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https://doi.org/10.1080/02841860802251567

has been cited by the following article:

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

  AUTHORS: Kiyoshi Yoda

  KEYWORDS: Treatment Margin, Systematic Positioning Errors, Random Positioning Errors

  JOURNAL NAME: International Journal of Medical Physics, Clinical Engineering and Radiation Oncology, Vol.6 No.2, May 23, 2017

  ABSTRACT: A radiotherapy treatment margin formula has been analytically derived when a standard deviation (SD) of systematic positioning errors Ʃ is relatively small compared to an SD of random positioning errors σ. The margin formula for 0 ≤ Ʃ ≤ σ was calculated by linearly interpolating two boundaries at Ʃ = 0 and Ʃ = σ, assuming that the van Herk margin approximation of k1Ʃ + k2σ is valid at Ʃ = σ. It was shown that a margin formula for 0 ≤ Ʃ ≤ σ may be approximated by k1σ + k2Ʃ, leading to a more general form of k1 max(Ʃ,σ) + k2 min(Ʃ,σ) which is a piecewise linear approximation for any values of Ʃ and σ.