Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical solution of partial differential equations
Numerical solution of partial differential equations
Simplified PN approximations to the equations of radiative heat transfer and applications
Journal of Computational Physics
The inverse source problem based on the radiative transfer equation in optical molecular imaging
Journal of Computational Physics
Spatial differencing of the transport equation: Positivity vs. accuracy
Journal of Computational Physics
Improving the accuracy of the diffusion model in highly absorbing media
Journal of Biomedical Imaging
Study on photon transport problem based on the platform of molecular optical simulation environment
Journal of Biomedical Imaging - Special issue on mathematical methods for images and surfaces
Journal of Biomedical Imaging - Special issue on Mathematical Methods for Images and Surfaces 2011
Applied Numerical Mathematics
Asymptotic derivation and numerical investigation of time-dependent simplified P N equations
Journal of Computational Physics
Iterative performance of various formulations of the SPN equations
Journal of Computational Physics
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In this work, we demonstrate the validity of the simplified spherical harmonics equations to approximate the more complicated equation of radiative transfer for modeling light propagation in biological tissue. We derive the simplified spherical harmonics equations up to order N=7 for anisotropic scattering and partially reflective boundary conditions. We compare numerical results with diffusion and discrete ordinates transport solutions. We find that the simplified spherical harmonics methods significantly improve the diffusion solution in transport-like domains with high absorption and small geometries, and are computationally less expensive than the discrete ordinates transport method. For example, the simplified P"3 method is approximately two orders of magnitude faster than the discrete ordinates transport method, but only 2.5 times computationally more demanding than the diffusion method. We conclude that the simplified spherical harmonics methods can accurately model light propagation in small tissue geometries at visible and near-infrared wavelengths, yielding transport-like solutions with only a fraction of the computational cost of the transport calculation.