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Analytic representation of electron central‐axis depth dose data
Author(s) -
Jette David,
Lanzl Lawrence H.,
Rozenfeld Martin,
Pagnamenta Antonio
Publication year - 1981
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.595038
Subject(s) - mathematics , polynomial , standard deviation , curve fitting , interpolation (computer graphics) , mathematical analysis , range (aeronautics) , data point , percentage depth dose curve , statistics , physics , motion (physics) , materials science , classical mechanics , composite material , ion , quantum mechanics , ionization chamber , ionization
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 (∼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 × 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. Key words: electron teletherapy, central‐axis depth dose, polynomial model, interpolation