An Accelerated Multistart Derivative-Free Framework for the Beam Angle Optimization Problem in IMRT

Radiation therapy, either alone or combined with surgery or chemotherapy, is one of the main treatment modalities for cancer. Intensity-modulated radiation therapy (IMRT) is an advanced form of radiation therapy, where the patient is irradiated using non-uniform radiation fields from selected beam angle directions. The goal of IMRT is to eradicate all cancer cells by delivering a radiation dose to the tumor volume, while attempting to spare, simultaneously, the surrounding organs and tissues. Although the use of non-uniform radiation fields can favor organ sparing, the selection of appropriate irradiation beam angle directions – beam angle optimization – is the best way to enhance organ sparing. The beam angle optimization (BAO) problem is an extremely challenging continuous non-convex multi-modal optimization problem. In this study, we present a novel approach for the resolution of the BAO problem, using a multistart derivative-free framework for a more thoroughly exploration of the search space of the highly non-convex BAO problem. As the objective function that drives the BAO problem is expensive in terms of computational time, and a multistart approach typically implies a large number of function evaluations, an accelerated framework is explored. A clinical case of an intra-cranial tumor treated at the Portuguese Institute of Oncology of Coimbra is used to discuss the benefits of the accelerated multistart approach proposed for the BAO problem.