The diffusion equation in multilayered rectangular biological tissue with finite thickness

Abstract

In biomedical optics, the diffusion model of biological tissue plays an important role. In the biological tissue of any multi-layer rectangular non-matching slab medium, under the rectangular boundary condition, based on the diffusion equation of light propagation in the biological medium, using the extrapolation boundary condition, the exact solution of the diffusion equation Green function of the light in any multi-layer rectangular medium of finite thickness is established and given, and the spatial resolution diffuse reflectivity and transmittance and time resolved diffuse reflectivity and transmittance are calculated in this paper. Different formulas for calculating transmittance are given. We use Monte Carlo to verify our model. The results show that our equation is in good agreement with Monte Carlo simulation. The equation can not only solve the problem of medium which is rectangular laterally, but also solve the problem that the x axis and y axis are infinite in transverse direction, and the medium is semi-infinite in longitudinal direction, and it can also solve the problem that the x, y and z coordinate axes are finite in size. So it's more universal.