Mesh optimization for Monte Carlo based optical tomography

Abstract

In this thesis, iterative mesh adaptation techniques are applied towards two separate goals within the MC and FMT techniques. First, mesh discretizations are coarsened for the MC simulations in regions where few simulated photons are able to reach. This allows for more photons to reach these areas and subsequently reduce the errors in the Jacobians. These coarsened meshes, subsequently, can be used with less photons to improve computational load of the techniques. Next, the mesh discretizations are refined in the areas where the fluorescent markers exist to improve resolution. By analytically rescaling the forward model for each iteration instead of repeating the MC simulations, the improvements in resolution come with a minimal increase in computational load.

Optical imaging is an essential pre-clinical tool, especially in small animal imaging, due to its high sensitivity and low costs. Techniques such as Fluorescence Molecular Tomography (FMT) allow for three dimensional quantification and visualization of molecular probes in vivo, providing important information in fields such as drug delivery. However, these techniques demand accurate forward models of light propagation in order to achieve accurate reconstructions. Monte Carlo (MC) methods simulate a large number of photons through discretized tissues in order to determine how light propagates between each source and detector pair. Recently, finite element methods have been used for the tissue discretizations, allowing for efficient computation and improved boundary accuracies. Using a mesh discretization also allows for strategic refining and coarsening of the elements to improve the computational demand of the process or the reconstruction accuracies.