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.