Effect of roughness in nondiffusive regions within diffusive media

Abstract

Recently it has been shown that clear regions within diffusive media can be accurately modeled within the diffusion approximation by means of a novel boundary condition [J. Opt. Soc. Am. A17, 1671 (2000)] or by an approximation to it [Phys. Med. Biol.41, 767 (1996); Med. Phys.27, 252 (2000)]. This can be directly applied to the study of light propagation in brain tissue, in which there exist clear regions, and in particular in the cerebrospinal fluid (CSF) layer under the skull. In this work we present the effect that roughness in the boundary of nondiffusive regions has on the measured average intensity, since, in practice, the CSF layer is quite rough. The same conclusions can be extended to any diffusive medium that encloses rough nondiffusive regions. We will demonstrate with numerical calculations that the roughness statistics of the interfaces (although not their actual profiles) must be known a priori to correctly predict the shape of the average intensity. We show that as the roughness increases, the effect of the nondiffusive region diminishes until it disappears, thus yielding data similar to those of a fully diffusive region. We also present a numerical study of the diffuse light scattered in the presence of both diffusive and nondiffusive regions and the interaction between the two, showing that when the nondiffusive region is rough, the spatial-intensity distribution produced by the two regions can be very similar.