An overview of the bipartition model for charged particle transport

A semi-analytical model for calculating the penetration depth of a high energy electron beam in a water phantom with a magnetic field

PURPOSE

As an electron beam is incident on a uniform water phantom in the presence of a lateral magnetic field, the depth-dose distribution of the electron beam changes significantly and forms the well-known 'Bragg peak', with a depth-dose distribution similar to that of heavy ions. This phenomenon has pioneered a new field in the clinical application of electron beams. For such clinical applications, evaluating the penetration depth of electron beams quickly and accurately is the critical problem.

METHODS

This paper describes a model for calculating the penetration depth of an electron beam rapidly and correctly in a water phantom under the influence of a magnetic field. The model was used to calculate the penetration depths under different conditions: the energies of electron beams of 6, 8, 12 and 15 MeV and the magnetic induction intensities of 0.75, 1.0, 1.5, 2.0 and 3.0 T. In addition, the calculation results were compared with the results of a Monte Carlo simulation.

RESULTS

The comparison results indicate that the difference between the two calculation methods was less than 0.5 cm. Moreover, the computing time of the calculation model was less than a second.

CONCLUSIONS

The semi-analytical model proposed in the present study enables the penetration depth of the electron beam in the presence of a magnetic field to be obtained with a computational efficiency higher than that of the Monte Carlo approach; thus, the proposed model has high potential for application.

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.