Implementation of the radiative transfer equation on block-structured grids for modeling fluorescence light propagation in tissue with arbitrary shape

We developed a method for solving the fluorescence equation of radiative transfer in the frequency domain on block-structured grids. In this way fluorescence light propagation in arbitrarily shaped tissue can be modeled with high accuracy without compromising on the convergence speed of these codes. The block-structure grid generator is developed as a multi-purpose tool that can be used with many numerical schemes. We present results from numerical studies that show that it is possible to resolve curved boundaries with grids that maintain much of the intrinsic structure of Cartesian grids. The natural ordering of this grid allows for simplified algorithms. In simulation studies we found that we can reduce the error in boundary fluence by a factor of five by using a two-level block structured grid. The increase in computational cost is only two-fold. We compare benchmark solutions to results with various levels of refinement, boundary conditions, and different geometries.