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Beam orientation optimization for intensity-modulated radiation therapy using mixed integer programming

The purpose of this study is to extend an algorithm proposed for beam orientation optimization in classical conformal radiotherapy to intensity-modulated radiation therapy (IMRT) and to evaluate the algorithm's performance in IMRT scenarios. In addition, the effect of the candidate pool of beam orientations, in terms of beam orientation resolution and starting orientation, on the optimized beam configuration, plan quality and optimization time is also explored. The algorithm is based on the technique of mixed integer linear programming in which binary and positive float variables are employed to represent candidates for beam orientation and beamlet weights in beam intensity maps. Both beam orientations and beam intensity maps are simultaneously optimized in the algorithm with a deterministic method. Several different clinical cases were used to test the algorithm and the results show that both target coverage and critical structures sparing were significantly improved for the plans with optimized beam orientations compared to those with equi-spaced beam orientations. The calculation time was less than an hour for the cases with 36 binary variables on a PC with a Pentium IV 2.66 GHz processor. It is also found that decreasing beam orientation resolution to 10° greatly reduced the size of the candidate pool of beam orientations without significant influence on the optimized beam configuration and plan quality, while selecting different starting orientations had large influence. Our study demonstrates that the algorithm can be applied to IMRT scenarios, and better beam orientation configurations can be obtained using this algorithm. Furthermore, the optimization efficiency can be greatly increased through proper selection of beam orientation resolution and starting beam orientation while guaranteeing the optimized beam configurations and plan quality.