OPTIMIZATION OF PENCIL BEAM WIDTHS FOR ELECTRON-BEAM DOSE CALCULATIONS

The pencil beam method of calculating dose distributions for electron-beam radiotherapy has been very useful, however, several limitations in the approach have been recognized. One such limitation is the lack of a mechanism to model range straggling of electrons. For stationary electron-beam calculations, range straggling is incorporated incompletely in the planar-fluence-to-dose conversion factor, which uses measured percentage depth dose curves to force the calculated percentage depth dose to reproduce the measurement. When calculating the dose distribution for an arced beam using a pencil beam algorithm, insufficient modeling of the pencil beams leads to larger errors than when using a stationary beam algorithm. The calculated depth of maximum dose is systematically overestimated by the pencil beam calculations. We will show that the lack of a way to account for range straggling in the arc-electron pencil beam calculation is primarily responsible for this discrepancy. Methods of incorporating range straggling into the electron pencil beam dose calculation have been presented before, but no data have been shown to support their use for heterogeneous phantoms (patients). This paper presents a similar range-straggling modification, as well as data to show that this model can predict pencil beam width to within 20% for heterogeneous slab phantoms. For stationary electron-beam calculations, the calculated isodose lines follows the measured isodose lines to within 1 mm down to the 10% dose level. Incorporating this modification into the arc-electron pencil beam calculation improves the agreement between the depths of the calculated and measured maximum doses to within 2 mm; however, the magnitude of the maximum dose is as much as 3%-4% lower for the calculated arc-electron beams. This study discusses reasons for these discrepancies and presents possible improvements. © 1995, American Association of Physicists in Medicine. All rights reserved.