Solution of Radiative Transfer Equation in Heterogeneous Tissue Based on Kubelka-Munk Theory

The interaction of electromagnetic waves with biological tissues is the most fundamental physical interaction in biology, and its study is expected to have a significant impact on the regulation of the life process, but due to the heterogeneity of the molecules in the biological hull environment, it is not possible to apply Maxwell’s equations analytically, so approximate methods and radiation transfer theory should be used. In this paper, an approximate solution for the propagation of electromagnetic waves in biological tissues has been presented by a mathematical modeling based on Kubelka-Munk (K.M.) theory. This theory is an approximation of the radiation transfer equation that explains the emission of diffuse and isotropic radiation through a homogeneous medium to a thickness d along the z-axis, regardless of the reflection of light from the tissue boundary surface. In mathematical calculations and modeling, the thermal effects due to the interaction of the electromagnetic wave with the heterogeneous tissue have been neglected and the intensity of the beam within the tissue is considered according to Lambert s law.