The energy-dependent electron loss model for pencil beam dose kernels

Three-dimensional electron dose calculation using an improved hybrid pencil beam model

An improved hybrid-pencil beam model (HPBM) for electron-beam three-dimensional dose calculation has been studied. The model is based on the fact that away from the edges of a large field, the electron distribution function exactly equals that for an infinitely wide electron beam. In the present model, we use the bipartition model to calculate the longitudinal part of the pencil-beam distribution function, and Fermi-Eyges multiple-scattering theory to calculate its transverse part. In order to describe the electron beam characteristics accurately, we introduce a new parameter, which is extracted from measured profile data near the surface of a water phantom, to correct the transverse distribution determined by the Fermi-Eyges theory. Furthermore, we introduce an effective energy spectrum to describe the effect on the collimated electron beam of the accelerator head. The dose distributions calculated with the improved HPBM were compared with the experimental data, and the agreement was within 1% in most of cases. This preliminary study has demonstrated the potential for use of the model in the clinical therapy.

The energy-dependent electron loss model: backscattering and application to heterogeneous slab media

Electron backscattering has been incorporated into the energy-dependent electron loss (EL) model and the resulting algorithm is applied to predict dose deposition in slab heterogeneous media. This algorithm utilizes a reflection coefficient from the interface that is computed on the basis of Goudsmit-Saunderson theory and an average energy for the backscattered electrons based on Everhart's theory. Predictions of dose deposition in slab heterogeneous media are compared to the Monte Carlo based dose planning method (DPM) and a numerical discrete ordinates method (DOM). The slab media studied comprised water/Pb, water/Al, water/bone, water/bone/water, and water/lung/water, and incident electron beam energies of 10 MeV and 18 MeV. The predicted dose enhancement due to backscattering is accurate to within 3% of dose maximum even for lead as the backscattering medium. Dose discrepancies at large depths beyond the interface were as high as 5% of dose maximum and we speculate that this error may be attributed to the EL model assuming a Gaussian energy distribution for the electrons at depth. The computational cost is low compared to Monte Carlo simulations making the EL model attractive as a fast dose engine for dose optimization algorithms. The predictive power of the algorithm demonstrates that the small angle scattering restriction on the EL model can be overcome while retaining dose calculation accuracy and requiring only one free variable, chi, in the algorithm to be determined in advance of calculation.