Analytic representation of electron central-axis depth dose data.

Abstract

We have examined a number of analytic representations of electron central-axis depth dose data current in the literature, testing them against sets of standard depth dose data. One of them, a two-parameter model of Shabason and Hendee, is recommended in situations in which good accuracy (approximately 2%) is desired, with the values of the parameters determined by an approximation formula which we have developed elsewhere. For higher accuracy, we have developed a polynomial model which gives, typically, a standard deviation of the fitting polynomial from the data points of 1%, and a maximum deviation of 2%. Fitting polynomials obtained with this method possess the property of having zero slope at the position of actual maximum dose, and generally a fifth-order polynomial (requiring four nonzero coefficients) provided the most acceptable fit. The four parameters involved are determined through inversion of a 4 x 4 matrix, and we have tabulated these four coefficients for the standard data sets. The polynomial model is designed for interpolation in the range between the 100% dose depth and the 10% dose depth, and another fitting curve of the same type can be adjoined to cover depths less than the 100% dose depth.