Simulation of Light Propagation in Media with Air-Filled Structures Using the Radiative Transfer Equation: Implications for Diffuse Optical Tomography for Thyroid Cancer

For image reconstruction in diffuse optical tomography (DOT), both accurate mathematical modeling of light propagation in biological tissue and robust inverse modeling are essential. This study evaluates the validity of the radiative transfer equation (RTE) as a forward model for DOT of the thyroid gland, which surrounds the air-filled trachea anteriorly, by comparing it with the photon diffusion equation (PDE). Distributions of photon time-of-flight (DTOFs) were obtained from numerical solutions of the RTE and the PDE in a homogeneous phantom and in a phantom containing four cylindrical holes. The refractive-index mismatch at the cylindrical hole walls (refractive index 1.511) was explicitly modeled by incorporating boundary conditions into the RTE solver, where refraction angles were determined using Snell’s law and the reflection coefficient was calculated based on Fresnel’s law. These simulated DTOFs were compared with experimental measurements acquired using a time-domain near-infrared spectroscopy (TD-NIRS) system. The results demonstrate that the RTE describes light propagation in media containing hollow regions more accurately than the PDE. Future work will apply this RTE framework to model light propagation in the human thyroid gland and improve the diagnostic accuracy of thyroid nodules.