A revised Gaussian pencil beam model for calculation of the in-water dose caused by clinical electron-beam irradiation

Purposes: The dose in water caused by clinical electron-beam irradiation is mainly composed of the doses due to the direct electrons, the indirect electrons, and the contaminant X-rays. In this paper, an analytical method for 3-dimensional (3D) dose calculation in water for the direct electrons and for the direct-plus-indirect electrons is proposed in light of the electron Monte Carlo (eMC) datasets. Methods: The dose calculation was performed for square fields, based on a revised Gaussian pencil beam model, where the parallel beam depth-dose dataset under an infinitely large field was reconstructed from the depth-dose dataset of a fan beam with a finite field. We used a semi-infinite water phantom, setting the beam incident surface on the isocenter plane that is perpendicular to the beam axis. The dose calculation model sets an effective field at each dose calculation depth, where the effective field is larger than the geometrical field that the electron applicator forms on the basis of its divergent spread under the effective source-surface distance (SSDeff). Results and conclusions: By comparing the calculated datasets of depth dose (DD) and off-axis dose (OAD) in water with the eMC datasets for electron beams of E=6, 12, and 18 MeV by Wieslander and Knöös (2006), it has been found that the revised Gaussian pencil beam model is of practical use and has a bright prospect to give almost the same calculation results as the eMC datasets.