Empirical model description of photon path length for differential path length spectroscopy: combined effect of scattering and absorption.

Differential path length spectroscopy (DPS) is a method of reflectance spectroscopy that utilizes a specialized fiber geometry to make the photon path length (tau) insensitive to variations in tissue optical properties over a wide range of absorption (mu(a)) and total scattering (mu(s)) coefficients, which are common within the ultraviolet/visible (UV/VIS) wavelength region. This study extends the description of tau to larger mu(a) and smaller mu(s) values, optical properties that are representative of the near-infrared region (NIR), a region where the DPS path length may be dependent on both coefficients. This study presents a novel empirical relationship between tau and the combined effect of both mu(a) (range: 0.1-12 mm(-1)) and mu(s) (range: 1.5-42 mm(-1)), anisotropy of 0.8, and is applicable to DPS probes containing a wide range of fiber diameters (range: 100-1000 microm). The results indicate that the simple empirical formula, including only one fitted parameter, is capable of accurately predicting tau over a wide range (r=0.985; range: 80-940 microm) and predictions are not biased versus mu(a) or mu(s). This novel relationship is applicable to analysis of DPS measurements of tissue in both the UV/VIS and NIR wavelength regions and may provide information about the wavelength-specific tissue volume optically sampled during measurement.