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

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Document pages: 4 pages

Abstract: Aradiotherapy treatment margin formula has been analytically derived when astandard deviation (SD) of systematic positioning errors Ʃ isrelatively small compared to an SD of random positioning errors σ.The margin formula for 0 ≤ Ʃ ≤ σ was calculated by linearly interpolating two boundaries atƩ = 0 and Ʃ = σ, assuming that the van Herk marginapproximation of k1Ʃ +k2σ is valid at Ʃ= σ. It was shown that a margin formula for 0 ≤ Ʃ ≤ σ may be approximatedby k1σ +k2Ʃ, leading to a moregeneral form of k1max(Ʃ,σ) + k2min(Ʃ,σ) which is a piecewise linear approximation for anyvalues of Ʃ and σ.

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