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Proceedings Paper

Simplified spherical harmonics approximation of the time-dependent equation of radiative transfer for the forward problem in time-domain diffuse optical tomography
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Paper Abstract

The equation of radiative transfer (ERT) is generally accepted as the most accurate model for light propagation in biological tissues. The ERT is notoriously expensive to solve numerically. Recently, Klose and Larsen have approximated the time-independent ERT using the simplified spherical harmonics equations ( SPN approximation). In this work, we outline how to derive the SPN approximation of the time-dependent ERT and obtain the associated integro- partial differential equations involving temporal convolution integrals. No approximation is made as regards the time variable in our derivation. To simplify the numerical solution of these equations, we introduce a "memory function". We discuss the numerical solution for N = 1 in the 2D and homogeneous case. We provide time evolution maps of the solution and compare it with the diffusion approximation of the ERT. The findings presented here straightforwardly extend to 3D inhomogeneous media and for higher values of N. These more complicated cases along with further details will be reported elsewhere.

Paper Details

Date Published: 23 February 2009
PDF: 11 pages
Proc. SPIE 7174, Optical Tomography and Spectroscopy of Tissue VIII, 717403 (23 February 2009); doi: 10.1117/12.810178
Show Author Affiliations
Yves Bérubé-Lauzière, Univ. de Sherbrooke (Canada)
Vivian Issa, Univ. de Sherbrooke (Canada)
Jorge Bouza Dominguez, Univ. de Sherbrooke (Canada)

Published in SPIE Proceedings Vol. 7174:
Optical Tomography and Spectroscopy of Tissue VIII
Bruce J. Tromberg; Arjun G. Yodh; Mamoru Tamura; Eva M. Sevick-Muraca; Robert R. Alfano, Editor(s)

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