Number and orientations of beams in intensity-modulated radiation treatments.

The fundamental question of how many equispaced coplanar intensity-modulated photon beams are required to obtain an optimum treatment plan is investigated in a dose escalation study for a typical prostate tumor. Furthermore, optimization of beam orientations to improve dose distributions is explored. A dose-based objective function and a fast gradient technique are employed for optimizing the intensity profiles (inverse planning). An exhaustive search and fast simulated annealing techniques (FSA) are used to optimize beam orientations. However, to keep computation times reasonable, the intensity profiles for each beam arrangement are still optimized using inverse planning. A pencil beam convolution algorithm is employed for dose calculation. All calculations are performed in three-dimensional (3D) geometry for 15 MV photons. DVHs, dose displays, TCP, NTCP, and biological score functions are used for evaluation of treatment plans. It is shown that for the prostate case presented here, the minimum required number of equiangular beams depends on the prescription dose level and ranges from three beams for 70 Gy plans to seven to nine beams for 81 Gy plans. For the highest dose level (81 Gy), beam orientations are optimized and compared to equiangular spaced arrangements. It is shown that (1) optimizing beam orientations is most valuable for a small numbers of beams (< or = 5) and the gain diminishes rapidly for higher numbers of beams; (2) if sensitive structures (for example rectum) are partially enclosed by the target volume, beams coming from their direction tend to be preferable, since they allow greater control over dose distributions; (3) while FSA and an exhaustive search lead to the same results, computation times using FSA are reduced by two orders of magnitude to clinically acceptable values. Moreover, characteristics of and demands on biology-based and dose-based objective functions for optimization of intensity-modulated treatments are discussed.