Pattern search methods framework for beam angle optimization in radiotherapy design

The selection of appropriate beam directions is decisive for the quality of the treatment, both for maximizing tumor doses and for organs sparing. However, the beam angle optimization (BAO) problem is still an open problem and, most of the time, beam directions continue to be manually selected in clinical practice which requires many trial and error iterations between selecting beam angles and computing fluence patterns until a suitable treatment is achieved. The goal of BAO is to improve the quality of the directions used and, at the same time, release the treatment planner for other tasks. The objective of this paper is to introduce a new approach for the resolution of the BAO problem, using pattern search methods to tackle this highly non-convex optimization problem. Pattern search methods are derivative-free optimization methods with the ability to avoid local entrapment. Moreover, they require few function value evaluations to progress and converge. These two characteristics gathered together make pattern search methods suited to address the BAO problem. A set of clinical examples of head-and-neck cases is used to discuss the benefits of using pattern search methods in the optimization of the BAO problem.