Comparison of methods to determine electron pencil beam spread in tissue-equivalent media

This study has intercompared the predictions of Fermi-Eyges theory for the rms spatial spread (sigma) of an electron pencil beam scattering in muscle-, lung- and bone-equivalent media with those of; two range straggling modifications to the theory, Monte Carlo simulations, and an empirical method based on broad beam penumbra. Systematic differences among the results obtained by these methods for the values of sigma have been identified. Monte Carlo simulations are lower than the predictions of Fermi-Eyges theory for sigma at all depths whereas the broad beam penumbra method results are in reasonable agreement with Fermi-Eyges theory at depths less than approximately 0.7 times the range of the incident electrons. All of the methods investigated have an increasing discrepancy from the predictions of Fermi-Eyges theory with depth, especially close to the end of the electron range. The two range-straggling modifications to Fermi-Eyges theory developed for soft tissue do not agree with either measured or Monte Carlo results for sigma in homogeneous scattering media of lung and bone.