Abstract
This paper describes an extension of the perturbation Monte Carlo method to model light transport when the phase function is arbitrarily perturbed. Current perturbation Monte Carlo methods allow perturbation of both the scattering and absorption coefficients, however, the phase function can not be varied. The more complex method we develop and test here is not limited in this way. We derive a rigorous perturbation Monte Carlo extension that can be applied to a large family of important biomedical light transport problems and demonstrate its greater computational efficiency compared with using conventional Monte Carlo simulations to produce forward transport problem solutions. The gains of the perturbation method occur because only a single baseline Monte Carlo simulation is needed to obtain forward solutions to other closely related problems whose input is described by perturbing one or more parameters from the input of the baseline problem. The new perturbation Monte Carlo methods are tested using tissue light scattering parameters relevant to epithelia where many tumors originate. The tissue model has parameters for the number density and average size of three classes of scatterers; whole nuclei, organelles such as lysosomes and mitochondria, and small particles such as ribosomes or large protein complexes. When these parameters or the wavelength is varied the scattering coefficient and the phase function vary. Perturbation calculations give accurate results over variations of ∼15-25% of the scattering parameters.
Highlights
There has been interest in analyzing optical reflectance spectra to obtain information about tissue microstructure
This paper focuses on the extension of perturbation Monte Carlo methods [14] to arbitrary variations of the phase function
The underlying idea of perturbation Monte Carlo, pMC, is to generate a single set of photon biographies according to the probability measure M and define a new estimator that can be used to estimate collected light intensity using the same photon biographies for different conditions
Summary
There has been interest in analyzing optical reflectance spectra to obtain information about tissue microstructure. The source-detector separations in optical reflectance measurements to study tissue microstructure are frequently small enough to preclude the use of diffusion theory. Solutions of the RTE can be obtained through Monte Carlo (MC) simulations These MC simulations can provide RTE solutions for any set of boundary conditions, light source and detector configurations and arbitrary tissue properties including any phase function. Obtaining accurate solutions to the RTE with Monte Carlo simulations typically uses much more computer time than, say, diffusion-based modeling. This paper focuses on the extension of perturbation Monte Carlo methods [14] to arbitrary variations of the phase function In this initial work, scattering through all azimuthal angles is assumed to be likely in both the baseline and perturbed simulations. The MC simulations are restricted to unpolarized scattering from spherical particles
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