On the tradeoff between treatment time and plan quality in rotational arc radiation delivery

A new delivery option for cancer centers equipped with linear accelerators fitted with multi-leaf collimators (MLC) -- i.e. centers which can perform intensity modulated radiation therapy (IMRT) -- is rotational delivery. In rotational delivery, the beam is on while the gantry is rotating and the MLC leaves are moving, thus treating the patient more efficiently (regarding time) than in IMRT. A consideration that should be examined when evaluating this new type of delivery method is the tradeoff between treatment plan quality and delivery time: what do we sacrifice in terms of plan quality by guaranteeing a 2 minute delivery, for example? In this paper we examine this question by studying a simplified 2D phantom where leaf and gantry motion are directly included in the optimization model. We formulate the model as a linear mixed integer program. Because of the difficulty in solving to optimality, we employ additional models which allow us to trap the true optimal solution between upper and lower bounds. The lower bound solutions reveal which beam directions are most useful for treatment (i.e. where the gantry should slow down), and this information is used to produce deliverable solutions close to the lower bound solutions. For the phantom cases studied, we show that when time is not an issue, IMRT solutions are optimal, but when allowable treatment time is constrained sufficiently, rotational delivery is the preferred choice.