Simulation of diffuse photon migration in tissue by a Monte Carlo method derived from the optical scattering of spheroids

Abstract

A Monte Carlo method was derived from the optical scattering properties of spheroidal particles and used for modeling diffuse photon migration in biological tissue. The spheroidal scattering solution used a separation of variables approach and numerical calculation of the light intensity as a function of the scattering angle. A Monte Carlo algorithm was then developed which utilized the scattering solution to determine successive photon trajectories in a three-dimensional simulation of optical diffusion and resultant scattering intensities in virtual tissue. Monte Carlo simulations using isotropic randomization, Henyey-Greenstein phase functions, and spherical Mie scattering were additionally developed and used for comparison to the spheroidal method. Intensity profiles extracted from diffusion simulations showed that the four models differed significantly. The depth of scattering extinction varied widely among the four models, with the isotropic, spherical, spheroidal, and phase function models displaying total extinction at depths of 3.62, 2.83, 3.28, and 1.95 cm, respectively. The results suggest that advanced scattering simulations could be used as a diagnostic tool by distinguishing specific cellular structures in the diffused signal. For example, simulations could be used to detect large concentrations of deformed cell nuclei indicative of early stage cancer. The presented technique is proposed to be a more physical description of photon migration than existing phase function methods. This is attributed to the spheroidal structure of highly scattering mitochondria and elongation of the cell nucleus, which occurs in the initial phases of certain cancers. The potential applications of the model and its importance to diffusive imaging techniques are discussed.