Elementary Monte Carlo Methods in Turbid Media

The Monte Carlo (MC) method has been employed through the years as a gold-standard method to reconstruct numerical solutions of the RTE. The MC method provides a physical simulation of light propagation; i.e., photon trajectories are generated by using the same statistical rules that govern propagation in random media. In practice, the MC method estimates the expected characteristics of the photon population as statistical averages over a large number of case histories of photon life that are simulated by a computer. These average statistical characteristics of the photon population are exactly what the RTE describes, and, intuitively, this is why the MC method allows one to estimate numerically solutions of the RTE. In fact, comparisons of MC-based results with exact analytical solutions of the RTE demonstrate that for the limit of an infinite number of photons used, the simulated data converge rigorously to the analytical results. The existing literature shows that the MC method can be implemented by using different approaches. In this chapter, the approaches usually employed are briefly reviewed by illustrating their main peculiarities. These approaches are also the basis of more complex MC procedures, such as perturbation MC methods, voxel-based MC methods, mesh-based MC methods, or GPU-accelerated MC codes.