Abstract
We study the modeling and simulation of steady-state measurements of light scattered by a turbid medium taken at the boundary. In particular, we implement the recently introduced corrected diffusion approximation in two spatial dimensions to model these boundary measurements. This implementation uses expansions in plane wave solutions to compute boundary conditions and the additive boundary layer correction, and a finite element method to solve the diffusion equation. We show that this corrected diffusion approximation models boundary measurements substantially better than the standard diffusion approximation in comparison to numerical solutions of the radiative transport equation.
Highlights
Non-invasive boundary measurements of light scattered by tissues are important for biomedical applications [1, 2]
We implement the recently introduced corrected diffusion approximation in two spatial dimensions to model these boundary measurements. This implementation uses expansions in plane wave solutions to compute boundary conditions and the additive boundary layer correction, and a finite element method to solve the diffusion equation. We show that this corrected diffusion approximation models boundary measurements substantially better than the standard diffusion approximation in comparison to numerical solutions of the radiative transport equation
The performance of the corrected diffusion approximation (cDA) was tested with 2D simulations
Summary
Non-invasive boundary measurements of light scattered by tissues are important for biomedical applications [1, 2]. There have been some works that have taken into account sources and boundaries correctly by combining the solutions of the RTE and the DA to form a hybrid method. Tarvainen et al [18] developed a coupled method combining solutions of the RTE and DA both within a finite element framework for both space and angle This coupled method can take into account correctly boundaries, sources as well as low-scattering regions in the interior of the domain. By computing the boundary layer solution only for boundary points where we are modeling measurements, we show that the cDA provides a superior approximation to the solution of the RTE requiring only a small amount of more work than solving the DA itself.
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