Scaling relationships for theories of anisotropic random walks applied to tissue optics

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Abstract
Monte Carlo simulations are used to discern scaling relationships for photon migration occurring within homogeneous, anisotropic scattering media of semi-infinite extent. Special attention is given to events associated with short path lengths. Empirical scaling relationships for path lengths and surface intensities are shown to agree with a consistency equation derived in an earlier study of anisotropic random walks. They are augmented here by a procedure that accounts for concomitant scaling of optical absorption coefficients. Results then are used to transform expressions that were obtained previously by analytical random-walk theory developed for an isotropic scattering model of photon migration. Quantities that are studied include the diffuse surface reflectance, the depth distribution of the fluence, and the time-resolved intensity of backreflected photons.