A novel energy layer optimization strategy based on machine specific delivery sequence for proton arc therapy

Objective. Due to the magnetic hysteresis effect, it normally takes more time to switch the energy layer upward compared to downward in proton arc therapy (PAT), e.g. 5.5 s for energy layer switching upwards and 0.7 s for energy layer switching downwards. Therefore, previous studies have focused on reducing the number of energy jumps (NEJ) as a main direction. However, it is possible to reduce the energy layer switching time, for instance, by using magnetic field feedback in the energy layer switching system (ELSS) of the proton therapy system (PTS), especially for small energy jumps. Thus, we propose a new energy selection optimization strategy to improve the treatment delivery efficiency based on a fast ELSS, which allows energy jumps within a pre-defined threshold energy layer optimization (ELO-EJT). Approach. The ELO-EJT algorithm is based on two sequential steps: ELO and plan-quality re-optimization. The ELO problem was solved using the proximal forward-backward splitting method. The optimization problem of plan-quality re-optimization was solved by the alternating direction method of multipliers. Eight clinical cases were tested on the open-source treatment planning system matRad (German Cancer Research Center DKFZ), assessing plan quality and treatment delivery efficiency to evaluate the ELO-EJT algorithm. Main results. The ELO-EJT algorithm could achieve similar plan quality compared with the spot-scanning proton arc therapy _seq algorithm, which is based on the energy layer sorting and re-distribution mechanisms. Meanwhile, it reduces the beam delivery time without the need to limit energy jumps. More specifically, it reduces BDT by 23.93 +/- 4.12% (from 123.95 +/- 11.94 s to 94.14 +/- 8.82 s). Significance. A new ELO strategy could effectively reduce the treatment delivery time by minimizing the NEJ exceeding a threshold NEJT, which paves the way for the clinical application of spot-scanning PAT.