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

Yves Bérubé-Lauzière; Vivian Issa; Jorge Bouza Dominguez

doi:10.1117/12.810178

23 February 2009 Simplified spherical harmonics approximation of the time-dependent equation of radiative transfer for the forward problem in time-domain diffuse optical tomography

Yves Bérubé-Lauzière, Vivian Issa, Jorge Bouza Dominguez

Author Affiliations +

Proceedings Volume 7174, Optical Tomography and Spectroscopy of Tissue VIII; 717403 (2009) https://doi.org/10.1117/12.810178
Event: SPIE BiOS, 2009, San Jose, California, United States

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 ( SP_N approximation). In this work, we outline how to derive the SP_N 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.

Citation Download Citation

Yves Bérubé-Lauzière, Vivian Issa, and Jorge Bouza Dominguez "Simplified spherical harmonics approximation of the time-dependent equation of radiative transfer for the forward problem in time-domain diffuse optical tomography", Proc. SPIE 7174, Optical Tomography and Spectroscopy of Tissue VIII, 717403 (23 February 2009); https://doi.org/10.1117/12.810178

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