A multi-arc and constant-energy-per-arc treatment planning method for efficient proton arc therapy

Proton arc therapy is an emerging proton modality with enhanced dose and linear energy transfer (LET) conformality to treatment targets. However, its delivery efficiency can be negatively impacted by frequent energy changes.

This work will develop a novel proton arc treatment planning method that has constant energy and thus does not require energy changes per arc, that is, a multi-arc and constant-energy-per-arc approach, for achieving efficient delivery of proton arc while optimizing its plan quality.

The proposed method is based on a novel block orthogonal matching pursuit (BOMP) optimization algorithm. The optimization process involves an iterative approach that alternates between BOMP-based energy selection and the optimization of spot weights on the selected arcs subject to the minimum-monitor-unit deliverability constraint. For method validation, the proposed BOMP is compared with (1) the heuristic-search (HS) method, in which each arc is optimized individually and then arcs with the best plan quality are jointly selected to optimize the final plan; (2) the conventional (CONV) method, which has a variable-energy arc, serving as the ground truth for plan quality; (3) the energy layer optimization (ELO) method, which minimizes the number of energy jumps for CONV.

BOMP had better plan quality than HS for multi-arc planning (e.g., 5-arc) in this work, which validates the efficacy of the BOMP method. Compared to IMPT, BOMP5 offers superior plan quality while also being comparable in total plan delivery time. For example, in a liver case, BOMP5 increased the conformity index (CI) from 0.80 to 0.86, reduced the max target dose from 130.1% to 116.4%, and also decreased the total plan delivery time from 354.4 to 259.9 s. Compared to CONV and ELO, BOMP substantially reduced energy layer switching time without sacrificing the plan quality. For example, compared to CONV, BOMP reduced the optimization objective value from 0.358-0.231, reduced max target dose from 116.3% to 110.8%, reduced the ≥10 Gy volume of brainstem from 0.84cc to 0.43cc and improved the CI from 0.83 to 0.84 for a head-and-neck case. Compared to CONV, the energy layer switching times for the head-and-neck case, liver case, and lung case have been significantly reduced from 759.4, 1918.6, and 916.2 to 2.8 s, respectively. And the total plan delivery time significantly reduced from 790.7 to 149.2 s, 2184.9 to 259.9 s, and 1017.6 to 125.0 s, respectively.

A novel multi-arc and constant-energy-per-arc proton arc treatment planning method is proposed that can eliminate the need of energy switching per arc, without sacrificing the plan quality, compared to CONV and ELO.