Analytical solution of the time-dependent photon diffusion equation for a layered medium

The scattering and the absorption coefficients of tissue can provide important information about the physiological condition of tissue. Living bodies have a complex structure, therefore in most cases tissue cannot be regarded as a homogeneous medium. In some cases biological tissue have layered structures (head, skin, bone, etc.), consequently in order to measure the optical properties in vivo it is necessary to formulate the photon migration in layered media. Making use of the diffusion equation a theoretical time domain model for photon migration through a highly scattering layered slab has been elaborated. A pencil pulsed light beam is normally incident upon the surface of the first diffusing layer. The effect of the refractive index mismatch with the external medium is taken into account and proper boundary conditions between the diffusing layers are considered. Analytical solutions of the fluence rate inside the layers have been obtained. A Monte Carlo program for the photon migration through a two or a three layered slab has been also developed. The results obtained by using the analytical solution and Monte Carlo simulations are compared and presented. The main goal of this work is the future application of the model on retrieving the optical properties of layered media.