Pencil-beam Delivery Pattern Optimization Increases Dose Rate for Stereotactic FLASH Proton Therapy

Purpose: FLASH dose rates >40 Gy/s are readily available in proton therapy (PT) with cyclotron-accelerated beams and pencil-beam scanning (PBS). The PBS delivery pattern will affect the local dose rate, as quantified by the PBS dose rate (PBS-DR), and therefore needs to be accounted for in FLASH-PT with PBS, but it is not yet clear how. Our aim was to optimize patient-specific scan patterns for stereotactic FLASH-PT of early-stage lung cancer and lung metastases, maximizing the volume irradiated with PBS-DR >40 Gy/s of the organs at risk voxels irradiated to >8 Gy (FLASH coverage). Methods and Materials: Plans to 54 Gy/3 fractions with 3 equiangular coplanar 244 MeV proton shoot-through transmission beams for 20 patients were optimized with in-house developed software. Planning target volume-based planning with a 5 mm margin was used. Planning target volume ranged from 4.4 to 84 cc. Scan-pattern optimization was performed with a Genetic Algorithm, run in parallel for 20 independent populations (islands). Mapped crossover, inversion, swap, and shift operators were applied to achieve (local) optimality on each island, with migration between them for global optimality. The cost function was chosen to maximize the FLASH coverage per beam at >8 Gy, >40 Gy/s, and 40 nA beam current. The optimized patterns were evaluated on FLASH coverage, PBS-DR distribution, and population PBS-DR-volume histograms, compared with standard line-by-line scanning. Robustness against beam current variation was investigated. Results: The optimized patterns have a snowflake-like structure, combined with outward swirling for larger targets. A population median FLASH coverage of 29.0% was obtained for optimized patterns compared with 6.9% for standard patterns, illustrating a significant increase in FLASH coverage for optimized patterns. For beam current variations of 5 nA, FLASH coverage varied between –6.1%-point and 2.2%-point for optimized patterns. Conclusions: Significant improvements on the PBS-DR and, hence, on FLASH coverage and potential healthy-tissue sparing are obtained by sequential scan-pattern optimization. The optimizer is flexible and may be further fine-tuned, based on the exact conditions for FLASH.