SU-E-T-634: Convex Direct Aperture Optimization for Sliding Window IMRT

To introduce a convex Direct Aperture Optimization (DAO) technique for sliding window IMRT. This method combines the accuracy of aperture-based dose calculations, which include leaf end effect, scatter, and leakage, with the convexity, and hence efficient solvability, of classic two phase IMRT optimization (fluence map optimization followed by sliding window leaf sequencing).

Artificial pencil beam profiles used in fluence map optimization are replaced with sigmoid-like profiles representing the dose "blocked" by a leaf while at some incremental position, per MU. More precisely, the profiles represent the dose from photons blocked minus that from photons leaked through or scattered by the leaf. These profiles can be computed by any clinically validated IMRT dose engine, and the scatter component for an individual leaf can be accurately included to the extent that it is independent of positions of other leaves. Variables of the resulting convex optimization are the MUs delivered while each leaf is at each incremental position. All constraints necessary to ensure a deliverable sliding window solution, such as those preventing leaf collision, are linear. Thus, provided the dose objective functions are convex, the entire IMRT optimization is convex, and therefore can be efficiently solved to provable optimality.

Our derivations prove that DAO is convex for sliding window IMRT, and we demonstrate the technique on a clinical prostate case.

By moving from the standard idealized fluence beamlet approach to a'fluence blocked by a leaf at position x' approach, we fully convexify the sliding window IMRT optimization problem, and thus avoid the dose degradation observed in two-step IMRT optimization and the non-convexity of the traditionally posed DAO problem.