Electron dose calculation using multiple-scattering theory: localized inhomogeneities--a new theory

In this fourth article in a series on the calculation of electron dose using multiple-scattering theory, we deal with localized inhomogeneities by solving the Fermi equation for scattering power which is an arbitrary function of position. In fact, we go further, by solving the second-order multiple-scattering equation which supersedes the (first-order) Fermi equation, again for scattering power which is an arbitrary function of position. Thus, we are no longer restricted to a horizontally layered medium, as is the case with the Fermi-Eyges theory. Our general solution is in the form of a perturbation series which evidently converges rapidly enough that only its first two or three terms need be taken for accurate dose calculation. Regarding the energy directly deposited by the primary electrons, the formulas developed in this article give very good agreement with Monte Carlo calculations for the thick half-slab configuration, as will be seen in the next article in this series. Moreover, our first-rank, second-order formulas, when expressed in Fourier-transformed space, are simple enough to be implemented in a treatment planning system providing full three-dimensional electron dose calculation for arbitrary configurations of inhomogeneities.