` CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 ``` #### 3.3 Resampling and Viewing Glyphs ``` After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using theReadFieldmodule and the data will be translated into a LatVolMesh again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network:ResampleRegularMesh,Map- FieldDataOntoNodes,CalculateFieldData2, andShowFieldGlyphs. TheResampleRegularMeshmodule resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply theMapFieldDataOntoNodesto map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, calledCalculateFieldData. There are currently three versions of this module available calledCalculateFieldData, CalculateFieldData2, andCalculateFieldData3. The sole difference between these modules is the number of field input ports. As in this case we want to use two fields as input we use theCalculateFieldData2module. TheCalculateFieldData2operates by taking data from the two input fields as two input streams and applying the operation specified inside theUIof the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formulaDATA1is the data from the first field andDATA2is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. TheCalculateFieldData2defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press theParser Helpbutton in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Typein the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output ``` **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally theShowFieldGlyphsallows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the properUI. To display the vectors select theVectorstab and enable the check buttonShow Vectors. Also disable theRender glyphs below thresholdsetting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below theVectorThreshold. In this example we will render Vectors as cones by selecting theVector Display Type in the UI and we useRGB Conversionas the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the the size of theVectorScale to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the ``` CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 ``` ``` Figure 3.9. The UI of the ShowFieldGlyphs Module ``` ``` vectors are pointing along that matters in this case. To make the vectors point in both directions, set the optionRender bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. ``` **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data ``` CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 ``` #### Chapter 4 # Building a Tetrahedral Mesh ``` Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes ``` #### 4.1 Building a Tetrahedral Mesh ``` In order to build a physical model out of the imaging data, we need to generate a computa- tional mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules calledInterfaceWithTetGenand WriteField. TheInterfaceWithTetGenmodule lets SCIRun communicate with TetGen for gen- erating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated byExtractIsosurfaceneeds to be smoothed. We use theFairMeshmodule for this again. When opening theUIof theInterfaceWithTetGenmodule, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the-Y,-q, and the-aoption in theUI. The-Yoption lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag-qenforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the-aflag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct theReadFieldmodule to read the fileHeartMRI-Segmentation.nrrd; theResampleRegularMeshmodule can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes in stead of hours. ``` **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh ``` CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 ``` ``` Figure 4.2. Image of the Tetrahedral Mesh ``` ``` TheExtractIsosurfacemodule should be set to theQuantitytap and we should be com- puting only one isosurface. TheInterfaceWithTetGenmodule options should be set as indicated in figure 4.1. Finally, theWriteFieldmodule should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in theUIof the module and pressSetto set the name of the file that will be written. Also open up theShowFieldmodule and disable theShow Nodesand Show Edges, although SCIRun can renderer these without any problems. After pressingExecute Allto execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). ``` **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. ``` CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 ``` ``` Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields ``` **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. ``` The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition ``` ``` CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 ``` ``` of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, ``` **30 Chapter 5** Figure 5.3. UI settings of modules ``` CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 ``` ``` Figure 5.4. UI settings of modules ``` ``` and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. ``` **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials ``` CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 ``` #### Chapter 6 # Finite Element Modeling ``` Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData ``` #### 6.1 Creating The Simulation ``` We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : ``` ``` −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) ``` ``` in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the ``` **34 Chapter 6** Figure 6.1. Full network for running simulation ``` CHAPTER 6. FINITE ELEMENT MODELING 35 ``` ``` Figure 6.2. UI settings of modules ``` ``` GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. ``` **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. ``` To efficiently project the data onto the same mesh as the data, we use theApplyMap- ``` ``` CHAPTER 6. FINITE ELEMENT MODELING 37 ``` ``` Figure 6.4. UI settings of modules ``` ``` pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to ``` **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. ``` CHAPTER 6. FINITE ELEMENT MODELING 39 ``` ``` Figure 6.6. Visualizing Results ``` **40 Chapter 6** \ No newline at end of file From 36d2d41f6a1b052905de09ae1db353eeeb909c01 Mon Sep 17 00:00:00 2001 From: williamfreigang <40257048+williamfreigang@users.noreply.github.com> Date: Tue, 28 Aug 2018 15:05:06 -0600 Subject: [PATCH 02/32] Ischemia Tutorial WIP Fixed Quotation Issues --- IschemiaTutorial.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index 1f54199..09dd17e 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -1 +1 @@ -# Ischemia Model tutorial #### SCIRun 4.7 Documentation ``` Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah ``` ``` SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc ``` This project was supported by grants from the National Center for Research Resources **(5P41RR012553-14)** and the National Institute of General Medical Sciences **(8 P41 GM103545-14)** from the National Institutes of Health. ``` Author(s): Jeroen Stinstra, Darrell Swenson ``` ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. ``` CHAPTER 1. OVERVIEW 3 ``` ``` In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ``` ``` ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: ``` ``` φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ``` ``` ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. ``` #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility ``` The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. ``` **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. ``` CHAPTER 1. OVERVIEW 5 ``` #### Chapter 2 # Reading and Visualization of Image # Data ``` Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets ``` #### 2.1 Loading The Dataset ``` We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in theBasicTutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main ``` ``` Figure 2.1. The main SCIRun window (File #1) ``` **6 Chapter 2** Figure 2.2. Finding a module and opening its GUI (File #2) SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. ``` CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 ``` ``` Figure 2.3. Select a file name and a file type (File #3) ``` ``` By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type ``` **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which ``` CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 ``` ``` Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) ``` ``` will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modulesConvertFieldsToTexture,ShowTextureS- lices,CreateStandardColorMaps,ShowSceneand connect the modules as depicted in figure 2.5. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figure 2.5 has been entered in the Network Editor, open up theUI of theShowTextureSlicesmodule and select to show the X, Y, and Z plane as indicated in the figure. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoviewin the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.6. By pressingShiftand clicking with the left mouse button on the light blue widget in the center of the viewer, the currently visible plane of the of 3D dataset can be altered. By clicking on theUIofGenerateStandardColorMapsmodule, the colormap of the current visualization can be altered (illustrated in figure 2.7). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In ``` **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. ``` CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 ``` ``` Figure 2.7. Network for checking contents of the file ``` **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets ``` CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 ``` ``` Figure 3.2. Reading in two datasets ``` #### 3.1 Volume Renderer and Clipping Planes ``` In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use theShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as theShowTextureSlicesmodule, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use theHeartMRI.nrrdand HeartMRI-Perfusionbed.nrrdas the two datasets for the two ReadFieldmodules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left ``` **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrdand a diffusion tensor image (DTI)HeartMRI-FiberOrientation.nrrd. Using theSeg3Dprogram the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrdandHeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up theViewScenemodule and pressConfigure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select theObjectstab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try theClippingtab, which will allow to clip the visualization. Open up the Clippingtab and switch on theClipping Plane Visiblebutton, next drag theXslider to 1.0. Now use theDslider to slide the clipping plane along the X-axis. The clipping widget has been configured, so thatDcorresponds to the full range of X that is spanned ``` CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 ``` ``` Figure 3.4. Slicing the dataset ``` ``` by the two images that are displayed in the viewer window. By draggingDfrom -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, pressPlane 2and then activate this plane by selecting theClipping Plane Visibleonce more. To make it easier to generate a thin slice, select the theReverse Clipping Plane Normaloption for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up theUIof theShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. ``` #### 3.2 Isosurfacing and Mesh Fairing ``` In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding theExtractIsosurface,FairMeshandShowFieldmodules to the network, as depicted in figure 3.5. TheExtractIsosurfaceshould get its input from the module that reads the perfusion bed field. Make sure to select theQuantitytab in the UIof the ExtractIsosurfacemodule as depicted in figure 3.5. TheExtractIsosurfacemodule extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the ``` **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. TheFairMesh module takes the output from theExtractIsosurfacemodule and smoothes out the surface. Because the data is discretized the isosurface will bestair-stepped. TheFairMeshmodule takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use theShowTextureVolumeto display the surface. Instead we use ``` CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 ``` ``` Figure 3.6. Coupling Two ViewScene Windows ``` ``` theShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into theViewScenemodule, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, theViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from theViewScenemodule. Press theNewWindowbutton to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the VolumeRendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press theLockViewbutton to unlock the window. When pressing the button theLockViewbutton changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the ``` **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select theViewsmenu at the top of the window and select theOther Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressingLon the keyboard when the window is selected. Likewise a view from an other window can be copied by pressingctrl 1to copy the view from the first window,ctrl 2for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Autoview also has a keyboard shortcut and is activated by pressing 0. ``` CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 ``` #### 3.3 Resampling and Viewing Glyphs ``` After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using theReadFieldmodule and the data will be translated into a LatVolMesh again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network:ResampleRegularMesh,Map- FieldDataOntoNodes,CalculateFieldData2, andShowFieldGlyphs. TheResampleRegularMeshmodule resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply theMapFieldDataOntoNodesto map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, calledCalculateFieldData. There are currently three versions of this module available calledCalculateFieldData, CalculateFieldData2, andCalculateFieldData3. The sole difference between these modules is the number of field input ports. As in this case we want to use two fields as input we use theCalculateFieldData2module. TheCalculateFieldData2operates by taking data from the two input fields as two input streams and applying the operation specified inside theUIof the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formulaDATA1is the data from the first field andDATA2is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. TheCalculateFieldData2defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press theParser Helpbutton in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Typein the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output ``` **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally theShowFieldGlyphsallows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the properUI. To display the vectors select theVectorstab and enable the check buttonShow Vectors. Also disable theRender glyphs below thresholdsetting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below theVectorThreshold. In this example we will render Vectors as cones by selecting theVector Display Type in the UI and we useRGB Conversionas the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the the size of theVectorScale to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the ``` CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 ``` ``` Figure 3.9. The UI of the ShowFieldGlyphs Module ``` ``` vectors are pointing along that matters in this case. To make the vectors point in both directions, set the optionRender bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. ``` **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data ``` CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 ``` #### Chapter 4 # Building a Tetrahedral Mesh ``` Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes ``` #### 4.1 Building a Tetrahedral Mesh ``` In order to build a physical model out of the imaging data, we need to generate a computa- tional mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules calledInterfaceWithTetGenand WriteField. TheInterfaceWithTetGenmodule lets SCIRun communicate with TetGen for gen- erating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated byExtractIsosurfaceneeds to be smoothed. We use theFairMeshmodule for this again. When opening theUIof theInterfaceWithTetGenmodule, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the-Y,-q, and the-aoption in theUI. The-Yoption lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag-qenforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the-aflag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct theReadFieldmodule to read the fileHeartMRI-Segmentation.nrrd; theResampleRegularMeshmodule can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes in stead of hours. ``` **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh ``` CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 ``` ``` Figure 4.2. Image of the Tetrahedral Mesh ``` ``` TheExtractIsosurfacemodule should be set to theQuantitytap and we should be com- puting only one isosurface. TheInterfaceWithTetGenmodule options should be set as indicated in figure 4.1. Finally, theWriteFieldmodule should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in theUIof the module and pressSetto set the name of the file that will be written. Also open up theShowFieldmodule and disable theShow Nodesand Show Edges, although SCIRun can renderer these without any problems. After pressingExecute Allto execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). ``` **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. ``` CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 ``` ``` Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields ``` **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. ``` The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition ``` ``` CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 ``` ``` of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, ``` **30 Chapter 5** Figure 5.3. UI settings of modules ``` CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 ``` ``` Figure 5.4. UI settings of modules ``` ``` and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. ``` **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials ``` CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 ``` #### Chapter 6 # Finite Element Modeling ``` Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData ``` #### 6.1 Creating The Simulation ``` We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : ``` ``` −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) ``` ``` in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the ``` **34 Chapter 6** Figure 6.1. Full network for running simulation ``` CHAPTER 6. FINITE ELEMENT MODELING 35 ``` ``` Figure 6.2. UI settings of modules ``` ``` GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. ``` **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. ``` To efficiently project the data onto the same mesh as the data, we use theApplyMap- ``` ``` CHAPTER 6. FINITE ELEMENT MODELING 37 ``` ``` Figure 6.4. UI settings of modules ``` ``` pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to ``` **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. ``` CHAPTER 6. FINITE ELEMENT MODELING 39 ``` ``` Figure 6.6. Visualizing Results ``` **40 Chapter 6** \ No newline at end of file +# Ischemia Model tutorial #### SCIRun 4.7 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by grants from the National Center for Research Resources **(5P41RR012553-14)** and the National Institute of General Medical Sciences **(8 P41 GM103545-14)** from the National Institutes of Health. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main Figure 2.1. The main SCIRun window (File #1) **6 Chapter 2** Figure 2.2. Finding a module and opening its GUI (File #2) SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modulesConvertFieldsToTexture,ShowTextureS- lices,CreateStandardColorMaps,ShowSceneand connect the modules as depicted in figure 2.5. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figure 2.5 has been entered in the Network Editor, open up theUI of theShowTextureSlicesmodule and select to show the X, Y, and Z plane as indicated in the figure. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoviewin the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.6. By pressingShiftand clicking with the left mouse button on the light blue widget in the center of the viewer, the currently visible plane of the of 3D dataset can be altered. By clicking on theUIofGenerateStandardColorMapsmodule, the colormap of the current visualization can be altered (illustrated in figure 2.7). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use theShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as theShowTextureSlicesmodule, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use theHeartMRI.nrrdand HeartMRI-Perfusionbed.nrrdas the two datasets for the two ReadFieldmodules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left ``` **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrdand a diffusion tensor image (DTI)HeartMRI-FiberOrientation.nrrd. Using theSeg3Dprogram the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrdandHeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up theViewScenemodule and pressConfigure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select theObjectstab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try theClippingtab, which will allow to clip the visualization. Open up the Clippingtab and switch on theClipping Plane Visiblebutton, next drag theXslider to 1.0. Now use theDslider to slide the clipping plane along the X-axis. The clipping widget has been configured, so thatDcorresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By draggingDfrom -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, pressPlane 2and then activate this plane by selecting theClipping Plane Visibleonce more. To make it easier to generate a thin slice, select the theReverse Clipping Plane Normaloption for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up theUIof theShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding theExtractIsosurface,FairMeshandShowFieldmodules to the network, as depicted in figure 3.5. TheExtractIsosurfaceshould get its input from the module that reads the perfusion bed field. Make sure to select theQuantitytab in the UIof the ExtractIsosurfacemodule as depicted in figure 3.5. TheExtractIsosurfacemodule extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. TheFairMesh module takes the output from theExtractIsosurfacemodule and smoothes out the surface. Because the data is discretized the isosurface will bestair-stepped. TheFairMeshmodule takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use theShowTextureVolumeto display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows theShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into theViewScenemodule, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, theViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from theViewScenemodule. Press theNewWindowbutton to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the VolumeRendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press theLockViewbutton to unlock the window. When pressing the button theLockViewbutton changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select theViewsmenu at the top of the window and select theOther Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressingLon the keyboard when the window is selected. Likewise a view from an other window can be copied by pressingctrl 1to copy the view from the first window,ctrl 2for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Autoview also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using theReadFieldmodule and the data will be translated into a LatVolMesh again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network:ResampleRegularMesh,Map- FieldDataOntoNodes,CalculateFieldData2, andShowFieldGlyphs. TheResampleRegularMeshmodule resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply theMapFieldDataOntoNodesto map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, calledCalculateFieldData. There are currently three versions of this module available calledCalculateFieldData, CalculateFieldData2, andCalculateFieldData3. The sole difference between these modules is the number of field input ports. As in this case we want to use two fields as input we use theCalculateFieldData2module. TheCalculateFieldData2operates by taking data from the two input fields as two input streams and applying the operation specified inside theUIof the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formulaDATA1is the data from the first field andDATA2is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. TheCalculateFieldData2defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press theParser Helpbutton in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Typein the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally theShowFieldGlyphsallows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the properUI. To display the vectors select theVectorstab and enable the check buttonShow Vectors. Also disable theRender glyphs below thresholdsetting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below theVectorThreshold. In this example we will render Vectors as cones by selecting theVector Display Type in the UI and we useRGB Conversionas the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the the size of theVectorScale to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the ShowFieldGlyphs Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the optionRender bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computa- tional mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules calledInterfaceWithTetGenand WriteField. TheInterfaceWithTetGenmodule lets SCIRun communicate with TetGen for gen- erating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated byExtractIsosurfaceneeds to be smoothed. We use theFairMeshmodule for this again. When opening theUIof theInterfaceWithTetGenmodule, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the-Y,-q, and the-aoption in theUI. The-Yoption lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag-qenforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the-aflag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct theReadFieldmodule to read the fileHeartMRI-Segmentation.nrrd; theResampleRegularMeshmodule can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes in stead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh TheExtractIsosurfacemodule should be set to theQuantitytap and we should be com- puting only one isosurface. TheInterfaceWithTetGenmodule options should be set as indicated in figure 4.1. Finally, theWriteFieldmodule should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in theUIof the module and pressSetto set the name of the file that will be written. Also open up theShowFieldmodule and disable theShow Nodesand Show Edges, although SCIRun can renderer these without any problems. After pressingExecute Allto execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file From 30a96815ccab40af50c9da2210c8a9931f53f74d Mon Sep 17 00:00:00 2001 From: williamfreigang <40257048+williamfreigang@users.noreply.github.com> Date: Tue, 28 Aug 2018 15:07:13 -0600 Subject: [PATCH 03/32] Ischemia Tutorial WIP Fixed Quotation Issues --- IschemiaTutorial.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index 09dd17e..d728452 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -1 +1 @@ -# Ischemia Model tutorial #### SCIRun 4.7 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by grants from the National Center for Research Resources **(5P41RR012553-14)** and the National Institute of General Medical Sciences **(8 P41 GM103545-14)** from the National Institutes of Health. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main Figure 2.1. The main SCIRun window (File #1) **6 Chapter 2** Figure 2.2. Finding a module and opening its GUI (File #2) SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modulesConvertFieldsToTexture,ShowTextureS- lices,CreateStandardColorMaps,ShowSceneand connect the modules as depicted in figure 2.5. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figure 2.5 has been entered in the Network Editor, open up theUI of theShowTextureSlicesmodule and select to show the X, Y, and Z plane as indicated in the figure. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoviewin the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.6. By pressingShiftand clicking with the left mouse button on the light blue widget in the center of the viewer, the currently visible plane of the of 3D dataset can be altered. By clicking on theUIofGenerateStandardColorMapsmodule, the colormap of the current visualization can be altered (illustrated in figure 2.7). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use theShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as theShowTextureSlicesmodule, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use theHeartMRI.nrrdand HeartMRI-Perfusionbed.nrrdas the two datasets for the two ReadFieldmodules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left ``` **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrdand a diffusion tensor image (DTI)HeartMRI-FiberOrientation.nrrd. Using theSeg3Dprogram the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrdandHeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up theViewScenemodule and pressConfigure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select theObjectstab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try theClippingtab, which will allow to clip the visualization. Open up the Clippingtab and switch on theClipping Plane Visiblebutton, next drag theXslider to 1.0. Now use theDslider to slide the clipping plane along the X-axis. The clipping widget has been configured, so thatDcorresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By draggingDfrom -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, pressPlane 2and then activate this plane by selecting theClipping Plane Visibleonce more. To make it easier to generate a thin slice, select the theReverse Clipping Plane Normaloption for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up theUIof theShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding theExtractIsosurface,FairMeshandShowFieldmodules to the network, as depicted in figure 3.5. TheExtractIsosurfaceshould get its input from the module that reads the perfusion bed field. Make sure to select theQuantitytab in the UIof the ExtractIsosurfacemodule as depicted in figure 3.5. TheExtractIsosurfacemodule extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. TheFairMesh module takes the output from theExtractIsosurfacemodule and smoothes out the surface. Because the data is discretized the isosurface will bestair-stepped. TheFairMeshmodule takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use theShowTextureVolumeto display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows theShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into theViewScenemodule, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, theViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from theViewScenemodule. Press theNewWindowbutton to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the VolumeRendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press theLockViewbutton to unlock the window. When pressing the button theLockViewbutton changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select theViewsmenu at the top of the window and select theOther Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressingLon the keyboard when the window is selected. Likewise a view from an other window can be copied by pressingctrl 1to copy the view from the first window,ctrl 2for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Autoview also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using theReadFieldmodule and the data will be translated into a LatVolMesh again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network:ResampleRegularMesh,Map- FieldDataOntoNodes,CalculateFieldData2, andShowFieldGlyphs. TheResampleRegularMeshmodule resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply theMapFieldDataOntoNodesto map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, calledCalculateFieldData. There are currently three versions of this module available calledCalculateFieldData, CalculateFieldData2, andCalculateFieldData3. The sole difference between these modules is the number of field input ports. As in this case we want to use two fields as input we use theCalculateFieldData2module. TheCalculateFieldData2operates by taking data from the two input fields as two input streams and applying the operation specified inside theUIof the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formulaDATA1is the data from the first field andDATA2is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. TheCalculateFieldData2defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press theParser Helpbutton in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Typein the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally theShowFieldGlyphsallows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the properUI. To display the vectors select theVectorstab and enable the check buttonShow Vectors. Also disable theRender glyphs below thresholdsetting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below theVectorThreshold. In this example we will render Vectors as cones by selecting theVector Display Type in the UI and we useRGB Conversionas the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the the size of theVectorScale to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the ShowFieldGlyphs Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the optionRender bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computa- tional mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules calledInterfaceWithTetGenand WriteField. TheInterfaceWithTetGenmodule lets SCIRun communicate with TetGen for gen- erating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated byExtractIsosurfaceneeds to be smoothed. We use theFairMeshmodule for this again. When opening theUIof theInterfaceWithTetGenmodule, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the-Y,-q, and the-aoption in theUI. The-Yoption lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag-qenforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the-aflag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct theReadFieldmodule to read the fileHeartMRI-Segmentation.nrrd; theResampleRegularMeshmodule can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes in stead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh TheExtractIsosurfacemodule should be set to theQuantitytap and we should be com- puting only one isosurface. TheInterfaceWithTetGenmodule options should be set as indicated in figure 4.1. Finally, theWriteFieldmodule should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in theUIof the module and pressSetto set the name of the file that will be written. Also open up theShowFieldmodule and disable theShow Nodesand Show Edges, although SCIRun can renderer these without any problems. After pressingExecute Allto execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file +# Ischemia Model tutorial #### SCIRun 4.7 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by grants from the National Center for Research Resources **(5P41RR012553-14)** and the National Institute of General Medical Sciences **(8 P41 GM103545-14)** from the National Institutes of Health. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main Figure 2.1. The main SCIRun window (File #1) **6 Chapter 2** Figure 2.2. Finding a module and opening its GUI (File #2) SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modulesConvertFieldsToTexture,ShowTextureS- lices,CreateStandardColorMaps,ShowSceneand connect the modules as depicted in figure 2.5. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figure 2.5 has been entered in the Network Editor, open up theUI of theShowTextureSlicesmodule and select to show the X, Y, and Z plane as indicated in the figure. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoviewin the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.6. By pressingShiftand clicking with the left mouse button on the light blue widget in the center of the viewer, the currently visible plane of the of 3D dataset can be altered. By clicking on theUIofGenerateStandardColorMapsmodule, the colormap of the current visualization can be altered (illustrated in figure 2.7). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use theShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as theShowTextureSlicesmodule, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use theHeartMRI.nrrdand HeartMRI-Perfusionbed.nrrdas the two datasets for the two ReadFieldmodules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrdand a diffusion tensor image (DTI)HeartMRI-FiberOrientation.nrrd. Using theSeg3Dprogram the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrdandHeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up theViewScenemodule and pressConfigure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select theObjectstab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try theClippingtab, which will allow to clip the visualization. Open up the Clippingtab and switch on theClipping Plane Visiblebutton, next drag theXslider to 1.0. Now use theDslider to slide the clipping plane along the X-axis. The clipping widget has been configured, so thatDcorresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By draggingDfrom -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, pressPlane 2and then activate this plane by selecting theClipping Plane Visibleonce more. To make it easier to generate a thin slice, select the theReverse Clipping Plane Normaloption for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up theUIof theShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding theExtractIsosurface,FairMeshandShowFieldmodules to the network, as depicted in figure 3.5. TheExtractIsosurfaceshould get its input from the module that reads the perfusion bed field. Make sure to select theQuantitytab in the UIof the ExtractIsosurfacemodule as depicted in figure 3.5. TheExtractIsosurfacemodule extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. TheFairMesh module takes the output from theExtractIsosurfacemodule and smoothes out the surface. Because the data is discretized the isosurface will bestair-stepped. TheFairMeshmodule takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use theShowTextureVolumeto display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows theShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into theViewScenemodule, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, theViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from theViewScenemodule. Press theNewWindowbutton to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the VolumeRendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press theLockViewbutton to unlock the window. When pressing the button theLockViewbutton changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select theViewsmenu at the top of the window and select theOther Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressingLon the keyboard when the window is selected. Likewise a view from an other window can be copied by pressingctrl 1to copy the view from the first window,ctrl 2for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Autoview also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using theReadFieldmodule and the data will be translated into a LatVolMesh again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network:ResampleRegularMesh,Map- FieldDataOntoNodes,CalculateFieldData2, andShowFieldGlyphs. TheResampleRegularMeshmodule resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply theMapFieldDataOntoNodesto map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, calledCalculateFieldData. There are currently three versions of this module available calledCalculateFieldData, CalculateFieldData2, andCalculateFieldData3. The sole difference between these modules is the number of field input ports. As in this case we want to use two fields as input we use theCalculateFieldData2module. TheCalculateFieldData2operates by taking data from the two input fields as two input streams and applying the operation specified inside theUIof the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formulaDATA1is the data from the first field andDATA2is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. TheCalculateFieldData2defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press theParser Helpbutton in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Typein the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally theShowFieldGlyphsallows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the properUI. To display the vectors select theVectorstab and enable the check buttonShow Vectors. Also disable theRender glyphs below thresholdsetting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below theVectorThreshold. In this example we will render Vectors as cones by selecting theVector Display Type in the UI and we useRGB Conversionas the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the the size of theVectorScale to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the ShowFieldGlyphs Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the optionRender bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computa- tional mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules calledInterfaceWithTetGenand WriteField. TheInterfaceWithTetGenmodule lets SCIRun communicate with TetGen for gen- erating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated byExtractIsosurfaceneeds to be smoothed. We use theFairMeshmodule for this again. When opening theUIof theInterfaceWithTetGenmodule, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the-Y,-q, and the-aoption in theUI. The-Yoption lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag-qenforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the-aflag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct theReadFieldmodule to read the fileHeartMRI-Segmentation.nrrd; theResampleRegularMeshmodule can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes in stead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh TheExtractIsosurfacemodule should be set to theQuantitytap and we should be com- puting only one isosurface. TheInterfaceWithTetGenmodule options should be set as indicated in figure 4.1. Finally, theWriteFieldmodule should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in theUIof the module and pressSetto set the name of the file that will be written. Also open up theShowFieldmodule and disable theShow Nodesand Show Edges, although SCIRun can renderer these without any problems. After pressingExecute Allto execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file From cc277f256864381a82c913c76ed3a52bec298962 Mon Sep 17 00:00:00 2001 From: williamfreigang <40257048+williamfreigang@users.noreply.github.com> Date: Fri, 14 Sep 2018 17:00:27 -0600 Subject: [PATCH 04/32] Heart Ischemia Tutorial WIP Fixed formatting errors and corrected mistakes in the texture slices & fiber orientation sections. --- IschemiaTutorial.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index d728452..24d9556 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -1 +1 @@ -# Ischemia Model tutorial #### SCIRun 4.7 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by grants from the National Center for Research Resources **(5P41RR012553-14)** and the National Institute of General Medical Sciences **(8 P41 GM103545-14)** from the National Institutes of Health. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main Figure 2.1. The main SCIRun window (File #1) **6 Chapter 2** Figure 2.2. Finding a module and opening its GUI (File #2) SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modulesConvertFieldsToTexture,ShowTextureS- lices,CreateStandardColorMaps,ShowSceneand connect the modules as depicted in figure 2.5. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figure 2.5 has been entered in the Network Editor, open up theUI of theShowTextureSlicesmodule and select to show the X, Y, and Z plane as indicated in the figure. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoviewin the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.6. By pressingShiftand clicking with the left mouse button on the light blue widget in the center of the viewer, the currently visible plane of the of 3D dataset can be altered. By clicking on theUIofGenerateStandardColorMapsmodule, the colormap of the current visualization can be altered (illustrated in figure 2.7). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use theShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as theShowTextureSlicesmodule, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use theHeartMRI.nrrdand HeartMRI-Perfusionbed.nrrdas the two datasets for the two ReadFieldmodules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrdand a diffusion tensor image (DTI)HeartMRI-FiberOrientation.nrrd. Using theSeg3Dprogram the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrdandHeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up theViewScenemodule and pressConfigure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select theObjectstab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try theClippingtab, which will allow to clip the visualization. Open up the Clippingtab and switch on theClipping Plane Visiblebutton, next drag theXslider to 1.0. Now use theDslider to slide the clipping plane along the X-axis. The clipping widget has been configured, so thatDcorresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By draggingDfrom -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, pressPlane 2and then activate this plane by selecting theClipping Plane Visibleonce more. To make it easier to generate a thin slice, select the theReverse Clipping Plane Normaloption for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up theUIof theShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding theExtractIsosurface,FairMeshandShowFieldmodules to the network, as depicted in figure 3.5. TheExtractIsosurfaceshould get its input from the module that reads the perfusion bed field. Make sure to select theQuantitytab in the UIof the ExtractIsosurfacemodule as depicted in figure 3.5. TheExtractIsosurfacemodule extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. TheFairMesh module takes the output from theExtractIsosurfacemodule and smoothes out the surface. Because the data is discretized the isosurface will bestair-stepped. TheFairMeshmodule takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use theShowTextureVolumeto display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows theShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into theViewScenemodule, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, theViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from theViewScenemodule. Press theNewWindowbutton to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the VolumeRendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press theLockViewbutton to unlock the window. When pressing the button theLockViewbutton changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select theViewsmenu at the top of the window and select theOther Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressingLon the keyboard when the window is selected. Likewise a view from an other window can be copied by pressingctrl 1to copy the view from the first window,ctrl 2for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Autoview also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using theReadFieldmodule and the data will be translated into a LatVolMesh again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network:ResampleRegularMesh,Map- FieldDataOntoNodes,CalculateFieldData2, andShowFieldGlyphs. TheResampleRegularMeshmodule resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply theMapFieldDataOntoNodesto map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, calledCalculateFieldData. There are currently three versions of this module available calledCalculateFieldData, CalculateFieldData2, andCalculateFieldData3. The sole difference between these modules is the number of field input ports. As in this case we want to use two fields as input we use theCalculateFieldData2module. TheCalculateFieldData2operates by taking data from the two input fields as two input streams and applying the operation specified inside theUIof the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formulaDATA1is the data from the first field andDATA2is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. TheCalculateFieldData2defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press theParser Helpbutton in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Typein the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally theShowFieldGlyphsallows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the properUI. To display the vectors select theVectorstab and enable the check buttonShow Vectors. Also disable theRender glyphs below thresholdsetting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below theVectorThreshold. In this example we will render Vectors as cones by selecting theVector Display Type in the UI and we useRGB Conversionas the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the the size of theVectorScale to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the ShowFieldGlyphs Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the optionRender bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computa- tional mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules calledInterfaceWithTetGenand WriteField. TheInterfaceWithTetGenmodule lets SCIRun communicate with TetGen for gen- erating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated byExtractIsosurfaceneeds to be smoothed. We use theFairMeshmodule for this again. When opening theUIof theInterfaceWithTetGenmodule, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the-Y,-q, and the-aoption in theUI. The-Yoption lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag-qenforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the-aflag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct theReadFieldmodule to read the fileHeartMRI-Segmentation.nrrd; theResampleRegularMeshmodule can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes in stead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh TheExtractIsosurfacemodule should be set to theQuantitytap and we should be com- puting only one isosurface. TheInterfaceWithTetGenmodule options should be set as indicated in figure 4.1. Finally, theWriteFieldmodule should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in theUIof the module and pressSetto set the name of the file that will be written. Also open up theShowFieldmodule and disable theShow Nodesand Show Edges, although SCIRun can renderer these without any problems. After pressingExecute Allto execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file +# Ischemia Model tutorial #### SCIRun 4.7 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by grants from the National Center for Research Resources **(5P41RR012553-14)** and the National Institute of General Medical Sciences **(8 P41 GM103545-14)** from the National Institutes of Health. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main Figure 2.1. The main SCIRun window (File #1) **6 Chapter 2** Figure 2.2. Finding a module and opening its GUI (File #2) SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computa- tional mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules calledInterfaceWithTetGenand WriteField. TheInterfaceWithTetGenmodule lets SCIRun communicate with TetGen for gen- erating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated byExtractIsosurfaceneeds to be smoothed. We use theFairMeshmodule for this again. When opening theUIof theInterfaceWithTetGenmodule, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the-Y,-q, and the-aoption in theUI. The-Yoption lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag-qenforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the-aflag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct theReadFieldmodule to read the fileHeartMRI-Segmentation.nrrd; theResampleRegularMeshmodule can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes in stead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh TheExtractIsosurfacemodule should be set to theQuantitytap and we should be com- puting only one isosurface. TheInterfaceWithTetGenmodule options should be set as indicated in figure 4.1. Finally, theWriteFieldmodule should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in theUIof the module and pressSetto set the name of the file that will be written. Also open up theShowFieldmodule and disable theShow Nodesand Show Edges, although SCIRun can renderer these without any problems. After pressingExecute Allto execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file From dbe76bb61eee65dbbb8e6a9b815aba2292afcae6 Mon Sep 17 00:00:00 2001 From: williamfreigang <40257048+williamfreigang@users.noreply.github.com> Date: Wed, 3 Oct 2018 15:36:26 -0600 Subject: [PATCH 05/32] Update index.md Add link for Ischemia Tutorial --- index.md | 1 + 1 file changed, 1 insertion(+) diff --git a/index.md b/index.md index 0684849..667d51a 100644 --- a/index.md +++ b/index.md @@ -17,6 +17,7 @@ SCIRun 5 is a complete rewrite of the GUI front end and graphical components of - [Module Reference](modules.html) - [Python API 0.2](python.html) - [Basic Tutorial](BasicTutorial.html) + - [Ischemia Tutorial](IschemiaTutorial.html) - [SCIRun5 Module Generation](SCIRun5ModuleGeneration.html) Doc v1.0c From 34dc34f649dc0277a886ed6e6dcb719553820ed5 Mon Sep 17 00:00:00 2001 From: williamfreigang <40257048+williamfreigang@users.noreply.github.com> Date: Wed, 3 Oct 2018 15:43:12 -0600 Subject: [PATCH 06/32] Ischemia Tutorial WIP Fixed title section and Tetrahedral Chapter --- IschemiaTutorial.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index 24d9556..8fdd4f1 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -1 +1 @@ -# Ischemia Model tutorial #### SCIRun 4.7 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by grants from the National Center for Research Resources **(5P41RR012553-14)** and the National Institute of General Medical Sciences **(8 P41 GM103545-14)** from the National Institutes of Health. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main Figure 2.1. The main SCIRun window (File #1) **6 Chapter 2** Figure 2.2. Finding a module and opening its GUI (File #2) SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computa- tional mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules calledInterfaceWithTetGenand WriteField. TheInterfaceWithTetGenmodule lets SCIRun communicate with TetGen for gen- erating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated byExtractIsosurfaceneeds to be smoothed. We use theFairMeshmodule for this again. When opening theUIof theInterfaceWithTetGenmodule, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the-Y,-q, and the-aoption in theUI. The-Yoption lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag-qenforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the-aflag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct theReadFieldmodule to read the fileHeartMRI-Segmentation.nrrd; theResampleRegularMeshmodule can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes in stead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh TheExtractIsosurfacemodule should be set to theQuantitytap and we should be com- puting only one isosurface. TheInterfaceWithTetGenmodule options should be set as indicated in figure 4.1. Finally, theWriteFieldmodule should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in theUIof the module and pressSetto set the name of the file that will be written. Also open up theShowFieldmodule and disable theShow Nodesand Show Edges, although SCIRun can renderer these without any problems. After pressingExecute Allto execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file +# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main Figure 2.1. The main SCIRun window (File #1) **6 Chapter 2** Figure 2.2. Finding a module and opening its GUI (File #2) SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. 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z2`APIPjc1u7;?wHM0+mN89D_CyUL`Qj0nJAixp?f?$?EuM)P*HgVzjKu=g?27|@(X zOC^rwGG_}Tr9r*UEZ8?{*n3Pgg)GNYVg41T^r>A`I^|P>|KI3nb#}6|ViL|7COAO$ z)m!7`&I7-h;MB-1QRSD9$9FA=zFnfXB&$UXM+%0BZYJjg`!0Z;0@C=#Y?LT(tOB3j2(f0E90!@sC4ok}_a$XK}8)XS#aUFnK zDLu(WQylpUN2el1wFGsFk?p9YrIfVuQI0f7*rr20G5=&WGzJHUJ2B>$di$Xrm_zv~q{7KI^xw_0VN93hh<_Kdtkp zgY*b)b)Ji8g2tl)z6w!Gj5NAjh9}ssxAT7m2^aMIQ*iy&?3IvA(Kf{ztyrTa9*ipn z%Ru#ZrNf^z(=EyC_gf4Lu9ku+QP$KSuh15Q3Q8W8tW3?LpA;7C`8kA4J^}~}xG)M! zNRVScI3)bO-L-CgF9T5XH)DnO3%rKLF%^xTu}qn{5;Slz_wi(W;RnIJRsrsGS6(5= zi7Ah26W~BU-78SP=sz1)i%(~fW4mu)#L@%n?o-21hnV9-ygi)x`h7|UdT!ANLoB2; je)Z@)_Imwp7yS8+3E`L&N{a{d-v=vJy<7D5`mg>U6qdFE From 5ce364c304ac2fdd0c6ea7393d6bc127104d930f Mon Sep 17 00:00:00 2001 From: williamfreigang <40257048+williamfreigang@users.noreply.github.com> Date: Mon, 10 Dec 2018 13:09:45 -0700 Subject: [PATCH 09/32] Update IschemiaTutorial.md --- IschemiaTutorial.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index 8fdd4f1..3a58187 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -1 +1 @@ -# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main Figure 2.1. The main SCIRun window (File #1) **6 Chapter 2** Figure 2.2. Finding a module and opening its GUI (File #2) SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file +# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main Figure 2.1. The main SCIRun window Date: Mon, 10 Dec 2018 13:15:46 -0700 Subject: [PATCH 10/32] Update IschemiaTutorial.md --- IschemiaTutorial.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index 3a58187..6909c6f 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -1 +1 @@ -# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main Figure 2.1. The main SCIRun window **6 Chapter 2** Figure 2.2. Finding a module and opening its GUI (File #2) SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file From 19fa1cae92cca2eb173ee5b58a470d348c448361 Mon Sep 17 00:00:00 2001 From: williamfreigang <40257048+williamfreigang@users.noreply.github.com> Date: Mon, 10 Dec 2018 13:17:29 -0700 Subject: [PATCH 11/32] Update IschemiaTutorial.md --- IschemiaTutorial.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index 6909c6f..6f98a7f 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -1 +1 @@ -# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main Figure 2.1. The main SCIRun window **6 Chapter 2** Figure 2.2. Finding a module and opening its GUI (File #2) SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file +# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main The main SCIRun window Figure 2.1 - The Main SCIRun Window **6 Chapter 2** Figure 2.2. Finding a module and opening its GUI (File #2) SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file From 24d500b1942831d415954f887363ce289c8cfc10 Mon Sep 17 00:00:00 2001 From: williamfreigang <40257048+williamfreigang@users.noreply.github.com> Date: Mon, 10 Dec 2018 13:22:25 -0700 Subject: [PATCH 12/32] Update IschemiaTutorial.md --- IschemiaTutorial.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index 6f98a7f..bfe7d0a 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -1 +1 @@ -# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main The main SCIRun window Figure 2.1 - The Main SCIRun Window **6 Chapter 2** Figure 2.2. Finding a module and opening its GUI (File #2) SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file +# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main The main SCIRun window Figure 2.1 - The Main SCIRun Window **6 Chapter 2** Adding_and_opening_module Figure 2.2. Finding the ReadField module and opening its GUI (File #2) SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file From 5d1fef2b46a0b942a0268c21330a84c348132833 Mon Sep 17 00:00:00 2001 From: williamfreigang <40257048+williamfreigang@users.noreply.github.com> Date: Mon, 10 Dec 2018 13:24:35 -0700 Subject: [PATCH 13/32] Update IschemiaTutorial.md --- IschemiaTutorial.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index bfe7d0a..c044853 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -1 +1 @@ -# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main The main SCIRun window Figure 2.1 - The Main SCIRun Window **6 Chapter 2** Adding_and_opening_module Figure 2.2. Finding the ReadField module and opening its GUI (File #2) SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file +# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main The main SCIRun window Figure 2.1 - The Main SCIRun Window **6 Chapter 2** Adding_and_opening_module Figure 2.2. Finding the ReadField module and opening its GUI (File #2) SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. Adding_and_opening_module Figure 2.2. Finding the ReadField module and opening its GUI (File #2) The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file From d49a4ff388132acd311e1f0386df13680dedfaa1 Mon Sep 17 00:00:00 2001 From: williamfreigang <40257048+williamfreigang@users.noreply.github.com> Date: Mon, 10 Dec 2018 13:26:06 -0700 Subject: [PATCH 14/32] Update IschemiaTutorial.md --- IschemiaTutorial.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index c044853..185a831 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -1 +1 @@ -# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main The main SCIRun window Figure 2.1 - The Main SCIRun Window **6 Chapter 2** Adding_and_opening_module Figure 2.2. Finding the ReadField module and opening its GUI (File #2) SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. Adding_and_opening_module Figure 2.2. Finding the ReadField module and opening its GUI (File #2) The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file +# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main The main SCIRun window **Figure 2.1 - The Main SCIRun Window** **6 Chapter 2** SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. Adding_and_opening_module **Figure 2.2. Finding the ReadField module and opening its GUI (File #2)** The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file From 450ae9a2167d990fa9d27e36f1e396001c37e7b7 Mon Sep 17 00:00:00 2001 From: williamfreigang <40257048+williamfreigang@users.noreply.github.com> Date: Mon, 10 Dec 2018 13:28:39 -0700 Subject: [PATCH 15/32] Update IschemiaTutorial.md --- IschemiaTutorial.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index 185a831..331e50a 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -1 +1 @@ -# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main The main SCIRun window **Figure 2.1 - The Main SCIRun Window** **6 Chapter 2** SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. Adding_and_opening_module **Figure 2.2. Finding the ReadField module and opening its GUI (File #2)** The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file +# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main The main SCIRun window _Figure 2.1 - The Main SCIRun Window_ **6 Chapter 2** SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. Adding_and_opening_module **Figure 2.2. Finding the ReadField module and opening its GUI** The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file From c97fe29a89aa49cdba3d357790eb3ebbdc189197 Mon Sep 17 00:00:00 2001 From: williamfreigang <40257048+williamfreigang@users.noreply.github.com> Date: Mon, 10 Dec 2018 13:29:44 -0700 Subject: [PATCH 16/32] Update IschemiaTutorial.md --- IschemiaTutorial.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index 331e50a..d1b1ef9 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -1 +1 @@ -# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main The main SCIRun window _Figure 2.1 - The Main SCIRun Window_ **6 Chapter 2** SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. Adding_and_opening_module **Figure 2.2. Finding the ReadField module and opening its GUI** The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file +# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main The main SCIRun window _Figure 2.1 - The Main SCIRun Window_ **6 Chapter 2** SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. Adding_and_opening_module _Figure 2.2 - Finding the ReadField module and opening its GUI_ The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file From c5063d4fd2434041c833d0ba9e58f06edfea7a0e Mon Sep 17 00:00:00 2001 From: williamfreigang <40257048+williamfreigang@users.noreply.github.com> Date: Mon, 10 Dec 2018 13:34:48 -0700 Subject: [PATCH 17/32] Update IschemiaTutorial.md --- IschemiaTutorial.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index d1b1ef9..4c8dfdd 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -1 +1 @@ -# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main The main SCIRun window _Figure 2.1 - The Main SCIRun Window_ **6 Chapter 2** SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. Adding_and_opening_module _Figure 2.2 - Finding the ReadField module and opening its GUI_ The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file +# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main The main SCIRun window _Figure 2.1 - The Main SCIRun Window_ **6 Chapter 2** SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. Adding_and_opening_module _Figure 2.2 - Finding the ReadField module and opening its GUI_ The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file From 8d32377ab457997323f371d020aa6ec59d361853 Mon Sep 17 00:00:00 2001 From: williamfreigang <40257048+williamfreigang@users.noreply.github.com> Date: Mon, 10 Dec 2018 13:42:48 -0700 Subject: [PATCH 18/32] Update IschemiaTutorial.md --- IschemiaTutorial.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index 4c8dfdd..30aeca0 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -1 +1 @@ -# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main The main SCIRun window _Figure 2.1 - The Main SCIRun Window_ **6 Chapter 2** SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. Adding_and_opening_module _Figure 2.2 - Finding the ReadField module and opening its GUI_ The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file +# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main The main SCIRun window _Figure 2.1 - The Main SCIRun Window_ **6 Chapter 2** SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. Adding_and_opening_module _Figure 2.1 - The Main SCIRun Window_ _Figure 2.2 - Finding the ReadField module and opening its GUI_ The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file From ab755b7845656d8024aec43df96a9ae8a6a934b7 Mon Sep 17 00:00:00 2001 From: williamfreigang <40257048+williamfreigang@users.noreply.github.com> Date: Mon, 10 Dec 2018 13:44:07 -0700 Subject: [PATCH 19/32] Update IschemiaTutorial.md --- IschemiaTutorial.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index 30aeca0..8b1acff 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -1 +1 @@ -# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main The main SCIRun window _Figure 2.1 - The Main SCIRun Window_ **6 Chapter 2** SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. Adding_and_opening_module _Figure 2.1 - The Main SCIRun Window_ _Figure 2.2 - Finding the ReadField module and opening its GUI_ The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file +# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main The main SCIRun window _Figure 2.1 - The Main SCIRun Window_ **6 Chapter 2** SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. Adding_and_opening_module _Figure 2.2 - Finding the ReadField module and opening its GUI_ The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file From 82c33772de4d4a20f4485caeb05c0cce51785303 Mon Sep 17 00:00:00 2001 From: williamfreigang <40257048+williamfreigang@users.noreply.github.com> Date: Mon, 10 Dec 2018 14:07:57 -0700 Subject: [PATCH 20/32] Update IschemiaTutorial.md --- IschemiaTutorial.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index 8b1acff..86adba7 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -1 +1 @@ -# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main The main SCIRun window _Figure 2.1 - The Main SCIRun Window_ **6 Chapter 2** SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. Adding_and_opening_module _Figure 2.2 - Finding the ReadField module and opening its GUI_ The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file +# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main The main SCIRun window _Figure 2.1 - The Main SCIRun Window_ **6 Chapter 2** SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. Adding_and_opening_module _Figure 2.2 - Finding the ReadField module and opening its GUI_ The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file From be50651288810330f402817fc5e585dd09bd7cae Mon Sep 17 00:00:00 2001 From: Nidhi Patel Date: Mon, 14 Oct 2019 14:53:44 -0600 Subject: [PATCH 21/32] Fix spelling errors --- BasicTutorial.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/BasicTutorial.md b/BasicTutorial.md index fa0f87d..06d3f1c 100644 --- a/BasicTutorial.md +++ b/BasicTutorial.md @@ -86,7 +86,7 @@ To visualize the field geometry, instantiate module **ShowField** in the **Visua

Figure 2.5 SCIRun can be used to visualize the structured mesh.
-Apply a colored scale to the data values on the geometry using **CreateStandardColorMaps** and **RescaleColorMaps** modules in **Visualization** (Figure 2.6). Colors can be manipulated using the CreateStandardColorMap UI and RescaleColorMap UI (Figure 2.7). Change the coloring scheme to Blackbody using the drop-down menu in the CreatSrandardColorMap UI. +Apply a colored scale to the data values on the geometry using **CreateStandardColorMaps** and **RescaleColorMaps** modules in **Visualization** (Figure 2.6). Colors can be manipulated using the CreateStandardColorMap UI and RescaleColorMap UI (Figure 2.7). Change the coloring scheme to Blackbody using the drop-down menu in the CreateStandardColorMap UI.
Apply and rescale a colormap to data values on the geometry. @@ -100,7 +100,7 @@ Apply a colored scale to the data values on the geometry using **CreateStandardC Return to the default color scale. Use the sliders in the GetSlicesFromStructuredFieldByIndices UI to change slice position within the geometry. Compare with Figure 2.6. -
+
Different cross sections can be visualized within the geometry using GetSlicesFromStructuredFieldbyIndices.
Figure 2.8 Different cross sections can be visualized within the geometry using GetSlicesFromStructuredFieldbyIndices.
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zOaJb6etd?#l@>=yEmilewVKZCvxA;fYS>8x9t2JH5ws?4H`PJCpq0nSZw+Y^G7tD0 z?qa~Yxa#YCXqyXmmzy0ZJI@>94Q5Jv4lpIwz|^Jl`M3de+ehxRK7Pd%Vc@$;0ZNhL z-{E$sa5c{f1e%#z%$Sh?iu~dh9}XvWTKD=`Zx9voByO?V6eRFN(lVS<>wEP!y{x}E z*H5e_deKQ)k4#Q2tUaqu$|(yg6ACJe2mld31v_YcyxA>Ya}Fd_q0aFiH!DiLt!4_) z>%)B5t9|_vS@u>*O5=0&f^<1&C@;!@KkE5C)>sV$4>r=~1h263+~DyWY;9~`H+*WNh4|JY&-ty6!|=I)vrOJzrG*beYgY{&q)lhJFt2dS1yO zSKz$(4S&+5_>eQH!0fA;m1Bi|lK(KGmwV1qT;yn-Ij~(TG#LKV>H&6WIDm2mkTqgo z!yQrMEX+>cth&)(5Hc&C-Y60ly}a|?^a4Sznp`6vv9WJmv7GfYb(g#bi)*!g#cA1D zG#eXkjM^#*3xq2Xv1oTqvdGp)gyitl4z%_@&u#@S(DFx=@?Z0jaGkG<|&V GKjELj=E7e9 literal 0 HcmV?d00001 From b915b8990002ba122344aec01e3a6b05adfdf302 Mon Sep 17 00:00:00 2001 From: Nidhi Patel Date: Mon, 21 Oct 2019 15:16:37 -0600 Subject: [PATCH 23/32] Add Updates to IschemiaTutorial.md --- IschemiaTutorial.md | 883 +++++++++++++++++++++++++++++++++++++++++++- 1 file changed, 882 insertions(+), 1 deletion(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index 86adba7..073ebda 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -1 +1,882 @@ -# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing Scientific Computing & Imaging Institute University of Utah SCIRun software download: http://software.sci.utah.edu Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. Author(s): Jeroen Stinstra, Darrell Swenson ## Contents - 1 Overview - 1.1 Ischemia Model - 1.2 Software requirements - 1.2.1 SCIRun module compatibility - 1.2.2 Required Datasets - 2 Reading and Visualization of Image Data - 2.1 Loading The Dataset - 2.2 Visualization of Dataset - 3 Visualization of Image Data - 3.1 Volume Renderer and Clipping Planes - 3.2 Isosurfacing and Mesh Fairing - 3.3 Resampling and Viewing Glyphs - 4 Building a Tetrahedral Mesh - 4.1 Building a Tetrahedral Mesh - 5 Tensors and Conductivities - 5.1 Creation of Model Parameters - 6 Finite Element Modeling - 6.1 Creating The Simulation - 6.2 Visualization of Simulation Results - #### Chapter 1 # Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an is- chemic heart based on data from actual experiments. The goal of this modeling pipeline is to generate experiment-specific models of the myocardium. The MR images that will be used in this example have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and the perfusion bed of left anterior descending artery. The goal of the simulations is to render a model that can be used to predict extracellular cardiac potentials as measured by electrodes onto on an isolated heart or with needles inserted into the heart. The background behind this research is to provide insight into the question how reduced flow or additional load affect regional acute ischemia. By measuring many anatomic details and electrical measurements we hope to provide insight in what is going on in the border zones between the healthy and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the creation of a forward model of ischemia based on measured anatomical data such as muscle fiber orientation and perfusion beds of the coronary arteries. The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain model one assumes that all electrical sources within the heart are located within the cell membranes of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each other by means of gap junctions (a protein that connects the insides of two cells together), the intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each location by a cell membrane. During the plateau phase of the action potential all cells can be assumed to be in a depolarized state, however the transmembrane potential (the potential difference between the intracellular and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes so called injury currents to flow within the intracellular and extracellular spaces. These currents can be observed at the surface of the heart as potential differences that translate to so called ST shifts in the ECG. CHAPTER 1. OVERVIEW 3 In order to model these currents one needs a description of the electrical properties of both the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors that have the shape of the heart and where the anisotropy is caused by the fiber structure of the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: ∇·Σi∇φi = imem (1.1) ∇·Σe∇φe = −imem (1.2) whereφiandφeare the intracellular and extracellular potentials respectively and Σi, and Σeare the conductivity tensors of both spaces. Finally,imemis the current through the membrane. We can define the transmembrane potential as: φm=φi−φe (1.3) Combining this equation with the previous set of equations results in the system to solve being: ∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potentialφm. To solve this for a specific heart, one needs to have a description of Σiandσeas a function of space and one needs to have a description of howφm changes throughout the border zone. In this tutorial we will first describe how to load the imaging data and how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, andφm, which in the final chapter then is used to solve the extracellular potentialφe. #### 1.2 Software requirements ##### 1.2.1 SCIRun module compatibility The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version to the latest built available from the SCI software portal, which will include the latest bug fixes and will make sure that the capabilities demonstrated in this tutorial are up to date. Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is necessary to obtain a version of SCIRun that includes the meshing tools (currently an interface to TetGen). The easiest way to obtain a SCIRun version that includes these tools is to download a binary version of the software, which is available for both OS X and Windows at the SCI software portal. Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing tools enabled by default. **4 Chapter 1** ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. Note the latter is available as a Windows zip file or as a Linux gzip file. Both however contain the same datasets and only one of them has to be downloaded. CHAPTER 1. OVERVIEW 5 #### Chapter 2 # Reading and Visualization of Image # Data Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. Figure 2.1 shows the main The main SCIRun window _Figure 2.1 - The Main SCIRun Window_ **6 Chapter 2** SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module selector. This menu is used for inserting modules into the network editor. In order to run this tutorial you need to have a SCIRun 5.x version or greater with a revision numberof 42612 or higher, the SCIRun version and revision number can be found in the upper right corner of the SCIRun editor window. Besides walking through the Module selector and finding a specific module by navigating through every submenu, a module can simply be found by typing the name of the module into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in figure 2.2. Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. Adding_and_opening_module _Figure 2.2 - Finding the ReadField module and opening its GUI_ The Dataset that is used in this example is called heart-ischemia and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with theheart-ischemiadatasets. If this dataset is not available in your copy of the SCIRunData bundle, please download the latest version from the website to obtain a copy. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 7 Figure 2.3. Select a file name and a file type (File #3) By pressing on the UI button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used in this example were generated by the Seg3D software and are in the .nnrdfile format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format allows for either a header be appended to the start of the file (.nrrd format) with header and data being in one file or having a separate header file that wraps the data found in a general binary data file (.nhdr format). More information on the .nrrd format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select theNrrdFilefile type **8 Chapter 2** Figure 2.4. & 2.5 Network for checking contents of the file (File # 4 & 5) and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the heart-ischemia directory and select **HeartMRI.nrrd** file. Then press Set at the bottom of the UI to store the file name and type in the module. This process is illustrated in figure 2.3. Now use the Show Module menu again and find the ReportFieldInfo. Insert this module into the network editor. Connect the two modules by clicking and dragging from one of the yellow ports of either module. By dragging the connection from the port from the first module to the second module, the two modules can be connected. Now press Execute All (The green arrowhead at the top of the screen) to execute the modules in the network, as is illustrated in figure 2.5. After the network has been executed, one can open the UI of the **ReportFieldInfo** module to inspect the type of data that has been loaded. In this case the data is represented as aLatVolMesh, the latter mesh type is used by SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data inside the pipeline, the module also shows the dimensions of the grid and the location in space derived from the original imaging data. An example of all the information displayed is shown in figure 2.5. #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking on the module with the right mouse button. This will show a menu, select **Destroy** from the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 9 Figure 2.6 & 2.7 Building the visualization network (File # 6 & 7) will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: GetSliceFromStructuredFieldByIndices, ShowField, RescaleColorMap, and CreateStandardColorMap, and connect the modules as depicted in figures 2.6 and 2.7. Note that not the full name needs to be entered each time in the Show Module text field: if a part of a module name is entered all the modules that match that part of the name will show up. This can be useful to search for new modules that for instance operate on a Field (e.g.by typing Field). After the network of figures 2.6 and 2.7 have been entered in the Network Editor, open up theUI of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the ViewScene module, press theVIEWbutton of the module to see the visualization. When the ViewScene Window depicts a black space after it has been opened, press Autoview in the viewer to ensure that the viewer is looking at the loaded data set. Once Autoviewhas been pressed the resulting dataset should look like the image depicted in figure 2.8. By clicking on the UI of the **GenerateStandardColorMaps** module, the colormap of the current visualization can be altered (illustrated in figure 2.8). The transparency of the colors can be edited by clicking on the red line in the center of the colorbar. When the line is at the top the color is opaque and when the color is at the bottom the color is transparent. Try to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In **10 Chapter 2** Figure 2.6. Network for checking contents of the file the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. CHAPTER 2. READING AND VISUALIZATION OF IMAGE DATA 11 Figure 2.7. Network for checking contents of the file **12 Chapter 2** #### Chapter 3 # Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** Figure 3.1. Reading in two datasets CHAPTER 3. VISUALIZATION OF IMAGE DATA 13 Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the previous example. However instead of viewing slices we will use the ShowTextureVolume module to volume render multiple datasets into the viewer. This module requires the same inputs as the ShowTextureSlices module, but now renders the full volume transparent. Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left **14 Chapter 3** Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- PerfusionBed.nrrd). Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up the ViewScene module and press Configure. This will add a tray below the current win- dow, with different tabs to edit different aspects of the image. Select the Objects tab. This tab shows the current components displayed in the view window. Pressing selection buttons as highlighted in figure 3.3 will switch on and off the displaying of a certain component. Also try the Clipping tab, which will allow to clip the visualization. Open up the Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping widget has been configured, so that D corresponds to the full range of X that is spanned CHAPTER 3. VISUALIZATION OF IMAGE DATA 15 Figure 3.4. Slicing the dataset by the two images that are displayed in the viewer window. By dragging D from -1 to + one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. The figure on the left shows the result of one slicing plane, the result on the right shows two slicing planes. To activate the second slicing plane, press Plane 2 and then activate this plane by selecting the Clipping Plane Visible once more. To make it easier to generate a thin slice, select the the Reverse Clipping Plane Normal option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing In order to build a model out of the datasets we need to translate the volumes into para- metric surfaces. One way to do this is to generate an isosurface. Modify the network by adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as depicted in figure 3.5. The ExtractIsosurface should get its input from the module that reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the ExtractIsosurface module as depicted in figure 3.5. TheExtractIsosurface module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the **16 Chapter 3** Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. The FairMesh module takes the output from the ExtractIsosurface module and smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. The FairMesh module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface that is tessalated by triangles. Because this field is no longer structured like a regular grid, one cannot use the ShowTextureVolume to display the surface. Instead we use CHAPTER 3. VISUALIZATION OF IMAGE DATA 17 Figure 3.6. Coupling Two ViewScene Windows the ShowFieldmodule that is a general module for visualizing any field. The output of this module can again be displayed into the ViewScene module, which now combines visualizations of all three modules. To compare the volume rendering against the smoothed surface model, the ViewScene module has the option to display two coupled Viewer windows. Open up the Viewer win- dow from the ViewScene module. Press the New Window button to generate a similar ViewScene window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the difference between the two visualizations, as depicted by figure 3.6. By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both images manually. This option can however be switched off. Press the Lock View button to unlock the window. When pressing the button the Lock View button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the **18 Chapter 3** Figure 3.7. Network for Visualizing the Fiber Orientation of the Data windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view to the view of the other window. Locking can also be activated by pressing on the keyboard when the window is selected. Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view from the first window, ctrl 2 for the second window and so on. The viewer also as predefined views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also has a keyboard shortcut and is activated by pressing 0. CHAPTER 3. VISUALIZATION OF IMAGE DATA 19 #### 3.3 Resampling and Viewing Glyphs After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and extracting the dominant direction from the data. This data can however still be loaded using the **ReadField** module and the data will be translated into a **LatVolMesh** again, however this time the data located at each node is a vector instead. In order to visualize the vector data we use the network depicted in figure 3.7. This network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. The **ResampleRegularMesh** module resamples the data. Its default settings down- sample the data by a factor 2 in each direction. This module has been added here to ensure that the network executes relatively fast and that the visualization is not clobber by a huge amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. Because the Diffusion Tensor Image was recorded at a different resolution as the anatom- ical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. The module operates by looking up the value of the data in the segmentation for node in the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. The **CalculateFieldData** operates by taking data from the two input fields as two input streams and applying the operation specified inside the UI of the module to each pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an operator that works on a stream of input data. In this case specify the input function as RESULT = DATA1 * DATA2;. In this formula DATA1 is the data from the first field and DATA2 is the data from the second field. As the segmentation defines the outside by a value zero and the inside as a value one, this expression masks the data and will generate vectors of zero length outside of the heart and keeps the input vector value for the vectors inside the heart. The **CalculateFieldData** defines a whole range of mathematical operators that can be applied to a fields and a range of possible input streams that range from the location of nodes to the data values located in the field. To obtain more information on the actual operators that are available for this calculator module press the Parser Help button in the module. This opens a document describing the expression language that has been integrated into SCIRun. Note that the module has build in logic to determine the output type, even though the output type is set to Scalar it will in fact render a Vector output. The Output Data Type in the latest version of SCIRun is thence no more than a hint of what output type would be preferred. In most cases the user should not need to set an output **20 Chapter 3** Figure 3.8. The UI of The CalculateFieldData2 Module type, only when for memory reasons the data should be different from a double precision representation, this type should be set. Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see fig- ure 3.9). This module is primarily used to display Vectors or Tensors that are located inside a field. As this module takes many different inputs, one needs to execute the module be- fore one can select displaying Vectors. The reason for this is that the module first needs to examine the contents of the input before it can display the proper UI. To display the vectors select the Vectors tab and enable the check button Show Vectors. Also disable the Render glyphs below threshold setting. This will prevent SCIRun from rendering glyphs whose size (for Vectors we look at the vector length) is below the _Vector Threshold_. In this example we will render Vectors as cones by selecting the Vector Display Type in the UI and we use RGB Conversion as the vector coloring. The latter option colors a vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for the z-axis. Depending on the orientation of the vector the red, green, and blue colors are mixed together to indicate the orientation. Also increase the size of the _Vector Scale_ to render glyphs that are larger. Also as these vectors represent the fiber direction, the actual direction they are pointing is arbitrary as they could just as well point in the opposite direction. It is the line the CHAPTER 3. VISUALIZATION OF IMAGE DATA 21 Figure 3.9. The UI of the **ShowFieldGlyphs** Module vectors are pointing along that matters in this case. To make the vectors point in both directions, set the option Render bidirectionally. The final image that is rendered is displayed in figure 3.10. In this image we applied the slicing from the previous section, to highlight the fibers in a cross section through the left ventricle of the heart. By combing the networks examined in this tutorial one can visualize the different aspects of the data. **22 Chapter 3** Figure 3.10. Visualizing the Fiber Orientation of the Data CHAPTER 3. VISUALIZATION OF IMAGE DATA 23 #### Chapter 4 # Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. When opening the UI of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in the UI. The -Y option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in this example we switch it off. The next flag -q enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. The final flag that is of interest is the -a flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not want that in this case, we supply a volumetric maximum. In this case a value of 5 is reasonable value. In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. **24 Chapter 4** Figure 4.1. Network for building a Tetrahedral Mesh CHAPTER 4. BUILDING A TETRAHEDRAL MESH 25 Figure 4.2. Image of the Tetrahedral Mesh The **ExtractIsosurface** module should be set to the Quantitytap and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in figure 4.1. Finally, the WriteField module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. Supply a filename in the UI of the module and press **Set to** set the name of the file that will be written. Also open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of how long it takes to render the mesh, hence even while the progress bar in the module is not moving progress is made and SCIRun will return within a several minutes and display the mesh. Use the slicing planes to examine the mesh (see figure 4.2). **26 Chapter 4** #### Chapter 5 # Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters The next step in building the simulation is the creation of the model parameter spaces. In this example the model is defined by the conductivities of the intracellular and extracellular spaces as a function of space and the transmembrane potential as a function of space. To generate these model spaces we start with a clean canvas, and add aReadField module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in figure 5.1 with Figures 5.2-5.4 detailing the setting of the variousUIs. Only those modules that need modifications to the default settings are listed in the figures. This network starts by loading the previously generated mesh, and also loads the per- fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first step is to downsample the data by a factor 2 to make the computations more interactive for this tutorial. The next step is the extraction of the isosurface that defines the boundary of the ischemic zone. This boundary subsequently fed into theFairMeshmodule to smooth out discretization effects, leaving a relative smooth definition of the ischemic border zone. This definition of the border zone is used for two purposes: (1) the definition of the trans- membrane potential as a function of space and (2) the definition of the conductivity which changes as a function of space. In order to define a volumetric function based on a surface we compute the distance to the surface for each node located in the mesh. As the ischemic zone is a closed volume we can use theCalculateSignedDistanceToFieldmodule to determine the distance of each node to the surface. In this case a positive distance is rendered for each node inside the ischemic zone and a negative distance is rendered for each node outside of the surface. Although the computation of the distance fields for unstructured grids is generally a slow operation, the SCIRun code inside the module uses a parallel algorithm that should solve this distance field with a timeframe of less than a minute. However note that when the objects get more complex this operation can be relatively slow. CHAPTER 5. TENSORS AND CONDUCTIVITIES 27 Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the transmembrane potential fields **28 Chapter 5** Figure 5.2. UI settings of modules Below theCalculateSignedDistanceToFieldmodule, the distance field is inserted into theCalculateFieldDatamodule. The latter module evaluates a mathematical ex- pression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the in- duced currents, the choice of the reference membrane potential does not matter. However if one wanted to one can add easily an additional term to equation. The equation displayed in figure 5.2 was chosen arbitrary to reflect a smooth transition CHAPTER 5. TENSORS AND CONDUCTIVITIES 29 of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the features of the built-in mathematical expression parser. It can parser a set of equations and one can define an arbitrary amount of additional parameters. The grammar of the parser requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. TheCalculateFieldData2module, which is based on the same mathematical expres- sion parser, is used to generate the conductivity tensors as well. In figure 5.3 the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a special function calledselectwhich treads the first argument as a boolean expression and based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use theMapFieldDataFromNodeToElemmodule. This module by default interpolates the data using a linear scheme to the center of each element of the mesh. The transformation of the fiber orientation data is a bit more complex as it is located inside a different mesh. In order to map data from one mesh type to another mesh type, two special modules have been designed to help with mapping data from one mesh to another mesh, namelyMapFieldDataOntoNodesandMapFieldDataOntoElems. In this case the latter module is used. By default the mapping of data onto elements is performed by choosing a range of sampling points inside each element and find the interpolated value for each location. The values are subsequently consolidated by averaging them. In case the user wanted a different integration scheme for the data, several methods are available for defining the data in the original, a variety of sampling schemes is available and several methods are available for combining the resulting values. In this case we use the default settings as they should render a good enough result. The mapped distance field and fiber orientation are then used to compute the conduc- tivity tensor. Within the math expression parser a full range of functions is available for defining the Tensor, in this case the first input into the Tensor function is the first eigen- vector and the two subsequent scalars are the conductivity along this first axis, and the next one is the conductivity across. A second eigenvector would be permitted as well by defining two input vectors and three conductivity scalars. However for cardiac tissue only the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. The last part of the network introduces a new concept called theBundle. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see figure 5.4) To generate a bundle theInsertFieldsIntoBundlemodule assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, en- quoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, **30 Chapter 5** Figure 5.3. UI settings of modules CHAPTER 5. TENSORS AND CONDUCTIVITIES 31 Figure 5.4. UI settings of modules and the extracellular conductivity respectively. The bundle subsequently saved on disk for the simulation network of the next chapter. Finally a small portion on the bottom left of the network is dedicated to displaying the transmembrane potential. This part of the network uses the modules from previous chapters to do generate a visualization of how the transmembrane potential looks like. Try for instance altering the “BLUR” parameter in the calculator module to see the effect of the blurring. An example of the output is given in figure 5.5. **32 Chapter 5** Figure 5.5. Visualization of assumed transmembrane potentials CHAPTER 5. TENSORS AND CONDUCTIVITIES 33 #### Chapter 6 # Finite Element Modeling Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- Matrix -GetFieldData - SetFieldData #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : −(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis the transmembrane potential andφeis the extracellular potential. In this network the transmembrane potentialφmis assumed to be the quantity that is known and the network computes the extracellular potentialsφethat are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. At the top of the network the bundle is split in two, one part is used to create the right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular and extracellular tensors. The moduleCalculateFieldData2is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ operator. The modules to the left of the creation of the stiffness matrix actually compute the right- hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the data inside the field needs to be represented as a vector. This is accomplished by the **34 Chapter 6** Figure 6.1. Full network for running simulation CHAPTER 6. FINITE ELEMENT MODELING 35 Figure 6.2. UI settings of modules GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary module. Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule solves the linear system using in iterative solver. The details of the solver can be entered in theUIof this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using theSetFieldDatamodule. An example of a reasonable number of iterations is given in figure 6.3. Everything below this module in the network is used for visualizing the data which is described in the next section. **36 Chapter 6** Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use theExtractIsosur- faceByFunctionmodule. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator module again and extracting the first eigenvector using theeigvec1()function. The data is subsequently moved to the elements of the mesh. To efficiently project the data onto the same mesh as the data, we use theApplyMap- CHAPTER 6. FINITE ELEMENT MODELING 37 Figure 6.4. UI settings of modules pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule to accomplish the same. Finally the vectors and the data are combined into one viewer. In order to render a sense or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary module extracts the outside of any mesh. In this case it renders the outer surface of the model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. Finally theViewScenemodule displays a result that show that the potentials tend to **38 Chapter 6** Figure 6.5. UI settings of modules stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. CHAPTER 6. FINITE ELEMENT MODELING 39 Figure 6.6. Visualizing Results **40 Chapter 6** \ No newline at end of file +# Ischemia Model tutorial + +#### SCIRun 5.0 Documentation + +Center for Integrative Biomedical Computing +Scientific Computing & Imaging Institute +University of Utah + + +SCIRun software download: +http://software.sci.utah.edu +Center for Integrative Biomedical Computing: +http://www.sci.utah.edu/cibc + +This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. + +Author(s): +Jeroen Stinstra, Darrell Swenson + + +## Contents + + - 1 Overview + - 1.1 Ischemia Model + - 1.2 Software requirements + - 1.2.1 SCIRun module compatibility + - 1.2.2 Required Datasets + - 2 Reading and Visualization of Image Data + - 2.1 Loading The Dataset + - 2.2 Visualization of Dataset + - 3 Visualization of Image Data //ended here + - 3.1 Volume Renderer and Clipping Planes + - 3.2 Isosurfacing and Mesh Fairing + - 3.3 Resampling and Viewing Glyphs + - 4 Building a Tetrahedral Mesh + - 4.1 Building a Tetrahedral Mesh + - 5 Tensors and Conductivities + - 5.1 Creation of Model Parameters + - 6 Finite Element Modeling + - 6.1 Creating The Simulation + - 6.2 Visualization of Simulation Results +- + +#### Chapter 1 + +# Overview + +**This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It +describes the pipeline starting from preprocessed images to generate a computational mesh and adapt +this mesh to meet the computational requirements. It then continues to set up a finite element bidomain +simulation, and demonstrates how results can be visualized.** + +#### 1.1 Ischemia Model + +This tutorial describes the generation of a quasi-static volume conductor model of an ischemic +heart based on data from actual experiments. The goal of this modeling pipeline is to generate +experiment-specific models of the myocardium. The MR images that will be used in this example +have been derived from a dog heart that was scanned to obtain anatomy, fiber orientation and +the perfusion bed of left anterior descending artery. The goal of the simulations is to render +a model that can be used to predict extracellular cardiac potentials as measured by electrodes +onto on an isolated heart or with needles inserted into the heart. + +The background behind this research is to provide insight into the question how reduced flow or +additional load affect regional acute ischemia. By measuring many anatomic details and electrical + measurements we hope to provide insight in what is going on in the border zones between the healthy + and ischemic tissue layers. This tutorial describes one specific aspect of that research namely the + creation of a forward model of ischemia based on measured anatomical data such as muscle fiber + orientation and perfusion beds of the coronary arteries. + +The electrical model that is described in this tutorial is a so called bidomain model. In the bidomain +model one assumes that all electrical sources within the heart are located within the cell membranes +of myocytes (heart cells). As the intracellular electrolytes of all the myocytes are connected to each +other by means of gap junctions (a protein that connects the insides of two cells together), the +intracellular and extracellular spaces can be assumed as two continuous spaces that are separated at each + location by a cell membrane. + +During the plateau phase of the action potential all cells can be assumed to be in a depolarized +state, however the transmembrane potential (the potential difference between the intracellular +and extracellular space) is not the same for ischemic and healthy cells. The latter effect causes +so called injury currents to flow within the intracellular and extracellular spaces. These currents +can be observed at the surface of the heart as potential differences that translate to so called ST +shifts in the ECG. + + + + +In order to model these currents one needs a description of the electrical properties of both +the intracellular and extracellular spaces. Both can be modeled as anisotropic volume conductors +that have the shape of the heart and where the anisotropy is caused by the fiber structure of +the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces +are the following: + +∇·Σi∇φi = imem (1.1) +∇·Σe∇φe = −imem (1.2) + +where φi and φe are the intracellular and extracellular potentials respectively and Σi, and Σe are +the conductivity tensors of both spaces. Finally, imem is the current through the membrane. We +can define the transmembrane potential as: + +φm=φi−φe (1.3) + +Combining this equation with the previous set of equations results in the system to solve being: + + +∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) + +The latter equation describes the potential of the extracellular space, as observed in measurements, +as a function of the membrane potential φm. To solve this for a specific heart, one needs to have a +description of Σi and σe as a function of space and one needs to have a description of how φm changes +throughout the border zone. In this tutorial we will first describe how to load the imaging data and +how visualize this, subsequently this imaging data is turned into a description of Σi, Σe, and φm, +which in the final chapter then is used to solve the extracellular potential φe. + + +#### 1.2 Software requirements + + +##### 1.2.1 SCIRun module compatibility + +The modules demonstrated in this tutorial are available in SCIRun version 4.0 and higher and this +tutorial is not compatible with any older version of SCIRun. Also be sure to update your SCIRun version +to the latest built available from the SCI software portal, which will include the latest bug fixes +and will make sure that the capabilities demonstrated in this tutorial are up to date. + +Because this tutorial demonstrates the meshing capabilities available within SCIRun, it is +necessary to obtain a version of SCIRun that includes the meshing tools (currently +an interface to TetGen). The easiest way to obtain a SCIRun version that includes these +tools is to download a binary version of the software, which is available for both OS X and +Windows at the SCI software portal. +Unfortunately for Linux users there is no binary yet available. Hence, to run this tutorial, +one has to compile SCIRun from scratch. Download SCIRun from the SCI software portal +at http://software.sci.utah.edu and follow the instructions in the InstallationGuide to build +SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with meshing +tools enabled by default. + + + +##### 1.2.2 Required Datasets + +This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain +these datasets, please go to the SCI software portal, follow theDownload SCIRunlink, +and instead of the SCIRun source or binary files, download one of the SCIRunData zip files. +Note the latter is available as a Windows zip file or as a Linux gzip file. Both however +contain the same datasets and only one of them has to be downloaded. + + + + +#### Chapter 2 + +# Reading and Visualization of Image + +# Data + + +Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets + +#### 2.1 Loading The Dataset + + +We start by opening the main SCIRun window by launching SCIRun by either double +clicking on the binary icon or by launching SCIRun from the command line. A detailed +description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been +launched the main Window with the Network editor is shown. *Figure 2.1* shows the main + +The main SCIRun window + +_Figure 2.1 - The Main SCIRun Window_ + + + +SCIRun network editor. For this tutorial we will be selecting modules from the +module selector, on the left side of the screen. If for some reason the module +selector is not there, open the dropdown menu titled **Window** to bring up the module +selector. This menu is used for inserting modules into the network editor. In order +to run this tutorial you need to have a SCIRun 5.x version or greater with a revision +number of 42612 or higher, the SCIRun version and revision number can be found in the +upper right corner of the SCIRun editor window. + +Besides walking through the Module selector and finding a specific module by navigating +through every submenu, a module can simply be found by typing the name of the module +into Show Module entry box located in the top menu bar. This will highlight the location +of a specific module within the Modules menu as is demonstrated in *Figure 2.2*. + +Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the +Modules menu and select the **ReadField** module form the menu. This will insert the +**ReadField** module in the upper left corner of the network editor. This module will now +be used to read in the first dataset. + +Adding and opening module + +_Figure 2.2 - Finding the ReadField module and opening its GUI_ + + +The Dataset that is used in this example is called **heart-ischemia** and it can be found +in the SCIRunData bundle that can be downloaded as well from the SCI software portal +(http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file +inside a directory and inside you will find a sub directory with the **heart-ischemia** datasets. +If this dataset is not available in your copy of the SCIRunData bundle, please download the +latest version from the website to obtain a copy. + + + + +Selecting file name and type + +_Figure 2.3. Select a file name and a file type_ + + +By pressing on the **UI** button of the **ReadField** module a browser window is opened +where one can enter the name of the file that needs to be loaded. The files that are used +in this example were generated by the **Seg3D** software and are in the *.nnrdfile* format. +This file format is used to represent regular spaced image data, such as MRI images or +segmentations. It consists of a simple text header specifying the dimensions of the data and +its location in space, followed by binary data representing the actual data. This file format +allows for either a header be appended to the start of the file (*.nrrd* format) with header +and data being in one file or having a separate header file that wraps the data found in a +general binary data file (*.nhdr* format). More information on the .nrrd format can be found +at http://teem.sourceforge.net/nrrd/format.html. + +Once the UI Window of the **ReadField** module opens, select the **NrrdFile** file type + + +Network for checking contents of file and information displayed when executed + +_Figure 2.4. Network for checking contents of the file_ + +and use the upper part of the UI to locate the dataset by browsing the directories to the +location where the SCIRunData has been saved. Open the **heart-ischemia** directory and +select **HeartMRI.nrrd** file. Then press **Set** at the bottom of the UI to store the file name +and type in the module. This process is illustrated in *Figure 2.3*. + +Now use the Show Module menu again and find the **ReportFieldInfo**. Insert this +module into the network editor. Connect the two modules by clicking and dragging from one of the yellow +ports of either module. By dragging the connection from the port from the first module to the second module, +the two modules can be connected. Now press **Execute All** (The green arrowhead at the top of the screen) to execute the modules in the +network, as is illustrated in *Figure 2.4*. After the network has been executed, one can open +the **UI** of the **ReportFieldInfo** module to inspect the type of data that has been loaded. + +In this case the data is represented as a **LatVolMesh**, the latter mesh type is used by +SCIRun to represent regularly spaced data like CT or MRI data. Besides the type of data +inside the pipeline, the module also shows the dimensions of the grid and the location in +space derived from the original imaging data. An example of all the information displayed +is shown in *Figure 2.4*. + +#### 2.2 Visualization of Dataset + +Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. +Because we do not need the **ReportFieldInfo** module for the next part of the tutorial we +can delete the module from the network. Destroy the **ReportFieldInfo** module by clicking +on the gear icon on the module. This will show a menu, select **Destroy** from +the menu and the module will be deleted from the network editor. + +To visualize the 3D dataset we convert the module into a 3D texture object, which + + + +Building visualization network + +_Figure 2.5 Building the visualization network_ + +will allow us to quickly browse through the dataset. Use the Show Module feature in the +menu bar to insert the following modules: **GetSliceFromStructuredFieldByIndices**, **ShowField**, **RescaleColorMap**, **CreateStandardColorMap**, and **ViewScene**, and connect the modules as depicted in +*Figure 2.5*. Note that not the full name needs to be entered each time in the Show Module +text field: if a part of a module name is entered all the modules that match that part of the +name will show up. This can be useful to search for new modules that for instance operate +on a Field (*e.g.* by typing Field). + +After the network of *Figure 2.5* have been entered in the Network Editor, open up the **UI** +of **GetSliceFromStructuredFieldByIndices** and select a slice of the axis, either I, J, or K. Now execute the network. The resulting visualization is now located in the +ViewScene module, press the **VIEW** button of the module to see the visualization. + +When the ViewScene Window depicts a black space after it has been opened, press the +**Autoview** icon in the viewer to ensure that the viewer is looking at the loaded data set. Once +**Autoview** has been pressed the resulting dataset should look like the image depicted in +*Figure 2.6*. + +By clicking on the UI of the **CreateStandardColorMap** module, the colormap of the +current visualization can be altered (illustrated in *Figure 2.6*). The transparency of the colors +can be edited by clicking on the red line in the center of the colorbar. When the line is at +the top the color is opaque and when the color is at the bottom the color is transparent. Try +to make the background transparent. The slider just below that controls where the largest +gradient in color should occur by sliding it to the left a higher contrast is generated. In + + +Network for checking contents of the file + +_Figure 2.6. Network for checking contents of the file_ + +the lower part of the menu one can now select from a series of predefined colormap lookup +tables to alter the appearance of the image. + +To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. +Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. + +Viewing multiple slices + + +_Figure 2.7. Viewing multiple slices_ + + + +#### Chapter 3 + +# Visualization of Image Data + +**Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** + +Figure 3.1. Reading in two datasets + + + +Figure 3.2. Reading in two datasets + +#### 3.1 Volume Renderer and Clipping Planes + + +In the previous chapter one dataset was explored, however the SCIRun viewer is capable +of rendering many datasets in the same viewer, so one can explore the correlation between +the data or combine them to build a model. In the next example we will be loading two +datasets into the viewer. To do this we start with a similar network as depicted in the +previous example. However instead of viewing slices we will use the ShowTextureVolume +module to volume render multiple datasets into the viewer. This module requires the same +inputs as the ShowTextureSlices module, but now renders the full volume transparent. +Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and +HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. +Once the network executes the data of the two datasets is combined into one visualization +of the data. Try to alter the transparency of the colormaps to highlight the needle markers +that were inserted into the heart and the perfusion bed of one of Left Anterior Descending +Artery. An example of such a visualization is given in figure 3.1. +The datasets in this example originate from an isolated dog heart in which the Left + + + +Figure 3.3. Opening the configuration tray + +Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an +MR scan. The heart was subsequently scanned to generate an anatomical image of the heart +HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. +Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- +mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- +PerfusionBed.nrrd). +Although displaying the two datasets into one image is useful, one does not always want +to see each component of the data. To edit what is actually displayed in the image, open up +the ViewScene module and press Configure. This will add a tray below the current win- +dow, with different tabs to edit different aspects of the image. Select the Objects tab. This +tab shows the current components displayed in the view window. Pressing selection buttons +as highlighted in figure 3.3 will switch on and off the displaying of a certain component. +Also try the Clipping tab, which will allow to clip the visualization. Open up the +Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider +to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping +widget has been configured, so that D corresponds to the full range of X that is spanned + + + + + +Figure 3.4. Slicing the dataset + + +by the two images that are displayed in the viewer window. By dragging D from -1 to + +one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. +The figure on the left shows the result of one slicing plane, the result on the right shows two +slicing planes. To activate the second slicing plane, press Plane 2 and then activate this +plane by selecting the Clipping Plane Visible once more. To make it easier to generate a +thin slice, select the the Reverse Clipping Plane Normal option for the second clipping +plane as this reverse the visible part of the image. By lining up the two clipping planes one +can generate a small thin slice. +If the slice becomes too transparent, open up the UI of the ShowTextureVolume +module. One of the main options is the Global Opacity. Changing this slider the volume +rendered object can be made more or less transparent. + +#### 3.2 Isosurfacing and Mesh Fairing + + +In order to build a model out of the datasets we need to translate the volumes into para- +metric surfaces. One way to do this is to generate an isosurface. Modify the network by +adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as +depicted in figure 3.5. The ExtractIsosurface should get its input from the module that +reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the +ExtractIsosurface module as depicted in figure 3.5. +TheExtractIsosurface module extracts an isosurface out of any field. In this case +we are extracting it out of the segmented perfusion bed by selecting a value between the + + + +Figure 3.5. Extracting an Isosurfacet + +maximum and minimum value in the field. In this case the background and the segmen- +tation have a different but constant value and hence the boundary between them will be +selected. The isosurface is extracted using the Marching Cubes method which will insert an +approximation of the isosurface for each element in the mesh. + +The FairMesh module takes the output from the ExtractIsosurface module and +smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. +The FairMesh module takes the surfaces and uses information about the neighborhood +of the surface to generate a smoother looking surface. The resulting surface is a surface +that is tessalated by triangles. Because this field is no longer structured like a regular +grid, one cannot use the ShowTextureVolume to display the surface. Instead we use + + + + +Figure 3.6. Coupling Two ViewScene Windows + + +the ShowFieldmodule that is a general module for visualizing any field. The output +of this module can again be displayed into the ViewScene module, which now combines +visualizations of all three modules. +To compare the volume rendering against the smoothed surface model, the ViewScene +module has the option to display two coupled Viewer windows. Open up the Viewer win- +dow from the ViewScene module. Press the New Window button to generate a similar +ViewScene window with the same dimensions. Now open up the configuration tab on both +windows. By selecting different objects in both windows, the windows can be customized +to display a different aspect of the Scene. Display the Faces of the Isosurface in one window +and the volume rendering of the Volume Rendering in the other window to examine the +difference between the two visualizations, as depicted by figure 3.6. +By zooming in into the model of the surface one can see the difference between the +two renderings. Note that by default the two windows are locked together. Meaning that +rotations in one window are automatically applied to the other window. This option allows +to highlight the same spot in space in both windows without the need to actually align both +images manually. This option can however be switched off. Press the Lock View button +to unlock the window. When pressing the button the Lock View button changes color to +indicate that it is switched off. One can now independently orient the windows. Locking the +windows together again will not align the windows but keep the relative change between the + + +Network for visualizing the fiber orientation of the data + + +_Figure 3.7. Network for Visualizing the Fiber Orientation of the Data_ + +windows. The changes are however applied to both windows. To align the windows again +select the Views menu at the top of the window and select the Other Viewer Windows +menu and select the option to get the view from the other window. This will align the view +to the view of the other window. + +Locking can also be activated by pressing on the keyboard when the window is selected. +Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view +from the first window, ctrl 2 for the second window and so on. The viewer also as predefined +views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also +has a keyboard shortcut and is activated by pressing 0. + + + + +#### 3.3 Resampling and Viewing Glyphs + + +After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot +easily be volume rendered as the data are not scalar, but are in fact vectors. This data was +derived from the Diffusion Weighted Images by doing a decomposition of the tensor and +extracting the dominant direction from the data. This data can however still be loaded +using the **ReadField** module and the data will be translated into a **LatVolMesh** again, +however this time the data located at each node is a vector instead. + +In order to visualize the vector data we use the network depicted in *Figure 3.7*. This +network adds the following new modules to the network: **ResampleRegularMesh**, **MapFieldDataOntoNodes**, **CalculateFieldData**, and **ShowFieldGlyphs**. + +The **ResampleRegularMesh** module resamples the data. Its default settings downsample +the data by a factor 2 in each direction. This module has been added here to ensure +that the network executes relatively fast and that the visualization is not clobber by a huge +amount of vectors. The default settings in the UI of this module should do for demonstrating +displaying vectors. + +Because the Diffusion Tensor Image was recorded at a different resolution as the anatomical +MR image, the data in the segmentation which was derived from the anatomical scan +is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to +map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. +The module operates by looking up the value of the data in the segmentation for node in +the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation +projected onto the same grid as the vector data. + +The mapped segmentation can now be used to mask out any data that is located outside +of the heart. In order to mask the data we use the general purpose calculator module, +called **CalculateFieldData**. + +The **CalculateFieldData** operates by taking data from the two input fields as two +input streams and applying the operation specified inside the UI of the module to each +pair of data from the two fields, as depicted by Figure 3.8. Hence, this module defines an +operator that works on a stream of input data. In this case specify the input function as +*RESULT = DATA1 * DATA2;*. In this formula *DATA1* is the data from the first field +and *DATA2* is the data from the second field. As the segmentation defines the outside by +a value zero and the inside as a value one, this expression masks the data and will generate +vectors of zero length outside of the heart and keeps the input vector value for the vectors +inside the heart. + +The **CalculateFieldData** defines a whole range of mathematical operators that can +be applied to a fields and a range of possible input streams that range from the location +of nodes to the data values located in the field. To obtain more information on the actual +operators that are available for this calculator module press the **Parser Help** button in +the module. This opens a document describing the expression language that has been +integrated into SCIRun. Note that the module has build in logic to determine the output +type, even though the output type is set to Scalar it will in fact render a Vector output. The +**Output Data Type** in the latest version of SCIRun is thence no more than a hint of what +output type would be preferred. In most cases the user should not need to set an output + + +The UI of the CalculateFieldData module + +_Figure 3.8. The UI of The **CalculateFieldData** Module_ + +type, only when for memory reasons the data should be different from a double precision +representation, this type should be set. + +Finally the **ShowFieldGlyphs** allows for displaying the vectors in the viewer (see *Figure +3.9*). This module is primarily used to display Vectors or Tensors that are located inside +a field. As this module takes many different inputs, one needs to execute the module before +one can select displaying Vectors. The reason for this is that the module first needs +to examine the contents of the input before it can display the proper **UI**. To display the +vectors select the **Vectors** tab and enable the check button **Show Vectors**. Also disable +the **Render glyphs below threshold** setting. This will prevent SCIRun from rendering +glyphs whose size (for Vectors we look at the vector length) is below the **Vector Threshold**. + +In this example we will render Vectors as cones by selecting the **Vector Display Type** +in the UI and we use **RGB Conversion** as the vector coloring. The latter option colors a +vector red if it is aligned along the x-axis, green if it is aligned along the y-axis and blue for +the z-axis. Depending on the orientation of the vector the red, green, and blue colors are +mixed together to indicate the orientation. Also increase the size of the **VectorScale** +to render glyphs that are larger. + +Also as these vectors represent the fiber direction, the actual direction they are pointing +is arbitrary as they could just as well point in the opposite direction. It is the line the + + +The UI of the ShowFieldGlyphs module + +_Figure 3.9. The UI of the **ShowFieldGlyphs** Module_ + + +vectors are pointing along that matters in this case. To make the vectors point in both +directions, set the option **Render bidirectionally**. + +The final image that is rendered is displayed in *Figure 3.10*. In this image we applied the +slicing from the previous section, to highlight the fibers in a cross section through the left +ventricle of the heart. By combing the networks examined in this tutorial one can visualize +the different aspects of the data. + + + +Figure 3.10. Visualizing the Fiber Orientation of the Data + + + + +#### Chapter 4 + +# Building a Tetrahedral Mesh + + +Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes + +#### 4.1 Building a Tetrahedral Mesh + + +In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using +isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted +in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and +**WriteField**. + +The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a +constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of +tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated +by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. + +When opening the UI of the **InterfaceWithTetGen** module, one can select out of a +range of options to generate a mesh. The three options that are of interest in generating +a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in +the UI. The -Y option lets the user decide whether additional vertices are to be inserted +into the outer boundary. Suppressing splitting of the boundary facets often generates lower +quality elements at the boundary, and forces TetGen to do far more computations, so in +this example we switch it off. The next flag -q enforces quality of the elements, one can +specify a lower ratio for a better quality. Normally enforcing a higher quality comes at +the price of a longer computation and more elements. We keep this at its default setting. +The final flag that is of interest is the -a flag that allows the user to specify the size of the +elements. Besides element quality, element size is an important parameter for computing +electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will +enforce the largest size elements it can fit within the interior of the mesh. As we do not +want that in this case, we supply a volumetric maximum. In this case a value of 5 is +reasonable value. + +In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; +the **ResampleRegularMesh** module can keep its default settings. The reason for this +module being added to the pipeline is reduce the number of elements in the segmentation, +so that the example can be computed within a time frame of minutes instead of hours. + + + +Figure 4.1. Network for building a Tetrahedral Mesh + + + + + +Figure 4.2. Image of the Tetrahedral Mesh + + +The **ExtractIsosurface** module should be set to the Quantitytap and we should be +computing only one isosurface. The **InterfaceWithTetGen** module options should be set as +indicated in figure 4.1. Finally, the **WriteField** module should contain a name of a file that +will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. +Press **Save** in the UI of the module, supply the filename HeartMRI-TetrahedralMesh.fld, and select the desired location for the the file that will be written. Also open up the **ShowField** +module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render +these without any problems. Open the **FairMesh** UI and ensure that the number of +iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. + +After pressing **Execute All** to execute all modules allow for a few minutes for the model +to build. As TetGen is running as an external library, we do not have a good estimate of +how long it takes to render the mesh, hence even while the progress bar in the module is +not moving progress is made and SCIRun will return within a several minutes and display +the mesh. Use the slicing planes to examine the mesh (see *Figure 4.2*). + + + +#### Chapter 5 + +# Tensors and Conductivities + +**Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** + +#### 5.1 Creation of Model Parameters + +The next step in building the simulation is the creation of the model parameter spaces. In +this example the model is defined by the conductivities of the intracellular and extracellular +spaces as a function of space and the transmembrane potential as a function of space. + +To generate these model spaces we start with a clean canvas, and add a **ReadField** +module to read the mesh that was generated in the previous chapter. The full network for +generating the model is outlined in *Figure 5.1* with *Figures 5.2 - 5.4* detailing the setting of +the various UIs. Only those modules that need modifications to the default settings are +listed in the figures. + +This network starts by loading the previously generated mesh, and also loads the per- +fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at +the top of the network. This data serves as material to build the heart specific models. + +In the upper left corner of the network the perfusion bed dataset is loaded. The first +step is to downsample the data by a factor 2 to make the computations more interactive for +this tutorial. The next step is the extraction of the isosurface that defines the boundary of +the ischemic zone. This boundary subsequently fed into the **FairMesh** module to smooth +out discretization effects, leaving a relative smooth definition of the ischemic border zone. +This definition of the border zone is used for two purposes: (1) the definition of the trans- +membrane potential as a function of space and (2) the definition of the conductivity which +changes as a function of space. + +In order to define a volumetric function based on a surface we compute the distance +to the surface for each node located in the mesh. As the ischemic zone is a closed volume +we can use the **CalculateSignedDistanceToField** module to determine the distance of +each node to the surface. In this case a positive distance is rendered for each node inside +the ischemic zone and a negative distance is rendered for each node outside of the surface. +Although the computation of the distance fields for unstructured grids is generally a slow +operation, the SCIRun code inside the module uses a parallel algorithm that should solve +this distance field with a timeframe of less than a minute. However note that when the +objects get more complex this operation can be relatively slow. + + + + + +Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the +transmembrane potential fields + + + +Figure 5.2. UI settings of modules + +Below the **CalculateSignedDistanceToFieldmodule**, the distance field is inserted +into the **CalculateFieldData** module. The latter module evaluates a mathematical +expression based on the data of the field. In this case we define a function that blurs the +transmembrane potential based on the distance to the border zone. As the distance is +signed we define the transmembrane potential inside the ischemic zone as -15 mV and the +potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this +bidomain simulation we have altered the actual transmembrane potential to be centered +around 0mV for convenience. As the choice of a reference potential does not alter the +induced currents, the choice of the reference membrane potential does not matter. However +if one wanted to one can add easily an additional term to equation. + + +The equation displayed in *Figure 5.2* was chosen arbitrary to reflect a smooth transition + + + + +of the transmembrane potential. The function here just indicates one of many functions that +could have been chosen, as we are still in the process of actually determining what the shape +of the ischemic border zone is. The equations displayed in the figure show various of the +features of the built-in mathematical expression parser. It can parser a set of equations and +one can define an arbitrary amount of additional parameters. The grammar of the parser +requires that you separate each expression by a semi colon. Currently only expression as +supported by the parser and no functions, loops, or conditional statements are supported. + +The **CalculateFieldData** module, which is based on the same mathematical expression +parser, is used to generate the conductivity tensors as well. In *Figure 5.3* the example +functions for these conductivities are given. Note that we use two input fields here and +hence the function now is function of two spatial varying parameters. In this case we as a +special function called **select** which treads the first argument as a boolean expression and +based on the outcome decides to evaluate the first or the second argument. This in a sense +adds a conditional statement to the math parser. + +One difference with the function for the transmembrane potential is that the data now +has to be located at the centers of the elements, as the Finite Element computations are +currently restricted to conductivities defined for an element. In order to translate the +distance field from a representation on nodes to a representation onto elements, we use +the **MapFieldDataFromNodeToElem** module. This module by default interpolates the +data using a linear scheme to the center of each element of the mesh. + +The transformation of the fiber orientation data is a bit more complex as it is located +inside a different mesh. In order to map data from one mesh type to another mesh type, two +special modules have been designed to help with mapping data from one mesh to another +mesh, namely **MapFieldDataOntoNodes** and **MapFieldDataOntoElems**. In this case +the latter module is used. By default the mapping of data onto elements is performed by +choosing a range of sampling points inside each element and find the interpolated value for +each location. The values are subsequently consolidated by averaging them. In case the user +wanted a different integration scheme for the data, several methods are available for defining +the data in the original, a variety of sampling schemes is available and several methods are +available for combining the resulting values. In this case we use the default settings as they +should render a good enough result. + +The mapped distance field and fiber orientation are then used to compute the conductivity +tensor. Within the math expression parser a full range of functions is available for +defining the Tensor, in this case the first input into the Tensor function is the first +eigenvector and the two subsequent scalars are the conductivity along this first axis, and the +next one is the conductivity across. A second eigenvector would be permitted as well by +defining two input vectors and three conductivity scalars. However for cardiac tissue only +the conductivity ratio across versus along the myocardial fiber is known. It is assumed that +across the fiber in both directions one has the same conductivity. + +The last part of the network introduces a new concept called the **Bundle**. A bundle +is no more than a collection of Fields and other objects that are stored by name. The +advantage of bundling data is that one can store all the fields into one file. Which makes it +easier to maintain the simulation data, as well as that it saves diskspace when components +use common structures like an underlying mesh. (see *Figure 5.4*) + +To generate a bundle the *InsertFieldsIntoBundle* module assigns each of the input +ports to a new name in the bundle. In this case we choose the names enquoteVM, +enquoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, + + + +Figure 5.3. UI settings of modules + + + + + +Figure 5.4. UI settings of modules + + +and the extracellular conductivity respectively. The bundle subsequently saved on disk for +the simulation network of the next chapter. + +Finally a small portion on the bottom left of the network is dedicated to displaying +the transmembrane potential. This part of the network uses the modules from previous +chapters to do generate a visualization of how the transmembrane potential looks like. Try +for instance altering the “BLUR” parameter in the calculator module to see the effect of +the blurring. An example of the output is given in *Figure 5.5*. + + + +Figure 5.5. Visualization of assumed transmembrane potentials + + + + +#### Chapter 6 + +# Finite Element Modeling + + +Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- +Matrix -GetFieldData - SetFieldData + +#### 6.1 Creating The Simulation + + +We start with the bundle generated in the previous chapter. This bundle contains all the +fields for running the simulation. To run the simulation build the network as depicted in +figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The +modules that are not highlighted in these figures use the default settings of these modules. +The underlying idea of the this network is to solve the following equation : + + +−(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) + + +in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis +the transmembrane potential andφeis the extracellular potential. In this network the +transmembrane potentialφmis assumed to be the quantity that is known and the network +computes the extracellular potentialsφethat are actually measured in experiments. Hence, +based on a proposed transmembrane potential, this network now computes the extracellular +potentials. +At the top of the network the bundle is split in two, one part is used to create the +right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. +As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular +and extracellular tensors. The moduleCalculateFieldData2is used to sum the values +of the intracellular and extracellular conductivity fields for each location. The output of +this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix +for the Poisson equation. This stiffness matrix can be viewed as the discretization of the +anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ +operator. +The modules to the left of the creation of the stiffness matrix actually compute the right- +hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the +numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane +potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the +data inside the field needs to be represented as a vector. This is accomplished by the + + + +Figure 6.1. Full network for running simulation + + +CHAPTER 6. FINITE ELEMENT MODELING 35 + + + +Figure 6.2. UI settings of modules + + +GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a +column matrix. In order to now obtain the right-hand-side vector we need to multiply the +column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary +module. +Both the stiffness matrix and the right-hand-side vector now form a linear system that +needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule +solves the linear system using in iterative solver. The details of the solver can be entered +in theUIof this module. Once the linear system is solved the solution contained in a +column vector is reinserted into the field using theSetFieldDatamodule. An example of +a reasonable number of iterations is given in figure 6.3. Everything below this module in +the network is used for visualizing the data which is described in the next section. + + + +Figure 6.3. UI settings of modules + +#### 6.2 Visualization of Simulation Results + +In order to study the effect of anisotropy on the extracellular potentials we look at a certain +cross section of the model. In order extract a cross section we use theExtractIsosur- +faceByFunctionmodule. This module lets the user specify a function and subsequently +extracts an isosurface of this function and projects the data back onto this surface. In this +case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. +However displaying the data without the underlying fiber structure is of no use, therefore we +can reconstruct the fiber orientation from the tensor data sending it through the calculator +module again and extracting the first eigenvector using theeigvec1()function. The data is +subsequently moved to the elements of the mesh. + + +To efficiently project the data onto the same mesh as the data, we use theApplyMap- + + + + + +Figure 6.4. UI settings of modules + + +pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh +if the operation that generated the new mesh computed a so called mapping matrix. In this +case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will +be able to project the data onto the same grid. As often in SCIRun there are many ways to +do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule +to accomplish the same. +Finally the vectors and the data are combined into one viewer. In order to render a sense +or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary +module extracts the outside of any mesh. In this case it renders the outer surface of the +model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh +boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated +by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so +to highlight the cross section more clearly. Also increase the scale of the vectors so they +become clearly visible. +Finally theViewScenemodule displays a result that show that the potentials tend to + + + +Figure 6.5. UI settings of modules + +stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. + + + + +Figure 6.6. Visualizing Results From 1131368e411bdebf9db58849b31ae38bea2f0ab7 Mon Sep 17 00:00:00 2001 From: Nidhi Patel Date: Mon, 21 Oct 2019 15:20:26 -0600 Subject: [PATCH 24/32] Rename files --- IschemiaTutorial_images/2.4.png | Bin 262945 -> 303140 bytes IschemiaTutorial_images/2.5.png | Bin 303140 -> 309628 bytes IschemiaTutorial_images/2.6.png | Bin 309628 -> 680616 bytes IschemiaTutorial_images/2.7.png | Bin 680616 -> 445634 bytes IschemiaTutorial_images/2.8.png | Bin 445634 -> 0 bytes IschemiaTutorial_images/3.7.png | Bin 0 -> 337677 bytes IschemiaTutorial_images/3.8.png | Bin 0 -> 355548 bytes IschemiaTutorial_images/3.9.2.png | Bin 0 -> 374545 bytes IschemiaTutorial_images/3.9.png | Bin 0 -> 358684 bytes 9 files changed, 0 insertions(+), 0 deletions(-) delete mode 100644 IschemiaTutorial_images/2.8.png create mode 100644 IschemiaTutorial_images/3.7.png create mode 100644 IschemiaTutorial_images/3.8.png create mode 100644 IschemiaTutorial_images/3.9.2.png create mode 100644 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zZglCgO5^9gDnq*!&>)k?r&(;7yY{L$;{JuCM zfukV|HL@pe#6_MkUPD&w!Ydt{0&J(K`n_wU>UjpSIq6KrOS&AQO*B`^$ulZ+6PZ35Z`_U>WMdN+P)$e?`8l2Uo(Pz&c9$WnyaF4?La>OyoZp9LC zgqn*FD)*lihIHy5Y;&IrIr zUz*ra`;gMTPAKSJ8D3W9O0F%OBGRG@_u7#Pq7TY zo%p}W*1yyETJGeh!P1*NhaU*)FQqxgvtDK4y`j`1@pnb|XV@ja_beH5)(1L&?f!um pYxVT>#`)-5qCYO{|I0zAe8+;@?ikPj&sk2Eo{q6L=Dy>zKLL)*5y}7n literal 0 HcmV?d00001 From d6ec3ba78bb1cff18a3a9c2b2012867486b557b9 Mon Sep 17 00:00:00 2001 From: Nidhi Patel Date: Mon, 21 Oct 2019 15:47:54 -0600 Subject: [PATCH 25/32] Add in page links --- IschemiaTutorial.md | 42 +++++++++++++++++++++--------------------- 1 file changed, 21 insertions(+), 21 deletions(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index 073ebda..1ef4feb 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -20,30 +20,30 @@ Jeroen Stinstra, Darrell Swenson ## Contents - - 1 Overview - - 1.1 Ischemia Model - - 1.2 Software requirements - - 1.2.1 SCIRun module compatibility - - 1.2.2 Required Datasets - - 2 Reading and Visualization of Image Data - - 2.1 Loading The Dataset - - 2.2 Visualization of Dataset - - 3 Visualization of Image Data //ended here - - 3.1 Volume Renderer and Clipping Planes - - 3.2 Isosurfacing and Mesh Fairing - - 3.3 Resampling and Viewing Glyphs - - 4 Building a Tetrahedral Mesh - - 4.1 Building a Tetrahedral Mesh - - 5 Tensors and Conductivities - - 5.1 Creation of Model Parameters - - 6 Finite Element Modeling - - 6.1 Creating The Simulation - - 6.2 Visualization of Simulation Results -- + - [1 Overview](#1-overview) + - [1.1 Ischemia Model](#11-ischemia-model) + - [1.2 Software requirements](#12-software-requirements) + - [1.2.1 SCIRun module compatibility](#121-scirun-module-compatibility) + - [1.2.2 Required Datasets](#122-required-datasets) + - [2 Reading and Visualization of Image Data](#2-reading-and-visualization-of-image-data) + - [2.1 Loading The Dataset](#21-loading-the-dataset) + - [2.2 Visualization of Dataset](#22-visualization-of-dataset) + - [3 Visualization of Image Data](#3-visualization-of-image-data) + - [3.1 Volume Renderer and Clipping Planes](#31-volume-renderer-and-clipping-planes) + - [3.2 Isosurfacing and Mesh Fairing](#32-isosurfacing-and-mesh-fairing) + - [3.3 Resampling and Viewing Glyphs](#33-resampling-and-viewing-glyphs) + - [4 Building a Tetrahedral Mesh](#4-building-a-tetrahedral-mesh) + - [4.1 Building a Tetrahedral Mesh](#41-building-a-tetrahedral-mesh) + - [5 Tensors and Conductivities](#5-tensors-and-conductivities) + - [5.1 Creation of Model Parameters](#51-creation-of-model-parameters) + - [6 Finite Element Modeling](#6-finite-element-modeling) + - [6.1 Creating The Simulation](#61-creating-the-simulation) + - [6.2 Visualization of Simulation Results](#62-visualization-of-simulation-results) + #### Chapter 1 -# Overview +# 1 Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt From 2cf3852a3befb89f9c26cb81741a2dd7278d433e Mon Sep 17 00:00:00 2001 From: Nidhi Patel Date: Mon, 21 Oct 2019 15:53:26 -0600 Subject: [PATCH 26/32] Fix in-page links --- IschemiaTutorial.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index 1ef4feb..01a94d4 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -148,7 +148,7 @@ contain the same datasets and only one of them has to be downloaded. #### Chapter 2 -# Reading and Visualization of Image +# 2 Reading and Visualization of Image # Data @@ -302,7 +302,7 @@ _Figure 2.7. Viewing multiple slices_ #### Chapter 3 -# Visualization of Image Data +# 3 Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** @@ -545,7 +545,7 @@ Figure 3.10. Visualizing the Fiber Orientation of the Data #### Chapter 4 -# Building a Tetrahedral Mesh +# 4 Building a Tetrahedral Mesh Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes @@ -614,7 +614,7 @@ the mesh. Use the slicing planes to examine the mesh (see *Figure 4.2*). #### Chapter 5 -# Tensors and Conductivities +# 5 Tensors and Conductivities **Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** @@ -764,7 +764,7 @@ Figure 5.5. 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SCIRun is given in the Basic Tutorial. Once SCIRun has launched the main Window with the Network editor is shown. *Figure 2.1* shows the main -The main SCIRun window +The main SCIRun window _Figure 2.1 - The Main SCIRun Window_ @@ -188,7 +188,7 @@ Modules menu and select the **ReadField** module form the menu. This will insert be used to read in the first dataset. -Adding and opening module +Adding and opening module _Figure 2.2 - Finding the ReadField module and opening its GUI_ @@ -201,7 +201,7 @@ If this dataset is not available in your copy of the SCIRunData bundle, please d latest version from the website to obtain a copy. -Selecting file name and type +Selecting file name and type _Figure 2.3. Select a file name and a file type_ From 85e69d16f04ce64e0a320cc65c158135cc773ae4 Mon Sep 17 00:00:00 2001 From: nids2001 Date: Tue, 29 Oct 2019 16:54:53 -0600 Subject: [PATCH 32/32] Update Formatting --- IschemiaTutorial.md | 330 +++++++++++++++++++++----------------------- 1 file changed, 161 insertions(+), 169 deletions(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index adc26c0..b8ed71e 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -1,55 +1,63 @@ -# Ischemia Model tutorial + +# Ischemia Model tutorial #### SCIRun 5.0 Documentation Center for Integrative Biomedical Computing + Scientific Computing & Imaging Institute + University of Utah SCIRun software download: http://software.sci.utah.edu + Center for Integrative Biomedical Computing: http://www.sci.utah.edu/cibc + This project was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number **P41 GM103545-18**. -Author(s): +Author: Jeroen Stinstra, Darrell Swenson ## Contents - - [1 Overview](#1-overview) - - [1.1 Ischemia Model](#11-ischemia-model) - - [1.2 Software requirements](#12-software-requirements) - - [1.2.1 SCIRun module compatibility](#121-scirun-module-compatibility) - - [1.2.2 Required Datasets](#122-required-datasets) - - [2 Reading and Visualization of Image Data](#2-reading-and-visualization-of-image-data) - - [2.1 Loading The Dataset](#21-loading-the-dataset) - - [2.2 Visualization of Dataset](#22-visualization-of-dataset) - - [3 Visualization of Image Data](#3-visualization-of-image-data) - - [3.1 Volume Renderer and Clipping Planes](#31-volume-renderer-and-clipping-planes) - - [3.2 Isosurfacing and Mesh Fairing](#32-isosurfacing-and-mesh-fairing) - - [3.3 Resampling and Viewing Glyphs](#33-resampling-and-viewing-glyphs) - - [4 Building a Tetrahedral Mesh](#4-building-a-tetrahedral-mesh) - - [4.1 Building a Tetrahedral Mesh](#41-building-a-tetrahedral-mesh) - - [5 Tensors and Conductivities](#5-tensors-and-conductivities) - - [5.1 Creation of Model Parameters](#51-creation-of-model-parameters) - - [6 Finite Element Modeling](#6-finite-element-modeling) - - [6.1 Creating The Simulation](#61-creating-the-simulation) - - [6.2 Visualization of Simulation Results](#62-visualization-of-simulation-results) + - [1 Overview](#overview) + - [1.1 Ischemia Model](#11-ischemia-model) + - [1.2 Software requirements](#12-software-requirements) + - [1.2.1 SCIRun module compatibility](#121-scirun-module-compatibility) + - [1.2.2 Required Datasets](#122-required-datasets) + - [2 Reading and Visualization of Image Data](#reading-and-visualization-of-image-data) + - [2.1 Loading The Dataset](#21-loading-the-dataset) + - [2.2 Visualization of Dataset](#22-visualization-of-dataset) + - [3 Visualization of Image Data](#visualization-of-image-data) + - [3.1 Volume Renderer and Clipping Planes](#31-volume-renderer-and-clipping-planes) + - [3.2 Isosurfacing and Mesh Fairing](#32-isosurfacing-and-mesh-fairing) + - [3.3 Resampling and Viewing Glyphs](#33-resampling-and-viewing-glyphs) + - [4 Building a Tetrahedral Mesh](#building-a-tetrahedral-mesh) + - [4.1 Building a Tetrahedral Mesh](#41-building-a-tetrahedral-mesh) + - [5 Tensors and Conductivities](#tensors-and-conductivities) + - [5.1 Creation of Model Parameters](#51-creation-of-model-parameters) + - [6 Finite Element Modeling](#finite-element-modeling) + - [6.1 Creating The Simulation](#61-creating-the-simulation) + - [6.2 Visualization of Simulation Results](#62-visualization-of-simulation-results) + + --- #### Chapter 1 -# 1 Overview +# Overview **This tutorial demonstrates several tools within SCIRun for building models out of imaging data. It describes the pipeline starting from preprocessed images to generate a computational mesh and adapt this mesh to meet the computational requirements. It then continues to set up a finite element bidomain simulation, and demonstrates how results can be visualized.** + #### 1.1 Ischemia Model This tutorial describes the generation of a quasi-static volume conductor model of an ischemic @@ -134,7 +142,6 @@ SCIRun from scratch. The supplied build script (build.sh) will build SCIRun with tools enabled by default. - ##### 1.2.2 Required Datasets This tutorial relies on several datasets that are part of the SCIRunData bundle. To obtain @@ -148,16 +155,14 @@ contain the same datasets and only one of them has to be downloaded. --- #### Chapter 2 -# 2 Reading and Visualization of Image -# Data +# Reading and Visualization of Image Data +**Scope: [Finding Modules](#21-loading-the-dataset) - [Building Networks](#building-networks) - [Loading Data](#loading-data) - [Visualization of 3D Datasets](#22-visualization-of-dataset)** -Scope: Finding Modules - Building Networks - Loading Data - Visualization of 3D Datasets #### 2.1 Loading The Dataset - We start by opening the main SCIRun window by launching SCIRun by either double clicking on the binary icon or by launching SCIRun from the command line. A detailed description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been @@ -165,8 +170,7 @@ launched the main Window with the Network editor is shown. *Figure 2.1* shows th The main SCIRun window - -_Figure 2.1 - The Main SCIRun Window_ +*Figure 2.1 - The Main SCIRun Window* SCIRun network editor. For this tutorial we will be selecting modules from the @@ -182,18 +186,17 @@ through every submenu, a module can simply be found by typing the name of the mo into Show Module entry box located in the top menu bar. This will highlight the location of a specific module within the Modules menu as is demonstrated in *Figure 2.2*. -Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the + Enter “**ReadField**” in the upper menu bar and follow the highlighted menus in the Modules menu and select the **ReadField** module form the menu. This will insert the **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. Adding and opening module - -_Figure 2.2 - Finding the ReadField module and opening its GUI_ +*Figure 2.2 - Finding the ReadField module and opening its GUI* -The Dataset that is used in this example is called **heart-ischemia** and it can be found + The dataset that is used in this example is called **heart-ischemia** and it can be found in the SCIRunData bundle that can be downloaded as well from the SCI software portal (http://software.sci.utah.edu). After downloading the SCIRunData zip file, unzip the file inside a directory and inside you will find a sub directory with the **heart-ischemia** datasets. @@ -202,32 +205,30 @@ latest version from the website to obtain a copy. Selecting file name and type - -_Figure 2.3. Select a file name and a file type_ +*Figure 2.3. Select a file name and a file type* By pressing on the **UI** button of the **ReadField** module a browser window is opened where one can enter the name of the file that needs to be loaded. The files that are used -in this example were generated by the **Seg3D** software and are in the *.nnrdfile* format. +in this example were generated by the **Seg3D** software and are in the `.nnrdfile` format. This file format is used to represent regular spaced image data, such as MRI images or segmentations. It consists of a simple text header specifying the dimensions of the data and its location in space, followed by binary data representing the actual data. This file format -allows for either a header be appended to the start of the file (*.nrrd* format) with header +allows for either a header be appended to the start of the file (`.nrrd` format) with header and data being in one file or having a separate header file that wraps the data found in a -general binary data file (*.nhdr* format). More information on the .nrrd format can be found +general binary data file (*.nhdr* format). More information on the `.nrrd` format can be found at http://teem.sourceforge.net/nrrd/format.html. Once the UI Window of the **ReadField** module opens, select the **NrrdFile** file type Network for checking contents of file and information displayed when executed - -_Figure 2.4. Network for checking contents of the file_ +*Figure 2.4. Network for checking contents of the file* and use the upper part of the UI to locate the dataset by browsing the directories to the -location where the SCIRunData has been saved. Open the **heart-ischemia** directory and -select **HeartMRI.nrrd** file. Then press **Set** at the bottom of the UI to store the file name +location where the SCIRunData has been saved. Open the `heart-ischemia` directory and +select `HeartMRI.nrrd` file. Then press **Set** at the bottom of the UI to store the file name and type in the module. This process is illustrated in *Figure 2.3*. Now use the Show Module menu again and find the **ReportFieldInfo**. Insert this @@ -243,6 +244,7 @@ inside the pipeline, the module also shows the dimensions of the grid and the lo space derived from the original imaging data. An example of all the information displayed is shown in *Figure 2.4*. + #### 2.2 Visualization of Dataset Now we have the data loaded into SCIRun, we can actually visualize the 3D image dataset. @@ -255,8 +257,7 @@ To visualize the 3D dataset we convert the module into a 3D texture object, whic Building visualization network - -_Figure 2.5 Building the visualization network_ +*Figure 2.5 Building the visualization network* will allow us to quickly browse through the dataset. Use the Show Module feature in the @@ -282,9 +283,9 @@ the top the color is opaque and when the color is at the bottom the color is tra to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In -Network for checking contents of the file -_Figure 2.6. Network for checking contents of the file_ +Network for checking contents of the file +*Figure 2.6. Network for checking contents of the file* the lower part of the menu one can now select from a series of predefined colormap lookup @@ -295,103 +296,103 @@ Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and sele Viewing multiple slices +*Figure 2.7. Viewing multiple slices* -_Figure 2.7. Viewing multiple slices_ --- #### Chapter 3 -# 3 Visualization of Image Data +# Visualization of Image Data -**Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** +**Scope: [Volume Renderer](#31-volume-renderer-and-clipping-planes) - [ViewScene Module](#32-isosurfacing-and-mesh-fairing) - [Resampling](#33-resampling-and-viewing-glyphs) - [Rendering Glyphs](#rendering-glyphs) - [Calculator Module](#calculator-module)** Reading in two datasets - -_Figure 3.1. Reading in two datasets_ +*Figure 3.1. Reading in two datasets* Reading in two datasets -_Figure 3.2. Reading in two datasets_ +*Figure 3.2. Reading in two datasets* -#### 3.1 Volume Renderer and Clipping Planes +#### 3.1 Volume Renderer and Clipping Planes In the previous chapter one dataset was explored, however the SCIRun viewer is capable of rendering many datasets in the same viewer, so one can explore the correlation between the data or combine them to build a model. In the next example we will be loading two datasets into the viewer. To do this we start with a similar network as depicted in the -previous example. However instead of viewing slices we will use the ShowTextureVolume +previous example. However instead of viewing slices we will use the **ShowTextureVolume** module to volume render multiple datasets into the viewer. This module requires the same -inputs as the ShowTextureSlices module, but now renders the full volume transparent. -Create the network shown in Figures 3.1 - 3.2 , and use the HeartMRI.nrrd and -HeartMRI-Perfusionbed.nrrd as the two datasets for the two ReadField modules. +inputs as the **ShowTextureSlices** module, but now renders the full volume transparent. + +Create the network shown in *Figures 3.1 - 3.2* , and use the `HeartMRI.nrrd` and +`HeartMRI-Perfusionbed.nrrd` as the two datasets for the two **ReadField** modules. Once the network executes the data of the two datasets is combined into one visualization of the data. Try to alter the transparency of the colormaps to highlight the needle markers that were inserted into the heart and the perfusion bed of one of Left Anterior Descending -Artery. An example of such a visualization is given in figure 3.1. +Artery. An example of such a visualization is given in *Figure 3.1*. + The datasets in this example originate from an isolated dog heart in which the Left Opening the configuration tray] - -_Figure 3.3. Opening the configuration tray_ +*Figure 3.3. Opening the configuration tray* Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart -HeartMRI.nrrd and a diffusion tensor image (DTI) HeartMRI-FiberOrientation.nrrd. -Using the Seg3D program the ventricular myocardium and the perfusion bed were seg- -mented out of the anatomical image (HeartMRI-Segmentation.nrrd and HeartMRI- -PerfusionBed.nrrd). +`HeartMRI.nrrd` and a diffusion tensor image (DTI) `HeartMRI-FiberOrientation.nrrd`. +Using the **Seg3D** program the ventricular myocardium and the perfusion bed were segmented +out of the anatomical image (`HeartMRI-Segmentation.nrrd` and `HeartMRIPerfusionBed.nrrd`). + Although displaying the two datasets into one image is useful, one does not always want to see each component of the data. To edit what is actually displayed in the image, open up -the ViewScene module and press Configure. This will add a tray below the current win- -dow, with different tabs to edit different aspects of the image. Select the Objects tab. This +the **ViewScene** module and press **Configure**. This will add a tray below the current window, +with different tabs to edit different aspects of the image. Select the **Objects** tab. This tab shows the current components displayed in the view window. Pressing selection buttons -as highlighted in figure 3.3 will switch on and off the displaying of a certain component. -Also try the Clipping tab, which will allow to clip the visualization. Open up the -Clipping tab and switch on the Clipping Plane Visible button, next drag the X slider -to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The clipping -widget has been configured, so that D corresponds to the full range of X that is spanned +as highlighted in *Figure 3.3* will switch on and off the displaying of a certain component. +Also try the **Clipping** tab, which will allow to clip the visualization. Open up the +**Clipping** tab and switch on the **Clipping Plane Visible** button, next drag the **X** slider +to `1.0`. Now use the **D** slider to slide the clipping plane along the X-axis. The clipping +widget has been configured, so that **D** corresponds to the full range of **X** that is spanned -Slicing the dataset -_Figure 3.4. Slicing the dataset_ +Slicing the dataset +*Figure 3.4. Slicing the dataset* -by the two images that are displayed in the viewer window. By dragging D from -1 to + -one can slice the full rendering. An example of such a visualization is depicted in figure 3.4. +by the two images that are displayed in the viewer window. By dragging **D** from `-1` to `+1` +one can slice the full rendering. An example of such a visualization is depicted in *Figure 3.4*. The figure on the left shows the result of one slicing plane, the result on the right shows two -slicing planes. To activate the second slicing plane, press Plane 2 and then activate this -plane by selecting the Clipping Plane Visible once more. To make it easier to generate a -thin slice, select the the Reverse Clipping Plane Normal option for the second clipping +slicing planes. To activate the second slicing plane, press **Plane 2** and then activate this +plane by selecting the **Clipping Plane Visible** once more. To make it easier to generate a +thin slice, select the the **Reverse Clipping Plane Normal** option for the second clipping plane as this reverse the visible part of the image. By lining up the two clipping planes one can generate a small thin slice. -If the slice becomes too transparent, open up the UI of the ShowTextureVolume + +If the slice becomes too transparent, open up the **UI** of the **ShowTextureVolume** module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. #### 3.2 Isosurfacing and Mesh Fairing +In order to build a model out of the datasets we need to translate the volumes into +parametric surfaces. One way to do this is to generate an isosurface. Modify the network by +adding the **ExtractIsosurface**, **FairMesh** and **ShowField** modules to the network, as +depicted in *Figure 3.5*. The *ExtractIsosurface* should get its input from the module that +reads the perfusion bed field. Make sure to select the **Quantity** tab in the **UI** of the +**ExtractIsosurface** module as depicted in *Figure 3.5*. -In order to build a model out of the datasets we need to translate the volumes into para- -metric surfaces. One way to do this is to generate an isosurface. Modify the network by -adding the ExtractIsosurface, FairMesh and ShowField modules to the network, as -depicted in figure 3.5. The ExtractIsosurface should get its input from the module that -reads the perfusion bed field. Make sure to select the Quantity tab in the UI of the -ExtractIsosurface module as depicted in figure 3.5. -TheExtractIsosurface module extracts an isosurface out of any field. In this case +The **ExtractIsosurface** module extracts an isosurface out of any field. In this case we are extracting it out of the segmented perfusion bed by selecting a value between the Extracting an Isosurface - -_Figure 3.5. Extracting an Isosurface_ +*Figure 3.5. Extracting an Isosurface* maximum and minimum value in the field. In this case the background and the segmen- @@ -399,62 +400,59 @@ tation have a different but constant value and hence the boundary between them w selected. The isosurface is extracted using the Marching Cubes method which will insert an approximation of the isosurface for each element in the mesh. -The FairMesh module takes the output from the ExtractIsosurface module and -smooth out the surface. Because the data is discretized the isosurface will be stair-stepped. -The FairMesh module takes the surfaces and uses information about the neighborhood +The **FairMesh** module takes the output from the **ExtractIsosurface** module and +smooth out the surface. Because the data is discretized the isosurface will be *stair-stepped*. +The **FairMesh** module takes the surfaces and uses information about the neighborhood of the surface to generate a smoother looking surface. The resulting surface is a surface -that is tessalated by triangles. Because this field is no longer structured like a regular -grid, one cannot use the ShowTextureVolume to display the surface. Instead we use +that is tessellated by triangles. Because this field is no longer structured like a regular +grid, one cannot use the **ShowTextureVolume** to display the surface. Instead we use Coupling two ViewScene windows +*Figure 3.6. Coupling two ViewScene windows* -_Figure 3.6. Coupling two ViewScene windows_ - -the ShowFieldmodule that is a general module for visualizing any field. The output -of this module can again be displayed into the ViewScene module, which now combines +the **ShowField** module that is a general module for visualizing any field. The output +of this module can again be displayed into the **ViewScene** module, which now combines visualizations of all three modules. -To compare the volume rendering against the smoothed surface model, the ViewScene + +To compare the volume rendering against the smoothed surface model, the **ViewScene** module has the option to display two coupled Viewer windows. Open up the Viewer win- -dow from the ViewScene module. Press the New Window button to generate a similar -ViewScene window with the same dimensions. Now open up the configuration tab on both +dow from the **ViewScene** module. Press the **NewWindow** button to generate a similar +**ViewScene** window with the same dimensions. Now open up the configuration tab on both windows. By selecting different objects in both windows, the windows can be customized to display a different aspect of the Scene. Display the Faces of the Isosurface in one window and the volume rendering of the Volume Rendering in the other window to examine the -difference between the two visualizations, as depicted by figure 3.6. +difference between the two visualizations, as depicted by *Figure 3.6*. + By zooming in into the model of the surface one can see the difference between the two renderings. Note that by default the two windows are locked together. Meaning that rotations in one window are automatically applied to the other window. This option allows to highlight the same spot in space in both windows without the need to actually align both -images manually. This option can however be switched off. Press the Lock View button -to unlock the window. When pressing the button the Lock View button changes color to +images manually. This option can however be switched off. Press the **Lock View** button +to unlock the window. When pressing the button the **Lock View** button changes color to indicate that it is switched off. One can now independently orient the windows. Locking the windows together again will not align the windows but keep the relative change between the Network for visualizing the fiber orientation of the data - -_Figure 3.7. Network for Visualizing the Fiber Orientation of the Data_ +*Figure 3.7. Network for Visualizing the Fiber Orientation of the Data* windows. The changes are however applied to both windows. To align the windows again -select the Views menu at the top of the window and select the Other Viewer Windows +select the **Views** menu at the top of the window and select the **Other Viewer Windows** menu and select the option to get the view from the other window. This will align the view to the view of the other window. -Locking can also be activated by pressing on the keyboard when the window is selected. -Likewise a view from an other window can be copied by pressing ctrl 1 to copy the view -from the first window, ctrl 2 for the second window and so on. The viewer also as predefined -views along the axis that can be accessed by pressing1 - 8on the keyboard. Auto view also -has a keyboard shortcut and is activated by pressing 0. - - +Locking can also be activated by pressing `L` on the keyboard when the window is selected. +Likewise a view from an other window can be copied by pressing `ctrl+1` to copy the view +from the first window, `ctrl+2` for the second window and so on. The viewer also as predefined +views along the axis that can be accessed by pressing `1 - 8` on the keyboard. Auto view also +has a keyboard shortcut and is activated by pressing `0`. #### 3.3 Resampling and Viewing Glyphs - After viewing perfusion bed, the other data to explore is the fiber orientation. Fibers cannot easily be volume rendered as the data are not scalar, but are in fact vectors. This data was derived from the Diffusion Weighted Images by doing a decomposition of the tensor and @@ -471,7 +469,7 @@ that the network executes relatively fast and that the visualization is not clob amount of vectors. The default settings in the UI of this module should do for demonstrating displaying vectors. -Because the Diffusion Tensor Image was recorded at a different resolution as the anatomical +Because the Diffusion Tensor Image was recorded at a different resolution as the anatomical MR image, the data in the segmentation which was derived from the anatomical scan is not in the same grid as the vector data. We apply the **MapFieldDataOntoNodes** to map the data from the segmentation onto the mesh of the Diffusion Tensor Imaging data. @@ -479,7 +477,7 @@ The module operates by looking up the value of the data in the segmentation for the mesh of the Diffusion Tensor Image. The result is a field that has the segmentation projected onto the same grid as the vector data. -The mapped segmentation can now be used to mask out any data that is located outside +The mapped segmentation can now be used to mask out any data that is located outside of the heart. In order to mask the data we use the general purpose calculator module, called **CalculateFieldData**. @@ -504,9 +502,8 @@ type, even though the output type is set to Scalar it will in fact render a Vect output type would be preferred. In most cases the user should not need to set an output -The UI of the CalculateFieldData module - -_Figure 3.8. The UI of The **CalculateFieldData** Module_ +The UI of the CalculateFieldData module +*Figure 3.8. The UI of The **CalculateFieldData** Module* type, only when for memory reasons the data should be different from a double precision @@ -533,8 +530,7 @@ is arbitrary as they could just as well point in the opposite direction. It is t The UI of the ShowFieldGlyphs module - -_Figure 3.9. The UI of the **ShowFieldGlyphs** Module_ +*Figure 3.9. The UI of the **ShowFieldGlyphs** Module* vectors are pointing along that matters in this case. To make the vectors point in both @@ -547,31 +543,33 @@ the different aspects of the data. Visualizing the Fiber Orientation of the Data +*Figure 3.10. Visualizing the Fiber Orientation of the Data* -_Figure 3.10. Visualizing the Fiber Orientation of the Data_ --- #### Chapter 4 -# 4 Building a Tetrahedral Mesh +# Building a Tetrahedral Mesh +**Scope: [Isosurface](#41-building-a-tetrahedral-mesh) - [FairMesh](#fairmesh) - [ResampleMesh] - [InterfaceWithTetGen](#interfacewithtetgen) - [Visualizing Meshes](#visualizing-meshes)** -Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing Meshes #### 4.1 Building a Tetrahedral Mesh - -In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using -isosurfaces. Another way to generate a mesh is with a [InterfaceWithCleaver](https://github.com/nids2001/scirun.pages/blob/defibrillation-tutorial/InterfaceWithCleaver.md) module. To build an elementary tetrahedral mesh, generate the network that is depicted +In order to build a physical model out of the imaging data, we need to generate a computational +mesh. In this example we describe an easy way of generating a tetrahedral mesh using +isosurfaces. Another way to generate a mesh is with a +[InterfaceWithCleaver](https://github.com/nids2001/scirun.pages/blob/defibrillation-tutorial/InterfaceWithCleaver.md) +module. To build an elementary tetrahedral mesh, generate the network that is depicted in *Figure 4.1.* This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. -The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a +The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a constrained Delaunay Tetrahedralization and output a full volumetric mesh that consists of tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. -When opening the **UI** of the **InterfaceWithTetGen** module, one can select out of a +When opening the **UI** of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating a computational tetrahedral mesh for this problem are the *-Y*, *-q*, and the *-a* option in the **UI**. The *-Y* option lets the user decide whether additional vertices are to be inserted @@ -594,14 +592,15 @@ so that the example can be computed within a time frame of minutes instead of ho Network for building a Tetrahedral Mesh -_Figure 4.1. Network for building a Tetrahedral Mesh_ +*Figure 4.1. Network for building a Tetrahedral Mesh* + Image of the Tetrahedral Mesh -_Figure 4.2. Image of the Tetrahedral Mesh_ +*Figure 4.2. Image of the Tetrahedral Mesh* -The **ExtractIsosurface** module should be set to the **Quantity** tab and we should be +The **ExtractIsosurface** module should be set to the **Quantity** tab and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as indicated in *Figure 4.1*. Finally, the **WriteField** module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. @@ -620,9 +619,10 @@ the mesh. Use the slicing planes to examine the mesh (see *Figure 4.2*). --- #### Chapter 5 -# 5 Tensors and Conductivities +# Tensors and Conductivities + +**Scope: [SignedDistanceField](#51-creation-of-model-parameters) - [CalculateFieldData](#calculatefielddata) - [Bundles](#bundles1) - [Mapping FieldData](#mapping-fielddata)** -**Scope: SignedDistanceField - CalculateFieldData - Bundles - Mapping FieldData** #### 5.1 Creation of Model Parameters @@ -660,16 +660,15 @@ this distance field with a timeframe of less than a minute. However note that wh objects get more complex this operation can be relatively slow. -Full network for building extracellular, intracellular conductivity fields and the +<img src= +*Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the +transmembrane potential fields* -_Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the -transmembrane potential fields_ UI Settings of modules - -_Figure 5.2. UI settings of modules_ +*Figure 5.2. UI settings of modules* Below the **CalculateSignedDistanceToField** module, the distance field is inserted @@ -693,7 +692,7 @@ one can define an arbitrary amount of additional parameters. The grammar of the requires that you separate each expression by a semi colon. Currently only expression as supported by the parser and no functions, loops, or conditional statements are supported. -The **CalculateFieldData** module, which is based on the same mathematical expression +The **CalculateFieldData** module, which is based on the same mathematical expression parser, is used to generate the conductivity tensors as well. In *Figure 5.3* the example functions for these conductivities are given. Note that we use two input fields here and hence the function now is function of two spatial varying parameters. In this case we as a @@ -701,7 +700,7 @@ special function called **select** which treads the first argument as a boolean based on the outcome decides to evaluate the first or the second argument. This in a sense adds a conditional statement to the math parser. -One difference with the function for the transmembrane potential is that the data now +One difference with the function for the transmembrane potential is that the data now has to be located at the centers of the elements, as the Finite Element computations are currently restricted to conductivities defined for an element. In order to translate the distance field from a representation on nodes to a representation onto elements, we use @@ -729,25 +728,24 @@ defining two input vectors and three conductivity scalars. However for cardiac t the conductivity ratio across versus along the myocardial fiber is known. It is assumed that across the fiber in both directions one has the same conductivity. -The last part of the network introduces a new concept called the **Bundle**. A bundle +The last part of the network introduces a new concept called the **Bundle**. A bundle is no more than a collection of Fields and other objects that are stored by name. The advantage of bundling data is that one can store all the fields into one file. Which makes it easier to maintain the simulation data, as well as that it saves diskspace when components use common structures like an underlying mesh. (see *Figure 5.4*) -To generate a bundle the *InsertFieldsIntoBundle* module assigns each of the input +To generate a bundle the **InsertFieldsIntoBundle** module assigns each of the input ports to a new name in the bundle. In this case we choose the names enquoteVM, enquoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, UI settings of modules +*Figure 5.3. UI settings of modules* -_Figure 5.3. UI settings of modules_ UI settings of modules - -_Figure 5.4. UI settings of modules_ +*Figure 5.4. UI settings of modules* and the extracellular conductivity respectively. The bundle subsequently saved on disk for @@ -761,24 +759,21 @@ the blurring. An example of the output is given in *Figure 5.5*. Visualization of assumed transmembrane potentials - -_Figure 5.5. Visualization of assumed transmembrane potentials_ +*Figure 5.5. Visualization of assumed transmembrane potentials* --- #### Chapter 6 -# 6 Finite Element Modeling +# Finite Element Modeling +**Scope: [BuildFEMatrix](#buildfematrix) - [ExtractIsosurfaceByFunction](#extractisosurfacebyfunction) - [Bundles](#bundles2) - [SolveLinearSystem](#solvelinearsystem) - [ApplyMappingMatrix](#applymappingmatrix) -[GetFieldData](#getfielddata) - [SetFieldData](#setfielddata)** -**Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- -Matrix -GetFieldData - SetFieldData** #### 6.1 Creating The Simulation - -We start with the bundle generated in the previous chapter. This bundle contains all the +We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in *Figure 6.1*. *Figure 6.2 - 6.5* display the settings required in each of the module **UI** menus. The modules that are not highlighted in these figures use the default settings of these modules. @@ -795,7 +790,7 @@ computes the extracellular potentials φe that are actually measured in experime based on a proposed transmembrane potential, this network now computes the extracellular potentials. -At the top of the network the bundle is split in two, one part is used to create the +At the top of the network the bundle is split in two, one part is used to create the right-hand-side of *Equation 6.1* and the other part is used to compute the left-hand-side. As seen in *Equation 6.1* the left-hand-side depends on the summation of the intracellular and extracellular tensors. The module **CalculateFieldData** is used to sum the values @@ -805,7 +800,7 @@ for the Poisson equation. This stiffness matrix can be viewed as the discretizat anisotropic Poisson equation and hence it is the numeric equivalent of the ∇·(Σi+ Σe)∇ operator. -The modules to the left of the creation of the stiffness matrix actually compute the +The modules to the left of the creation of the stiffness matrix actually compute the right-hand-side vector. This is done again by using the **BuildFEMatrix** module to generate the numerical operator ∇·(Σi)∇ and multiplying this with the values from the transmembrane potential field. As the output of the **BuildFEMatrix** module is matrix (blue pipe), the @@ -813,12 +808,12 @@ data inside the field needs to be represented as a vector. This is accomplished Full network for running simulation +*Figure 6.1. Full network for running simulation* -_Figure 6.1. Full network for running simulation_ UI settings of modules -_Figure 6.2. UI settings of modules_ +*Figure 6.2. UI settings of modules* **GetFieldData** module that strips the data from the nodes in the field and inserts it into a @@ -826,23 +821,23 @@ column matrix. In order to now obtain the right-hand-side vector we need to mult column vector with the matrix. The latter is accomplished by the **EvaluateLinAlgBinary** module. -Both the stiffness matrix and the right-hand-side vector now form a linear system that +Both the stiffness matrix and the right-hand-side vector now form a linear system that needs to be solved to obtain the extracellular potentials. The **SolveLinearSystem** module solves the linear system using in iterative solver. The details of the solver can be entered -in the **UI** of this module. Once the linear system is solved the solution contained in a +in the **UI** of this module. Once the linear system is solved the solution contained in a column vector is reinserted into the field using the **SetFieldData** module. An example of a reasonable number of iterations is given in *Figure 6.3*. Everything below this module in the network is used for visualizing the data which is described in the next section. UI settings of modules +*Figure 6.3. UI settings of modules* -_Figure 6.3. UI settings of modules_ #### 6.2 Visualization of Simulation Results -In order to study the effect of anisotropy on the extracellular potentials we look at a certain +In order to study the effect of anisotropy on the extracellular potentials we look at a certain cross section of the model. In order extract a cross section we use the **ExtractIsosurfaceByFunction** module. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this @@ -852,13 +847,11 @@ can reconstruct the fiber orientation from the tensor data sending it through th module again and extracting the first eigenvector using the *eigvec1()* function. The data is subsequently moved to the elements of the mesh. - -To efficiently project the data onto the same mesh as the data, we use the **ApplyMap-** +To efficiently project the data onto the same mesh as the data, we use the **ApplyMap-** UI settings of modules - -_Figure 6.4. UI settings of modules_ +*Figure 6.4. UI settings of modules* **pingMatrixmodule**, this allows to quickly copy the data from one mesh to another mesh @@ -876,17 +869,16 @@ boundary. Disable the display of nodes and edges and alter the **Default Color** by *Figure 6.5*. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. + Finally the **ViewScene** module displays a result that show that the potentials tend to UI settings of modules - -_Figure 6.5. UI settings of modules_ +*Figure 6.5. UI settings of modules* stretch along the fiber orientation, as can be viewed by the results indicated in *Figure 6.6*. Visualizing Results - -_Figure 6.6. Visualizing Results_ +*Figure 6.6. Visualizing Results*

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z^L0J?TAQ@z#UXw9-%}L4y9cZ|gp_SILMP3mp^psRs7aET)(;+{=6WrAW|e6P1DJj{asoH97QIiwZp_+bbNkmU+TV>&; z<6q-qYjEOJaS@gMhq-^aSedUVdaHilUXAk$j9%ONXjyo1Fyu@kxVp%?|6D&Xj&boa zMRp>9__Gh2v!65F+*XvtH|#%lLNPjr6%k0!F1aZUe>g@uIAF5iRtW-v!<1kcW2_O$plw6WP7G77P54@7p71M5Y^ z@*+!OH*@TV@^W^cj)d(5D9OdV@s63luz-FyH#zd$m=8UPep(=P?+#)eTcU*7EE7aj z8I8F87#}CKc4^J>+b%q+xIwp7?z^O2-3h^kICW>V_Y7(_Fv7PC*P)KPK0*|PCE_l{ zk53zq&qgVEfb!?iz`qSdBp^%0*ZH=+E=^=jC6A5L5s!=Wk93YUzHY{OsMO7F@Ibp* zB$tubE$eI|jxJ$4`aF~W4+XeQNpV)Z zXw5>}bMV#w;g;_WnzMm>Hnu71^CZVV0N$4B�&pRanm<5B~(Ey>fQ90~agl=zf_}YcDr=xjaqgKr^>VKYloR9zj literal 0 HcmV?d00001 From fe821a1e33eb48635b9a4b8788999bfb6c11edd5 Mon Sep 17 00:00:00 2001 From: nids2001 Date: Thu, 24 Oct 2019 16:56:46 -0600 Subject: [PATCH 28/32] Update chapter 4 --- IschemiaTutorial.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index 01a94d4..13b9d5d 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -554,7 +554,7 @@ Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using -isosurfaces. To build an elementary tetrahedral mesh, generate the network that is depicted +isosurfaces. Another way to generate a mesh is with a [InterfaceWithCleaver](https://github.com/nids2001/scirun.pages/blob/defibrillation-tutorial/InterfaceWithCleaver.md) module. To build an elementary tetrahedral mesh, generate the network that is depicted in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. From be0bf6cecf13fbe12d8c33650b0f9e0beb133072 Mon Sep 17 00:00:00 2001 From: nids2001 Date: Thu, 24 Oct 2019 18:00:08 -0600 Subject: [PATCH 29/32] Fix chapter 4 & update formatting --- IschemiaTutorial.md | 244 +++++++++++++++++++++++--------------------- 1 file changed, 127 insertions(+), 117 deletions(-) diff --git a/IschemiaTutorial.md b/IschemiaTutorial.md index 13b9d5d..407f4ac 100644 --- a/IschemiaTutorial.md +++ b/IschemiaTutorial.md @@ -40,7 +40,7 @@ Jeroen Stinstra, Darrell Swenson - [6.1 Creating The Simulation](#61-creating-the-simulation) - [6.2 Visualization of Simulation Results](#62-visualization-of-simulation-results) - +--- #### Chapter 1 # 1 Overview @@ -90,19 +90,19 @@ that have the shape of the heart and where the anisotropy is caused by the fiber the myocardium (cardiac muscle tissue). The partial differential equations to solve in both spaces are the following: -∇·Σi∇φi = imem (1.1) -∇·Σe∇φe = −imem (1.2) +∇·Σi∇φi = imem *Equation (1.1)* +∇·Σe∇φe = −imem *Equation (1.2)* where φi and φe are the intracellular and extracellular potentials respectively and Σi, and Σe are the conductivity tensors of both spaces. Finally, imem is the current through the membrane. We can define the transmembrane potential as: -φm=φi−φe (1.3) +φm=φi−φe *Equation (1.3)* Combining this equation with the previous set of equations results in the system to solve being: -∇·(Σi+ Σe)∇φe=−∇·Σi∇φm (1.4) +∇·(Σi+ Σe)∇φe=−∇·Σi∇φm *Equation (1.4)* The latter equation describes the potential of the extracellular space, as observed in measurements, as a function of the membrane potential φm. To solve this for a specific heart, one needs to have a @@ -145,7 +145,7 @@ contain the same datasets and only one of them has to be downloaded. - +--- #### Chapter 2 # 2 Reading and Visualization of Image @@ -163,12 +163,12 @@ clicking on the binary icon or by launching SCIRun from the command line. A deta description of how to run SCIRun is given in the Basic Tutorial. Once SCIRun has been launched the main Window with the Network editor is shown. *Figure 2.1* shows the main + The main SCIRun window _Figure 2.1 - The Main SCIRun Window_ - SCIRun network editor. For this tutorial we will be selecting modules from the module selector, on the left side of the screen. If for some reason the module selector is not there, open the dropdown menu titled **Window** to bring up the module @@ -187,6 +187,7 @@ Modules menu and select the **ReadField** module form the menu. This will insert **ReadField** module in the upper left corner of the network editor. This module will now be used to read in the first dataset. + Adding and opening module _Figure 2.2 - Finding the ReadField module and opening its GUI_ @@ -200,8 +201,6 @@ If this dataset is not available in your copy of the SCIRunData bundle, please d latest version from the website to obtain a copy. - - Selecting file name and type _Figure 2.3. Select a file name and a file type_ @@ -225,6 +224,7 @@ Once the UI Window of the **ReadField** module opens, select the **NrrdFile** fi _Figure 2.4. Network for checking contents of the file_ + and use the upper part of the UI to locate the dataset by browsing the directories to the location where the SCIRunData has been saved. Open the **heart-ischemia** directory and select **HeartMRI.nrrd** file. Then press **Set** at the bottom of the UI to store the file name @@ -254,11 +254,11 @@ the menu and the module will be deleted from the network editor. To visualize the 3D dataset we convert the module into a 3D texture object, which - Building visualization network _Figure 2.5 Building the visualization network_ + will allow us to quickly browse through the dataset. Use the Show Module feature in the menu bar to insert the following modules: **GetSliceFromStructuredFieldByIndices**, **ShowField**, **RescaleColorMap**, **CreateStandardColorMap**, and **ViewScene**, and connect the modules as depicted in *Figure 2.5*. Note that not the full name needs to be entered each time in the Show Module @@ -282,35 +282,39 @@ the top the color is opaque and when the color is at the bottom the color is tra to make the background transparent. The slider just below that controls where the largest gradient in color should occur by sliding it to the left a higher contrast is generated. In - Network for checking contents of the file _Figure 2.6. Network for checking contents of the file_ + the lower part of the menu one can now select from a series of predefined colormap lookup tables to alter the appearance of the image. To view multiple angles or slices at the same time, create an additional **GetSliceFromStructuredFieldByIndices** and **ShowField** module, and connect them together. Link the **GetSliceFromStructuredFieldByIndices** to your original **ReadField** module and the **RescaleColorMap** module, and the **ShowField** module to the **RescaleColorMap** and **ViewScene** modules. Open the UI of the new **GetSliceFromStructuredFieldByIndices** module, and select an axis (I, J, or K) that is different from the one selected in the first **GetSliceFromStructuredFieldByIndices** module. -Viewing multiple slices +Viewing multiple slices _Figure 2.7. Viewing multiple slices_ - +--- #### Chapter 3 # 3 Visualization of Image Data **Scope: Volume Renderer - ViewScene Module - Resampling - Rendering Glyphs - Calculator Module** -Figure 3.1. Reading in two datasets + +Reading in two datasets + +_Figure 3.1. Reading in two datasets_ +Reading in two datasets +_Figure 3.2. Reading in two datasets_ -Figure 3.2. Reading in two datasets #### 3.1 Volume Renderer and Clipping Planes @@ -331,8 +335,10 @@ Artery. An example of such a visualization is given in figure 3.1. The datasets in this example originate from an isolated dog heart in which the Left +Opening the configuration tray] + +_Figure 3.3. Opening the configuration tray_ -Figure 3.3. Opening the configuration tray Anterior Descending Artery was perfused with Gadolinium preparation so it shows up in an MR scan. The heart was subsequently scanned to generate an anatomical image of the heart @@ -352,10 +358,9 @@ to 1.0. Now use the D slider to slide the clipping plane along the X-axis. The c widget has been configured, so that D corresponds to the full range of X that is spanned +Slicing the dataset - - -Figure 3.4. Slicing the dataset +_Figure 3.4. Slicing the dataset_ by the two images that are displayed in the viewer window. By dragging D from -1 to + @@ -370,6 +375,7 @@ If the slice becomes too transparent, open up the UI of the ShowTextureVolume module. One of the main options is the Global Opacity. Changing this slider the volume rendered object can be made more or less transparent. + #### 3.2 Isosurfacing and Mesh Fairing @@ -383,8 +389,10 @@ TheExtractIsosurface module extracts an isosurface out of any field. In this cas we are extracting it out of the segmented perfusion bed by selecting a value between the +Extracting an Isosurface + +_Figure 3.5. Extracting an Isosurface_ -Figure 3.5. Extracting an Isosurfacet maximum and minimum value in the field. In this case the background and the segmen- tation have a different but constant value and hence the boundary between them will be @@ -399,9 +407,9 @@ that is tessalated by triangles. Because this field is no longer structured like grid, one cannot use the ShowTextureVolume to display the surface. Instead we use +Coupling two ViewScene windows - -Figure 3.6. Coupling Two ViewScene Windows +_Figure 3.6. Coupling two ViewScene windows_ the ShowFieldmodule that is a general module for visualizing any field. The output @@ -427,9 +435,9 @@ windows together again will not align the windows but keep the relative change b Network for visualizing the fiber orientation of the data - _Figure 3.7. Network for Visualizing the Fiber Orientation of the Data_ + windows. The changes are however applied to both windows. To align the windows again select the Views menu at the top of the window and select the Other Viewer Windows menu and select the option to get the view from the other window. This will align the view @@ -500,6 +508,7 @@ output type would be preferred. In most cases the user should not need to set an _Figure 3.8. The UI of The **CalculateFieldData** Module_ + type, only when for memory reasons the data should be different from a double precision representation, this type should be set. @@ -537,12 +546,12 @@ ventricle of the heart. By combing the networks examined in this tutorial one ca the different aspects of the data. +Visualizing the Fiber Orientation of the Data -Figure 3.10. Visualizing the Fiber Orientation of the Data - - +_Figure 3.10. Visualizing the Fiber Orientation of the Data_ +--- #### Chapter 4 # 4 Building a Tetrahedral Mesh @@ -555,54 +564,51 @@ Scope: Isosurface - FairMesh - ResampleMesh - InterfaceWithTetGen - Visualizing In order to build a physical model out of the imaging data, we need to generate a computational mesh. In this example we describe an easy way of generating a tetrahedral mesh using isosurfaces. Another way to generate a mesh is with a [InterfaceWithCleaver](https://github.com/nids2001/scirun.pages/blob/defibrillation-tutorial/InterfaceWithCleaver.md) module. To build an elementary tetrahedral mesh, generate the network that is depicted -in figure 4.1. This network introduces two new modules called **InterfaceWithTetGen** and +in *Figure 4.1.* This network introduces two new modules called **InterfaceWithTetGen** and **WriteField**. The **InterfaceWithTetGen** module lets SCIRun communicate with TetGen for generating a tetrahedral mesh. This module takes a triangular mesh as input and performs a -constrained Delaunay Tetrahedralization and output a full volemtric mesh that consists of -tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated -by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. +constrained Delaunay Tetrahedralization and output a full volumetric mesh that consists of +tetrahedral elements. In order to for tetrahedralization to succeed the isosurface generated by **ExtractIsosurface** needs to be smoothed. We use the **FairMesh** module for this again. -When opening the UI of the **InterfaceWithTetGen** module, one can select out of a +When opening the **UI** of the **InterfaceWithTetGen** module, one can select out of a range of options to generate a mesh. The three options that are of interest in generating -a computational tetrahedral mesh for this problem are the -Y, -q, and the-a option in -the UI. The -Y option lets the user decide whether additional vertices are to be inserted +a computational tetrahedral mesh for this problem are the *-Y*, *-q*, and the *-a* option in +the **UI**. The *-Y* option lets the user decide whether additional vertices are to be inserted into the outer boundary. Suppressing splitting of the boundary facets often generates lower quality elements at the boundary, and forces TetGen to do far more computations, so in -this example we switch it off. The next flag -q enforces quality of the elements, one can +this example we switch it off. The next flag *-q* enforces quality of the elements, one can specify a lower ratio for a better quality. Normally enforcing a higher quality comes at the price of a longer computation and more elements. We keep this at its default setting. -The final flag that is of interest is the -a flag that allows the user to specify the size of the +The final flag that is of interest is the *-a* flag that allows the user to specify the size of the elements. Besides element quality, element size is an important parameter for computing -electromagnetic fields. Without a volume constraint the delaunay tetrahedralization will +electromagnetic fields. Without a volume constraint the Delaunay tetrahedralization will enforce the largest size elements it can fit within the interior of the mesh. As we do not -want that in this case, we supply a volumetric maximum. In this case a value of 5 is +want that in this case, we supply a volumetric maximum. In this case a value of `5` is reasonable value. -In this network, instruct the **ReadField** module to read the file HeartMRI-Segmentation.nrrd ; +In this network, instruct the **ReadField** module to read the file `HeartMRI-Segmentation.nrrd`; the **ResampleRegularMesh** module can keep its default settings. The reason for this module being added to the pipeline is reduce the number of elements in the segmentation, so that the example can be computed within a time frame of minutes instead of hours. - -Figure 4.1. Network for building a Tetrahedral Mesh - +Network for building a Tetrahedral Mesh +_Figure 4.1. Network for building a Tetrahedral Mesh_ +Image of the Tetrahedral Mesh +_Figure 4.2. Image of the Tetrahedral Mesh_ -Figure 4.2. Image of the Tetrahedral Mesh - - -The **ExtractIsosurface** module should be set to the Quantitytap and we should be +The **ExtractIsosurface** module should be set to the **Quantity** tab and we should be computing only one isosurface. The **InterfaceWithTetGen** module options should be set as -indicated in figure 4.1. Finally, the **WriteField** module should contain a name of a file that +indicated in *Figure 4.1*. Finally, the **WriteField** module should contain a name of a file that will be used to save the mesh, so we do not need to recompute for in the rest of the chapters. -Press **Save** in the UI of the module, supply the filename HeartMRI-TetrahedralMesh.fld, and select the desired location for the the file that will be written. Also open up the **ShowField** +Press **Save** in the UI of the module, supply the filename `HeartMRI-TetrahedralMesh.fld`, and select the desired location for the the file to be written. Also, open up the **ShowField** module and disable the **Show Nodes** and **Show Edges**, although SCIRun can render these without any problems. Open the **FairMesh** UI and ensure that the number of -iterations is at 40, for the **InterfaceWithTetGen** module to work correctly. +iterations is at `40`, for the **InterfaceWithTetGen** module to work correctly. After pressing **Execute All** to execute all modules allow for a few minutes for the model to build. As TetGen is running as an external library, we do not have a good estimate of @@ -611,7 +617,7 @@ not moving progress is made and SCIRun will return within a several minutes and the mesh. Use the slicing planes to examine the mesh (see *Figure 4.2*). - +--- #### Chapter 5 # 5 Tensors and Conductivities @@ -627,11 +633,11 @@ spaces as a function of space and the transmembrane potential as a function of s To generate these model spaces we start with a clean canvas, and add a **ReadField** module to read the mesh that was generated in the previous chapter. The full network for generating the model is outlined in *Figure 5.1* with *Figures 5.2 - 5.4* detailing the setting of -the various UIs. Only those modules that need modifications to the default settings are +the various **UIs**. Only those modules that need modifications to the default settings are listed in the figures. -This network starts by loading the previously generated mesh, and also loads the per- -fusion bed dataset and the fiber orientation dataset. All these three datasets are loaded at +This network starts by loading the previously generated mesh, and also loads the perfusion +bed dataset and the fiber orientation dataset. All these three datasets are loaded at the top of the network. This data serves as material to build the heart specific models. In the upper left corner of the network the perfusion bed dataset is loaded. The first @@ -654,22 +660,24 @@ this distance field with a timeframe of less than a minute. However note that wh objects get more complex this operation can be relatively slow. +Full network for building extracellular, intracellular conductivity fields and the +transmembrane potential fields +_Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the +transmembrane potential fields_ -Figure 5.1. Full network for building extracellular, intracellular conductivity fields and the -transmembrane potential fields +UI Settings of modules +_Figure 5.2. UI settings of modules_ -Figure 5.2. UI settings of modules - -Below the **CalculateSignedDistanceToFieldmodule**, the distance field is inserted +Below the **CalculateSignedDistanceToField** module, the distance field is inserted into the **CalculateFieldData** module. The latter module evaluates a mathematical expression based on the data of the field. In this case we define a function that blurs the transmembrane potential based on the distance to the border zone. As the distance is signed we define the transmembrane potential inside the ischemic zone as -15 mV and the -potential outside of the ischemic zone as +15mV, with the border zone at 0 mV. In this +potential outside of the ischemic zone as +1 5mV, with the border zone at 0 mV. In this bidomain simulation we have altered the actual transmembrane potential to be centered around 0mV for convenience. As the choice of a reference potential does not alter the induced currents, the choice of the reference membrane potential does not matter. However @@ -677,10 +685,6 @@ if one wanted to one can add easily an additional term to equation. The equation displayed in *Figure 5.2* was chosen arbitrary to reflect a smooth transition - - - - of the transmembrane potential. The function here just indicates one of many functions that could have been chosen, as we are still in the process of actually determining what the shape of the ischemic border zone is. The equations displayed in the figure show various of the @@ -736,14 +740,14 @@ ports to a new name in the bundle. In this case we choose the names enquoteVM, enquoteIC and enquoteEC for the transmembrane potential, the intracellular conductivity, +UI settings of modules -Figure 5.3. UI settings of modules - +_Figure 5.3. UI settings of modules_ +UI settings of modules - -Figure 5.4. UI settings of modules +_Figure 5.4. UI settings of modules_ and the extracellular conductivity respectively. The bundle subsequently saved on disk for @@ -756,127 +760,133 @@ for instance altering the “BLUR” parameter in the calculator module to see t the blurring. An example of the output is given in *Figure 5.5*. +Visualization of assumed transmembrane potentials -Figure 5.5. Visualization of assumed transmembrane potentials - +_Figure 5.5. Visualization of assumed transmembrane potentials_ +--- #### Chapter 6 # 6 Finite Element Modeling -Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- -Matrix -GetFieldData - SetFieldData +**Scope: BuildFEMatrix - ExtractIsosurfaceByFunction - Bundles - SolveLinearSystem - ApplyMapping- +Matrix -GetFieldData - SetFieldData** #### 6.1 Creating The Simulation We start with the bundle generated in the previous chapter. This bundle contains all the fields for running the simulation. To run the simulation build the network as depicted in -figure 6.1. Figure 6.2-6.5 display the settings required in each of the moduleUImenus. The +*Figure 6.1*. *Figure 6.2 - 6.5* display the settings required in each of the module **UI** menus. The modules that are not highlighted in these figures use the default settings of these modules. The underlying idea of the this network is to solve the following equation : -−(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm (6.1) +−(∇·(Σi+ Σe)∇φe) =∇·Σi∇φm *Equation (6.1)* -in which Σiand Σeare the intracellular and extracellular conductivity tensors andφmis -the transmembrane potential andφeis the extracellular potential. In this network the -transmembrane potentialφmis assumed to be the quantity that is known and the network -computes the extracellular potentialsφethat are actually measured in experiments. Hence, +in which Σi and Σe are the intracellular and extracellular conductivity tensors andφmis +the transmembrane potential and φe is the extracellular potential. In this network the +transmembrane potential φm is assumed to be the quantity that is known and the network +computes the extracellular potentials φe that are actually measured in experiments. Hence, based on a proposed transmembrane potential, this network now computes the extracellular potentials. + At the top of the network the bundle is split in two, one part is used to create the -right-hand-side of equation 6.1 and the other part is used to compute the left-hand-side. -As seen in equation 6.1 the left-hand-side depends on the summation of the intracellular -and extracellular tensors. The moduleCalculateFieldData2is used to sum the values +right-hand-side of *Equation 6.1* and the other part is used to compute the left-hand-side. +As seen in *Equation 6.1* the left-hand-side depends on the summation of the intracellular +and extracellular tensors. The module **CalculateFieldData** is used to sum the values of the intracellular and extracellular conductivity fields for each location. The output of -this module is subsequently fed into theBuildFEMatrixwhich builds the stiffness matrix +this module is subsequently fed into the **BuildFEMatrix** which builds the stiffness matrix for the Poisson equation. This stiffness matrix can be viewed as the discretization of the -anisotropic Poisson equation and hence it is the numeric equivalent of the∇·(Σi+ Σe)∇ +anisotropic Poisson equation and hence it is the numeric equivalent of the ∇·(Σi+ Σe)∇ operator. -The modules to the left of the creation of the stiffness matrix actually compute the right- -hand-side vector. This is done again by using theBuildFEMatrixmodule to generate the -numerical operator∇·(Σi)∇and multiplying this with the values from the transmembrane -potential field. As the output of theBuildFEMatrixmodule is matrix (blue pipe), the -data inside the field needs to be represented as a vector. This is accomplished by the - - -Figure 6.1. Full network for running simulation +The modules to the left of the creation of the stiffness matrix actually compute the +right-hand-side vector. This is done again by using the **BuildFEMatrix** module to generate the +numerical operator ∇·(Σi)∇ and multiplying this with the values from the transmembrane +potential field. As the output of the **BuildFEMatrix** module is matrix (blue pipe), the +data inside the field needs to be represented as a vector. This is accomplished by the -CHAPTER 6. FINITE ELEMENT MODELING 35 +Full network for running simulation +_Figure 6.1. Full network for running simulation_ -Figure 6.2. UI settings of modules +UI settings of modules +_Figure 6.2. UI settings of modules_ -GetFieldDatamodule that strips the data from the nodes in the field and inserts it into a +**GetFieldData** module that strips the data from the nodes in the field and inserts it into a column matrix. In order to now obtain the right-hand-side vector we need to multiply the -column vector with the matrix. The latter is accomplished by theEvaluateLinAlgBinary +column vector with the matrix. The latter is accomplished by the **EvaluateLinAlgBinary** module. + Both the stiffness matrix and the right-hand-side vector now form a linear system that -needs to be solved to obtain the extracellular potentials. TheSolveLinearSystemmodule +needs to be solved to obtain the extracellular potentials. The **SolveLinearSystem** module solves the linear system using in iterative solver. The details of the solver can be entered -in theUIof this module. Once the linear system is solved the solution contained in a -column vector is reinserted into the field using theSetFieldDatamodule. An example of -a reasonable number of iterations is given in figure 6.3. Everything below this module in +in the **UI** of this module. Once the linear system is solved the solution contained in a +column vector is reinserted into the field using the **SetFieldData** module. An example of +a reasonable number of iterations is given in *Figure 6.3*. Everything below this module in the network is used for visualizing the data which is described in the next section. +UI settings of modules + +_Figure 6.3. UI settings of modules_ -Figure 6.3. UI settings of modules #### 6.2 Visualization of Simulation Results In order to study the effect of anisotropy on the extracellular potentials we look at a certain -cross section of the model. In order extract a cross section we use theExtractIsosur- -faceByFunctionmodule. This module lets the user specify a function and subsequently +cross section of the model. In order extract a cross section we use the **ExtractIsosurfaceByFunction** +module. This module lets the user specify a function and subsequently extracts an isosurface of this function and projects the data back onto this surface. In this -case we use the functionRESULT=Y;which will generate cross sections in the XZ-plane. +case we use the function `RESULT=Y;` which will generate cross sections in the XZ-plane. However displaying the data without the underlying fiber structure is of no use, therefore we can reconstruct the fiber orientation from the tensor data sending it through the calculator -module again and extracting the first eigenvector using theeigvec1()function. The data is +module again and extracting the first eigenvector using the *eigvec1()* function. The data is subsequently moved to the elements of the mesh. -To efficiently project the data onto the same mesh as the data, we use theApplyMap- +To efficiently project the data onto the same mesh as the data, we use the **ApplyMap-** +UI settings of modules +_Figure 6.4. UI settings of modules_ -Figure 6.4. UI settings of modules - - -pingMatrixmodule, this allows to quickly copy the data from one mesh to another mesh +**pingMatrixmodule**, this allows to quickly copy the data from one mesh to another mesh if the operation that generated the new mesh computed a so called mapping matrix. In this -case theExtractIsosurfaceByFunctiondid compute such a mapping matrix and we will +case the **ExtractIsosurfaceByFunction** did compute such a mapping matrix and we will be able to project the data onto the same grid. As often in SCIRun there are many ways to -do the same thing, we could just as well have used theMapFieldDataOntoElemsmodule +do the same thing, we could just as well have used the **MapFieldDataOntoElems** module to accomplish the same. + Finally the vectors and the data are combined into one viewer. In order to render a sense -or orientation we also render a transparent shell of the mesh. TheGetFieldBoundary +or orientation we also render a transparent shell of the mesh. The **GetFieldBoundary** module extracts the outside of any mesh. In this case it renders the outer surface of the -model. TheShowFieldmodule can be setup so it renders a transparent version of the mesh -boundary. Disable the display of nodes and edges and alter theDefault Coloras indicated -by figure 6.5. By altering the Alpha value the mesh can be made far more transparent, so +model. The **ShowField** module can be setup so it renders a transparent version of the mesh +boundary. Disable the display of nodes and edges and alter the **Default Color** as indicated +by *Figure 6.5*. By altering the Alpha value the mesh can be made far more transparent, so to highlight the cross section more clearly. Also increase the scale of the vectors so they become clearly visible. -Finally theViewScenemodule displays a result that show that the potentials tend to +Finally the **ViewScene** module displays a result that show that the potentials tend to +UI settings of modules -Figure 6.5. UI settings of modules +_Figure 6.5. UI settings of modules_ -stretch along the fiber orientation, as can be viewed by the results indicated in figure 6.6. +stretch along the fiber orientation, as can be viewed by the results indicated in *Figure 6.6*. +Visualizing Results -Figure 6.6. Visualizing Results +_Figure 6.6. 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