A finite-volume algorithm for modeling light transport with the time-independent simplified spherical harmonics approximation to the equation of radiative transfer

Ludguier D. Montejo; Hyun-Keol K. Kim; Andreas H. Hielscher

doi:10.1117/12.875967

17 February 2011 A finite-volume algorithm for modeling light transport with the time-independent simplified spherical harmonics approximation to the equation of radiative transfer

Ludguier D. Montejo, Hyun-Keol K. Kim, Andreas H. Hielscher

Author Affiliations +

Proceedings Volume 7896, Optical Tomography and Spectroscopy of Tissue IX; 78960J (2011) https://doi.org/10.1117/12.875967
Event: SPIE BiOS, 2011, San Francisco, California, United States

Abstract

In this work we introduce the finite volume (FV) approximation to the simplified spherical harmonics (SP_N) equations for modeling light propagation in tissue. The SP_N equations, with partly reflective boundary conditions, are discretized on unstructured grids. The resulting system of linear equations is solved with a Krylov subspace iterative method called the generalized minimal residual (GMRES) algorithm. The accuracy of the FV-SP_N algorithm is validated through numerical simulations of light propagation in a numerical phantom with embedded inhomogeneities. We use a FV implementation of the equation of radiative transfer (ERT) as the benchmark algorithm. Solutions obtained using the FV-SP_N (N > 1) algorithm are compared to solutions obtained with the ERT and the diffusion equation (SP₁). Compared to the SP₁, the SP₃ solutions obtained using the FV-SP_N algorithm can better approximate ERT solutions near boundary sources and in the vicinity of void-like regions. Solutions using the SP₃ algorithm are obtained 9.95 times faster than solutions with the ERT-based algorithm.

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Ludguier D. Montejo, Hyun-Keol K. Kim, and Andreas H. Hielscher "A finite-volume algorithm for modeling light transport with the time-independent simplified spherical harmonics approximation to the equation of radiative transfer", Proc. SPIE 7896, Optical Tomography and Spectroscopy of Tissue IX, 78960J (17 February 2011); https://doi.org/10.1117/12.875967

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