Solution of Radiative Transfer Equation using Discrete Transfer Method for two-dimensional participating medium

The present work reports the development and application of a simplified numerical approach for solving the transient Radiative Transfer Equation (RTE) using Discrete Transfer Method (DTM) in two-dimensional coordinate system. The numerical formulation of the proposed scheme is discussed in detail and its application in the context of understanding light propagation phenomenon in laser-irradiated numerically simulated biological tissue phantoms has been demonstrated. The developed mathematical model has first been benchmarked against the results published in the literature for the same operating conditions. Thereafter, the results of a detailed parametric study have been presented to investigate the effects of optical properties of the biological phantom on the intensity distribution within the two-dimensional tissue phantom, net transmittance and reflectance, etc. The effect of anisotropy of the tissue medium has also been studied to understand the phenomenon of light propagation within the body of the sample. Based on the results of the study, it has been inferred that the developed numerical methodology for two-dimensional Discrete Transfer Method successfully predicts the physics of the phenomena of light propagation within the tissue phantom and compares well with the other conventionally employed numerical models for solving the Radiative Transfer Equation.