Effect of roughness in non-diffusive regions within diffusive media

摘要

Recently, it has been shown that clear regions within diffusive media can be accurately modelled within the diffusion approximation by means of a novel boundary condition or by an approximation to it. This can be directly applied to the study of light propagation in brain tissue, in which there exist clear regions, and in particular, the cerebro spinal fluid (CSF) layer under the skull. In this work, we present the effect that roughness in the boundary of non-diffusive regions has on the measured signal, since, in practice, the CSF layer is quite rough. The same conclusions can be extended to any diffusive medium which encloses rough non-diffusive regions. We will demonstrate with numerical calculations that the roughness statistics of the interfaces although not their actual profile must be known a priori in order to correctly predict the shape of the measured signal. We show that as the roughness increases, the effect of the non-diffusive region diminishes until it disappears, thus yielding data similar to those of a fully diffusive region.