Total-variation regularization based inverse planning for intensity modulated arc therapy

Intensity modulated arc therapy (IMAT) delivers conformal dose distributions through continuous gantry rotation with constant or variable speed while modulating the field aperture shape and weight. The enlarged angular space and machine delivery constraints make inverse planning of IMAT more intractable as compared to its counterpart of fixed gantry IMRT. Currently, IMAT inverse planning is being done using two extreme methods: the first one computes in beamlet domain with a subsequent arc leaf sequencing, and the second proceeds in machine parameter domain with entire emphasis placed on a pre-determined delivery method without exploring potentially better alternative delivery schemes. Towards truly optimizing the IMAT treatment on a patient specific basis, in this work we propose a total-variation based inverse planning framework for IMAT, which takes advantage of the useful features of the above two existing approaches while avoiding their shortcomings. A quadratic optimization algorithm has been implemented to demonstrate the performance and advantage of the proposed approach. Applications of the technique to a prostate case and a head and neck case indicate that the algorithm is capable of generating IMAT plans with patient specific numbers of arcs efficiently. Superior dose distributions and delivery time are achieved with a maximum number of apertures of three for each field. As compared to conventional beamlet-based algorithms, our method regularizes the field modulation complexity during optimization, and permits us to obtain the best possible plan with a pre-set modulation complexity of fluences. As illustrated in both prostate and head-and-neck case studies, the proposed method produces more favorable dose distributions than the segment-based algorithms, by optimally accommodating the clinical need of intensity modulation levels for each individual field. On a more fundamental level, our formulation preserves the convexity of optimization and makes the search of the global optimal solution possible with a deterministic method.