Photon dose calculation based on electron multiple-scattering theory: practical representation of dose and particle transport integrals.
In modern photon dose-calculation algorithms one is frequently called upon to evaluate the integral at various points throughout the irradiated material of a dose or particle transport quantity multiplied by a weighting factor. For example, for a given dose-calculation point one might be integrating the product of the dose deposited by a monoenergetic beam and the energy distribution of the actual beam, and want to do this throughout the treatment volume. We have developed explicit formulas for replacing such integrations with a weighted sum of two or three functions (of, for example, the point of dose calculation) in order to greatly reduce the calculation time for the algorithm being used. We demonstrate the accuracy of this method of representing dose and particle transport integrals through comparisons with Monte Carlo calculations of dose distributions for two typical problems, in dealing with the energy spectrum of the photon beam and with the energy deposited by all the Compton electrons emerging from a particular interaction point, respectively.