A Radiotherapy Treatment Margin Formula When Systematic Positioning Errors are Relatively Small Compared to Random Positioning Errors: A First-Order Approximation
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.
References
[1]
van Herk, M., Remeijer, P., Rasch, C. and Lebesque, J.V. (2000) The Probability of Correct Target Dosage: Dose-Population Histograms for Deriving Treatment Margins in Radiotherapy. International Journal of Radiation Oncology Biology Physics, 47, 1121-1135. https://doi.org/10.1016/S0360-3016(00)00518-6
[2]
van Herk, M. (2004) Errors and Margins in Radiotherapy. Seminars in Radiation Oncology, 14, 52-64. https://doi.org/10.1053/j.semradonc.2003.10.003
[3]
Jensen, H.R., Hansen, O., Hjelm-Hansen, M. and Brink, C. (2008) Inter- and Intra-fractional Movement of the Tumour in Extracranial Stereotactic Radiotherapy of NSCLC. Acta Oncologica, 47, 1432-1437. https://doi.org/10.1080/02841860802251567
[4]
Smitsmans, M.H., de Bois, J., Sonke, J.J., Betgen, A., Zijp, L.J., Jaffray, D.A., Lebesque, J.V. and van Herk, M. (2005) Automatic Prostate Localization on Cone-Beam CT Scans for High Precision Image-Guided Radiotherapy. International Journal of Radiation Oncology Biology Physics, 63, 975-984. https://doi.org/10.1016/j.ijrobp.2005.07.973
[5]
Mizukami, N. and Yoda, K. (2016) Intrafractional Positioning Accuracy during Stereotactic Brain Radiotherapy with a Modified Thermoplastic Mask System, On-Board Cone-Beam CT, and a Six-Degrees-of-Freedom Couch. Journal of Radiosurgery and SBRT, 4, 75-76.
[6]
Stroom, J.C. and Heijmen, B.J. (2002) Geometrical Uncertainties, Radiotherapy Planning Margins, and the ICRU-62 Report. Radiotherapy Oncology, 64, 75-83. https://doi.org/10.1016/S0167-8140(02)00140-8
