A higher order diffusion model for three-dimensional photon migration and image reconstruction in optical tomography

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Abstract
In this work, we derived three-dimensional simplified spherical harmonics approximated higher order diffusion equations. We also solved the higher order diffusion equations using a finite element method and compared the solutions from the first-order diffusion equation and Monte Carlo simulations. We found that the conducted model is able to improve the first-order diffusion solution in a transport-like homogeneous or heterogeneous medium. Reconstructed images based on the higher order diffusion model are also presented. We conclude that the developed higher order diffusion model is able to accurately describe light propagation in biological tissues and to offer improved image reconstruction.