Testing of radiative transfer equations for biomedical applications

The radiative transfer equation (RTE) is an important theoretical tool in biomedical optics for describing light propagation in tissues. The solutions to its derived diffusion equation (DE) are used, for example, for dose calculation in photodynamic therapy and for optical tomography. The RTE is valid for constant refractive index and zero ray divergence. These conditions limit its applicability in biomedical optics. To eliminate these drawbacks three new RTEs have been proposed. In this paper we test the standard RTE and the new RTES by solving them for the irradiance of rays propagating in an infinite medium with no scattering, no absorption and no amplification. The solutions to this problem must coincide with the irradiance laws of geometrical optics. We show that only one of those equations gives solutions, which are consistent with irradiance laws of geometrical optics due to its ability to model, the effect of spatially varying refractive index and non-negligible ray divergence. Consequently that equation gives a better description of light propagation in scattering media with spatially varying refractive index and near sources, a physical situation occurring frequently in biomedical optics.