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Light transport in biological tissue based on the simplified spherical harmonics equations. (English) Zbl 1122.78015
Light propagation models in biomedical optics are essential for tomographic imaging of biological tissues using visible and infrared light. These models predict light intensities which can be compared to actually measured light intensities on the tissue boundary. Combinations of predicted and measured data are the basis of image reconstruction algorithms. Light transport in scattering media is modeled in terms of suitable radiative transfer equations whose solvability is a major endavour. Discrete ordinates and spherical harmonics equations are among the reliable approximation methods to this end.
The main goal of the paper is to transfer from the neutron transport theory to the biomedical optics, the so-called simplified spherical harmonics approximation method. Suitable equations are formulated with partially reflective boundary conditions in anisotropically scattering media. Solutions are found to give better results than the standard diffusion model methods. The respective equations are numerically solved for the two-dimensional media mimicking typical small tissue properties. There is a significant computational time gain incurred, in comparison with the standard transport calculations.

MSC:
78A70 Biological applications of optics and electromagnetic theory
78A40 Waves and radiation in optics and electromagnetic theory
62P10 Applications of statistics to biology and medical sciences; meta analysis
92C55 Biomedical imaging and signal processing
78M20 Finite difference methods applied to problems in optics and electromagnetic theory
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