Inclusion of electron range straggling in the Fermi-Eyges multiple-scattering theory

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Abstract
In electron-beam treatment planning using pencil-beam models, the number and direction of the electrons at each point of the irradiated medium are often calculated with the Fermi-Eyges (FE) multiple-scattering theory. This theory does not account for the absorption of electrons with depth, i.e. it predicts a planar fluence constant with depth. This leads to a radial and angular spread of the pencil beam that increases continuously with depth. In order to eliminate these problems the authors have developed an analytical description for the range straggling of electrons along their path, based on Monte Carlo calculations and derived an expression from the FE theory for the mean pathlength travelled by the electrons that arrive at a point of the medium. This enables inclusion of electron range straggling in the multiple-scattering theory. Radial dose distributions of a pencil beam in water have been calculated with this model and are compared with the results of a complete Monte Carlo simulation.