Calibration iso-pathlength point in cylindrical tissue geometry: Comparing steady state photon diffusion to Monte Carlo simulation

Light-tissue interactions are commonly studied for near infra-red (NIR) spectroscopy for imaging and diagnosis. While imaging is bound to the surface due to the high tissue scattering, many diagnosis methods, such as the photoplethysmograph (PPG) and pulse oximeter, focus on sensing instead of imaging. There are two approaches for the investigation of light-tissue interactions: one numerical and the other analytical. The most common numerical method is the Monte Carlo (MC) simulation, which is a statistical study of photon migration from the optical properties of the different tissue regions. However, the yield of such statistical approaches is limited. Analytical methods are commonly based on the diffusion theory, yet they are inaccurate near the light source. There are several solution methods, where extrapolated boundary conditions lead to a more accurate solution. Previously, we proposed measuring the full scattering profile (FSP), which is the angular intensity distribution, of cylindrical tissues. MC simulations revealed that the FSP has a fixed intensity point, named the iso-pathlength (IPL) point, which does not depend on the reduced scattering coefficient. The location of this point depends solely on the geometry. In this study, we derived the FSP from the steady state diffusion theory based on the extrapolated zeroboundary condition. A comparison of different reduced scattering coefficients revealed the IPL point, where the intensity remains constant. Furthermore, a MC simulation was performed under the same geometry and optical properties. We show that the position of the IPL according to the diffusion theory is in agreement with the MC simulation.