Fast approximate delivery of fluence maps: the single map case

In this first paper of a two-paper series, we present a method for optimizing the dynamic delivery of fluence maps in radiation therapy. For a given fluence map and a given delivery time, the optimization of the leaf trajectories of a multi-leaf collimator to approximately form the given fluence map is a non-convex optimization problem. Its general solution has not been addressed in the literature, despite the fact that dynamic delivery of fluence maps has long been a common approach to intensity modulated radiation therapy. We model the leaf trajectory and dose rate optimization as a non-convex continuous optimization problem and solve it by an interior point method from randomly initialized feasible starting solutions. We demonstrate the method on a fluence map from a prostate case and a larger fluence map from a head-and-neck case. While useful for static beam IMRT delivery, our main motivation for this work is the extension to the case of sequential fluence map delivery, i.e. the case of VMAT, which is the topic of the second paper.