Beam orientation optimization for intensity modulated radiation therapy using adaptive l_2,1-minimization

Beam orientation optimization (BOO) is a key component in the process of intensity modulated radiation therapy treatment planning. It determines to what degree one can achieve a good treatment plan in the subsequent plan optimization process. In this paper, we have developed a BOO algorithm via adaptive l _{2, 1}-minimization. Specifically, we introduce a sparsity objective function term into our model which contains weighting factors for each beam angle adaptively adjusted during the optimization process. Such an objective function favors a small number of beam angles. By optimizing a total objective function consisting of a dosimetric term and the sparsity term, we are able to identify unimportant beam angles and gradually remove them without largely sacrificing the dosimetric objective. In one typical prostate case, the convergence property of our algorithm, as well as how beam angles are selected during the optimization process, is demonstrated. Fluence map optimization (FMO) is then performed based on the optimized beam angles. The resulting plan quality is presented and is found to be better than that of equiangular beam orientations. We have further systematically validated our algorithm in the contexts of 5-9 coplanar beams for five prostate cases and one head and neck case. For each case, the final FMO objective function value is used to compare the optimized beam orientations with the equiangular ones. It is found that, in the majority of cases tested, our BOO algorithm leads to beam configurations which attain lower FMO objective function values than those of corresponding equiangular cases, indicating the effectiveness of our BOO algorithm. Superior plan qualities are also demonstrated by comparing DVH curves between BOO plans and equiangular plans.