Planning target volumes for radiotherapy: how much margin is needed?

Abstract

Purpose: The radiotherapy planning target volume (PTV) encloses the clinical target volume (CTV) with anisotropic margins to account for possible uncertainties in beam alignment, patient positioning, organ motion, and organ deformation. Ideally, the CTV-PTV margin should be determined solely by the magnitudes of the uncertainties involved. In practice, the clinician usually also considers doses to abutting healthy tissues when deciding on the size of the CTV-PTV margin. This study calculates the ideal size of the CTV-PTV margin when only physical position uncertainties are considered. Methods and Materials: The position of the CTV for any treatment is assumed to be described by independent Gaussian distributions in each of the three Cartesian directions. Three strategies for choosing a CTV-PTV margin are analyzed. The CTV-PTV margin can be based on: 1. the probability that the CTV is completely enclosed by the PTV; 2. the probability that the projection of the CTV in the beam’s eye view (BEV) is completely enclosed by the projection of the PTV in the BEV; and 3. the probability that a point on the edge of the CTV is within the PTV. Cumulative probability distributions are derived for each of the above strategies. Results: Expansion of the CTV by 1 standard deviation (SD) in each direction results in the CTV being entirely enclosed within the PTV 24% of the time; the BEV projection of the CTV is enclosed within the BEV projection of the PTV 39% of the time; and a point on the edge of the CTV is within the PTV 84% of the time. To have the CTV enclosed entirely within the PTV 95% of the time requires a margin of 2.8 SD. For the BEV projection of the CTV to be within the BEV projection of the PTV 95% of the time requires a margin of 2.45 SD. To have any point on the surface of the CTV be within the PTV 95% of the time requires a margin of 1.65 SD. Conclusion: In the first two strategies for selecting a margin, the probability of finding the CTV within the PTV is unrelated to dose variations in the CTV. In the third strategy, the specified confidence limit is correlated with the minimum target dose. We recommend that the PTV be calculated from the CTV using a margin of 1.65 SD in each direction. This gives a minimum CTV dose that is greater than 95% of the minimum PTV dose. Additional sparing of adjoining healthy structures should be accomplished by modifying beam portals, rather than adjusting the PTV. Then, the dose distributions more accurately reflect the clinical compromise between treating the tumor and sparing the patient.