Electron dose calculations using the Method of Moments.
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.
Larsen
E W
EW
Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor 48109, USA.
Miften
M M
MM
Fraass
B A
BA
Bruinvis
I A
IA
D004583:Electrons / Q000627:therapeutic use*; D006801:Humans; D008962:Models, Theoretical; D009010:Monte Carlo Method; D009369:Neoplasms / Q000532:radiotherapy; D016011:Normal Distribution; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted; D011882:Radiotherapy, High-Energy / Q000295:instrumentation / Q000379:methods*