SU-E-T-619: A Network-Flow Solution Approach to VMAT Treatment Plan Optimization

To add mathematical rigor to the merging phase of the recently published two-stage VMAT optimization method called VMERGE. Using an exact merging method, we are able to better characterize the tradeoff between delivery efficiency and dose quality.

VMERGE begins with an IMRT plan that uses 180 equi-spaced beams and yields the "ideal" dose. Neighboring fluence maps are successively merged, meaning they are added together and delivered as one map. The merging process improves the delivery time at the expense of deviating from the initial high-quality dose distribution. We replace the original heuristic merging method by considering the merging problem as a bi-criteria optimization problem: maximize treatment efficiency and minimize the deviation from the ideal dose. We formulate this using a network-flow model where nodes represent the beam angles along with the starting MLC leaf position and arcs represent the possible merges. Since the problem is non-convex, we employ a customized box algorithm to obtain the Pareto approximation. We also evaluate the performance of several simple heuristics.

We test our exact and heuristic solution approaches on a pancreas and a prostate case. For both cases, the shape of the Pareto frontier suggests that starting from a high quality plan, we can obtain efficient VMAT plans through merging neighboring arcs without substantially deviating from the initial dose distribution. The trade-off curves obtained by the various heuristics are contrasted and shown to all be equally capable of initial plan simplifications, but to deviate in quality for more drastic efficiency improvements.

This work presents a bi-criteria network-flow solution approach to the merging problem. The obtained Pareto-frontier approximation is used as a benchmark to evaluate the performance of the proposed merging heuristics. The results validate that one of the heuristics in particular can achieve high-quality solutions.