Simultaneous Reduction of Number of Spots and Energy Layers in Intensity Modulated Proton Therapy for Rapid Spot Scanning Delivery

TL;DR

This paper introduces a reweighted l1 regularization method for proton therapy planning that significantly reduces treatment time by sparsifying spots and energy layers while maintaining plan quality.

Contribution

The study proposes a novel reweighted l1 regularization approach that outperforms standard methods in reducing spots and energy layers in proton therapy plans.

Findings

Reduced spots by 40% on average

Lowered energy layers by 35% on average

Achieved better delivery quality trade-offs

Abstract

Reducing proton treatment time improves patient comfort and decreases the risk of error from intra-fractional motion, but must be balanced against clinical goals and treatment plan quality. We 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 $l_1$ 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 was compared with existing standard $l_1$ and group $l_2$ regularization methods. We also compared the effectiveness of the three methods ($l_1$, group $l_2$, and reweighted $l_1$) 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. The reweighted $l_1$ regularization method reduced the number of spots and energy layers by an average over all patients of 40% and 35%, respectively, with an insignificant cost to dosimetric plan quality. From the Pareto surfaces, it is clear that reweighted $l_1$ provided a better trade-off between plan delivery efficiency and dosimetric plan quality than standard $l_1$ or group $l_2$ regularization, requiring the lowest cost to quality to achieve any given level of delivery efficiency. In summary, reweighted $l_1$ 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.