A Radiotherapy Treatment Margin Formula When Systematic Positioning Errors are Relatively Small Compared to Random Positioning Errors: A First-Order Approximation

摘要

A radiotherapy treatment margin formula has been analytically derived when a standard deviation (SD) of systematic positioning errors ? is relatively small compared to an SD of random positioning errors σ. The margin formula for 0 ≤ ? ≤ σ was calculated by linearly interpolating two boundaries at ? = 0 and ? = σ, assuming that the van Herk margin approximation of k1? + k2σ is valid at ? = σ. It was shown that a margin formula for 0 ≤ ? ≤ σ may be approximated by k1σ + k2?, leading to a more general form of k1 max(?,σ) + k2 min(?,σ) which is a piecewise linear approximation for any values of ? and σ.