30 May 1995 Finite-element-based higher order diffusion approximation of light propagation in tissues
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Diffusion approximation (first-order) and Monte Carlo methods have been widely used in modeling light propagation tissues. Diffusion theory can provide a reasonably accurate description of light distributions in regions some distance from boundaries and sources, whereas Monte Carlo methods can give a more accurate solution without these limitations, but are computationally time-consuming. A higher-order diffusion approximation of light propagation in 2D tissue geometries using a finite element method is presented in this paper. We demonstrate that higher-order diffusion approximation can provide more accurate solutions than the usual first-order diffusion model yet is still much lower in computational cost than Monte Carlo simulation. Two benchmark problems are tested. The first one which consists of a rectangular geometry has an exact analytical solution and confirms our higher-order diffusion model implementation. The second test problem is an optically homogeneous, 2D cylindrical geometry and the computed solutions are compared with measrued data along the boundary of a tissue-like liquid phantom. The agreement is found to be promising and potentially more accurate than the conventional first-order diffusion equation approximation.
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Huabei Jiang, Huabei Jiang, Keith D. Paulsen, Keith D. Paulsen, "Finite-element-based higher order diffusion approximation of light propagation in tissues", Proc. SPIE 2389, Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, (30 May 1995); doi: 10.1117/12.210007; https://doi.org/10.1117/12.210007

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