Computation of Electron Dose Distributions in Tissue Using Gaussian Pencil Beams

Abstract

Magnetically scanned therapeutic electron beams from the Sagittaire Therac 40 accelerator can be modelled using a collimated isotropic source in which the emitted electrons scatter according to Fermi-Eyges small angle multiple scattering theory. This theory predicts a Gaussian spatial and angular spread of an electron pencil beam with depth in tissue. A semiempirical method based on this theory can be used to derive the standard deviation a of this Gaussian with depth in a tissue-equivalent medium from broad electron beam penumbra. The results obtained with this semiempirical method at 16 and 22 Mev beam energies are compared to Fermi-Eyges theory and a range straggling modification to this theory (5), for homogeneous tissue-equivalent media corresponding to muscle, lung and bone. The semi-empirically derived values of delta demonstrate that neither Fermi-Eyges theory nor the range straggling modification to this theory possesses universal validity and this may lead to significant dose computation errors in the treatment planning of radiotherapy patients. A 'friction' term is introduced into the Fermi-Eyges electron transport equation to account for the effects of range straggling. This friction component is successful in modelling the measured variation of mean square scattering angle with depth in homogeneous media.