Numerical simulation of the interaction between light and tissue is important for the design and analysis of many optical imaging modalities. Most current simulations are based on the Transport Theory of light in a dielectric, and only calculate the intensity of light in a volume. These simulations do not provide phase information, which is important for many biomedical imaging systems. We are interested in obtaining the optical field, magnitude and phase, due to the interaction of light with tissue. Therefore, we need to solve the integral equation for scalar scattering in a volume of interest. Since the wavelength of light is in the order of nanometres, simulation of volumes of more than a few millimetres requires intensive computational resources. For large volumes, Monte Carlo methods are a suitable choice because their computational complexity is independent of the mathematical dimension of the problem. Also by a careful selection of the random sampling scheme the number of samples needed can be further reduced. In this paper we present an implementation of a method to solve Fredholm integral equations of the second kind using Reversible Jump Markov chain Monte Carlo (RJMCMC). This method could be used to simulate light in tissue with very large electrical size, meaning tissue whose physical dimensions are much larger than the wavelength of light, by solving the integral equation of scalar scattering over a large domain. We implemented this method based on RJMCMC and present in this paper the results of applying it to solve integral equations of one and two dimensions.
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Pedro F. Pereira and Sherif S. Sherif
Simulation of the interaction of light and tissue in a large volume using a Markov chain Monte Carlo method
", Proc. SPIE 8412, Photonics North 2012, 841218 (October 23, 2012); doi:10.1117/12.2001455; http://dx.doi.org/10.1117/12.2001455