A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy

In order to quantify near-infrared spectroscopic (NIRS) data on an inhomogeneous medium, knowledge of the contribution of the various parts of the medium to the total NIRS signal is required. This is particularly true in the monitoring of cerebral oxygenation by NIRS, where the contribution of the overlying tissues must be known. The concept of the time point spread function (TPSF), which is used extensively in NIRS to determine the effective optical pathlength, is expanded to the more general inhomogeneous case. This is achieved through the introduction of the partial differential pathlength, which is the effective optical pathlength in the inhomogeneous medium, and an analytical proof of the applicability of the modified Beer-Lambert law in an inhomogeneous medium is shown. To demonstrate the use of partial differential pathlength, a Monte Carlo simulation of a two-concentric-sphere medium representing a simplified structure of the head is presented, and the possible contribution of the overlying medium to the total NIRS signal is discussed.