Objective function surrogates for iterative beam angle selection

Abstract

Optimized non-coplanar beam ensembles may yield substantial improvements of radiation therapy treatment plan quality. However, beam angle selection (BAS) is a nontrivial process and automated beam ensemble optimization is not supported by most commercial treatment planning systems, in part due to the lack of efficient algorithms. We focus on iterative BAS, where a beam ensemble is sequentially constructed: the basis for BAS during iteration n is a treatment plan containing n-1 fixed beams. To select the nth beam, each remaining candidate beam is added one-by-one to the current beam ensemble and the fluence map optimization (FMO) problem is solved. The beam yielding the lowest objective function value is selected. In this work we investigate two alternative methods relying on objective function surrogates to score candidate beams in order to make iterative BAS computationally more efficient: Conventional iterative BAS is compared to (1) an approach where the FMO is not solved to optimality but stopped after five iterations of a gradient based algorithm and (2) an approach where candidate beams are scored based on a projected gradient of the FMO in the first iteration. In a treatment planning study including one pancreas, one prostate, and one intracranial case, it is observed that both iterative BAS methods using objective function surrogates yield similar plan quality compared to naïve iterative BAS with regard to the resulting the objective function values and DVHs. At the same time, the surrogates enable reductions in computation time by a factor of 50-100 making them highly attractive for clinical application.