Electron dose calculation using multiple-scattering theory: a new theory of multiple scattering

Starting from the Boltzmann-Fokker-Planck transport equation, we have developed a new theory of multiple scattering which incorporates the advances already made with our Gaussian multiple-scattering theory for electron dose calculation. This incorporation has been accomplished in a natural way, by modifying the scattering power T and by adding a convolution term to the distribution-function equation of the Gaussian theory. Our previous results concerning increasing the accuracy of the small-angle approximation used and dealing with localized tissue inhomogeneities have thus been maintained, and we have arrived at a complete distribution function in both transverse spatial and angular variables. When integrated over the transverse angular variables, for a first-order small-angle approximation this distribution function for a pencil beam is essentially the same as the Moliere multiple-scattering distribution, which includes large-angle single scattering. For a water phantom, we have used comparisons with EGS4 Monte Carlo calculations to demonstrate the greatly increased accuracy of our new multiple-scattering theory over the Gaussian theory, which includes the usual Fermi-Eyges theory. We have also presented a fairly accurate Gaussian approximation to the pencil-beam dose profiles given by our new theory, which can be used in order to maintain the mathematical simplicity of the predictions of the Fermi-Eyges theory.