Perturgation Theory of Photon Migration in the Presence of a Single Defect

We present an analytical perturbation analysis to study the sensitivity of diffusive photon flux to the addition of a small shperical defect object in multiple scattering media such as human tissues. As a first simple application of our perturbation method, we derive analytically the photon migration path distributions, and the shapes of the so called “banana” regions in which the photon migration paths are concentrated. We then derive analytically the sensitivity of detected photon flux densities to the inclusion of small spherical defects in the multiple scattering medium, for both single source and two-source configurations, at both steady state (DC) and frequency modulation conditions, and compare the results with Monte Carlo simulations.