Abstract

In this report we present preliminary results towards developing an efficient numerical scheme for computing photon migration in complex scattering media such as body tissues. Our motivation for these studies is the appreciation that development of practical imaging schemes will require that solutions to the forward problem be computationally tractable, physically accurate and have a format that maps well to the inverse problem. The object here is to optimize the tradeoffs and still obtain an acceptable answer. It is known, for example, that Monte Carlo methods can provide accurate estimates of photon distributions, even for complex media, but the computing times can be unacceptable long. Numerical solutions to the diffusion are computationally much more efficient, but of course, the physically accuracy of these solutions are subject to the constraints of the diffusion approximation (i.e., away from boundaries and source and the absence of strong discontinuities). We further recognize that for iterative inversion methods, solution of the forward problem on a uniform grid is desirable, as it permits use of global instead of local interpolation functions. Solutions to the forward problem that employ nonuniform grids certainly can be considered, but add to computing times for the inverse problem.

© 1994 Optical Society of America