RADIATIVE TRANSPORT IN THE DIFFUSION-APPROXIMATION - AN EXTENSION FORHIGHLY ABSORBING MEDIA AND SMALL SOURCE-DETECTOR SEPARATIONS

The diffusion approximation to the Boltzmann transport equation is com monly used to analyze data obtained from biomedical optical diagnostic techniques. Unfortunately, this approximation has significant Limitat ions to accurately predict radiative transport in turbid media, which constrains its applicability to highly scattering systems. Here we ext end the diffusion approximation in both stationary and frequency-domai n cases using an approach initially formulated independently by Prahl [Ph.D. thesis, University of Texas at Austin, 1988 (unpublished)] and Star [in Dosimetry of Laser Radiation in Medicine and Biology, edited by G. J. Muller and D. H. Sliney (SPIE, Bellingham, WA, 1989), pp. 146 -154; in Optical-Thermal Response of Laser-Irradiated Tissue, edited b y A. J. Welch and M. J. C. van Gemert (Plenum, New York, 1995), pp. 13 1-206]. The solution is presented in the stationary case for infinite media with a collimated source of finite size exhibiting spherical sym metry. The solution is compared to results given by standard diffusion theory as well as to measurements made in turbid phantoms with reduce d single scattering albedos a' ranging from 0.248 to 0.997. Unlike the conventional diffusion approximation, the approach presented here pro vides accurate descriptions of optical dosimetry in both low and high scattering media. Moreover, it accurately describes the transition fro m the highly anisotropic light distributions present close to collimat ed sources to the nearly isotropic light distribution present in the f ar field. It is postulated that the ability to measure the transition between this near and far field behavior and predict it within a singl e theoretical framework may allow the separation of the single scatter ing anisotropy g from the reduced scattering coefficient mu(s)'. The g eneralized formulation of diffusion theory presented here may enable t he quantitative application of present optical diagnostic techniques t o turbid systems which are more highly absorbing and allow these syste ms to be probed using smaller source-detector separations.