Solution of the time-dependent diffusion equation for a three-layer medium: application to study photon migration through a simplified adult head model

A diffusion-based model for photon migration through a three-layer medium is described. The main purpose of this work is to investigate the performance of a diffusion equation (DE)-based forward model for studying photon migration through a diffusive layered medium having a low scattering layer. This geometrical model can be used as a simple model of the adult head. Numerical results are shown for a set of values of the optical properties typical of the adult human head, where scalp and skull are lumped in the first layer while the second and third layer are associated with the cerebrospinal fluid (CSF) and the brain, respectively. Due to the presence of the CSF, which is a relatively clear layer, the diffusion-based model yields an approximate solution of photon migration. Nevertheless, comparisons with MC simulations show that the model can predict the total and the partial mean path length in the different layers with an error less than 20%. In particular, the partial mean path length in the third layer, representative of the brain, is calculated with an error less than 10% if the reduced scattering coefficient of the second layer, representative of the CSF, is assumed 0.25 mm−1.