Experimental tests of indicators for the degree of validness of the diffusion approximation

The diffusion approximation has been one of the central topics in near-infrared spectroscopy (NIRS). When NIRS measurements are analyzed by the diffusion theory, the measurements must be performed in the diffusive regime. However, since most of past researches have focused on theoretical or qualitative nature of the diffusion approximation, it is not easy to know if each measurement is designed in the diffusive regime. In this paper, we consider the diffusion approximation quantitatively and propose indicators that quantify the degree of validness of the diffusion approximation. The difference between the measurement and diffusion theory can be evaluated with the χ² value, ℓ¹ and ℓ² norms, and Kullback-Leibler divergence. We conduct a liquid phantom experiment to test the proposed χ² value. Moreover, the χ² value is further investigated by Monte Carlo simulations. We find the χ² value becomes significantly large when measurements are performed in the nondiffusive or transport regime. The proposed indicators similarly work. In particular, the χ² value is shown to work as an indicator which evaluates the degree of validness of the diffusion approximation. These indicators are general and can be used for different numerical, experimental, and clinical measurements in NIRS.