Pencil‐beam redefinition algorithm for electron dose distributions

Abstract

A pencil-beam redefinition algorithm has been developed for the calculation of electron-beam dose distributions on a three-dimensional grid utilizing 3-D inhomogeneity correction. The concept of redefinition was first used for both fixed and arced electron beams by Hogstrom et al. but was limited to a single redefinition. The success of those works stimulated the development of the pencil-beam redefinition algorithm, the aim of which is to solve the dosimetry problems presented by deep inhomogeneities through development of a model that redefines the pencil beams continuously with depth. This type of algorithm was developed independently by Storchi and Huizenga who termed it the "moments method." Such a pencil beam within the patient is characterized by a complex angular distribution, which is approximated by a Gaussian distribution having the same first three moments as the actual distribution. Three physical quantities required for dose calculation and subsequent radiation transport--namely planar fluence, mean direction, and root-mean-square spread about the mean direction--are obtained from these moments. The primary difference between the moments method and the redefinition algorithm is that the latter subdivides the pencil beams into multiple energy bins. The algorithm then becomes a macroscopic method for transporting the complete phase space of the beam and allows the calculation of physical quantities such as fluence, dose, and energy distribution. Comparison of calculated dose distributions with measured dose distributions for a homogeneous water phantom, and for phantoms with inhomogeneities deep relative to the surface, show agreement superior to that achieved with the pencil-beam algorithm of Hogstrom et al. in the penumbral region and beneath the edges of air and bone inhomogeneities. The accuracy of the redefinition algorithm is within 4% and appears sufficient for clinical use, and the algorithm is structured for further expansion of the physical model if required for site-specific treatment planning problems.