Perturbation Monte Carlo methods to solve inverse photon migration problems in heterogeneous tissues.

We introduce a novel and efficient method to provide solutions to inverse photon migration problems in heterogeneous turbid media. The method extracts derivative information from a single Monte Carlo simulation to permit the rapid determination of rates of change in the detected photon signal with respect to perturbations in background tissue optical properties. We then feed this derivative information to a nonlinear optimization algorithm to determine the optical properties of the tissue heterogeneity under examination. We demonstrate the use of this approach to solve rapidly a two-region inverse problem of photon migration in the transport regime, for which diffusion-approximation-based approaches are not applicable.