Electron beam dose planning using discrete Gaussian beams. Mathematical background.

A general method for computerized electron beam dose planning is proposed based on the use of a square or hexagonal grid or matrix of discrete Gaussian elementary beams. Using this method the distribution of absorbed dose in an electron beam of arbitrary cross-section incident on an irregular patient surface can be calculated taking the influence of tissue inhomogeneities into account. The derived expressions for the absorbed dose in narrow and broad uniform beams are compared with experimental data and Monte Carlo calculations. Good agreement is obtained over the clinically significant portion of the absorbed dose distribution at a fairly wide grid spacing of about 0.5 cm.