PETRA: A pencil beam trimming algorithm for analytical proton therapy dose calculations with the dynamic collimation system

The Dynamic Collimation System (DCS) has been shown to produce superior treatment plans to uncollimated pencil beam scanning (PBS) proton therapy using an in-house treatment planning system (TPS) designed for research. Clinical implementation of the DCS requires the development and benchmarking of a rigorous dose calculation algorithm that accounts for pencil beam trimming, performs monitor unit calculations to produce deliverable plans at all beam energies, and is ideally implemented with a commercially available TPS.To present an analytical Pencil bEam TRimming Algorithm (PETRA) for the DCS, with and without its range shifter, implemented in the Astroid TPS (.decimal, Sanford, Florida, USA).PETRA was derived by generalizing an existing pencil beam dose calculation model to account for the DCS-specific effects of lateral penumbra blurring due to the nickel trimmers in two different planes, integral depth dose variation due to the trimming process, and the presence and absence of the range shifter. Tuning parameters were introduced to enable agreement between PETRA and a measurement-validated Dynamic Collimation Monte Carlo (DCMC) model of the Miami Cancer Institute's IBA Proteus Plus system equipped with the DCS. Trimmer position, spot position, beam energy, and the presence or absence of a range shifter were all used as variables for the characterization of the model. The model was calibrated for pencil beam monitor unit calculations using procedures specified by International Atomic Energy Agency Technical Report Series 398 (IAEA TRS-398).The integral depth dose curves (IDDs) for energies between 70 MeV and 160 MeV among all simulated trimmer combinations, with and without the ranger shifter, agreed between PETRA and DCMC at the 1%/1 mm 1-D gamma criteria for 99.99% of points. For lateral dose profiles, the median 2-D gamma pass rate for all profiles at 1.5%/1.5 mm was 99.99% at the water phantom surface, plateau, and Bragg peak depths without the range shifter and at the surface and Bragg peak depths with the range shifter. The minimum 1.5%/1.5 mm gamma pass rates for the 2-D profiles at the water phantom surface without and with the range shifter were 98.02% and 97.91%, respectively, and, at the Bragg peak, the minimum pass rates were 97.80% and 97.5%, respectively.The PETRA model for DCS dose calculations was successfully defined and benchmarked for use in a commercially available TPS.