Radiative transport in the delta-P1 approximation for semi-infinite turbid media

We have developed an analytic solution for spatially resolved diffuse reflectance within the deltaP1 approximation to the radiative transport equation for a semi-infinite homogeneous turbid medium. We evaluate the performance of this solution by comparing its predictions with those provided by Monte Carlo simulations and the standard diffusion approximation. We demonstrate that the delta-P1 approximation provides accurate estimates for spatially resolved diffuse reflectance in both low and high scattering media. We also develop a multi-stage nonlinear optimization algorithm in which the radiative transport estimates provided by the delta-P1 approximation are used to recover the optical absorption (microa), reduced scattering (micros'), and single-scattering asymmetry coefficients (g1) of liquid and solid phantoms from experimental measurements of spatially resolved diffuse reflectance. Specifically, the delta-P1 approximation can be used to recover microa, micros', and g1 with errors within +/- 22%, +/- 18%, and +/- 17%, respectively, for both intralipid-based and siloxane-based tissue phantoms. These phantoms span the optical property range 4 < (micros' /microa) < 117. Using these same measurements, application of the standard diffusion approximation resulted in the recovery of microa and micros' with errors o f +/- 29% and +/- 25%, respectively. Collectively, these results demonstrate that the delta-P1 approximation provides accurate radiative transport estimates that can be used to determine accurately the optical properties of biological tissues, particularly in spectral regions where tissue may display moderate/low ratios of reduced scattering to absorption (micros'/microa).