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

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    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.

    Original languageEnglish (US)
    Title of host publicationOptical Tomography and Spectroscopy of Tissue IX
    DOIs
    StatePublished - 2011
    EventOptical Tomography and Spectroscopy of Tissue IX - San Francisco, CA, United States
    Duration: Jan 23 2011Jan 26 2011

    Publication series

    NameProgress in Biomedical Optics and Imaging - Proceedings of SPIE
    Volume7896
    ISSN (Print)1605-7422

    Conference

    ConferenceOptical Tomography and Spectroscopy of Tissue IX
    CountryUnited States
    CitySan Francisco, CA
    Period1/23/111/26/11

    Keywords

    • Diffuse optical tomography
    • equation of radiative transfer
    • finite volume method
    • light propagation
    • simplified spherical harmonics

    ASJC Scopus subject areas

    • Electronic, Optical and Magnetic Materials
    • Biomaterials
    • Atomic and Molecular Physics, and Optics
    • Radiology Nuclear Medicine and imaging

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