2.1 Workflow input models
Figure 4. Inversion algorithm applied to data generated by forward model (top row) to construct images (bottom row). Forward and reconstructed models are in SquareMesh_ScatteredDensityBreast folder.
Figure 5. (a) Input forward and reconstructed models with rectangular mesh elements. (b) Data path that points to parent folder that holds the data and configuration folders is entered in field shown in circle 1. User then selects format of forward and reconstruction models with Input model format toggle switch (circle 2). After selecting the ‘Input forward and reconstructed models for processing’ from the task list (circle 3), the ‘Press to Run’ button is clicked (circle 4) to start the task.
The first step is to input the forward and inversion (or reconstruction) models. A review of microwave breast imaging with tomography is provided in Appendix A3. Imaging is carried out in two steps. In the first step, the breast is illuminated successively with incident electromagnetic fields from each of the antennas. Hence, the breast is interrogated from multiple directions, and the resulting scattered and transmitted fields are received by antennas located on the breast’s periphery and recorded by the measurement system. For a numerical experiment, an electromagnetic forward model comprised of tissues with dielectric properties reported from large–scale studies [5,6]. The model is sequentially illuminated with numerical incident fields, and the calculated scattered and transmitted fields received by the numerical antenna are stored.
Once the experimental data are collected, the reconstruction step using the inversion algorithm is carried out. This second step starts with a trial guess of the distribution. The electromagnetic model of the breast is initialized with this guess. An array of numerical antennas within a simulated measurement chamber that approximates the actual experimental system surrounds the breast and sequentially illuminates the breast with numerical incident fields. The resulting calculated scattered and transmitted fields received at the numerical antennas are recorded. A cost functional measures the discrepancy between the measured and calculated fields, and an inverse solver computes the optimal change in the parameter profile of the electromagnetic model necessary to reduce the discrepancy between these data. The trial solution is updated with these changes, and the forward solver recalculates the electric fields. The process continues in this iterative manner—updating and refining the reconstructed profile (or inversion model)—until the calculated and measured fields match which, in turn, implies that the reconstructed profile closely matches the actual spatial distribution of dielectric properties of tissues in the breast interior. Different tissue types are distinguished from each other by their characteristic dielectric properties.
The test data provided in the testData folder are associated with a numerical studies. The forward model in the SquareMesh_ScatteredDensityBreast folder used to generate the numerical electromagnetic data is shown in the top row of figure 4. The inversion algorithm is applied to these data, resulting in the reconstructed images shown in the bottom row of figure 4.
In order to process these data, the data path that points to the parent folder of the data and configuration folders (see figure 5b, for example) is entered in the field shown in circle 1 of figure 5a. The format of the forward and reconstruction models is selected with the Input model format toggle switch. Either the Rectangular mesh elements (matlab) or Triangular mesh elements option is selected.
Figure 6. Configuration and data files used when models represented with rectangular mesh elements.
To accommodate microwave inversion results produced from various microwave breast imaging algorithms, forward and inverse models that use or have already been transformed to rectangular mesh elements are input by selecting this option. A frequency file (frequency.txt) that stores the incident field frequency measured in Hz used to collect the data must be supplied. X and Y axes node files (xNodes.txt, and yNodes.txt) used to mesh the imaging domain into rectangular elements and to identify coordinates of each element (or node) of the model must also be provided. It is assumed that these files represent distance along an axis in meters. The frequency and axes files are stored in the configuration folder.
Values of the electrical properties (complex permittivity) for each element (or node) of the meshed 2D space used to represent the forward and reconstruction models are stored in matrices with variable names input_forwardModel, and input_reconstructedModel, and are saved in matlab formatted files input_forwardModel.mat, and input_reconstructedModel.mat, respectively, in the data folder. Files stored in the configuration and data folders are shown in figure 6.
After entering the data path that points to the parent folder of the data and configuration folders, the user selects the ‘Rectangular mesh (Matlab)’ option with the ‘Input model format’ toggle switch (figure 5a circle 2). The user also selects the ‘Input forward and reconstruction models for processing’ from the task list (figure 5a circle 3), the color map to display the figures, and the format to save the figures.
Next, the user clicks on the ‘Press to run’ button to execute the task (figure 5a circle 4). After reading and validating the user information from the GUI (including error checking tasks that validate the existence of the data and configuration files), the task manager constructs the finite element object fe that implements methods to read the complex permittivity maps, and the mesh and frequency information from files in the data and configuration folders. These data are stored in the data structure of the finite element object. Object methods use these data to construct the forward and reconstructed models that are displayed for the user. Figure 4 shows an example of forward and reconstructed models for a scattered density breast represented with rectangular mesh elements that are stored in the SquareMesh_ScatteredDensityBreast folder of the test data set.
A final sub-task that is performed is to use the incident field frequency read from the frequency file to calculate threshold values for various tissue types that are used to segment the forward model. The finite element object fe is saved in the file named inputModels.mat in the results folder that is created by the task manager. All figures are saved in the figures folder that is created along with the results folder in the SquareMesh_ScatteredDensityBreast folder.
Figure 7. Configuration (left) and data (right) files used when forward and reconstructed models represented with triangular mesh elements.
Figure 8. Input forward and reconstructed models with triangular mesh elements. Data path that points to parent folder that holds the data and configuration folders entered in field shown in circle 1. ‘Triangular mesh’ selected with ‘Input format’ toggle (circle 2). Click on ‘Press to get contrast iteration file list’ (circle 3) to retrieve list of reconstructed contrast profiles.
Figure 9. Input forward and reconstructed models with triangular mesh elements. Select contrast profile for reconstruction model (circle 1). ‘Input forward and reconstructed models for processing’ task selected from task list (circle 2). Task is run by clicking on ‘Press to run’ button (circle 3).
Figure 10. Forward (top row) and reconstruction (bottom row) models for the test data in the TriangularMesh_HeterogenouslyDenseBreast folder.
The structure of the files in the configuration and data folders output by the finite-element-method contrast source inversion (FEM-CSI) technique [2] that uses triangular mesh elements is shown in figure 7. The method uses various sized triangular mesh elements to represent the forward and reconstruction models. An example of the forward model with triangular mesh elements is shown in figure 8. Mesh information and the value of the complex contrast at nodes of the model are provided for the forward model with the FwdMesh.msh and FwdMaterials.txt files, respectively. Likewise, mesh information for the inverse models is provided by the InvMesh.msh file. The complex permittivity of the background is provided by the PriorMaterials.txt file. More general information about how the data were collected is provided by the input_datacollect.xml (forward model) and input_csi_Img_Rec.xml (inverse model). A frequency file (frequency.txt) indicating the incident field frequency is provided. Information about the rectangular mesh for which the triangular elements are transformed to is furnished with the xNodes.txt, and yNodes.txt files. Finally, the contrast permittivity at nodes on the reconstructed model mesh at specific iterations of the inversion algorithm is provided in contrast files in the data folder.
The user first enters the forward and reconstruction models data path pointing to the parent folder of the data and configuration folders in the field identified with circle 1 in figure 8. The ‘input model format’ toggle switch is set to the ‘Triangular mesh’ option shown with circle 2 of figure 8. When this option is selected, a contrast iteration file list box is visible as shown in figure 8. To populate the list box, the user must click on the ‘Press to get contrast iteration file list’ button (circle 3 of figure 8). The GUI responds by reading file names of the contrast iteration files in the data folder. It extracts the iteration number from the file name and displays this information in the ‘Contrast iteration files’ list box. The user then selects the desired contrast iteration file to form the profile of the reconstruction model (figure 9 circle 1), selects the ‘Input forward and reconstructed model for processing’ from the task list box (figure 9 circle 2), and clicks on the ‘Press to run’ to execute the task (figure 9 circle 3).
After reading and validating user information from the GUI (including the existence of the data and configuration files), the task manager creates finite element object fe that implements methods to read files in the data and configuration folders. Object methods transform the forward and inverse triangular model elements to rectangular elements. The transformed models are stored in the data structure of finite element object fe. Figure 10 shows an example of forward and reconstructed models for an heterogeneously dense classified breast read from data and configuration files in the TriangularMesh_HeterogenouslyDenseBreast folder of the test data set.
The incident field frequency read from the frequency file is used to initialize the threshold values used to segment the forward model. The finite element object fe (saved in inputModels.mat) and the figures are saved in the results and figures folders, respectively, that are created in the TriangularMesh_HeterogenouslyDenseBreast folder.