Technical Note: Plan-delivery-time constrained inverse optimization method with minimum-MU-per-energy-layer (MMPEL) for efficient pencil beam scanning proton therapy

Purpose: This work aims to reduce dose delivery time of pencil beam scanning (PBS) proton plans, which is the dominant factor of total plan delivery time. A proton PBS system, such as Varian ProBeam proton therapy system, can be equipped with the proton dose rate that is linearly proportional to the minimum monitor unit (MU) (i.e., number of protons) of PBS spots before saturation. Thus dose delivery time can be potentially reduced by increasing the MU threshold. However, commercially available treatment planning systems and current methods only allow for a single MU threshold globally for all PBS spots (i.e., all energy layers), and consequently the room to increase this minimum-MU for reducing dose delivery time is very limited since higher minimum-MU can greatly degrade treatment plan quality.

Methods: Two major innovations of this work are the proposal of using variable MU thresholds locally adaptive to each energy layer, that is, minimum-MU-per-energy-layer (MMPEL), for reducing dose delivery time, and the joint optimization of plan delivery time and plan quality. Minimum-MU-per-energy-layer is formulated as a constrained optimization problem with objectives of dose-volume-histogram based planning constraints and plan delivery time, and minimum-MU constraints per energy layer for deliverable PBS spots. Minimum-MU-per-energy-layer is solved by iterative convex relaxations via alternating direction method of multipliers.

Results: Representative prostate, lung, brain, head-and-neck, breast, liver and pancreas cases were used to validate MMPEL. Minimum-MU-per-energy-layer reduced dose delivery time to 53%, 67%, 67%, 53%, 54%, 32%, and 14% respectively while maintaining a similar plan quality. Accepting a slightly degraded plan quality that still met all physician planning constraints, the treatment time could be further reduced to 26%, 35%, 41%, 34%, 32%, 16%, and 11% respectively, or in another word MMPEL accelerated the PBS plan delivery by 2-10 fold.

Conclusions: A new proton PBS treatment planning method MMPEL with variable energy-adaptive MU thresholds is developed to optimize dose delivery time jointly with plan quality. The preliminary results suggest that MMPEL could substantially reduce dose delivery time.