Author(s)

Kiyoshi Yoda

Research Physics, Elekta KK, Tokyo, Japan.

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.

Treatment Margin, Systematic Positioning Errors, Random Positioning Errors

Yoda, K. (2017) A Radiotherapy Treatment Margin Formula When Systematic Positioning Errors are Relatively Small Compared to Random Positioning Errors: A First-Order Approximation. International Journal of Medical Physics, Clinical Engineering and Radiation Oncology, 6, 193-196. doi: 10.4236/ijmpcero.2017.62017.