Comparison of Combinatorial and Continuous Frameworks for the Beam Angle Optimization Problem in IMRT

Radiation therapy (RT) is used nowadays for the majority of cancer patients. A technologically advanced type of RT is IMRT – intensity-modulated radiation therapy. With this RT modality the cancerous cells of the patient can be irradiated using non-uniform radiation maps delivered from different beam directions. Although non-uniform radiation maps allow, by themselves, an enhanced sparing of the neighboring healthy organs while properly irradiating the tumor with the prescribed dose, selection of appropriate irradiation directions play a decisive role on these conflicting tasks: deliver dose to the tumor while preventing (too much) dose to be deposited in the surrounding tissues. This paper focus on the problem of choosing the best set of irradiation directions, known as beam angle optimization (BAO) problem. Two completely different mathematical formulations of this problem can be found in the literature. A combinatorial formulation, widely used and addressed by many different algorithms and strategies, and a continuous formulation proposed by the authors and addressed by derivative-free algorithms. In this paper, a comparison of two of the most successful strategies to address each one of these formulations is done resorting to a set of ten clinical nasopharyngeal tumor cases already treated at the Portuguese Institute of Oncology of Coimbra.