Fast approximate delivery of fluence maps: the VMAT case

Abstract

In this article we provide a method to generate the trade-off between delivery time and fluence map matching quality for volumetric modulated arc therapy (VMAT). At the heart of our method lies a mathematical programming model that, for a given duration of delivery, optimizes leaf trajectories and dose rates such that the desired fluence map is reproduced as well as possible. This model was presented for the single map case in a companion paper (Fast approximate delivery of fluence maps: the single map case). The resulting large-scale, non-convex optimization problem was solved using a heuristic approach. The single-map approach cannot directly be applied to the full arc case due to the large increase in model size, the issue of allocating delivery times to each of the arc segments, and the fact that the ending leaf positions for one map will be the starting leaf positions for the next map. In this article the method proposed in \cite{dm1} is extended to solve the full map treatment planning problem. We test our method using a prostate case and a head and neck case, and present the resulting trade-off curves. Analysis of the leaf trajectories reveal that short time plans have larger leaf openings in general than longer delivery time plans. Our method allows one to explore the continuum of possibilities between coarse, large segment plans characteristic of direct aperture approaches and narrow field plans produced by sliding window approaches. Exposing this trade off will allow for an informed choice between plan quality and solution time. Further research is required to speed up the optimization process to make this method clinically implementable.