Theoretical investigation of photon partial pathlengths in multilayered turbid media

Functional near infrared spectroscopy (fNIRS) is a valuable tool for assessing oxy- and deoxyhemoglobin concentration changes (Δ[HbO] and Δ[HbR], respectively) in the human brain. To this end, photon pathlengths in tissue are needed to convert from light attenuation to Δ[HbO] and Δ[HbR]. Current techniques describe the human head as a homogeneous medium, in which case these pathlengths are easily computed. However, the head is more appropriately described as a layered medium; hence, the partial pathlengths in each layer are required. The current way to do this is by means of Monte Carlo (MC) simulations, which are time-consuming and computationally expensive. In this work, we introduce an approach to theoretically calculate these partial pathlengths, which are computed several times faster than MC simulations. Comparison of our approach with MC simulations show very good agreement. Results also suggest that these analytical expressions give much more specific information about light absorption in each layer than in the homogeneous case.