Finite element method for diffusive light propagations in index-mismatched media.

Near-infrared (NIR) light propagations in strongly scattering tissue have been studied in the past few decades and diffusion approximations (DA) have been extensively used under the assumption that the refractive index is constant throughout the medium. When the index is varying, the discontinuity of the fluence rate arises at the index-mismatched interface. We introduce the finite element method (FEM) incorporating the refractive index mismatch at the interface between the diffusive media without any approximations. Intensity, mean time, and mean optical path length were computed by FEM and by Monte Carlo (MC) simulations for a two-layer slab model and a good agreement between the data from FEM and from MC was found. The absorption sensitivity of intensity and mean time measurements was also analyzed by FEM. We have shown that mean time and absorption sensitivity functions vary significantly as the refractive index mismatch develops at the interface between the two layers.