TY - GEN

T1 - A finite-volume algorithm for modeling light transport with the time-independent simplified spherical harmonics approximation to the equation of radiative transfer

AU - Montejo, Ludguier D.

AU - Kim, Hyun Keol K.

AU - Hielscher, Andreas H.

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011

Y1 - 2011

N2 - In this work we introduce the finite volume (FV) approximation to the simplified spherical harmonics (SPN) equations for modeling light propagation in tissue. The SPN 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-SPN 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-SPN (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-SPN 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.

AB - In this work we introduce the finite volume (FV) approximation to the simplified spherical harmonics (SPN) equations for modeling light propagation in tissue. The SPN 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-SPN 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-SPN (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-SPN 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.

KW - Diffuse optical tomography

KW - equation of radiative transfer

KW - finite volume method

KW - light propagation

KW - simplified spherical harmonics

UR - http://www.scopus.com/inward/record.url?scp=79955724440&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955724440&partnerID=8YFLogxK

U2 - 10.1117/12.875967

DO - 10.1117/12.875967

M3 - Conference contribution

AN - SCOPUS:79955724440

SN - 9780819484338

T3 - Progress in Biomedical Optics and Imaging - Proceedings of SPIE

BT - Optical Tomography and Spectroscopy of Tissue IX

T2 - Optical Tomography and Spectroscopy of Tissue IX

Y2 - 23 January 2011 through 26 January 2011

ER -