No abstract

The diffusion approximation to the Boltzmann transport equation is commonly used to analyze data obtained from biomedical optical diagnostic techniques. Unfortunately, this approximation has significant limitations to accurately predict radiative transport in turbid media, which constrains its applicability to highly scattering systems. Here we extend the diffusion approximation in both stationary and frequency-domain cases using an approach initially formulated independently by Prahl ͓Ph.D. The solution is presented in the stationary case for infinite media with a collimated source of finite size exhibiting spherical symmetry. The solution is compared to results given by standard diffusion theory as well as to measurements made in turbid phantoms with reduced single scattering albedos aЈ ranging from 0.248 to 0.997. Unlike the conventional diffusion approximation, the approach presented here provides accurate descriptions of optical dosimetry in both low and high scattering media. Moreover, it accurately describes the transition from the highly anisotropic light distributions present close to collimated sources to the nearly isotropic light distribution present in the far field. It is postulated that the ability to measure the transition between this near and far field behavior and predict it within a single theoretical framework may allow the separation of the single scattering anisotropy g from the reduced scattering coefficient s Ј. The generalized formulation of diffusion theory presented here may enable the quantitative application of present optical diagnostic techniques to turbid systems which are more highly absorbing and allow these systems to be probed using smaller source-detector separations. ͓S1063-651X͑98͒13408-6͔

The use of perturbation and differential Monte Carlo (pMC/dMC) methods in conjunction with nonlinear optimization algorithms were proposed recently as a means to solve inverse photon migration problems in regionwise heterogeneous turbid media. We demonstrate the application of pMC/dMC methods for the recovery of optical properties in a two-layer extended epithelial tissue model from experimental measurements of spatially resolved diffuse reflectance. The results demonstrate that pMC/dMC methods provide a rapid and accurate approach to solve two-region inverse photon migration problems in the transport regime, that is, on spatial scales smaller than a transport mean free path and in media where optical scattering need not dominate absorption. The pMC/dMC approach is found to be effective over a broad range of absorption (50 to 400%) and scattering (70 to 130%) perturbations. The recovery of optical properties from spatially resolved diffuse reflectance measurements is examined for different sets of source-detector separation. These results provide some guidance for the design of compact fiber-based probes to determine and isolate optical properties from both epithelial and stromal layers of superficial tissues.