EUD-based margin selection in the presence of set-up uncertainties

To assess the impact of geometric uncertainties on treatment plan design, we have performed a numerical simulation in which both systematic and random errors were included. A clinical target volume (CTV) with an abutting organ at risk (OAR), both of 50 mm diameter, in a cubic phantom was modeled. A four-field conformal treatment plan was designed in which one pair of parallel-opposed beams traversed the OAR and CTV while the other pair intersected the CTV only. Field size, prescribed (isocenter) dose and systematic set-up uncertainty were varied in two orthogonal directions to examine their impact on the outcome as predicted by the dose volume histogram (DVH) and the phenomenological form of equivalent uniform dose (EUD). Of the systematic uncertainty levels considered (0, 2, 4, and 6 mm standard deviations of a Gaussian distribution), 10 mm margin (CTV-PTV) was adequate to maintain the integrity of the dose distribution within the CTV. However, reducing the margin (and hence field size) without reducing set-up errors required an increase in the isocenter dose to compensate for the loss in EUD. It was found that, in the direction containing both the CTV and OAR, with random and systematic uncertainties of 2 and 4 mm respectively, increasing the isocenter dose by about 3.5 Gy on a 6 mm-margin plan resulted in the statistically equivalent EUD value to that with a 10 mm-margin for the CTV, while the OAR EUD is dropped by 1 Gy. In general, though, the directional sensitivity to geometric uncertainties, and hence the required margin size in different directions, was dependent on beam geometries and the relative positions of the structures under consideration relative to the beam directions. Based on the validity of the EUD concept, our general conclusion is that modest dose escalation may result in plans that better achieve clinical objectives. Also, a simple single number plan quality index such as EUD5%, discussed in the paper, facilitates meaningful statistical comparisons between competing treatment strategies