Radiotherapy margin design with particular consideration of high curvature CTVs

In applying 3D conformal radiation therapy to a tumor clinical target volume (CTV), a margin is added around the CTV to account for any sources of error in the application of treatment which may result in misalignment between the CTV and the dose distribution actually delivered. The volume enclosed within the CTV plus the margin is known as the PTV, or planning target volume. The larger the errors are anticipated to be, the wider the margin will need to be to accommodate those errors. Based on the approach of van Herk et al. ["The probability of correct target dosage: Dose-population histograms for deriving treatment margins in radiotherapy," Int. J. Radiat. Oncol. Biol., Phys. 47(4), 1121-1135 (2000)] this paper develops the mathematical theory behind the calculation of the margin width required to ensure that the entire CTV receives sufficiently high dose with sufficiently high probability. The margin recipe developed not only considers the magnitude of the errors but also includes a term to adjust for curved CTV surfaces. In doing so, the accuracy of the margin recipe is enhanced yet remains mathematically concise enough to be readily implemented in the clinical setting. The results are particularly relevant for clinical situations in which the uncertainties in treatment are large relative to the size of the CTV.