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In recent years, volumetric modulated arc therapy (VMAT) has been becoming amore and more important radiation technique widely used in clinical applicationfor cancer treatment. One of the key problems in VMAT is treatment planoptimization, which is complicated due to the constraints imposed by theinvolved equipments. In this paper, we consider a model with four majorconstraints: the bound on the beam intensity, an upper bound on the rate of thechange of the beam intensity, the moving speed of leaves of the multi-leafcollimator (MLC) and its directional-convexity. We solve the model by atwo-stage algorithm: performing minimization with respect to the shapes of theaperture and the beam intensities alternatively. Specifically, the shapes ofthe aperture are obtained by a greedy algorithm whose performance is enhancedby random sampling in the leaf pairs with a decremental rate. The beamintensity is optimized using a gradient projection method with non-monotonicline search. We further improve the proposed algorithm by an incremental randomimportance sampling of the voxels to reduce the computational cost of theenergy functional. Numerical simulations on two clinical cancer date setsdemonstrate that our method is highly competitive to the state-of-the-artalgorithms in terms of both computational time and quality of treatmentplanning.

Randomized Algorithms For High Quality Treatment Planning in Volumetric Modulated Arc Therapy