Randomized algorithms for high quality treatment planning in volumetric modulated arc therapy

In recent years, volumetric modulated arc therapy (VMAT) has been becoming a more and more important radiation technique widely used in clinical application for cancer treatment. One of the key problems in VMAT is treatment plan optimization, which is complicated due to the constraints imposed by the involved equipments. In this paper, we consider a model with four major constraints: the bound on the beam intensity, an upper bound on the rate of the change of the beam intensity, the moving speed of leaves of the multi-leaf collimator (MLC) and its directional-convexity. We solve the model by a two-stage algorithm: performing minimization with respect to the shapes of the aperture and the beam intensities alternatively. Specifically, the shapes of the aperture are obtained by a greedy algorithm whose performance is enhanced by random sampling in the leaf pairs with a decremental rate. The beam intensity is optimized using a gradient projection method with non-monotonic line search. We further improve the proposed algorithm by an incremental random importance sampling of the voxels to reduce the computational cost of the energy functional. Numerical simulations on two clinical cancer date sets demonstrate that our method is highly competitive to the state-of-the-art algorithms in terms of both computational time and quality of treatment planning.