Purpose: Proton arc is a new treatment modality that delivers proton beams while continuously rotating the gantry. This study proposed a regularized l0-minimization primal dual active set with continuation (PDASC) algorithm for proton arc spot sparsity optimization to simultaneously optimize the plan quality and the beam delivery time (BDT). Methods: Based on the previously published beam delivery sequence model of IBA ProteusONE®, proton treatment delivery time is actually dominated by spot switching time (SSWT). SSWT is approximately linearly dependent on spot numbers. So we used a non-convex l0-norm to control the sparsity level of the regularized solution. The clinical objective is formulated as an l2-norm. The algorithm couples the primal dual active set method with a continuation strategy on the regularization parameter. Each inner iteration first identifies the active set from both primal and dual variables, then updates the primal variable by solving a (typically small) least-squares problem defined on the active set, from which the dual variable can be updated explicitly. Two representative clinical cases, including an intracranial and a lung target, were used for testing purposes. l2-norm value is calculated for evaluating the clinical objective. And DVH is plotted. Both the objective value and optimization time are compared with Spot-Scanning Proton Arc (SPArcoriginal) algorithm. Results: The results showed that PDASC can ensure both spot and plan quality. This new planning framework could effectively improve the optimization speed by a factor of about three hundred (8.8 times to 536.5 times from 20%-80% sparsity) compared to the SPArc-original implemented in RayStation. Conclusion: This study introduced the first simultaneously optimize the plan quality and BDT SPArc optimization platform utilizing the PDASC. Additionally, the successful implementation of the PDASC algorithm into SPArc can significantly improve the optimization time, which is a critical step forward in the era of proton arc therapy.
Zhao L, You J, Liu G, Lu X, Ding X. A novel simultaneous plan quality and beam delivery time SPArc optimization platform using primal dual active set with continuation (PDASC). Med Phys. 2022 June;49(6):E116.