An analytical method for 3-dimensional calculation of the contaminant X-ray dose in water caused by clinical electron-beam irradiation

Purposes: In this paper, an analytical method for 3-dimensional (3D) calculation of the contaminant X-ray dose in water caused by clinical electron-beam irradiation is proposed in light of the two groups of Monte Carlo (MC) datasets reported by Wieslander and Knöös (2006). Methods: The dose calculation was performed based on Clarkson’s sector method. We used a plane called the isocenter plane, which is set perpendicular to the beam axis, containing the isocenter on it. On the isocenter plane, we defined the applicator field formed by an electron applicator and the cerrobend area field formed by a cerrobend insert if any, as well as other physical terms that are important for the dose calculations. The original sector method was modified to consider the following terms: (a) the vague beam-field margins formed by the dual-foil system; (b) the in-air dose distribution of the contaminant X-ray beam; (c) the X-ray spectrum change between the contaminant X-ray PDD datasets and the published radiotherapy X-ray PDD datasets; and (d) the contaminant X-ray attenuation for the cerrobent insert, if any. Results and conclusions: By comparing the calculated datasets of depth dose (DD) and off-axis dose (OAD) with the MC results for electron beams of E =6, 12, and 18 MeV, it can be concluded that the analytical calculation method is of practical use for various irradiation conditions. In particular, it should be noted that the analytical method can give almost the same calculation results as the MC-based dose calculation algorithm used in a commercial treatment planning system (TPS). highlights Based on Clarkson’s sector method, we developed an analytical method for calculation of the contaminant X-ray dose in water caused by clinical electron-beam irradiation. The analytical method was constructed by considering the following terms: (a) the vague beam-field margins formed by the dual-foil system; (b) the in-air dose distribution of the contaminant X-ray beam; (c) the X-ray spectrum change between the contaminant X-ray PDD datasets and the published radiotherapy X-ray PDD datasets; and (d) the contaminant X-ray attenuation for the cerrobent insert, if any. The dose calculation was performed in light of the two groups of Monte Carlo (MC) datasets reported by Wieslander and Knöös (2006). We conclude that the analytical method can achieve accurate dose calculations, even for beams with cerrobent inserts.