A derivative‐free multistart framework for an automated noncoplanar beam angle optimization in IMRT

Abstract

The inverse planning of an intensity-modulated radiation therapy (IMRT) treatment requires decisions regarding the angles used for radiation incidence, even when arcs are used. The possibility of improving the quality of treatment plans by an optimized selection of the beam angle incidences-beam angle optimization (BAO)-is seldom done in clinical practice. The inclusion of noncoplanar beam incidences in an automated optimization routine is even more unusual. However, for some tumor sites, the advantage of considering noncoplanar beam incidences is well known. This paper presents the benefits of using a derivative-free multistart framework for the optimization of the noncoplanar BAO problem. Multistart methods combine a global strategy for sampling the search space with a local strategy for improving the sampled solutions. The proposed global strategy allows a thorough exploration of the continuous search space of the highly nonconvex BAO problem. To avoid local entrapment, a derivative-free method is used as local procedure. Additional advantages of the derivative-free method include the reduced number of function evaluations required to converge and the ability to use multithreaded computing. Twenty nasopharyngeal clinical cases were selected to test the proposed multistart framework. The planning target volumes included the primary tumor, the high and low risk lymph nodes. Organs-at-risk included the spinal cord, brainstem, optical nerves, chiasm, parotids, oral cavity, brain, thyroid, among others. For each case, a setup with seven equispaced beams was chosen and the resulting treatment plan, using a multicriteria optimization framework, was then compared against the coplanar and noncoplanar plans using the optimal beam setups obtained by the derivative-free multistart framework. The optimal noncoplanar beam setup obtained by the derivative-free multistart framework leads to high quality treatment plans with better target coverage and with improved organ sparing compared to treatment plans using equispaced or optimal coplanar beam angle setups. The noncoplanar treatment plans achieved, e.g., an average reduction in the mean dose of the oral cavity of 6.1 Gy and an average reduction in the maximum-dose of the brainstem of 7 Gy when compared to the equispaced treatment plans. The noncoplanar BAO problem is an extremely challenging multimodal optimization problem that can be successfully addressed through a thoughtful exploration of the continuous highly nonconvex BAO search space. The proposed framework is capable of calculating high quality treatment plans and thus can be an interesting alternative toward automated noncoplanar beam selection in IMRT treatment planning which is nowadays the natural trend in treatment planning.