A set cover approach to fast beam orientation optimization in intensity modulated radiation therapy for total marrow irradiation

The beam orientation optimization (BOO) problem in intensity modulated radiation therapy (IMRT) treatment planning is a nonlinear problem, and existing methods to obtain solutions to the BOO problem are time consuming due to the complex nature of the objective function and size of the solution space. These issues become even more difficult in total marrow irradiation (TMI), where many more beams must be used to cover a vastly larger treatment area than typical site-specific treatments (e.g., head-and-neck, prostate, etc). These complications result in excessively long computation times to develop IMRT treatment plans for TMI, so we attempt to develop methods that drastically reduce treatment planning time. We transform the BOO problem into the classical set cover problem (SCP) and use existing methods to solve SCP to obtain beam solutions. Although SCP is NP-Hard, our methods obtain beam solutions that result in quality treatments in minutes. We compare our approach to an integer programming solver for the SCP to illustrate the speed advantage of our approach.