toastpp Slab

Using TOAST++, the DOT problem is solved in a slab geometry. The forward solution at various detector positions is compared to the analytical solution to the diffusion equation. The analytical solution was calculated using different boundary conditions than those used by TOAST++, so the solutions are similar but not exactly the same.

The code is written in MATLAB, and the steps are split into .m files. The steps are:

1. Generate slab nodes
2a. Generate mesh with tetgen
2b. Check mesh and remove bad elements
3. Generate initial values
4a. Generate detector positions
4b. Generate source positions
5. Generate source-detector (QM) file
6a. Solve the forward solution in TOAST++ and compare to the analytical solution
6b. Generate the FEM file from synthetic data generated in 6a
7. Reconstruct mus and mua in the slab using TOAST++
8. Plot solution

tetgen: http://wias-berlin.de/software/tetgen/

This code is a starting point and can be expanded to complicated geometries.

Project Samples

Analytical transmittance solution to the diffusion equation assuming an infinite slab geometry. This solution was numerically forier transformed and the results compared to the forward solution generated in TOAST++.

Comparison of the fourier transform of the Transmittance and the forward solution generated by TOAST++ in the slab geometry. Each curve corresponds to a different source and detector pair, and they are randomly colored.

Isosurface showing the reconstructed inhomogeneities in a slab geometry. TK1 regularization was used with tau = 1.6e-3.

Isosurface showing two reconstructed inhomogeneities in a slab geometry. TK1 regularization was used with tau = 1.6e-3. Note that mua was not reconstructed successfuly.

Image slice in the z plane showing the two reconstructed inhomogeneities. Low discretization was used for fast reconstructions, which may have contributed to the errors.

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