Differential pathlength factor for diffuse photon scattering through tissue by a pulse-response method

Although near-infrared (NIR) spectroscopy may one day provide a noninvasive measurement of oxidative metabolism in tissue, the method cannot be fully quantitative until the mean pathlength traveled by photons between reference and output detectors (i.e, optrodes) is known. In NIR spectroscopy, photons are transported primarily by diffuse scattering, and their mean pathlength can be expressed by a differential path factor (DPF) whose value is greater than the interoptrode distance. Beginning with a P1 diffusion approximation of the Boltzmann equation, one-dimensional photon currents originating from plane, line, and point photon sources were analyzed. DPF was formulated from the attenuation of light intensity generated by constant sources, and an equation for the mean time of flight of photons between reference and output optrodes, delta tau, was derived for arbitrarily pulsed sources. The results indicate that (1) the attenuation of light in tissue does not, in general, vary with interoptrode distance in the manner predicted by Beer's law; (2) the relationship between DPF and interoptrode distance is nonlinear and geometry-dependent; and (3) in spite of these nonidealities, DPF is equal to the product of delta tau and the speed of light.