Simultaneous reduction of number of spots and energy layers in intensity modulated proton therapy for rapid spot scanning delivery

BackgroundReducing proton treatment time improves patient comfort and decreases the risk of error from intrafractional motion, but must be balanced against clinical goals and treatment plan quality.PurposeTo improve the delivery efficiency of spot scanning proton therapy by simultaneously reducing the number of spots and energy layers using the reweighted l1$l_1$ regularization method.MethodsWe formulated the proton treatment planning problem as a convex optimization problem with a cost function consisting of a dosimetric plan quality term plus a weighted l1$l_1$ regularization term. We iteratively solved this problem and adaptively updated the regularization weights to promote the sparsity of both the spots and energy layers. The proposed algorithm was tested on four head-and-neck cancer patients, and its performance, in terms of reducing the number of spots and energy layers, was compared with existing standard l1$l_1$ and group l2$l_2$ regularization methods. We also compared the effectiveness of the three methods (l1$l_1$, group l2$l_2$, and reweighted l1$l_1$) at improving plan delivery efficiency without compromising dosimetric plan quality by constructing each of their Pareto surfaces charting the trade-off between plan delivery and plan quality.ResultsThe reweighted l1$l_1$ regularization method reduced the number of spots and energy layers by an average over all patients of 40%$40\%$ and 35%$35\%$, respectively, with an insignificant cost to dosimetric plan quality. From the Pareto surfaces, it is clear that reweighted l1$l_1$ provided a better trade-off between plan delivery efficiency and dosimetric plan quality than standard l1$l_1$ or group l2$l_2$ regularization, requiring the lowest cost to quality to achieve any given level of delivery efficiency.ConclusionsReweighted l1$l_1$ regularization is a powerful method for simultaneously promoting the sparsity of spots and energy layers at a small cost to dosimetric plan quality. This sparsity reduces the time required for spot scanning and energy layer switching, thereby improving the delivery efficiency of proton plans.