Pulse-by-pulse treatment planning and its application to generic observations of ultra-high dose rate (FLASH) radiotherapy with photons and protons

<i>Objective.</i>The exact temporal characteristics of beam delivery affect the efficacy and outcome of ultra-high dose rate (UHDR or 'FLASH') radiotherapy, mainly due to the influence of the beam pulse structure on mean dose rate. Single beams may also be delivered in separate treatment sessions to elevate mean dose rate. This paper therefore describes a model for pulse-by-pulse treatment planning and demonstrates its application by making some generic observations of the characteristics of FLASH radiotherapy with photons and protons.<i>Approach.</i>A beam delivery model was implemented into the AutoBeam (v6.3) inverse treatment planning system, so that the individual pulses of the delivery system could be explicitly described during optimisation. The delivery model was used to calculate distributions of time-averaged and dose-averaged mean dose rate and the dose modifying factor for FLASH was then determined and applied to dose calculated by a discrete ordinates Boltzmann solver. The method was applied to intensity-modulated radiation therapy with photons as well as to passive scattering and pencil beam scanning with protons for the case of a simple phantom geometry with a prescribed dose of 36 Gy in 3 fractions.<i>Main results.</i>Dose and dose rate are highest in the target region, so FLASH sparing is most pronounced around the planning target volume (PTV). When using a treatment session per beam, OAR sparing is possible more peripherally. The sparing with photons is higher than with protons because the dose to OAR is higher with photons.<i>Significance.</i>The framework provides an efficient method to determine the optimal technique for delivering clinical dose distributions using FLASH. The most sparing occurs close to the PTV for hypofractionated treatments.