Condensed history methods for Monte Carlo solutions of photon transport problems

In this dissertation, we study fast yet accurate Condensed History (CH) Monte Carlo (MC) methods and show how they might be applied to problems in biomedical optics. CH modeling is routinely used to solve important problems involving charged particle transport, such as the design of radiation therapy plans for cancer patients undergoing radiation treatment, but has been little used for Monte Carlo modeling of photons. While the basic ideas used for charged particles can be carried over to the photon case, the CH techniques require modification and adaptation to be successful for photon transport.; Several different CH methods are studied and compared. The essence of the most useful of these is that the accuracy of the approximate solution can be controlled by preserving certain averages over the angular distribution of scattering, as described by the scattering kernel, in the model. Subtle differences between electron scattering kernels and those used to model photon collisions in tissue make this a challenging exercise. For maximum accuracy, it appears that the averaging in the CH model must be carried out in such a way that a large number of expansion coefficients of the exact and CH solutions agree. However, this criterion tends to conflict with the objective of making the CH simulation much faster than the detailed MC simulation. Success can only be achieved when a proper balance is struck.; We have considered CH averaging approaches that either preserve space-angular moments of the solution directly or do so indirectly by preserving the angular moments of an approximate scattering kernel. This is accomplished by requiring the exact and approximate scattering kernels to satisfy certain "similarity relationships" described in the dissertation.; We have compared the relative efficiencies of several different CH methods using model transport problems whose solutions can be found exactly. The error analysis has made use of advanced MC algorithms that are adaptive and converge geometrically to complete transport solutions for both the detailed and the CH models. Finally, the methods have been tested on an idealized, but representative, tissue problem. One of the CH methods studied seems most promising for practical tissue optics applications.