The Method of Moments is generalized to predict the dose deposited by a prescribed source of electrons in a homogeneous medium. The essence of this method is (i) to determine, directly from the linear Boltzmann equation, the exact mean fluence, mean spatial displacements, and mean-squared spatial displacements, as functions of energy; and (ii) to represent the fluence and dose distributions accurately using this information. Unlike the Fermi-Eyges theory, the Method of Moments is not limited to small-angle scattering and small angle of flight, nor does it require that all electrons at any specified depth z have one specified energy E(z). The sole approximation in the present application is that for each electron energy E, the scalar fluence is represented as a spatial Gaussian, whose moments agree with those of the linear Boltzmann solution. Numerical comparisons with Monte Carlo calculations show that the Method of Moments yields expressions for the depth-dose curve, radial dose profiles, and fluence that are significantly more accurate than those provided by the Fermi-Eyges theory.

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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 ( F E ) 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 we 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. Good agreement with the central part of the Monte Carlo dose profiles is obtained; the radial widths ( l / e dose level) agree to within 1 mm over the entire depth range.

A method for the calculation of absorbed dose distributions of arbitrarily shaped electron beams is presented. Isodose distributions and output factors of treatment fields can be predicted with good accuracy, without the need for any dose measurement in the actual field. A Gaussian pencil beam model is employed with two different pencil beams for each electron beam energy. The values of the parameters of the pencil beam dose distributions are determined from a set of measurements of broad beam distributions; in this way the influence of electrons scattered by the applicator walls is taken into account. The dose distribution of electrons scattered from high atomic number metal frames, which define the treatment field contour at the skin, is calculated separately and added. This calculation is based on experimentally derived data. The method has been tested for beams with 6, 10, 14 and 20 MeV electron energy. The distance between calculated and measured isodose lines with values between 10 and 90% is under 0.3 cm. The difference between calculated and measured output factors does not exceed 2%.