A beam model and Boltzmann solver for radiotherapy treatment planning of superficial brain metastases using a scanned electron beam at ultra-high (FLASH) dose rate

Contemporary particle accelerators allow for the generation of a narrow pencil beam of electrons which can be scanned to deliver a clinical dose distribution at an ultra-high (FLASH) dose rate. This study develops a radiotherapy beam model and discrete ordinates Boltzmann solver for such an accelerator and then applies the method to treatment planning for superficial brain metastases. Approach. Beam profiles for the quasi-monoenergetic 17.5 MeV electron beam from the Photo Injector Test facility at DESY in Zeuthen (PITZ) were measured at various depths in a water tank using radiochromic film. The incident radiation was modelled as a Gaussian source and the electron distribution in the patient was modelled using classical observations with continuous slowing down approximation. This distribution then formed the fixed source component in a discrete ordinates Boltzmann solver. The dose calculation method was then applied to a retrospective study of six patients with superficial brain metastases. The dose due to scanned electrons was compared with that from a single passively scattered proton beam at ultra-high dose rate, a proton arc, and a robotic photon treatment. Main results. The calculated dose distribution in a homogeneous water phantom agreed with the measured data to within the 3% experimental uncertainty at all depths. Scanned electron beams were able to provide dose distributions for superficial brain metastases that had a better conformity index than either passively scattered protons or robotic photon treatment (1.02±0.13 versus 1.54±0.13 and 1.35±0.26 respectively; median±hemi-range; p<0.05). Brain V12Gy and skin dose were acceptable for all treatments. Significance. The dose calculation provides a fast and efficient method for inverse planning in the potential clinical application of a scanned electron beam at ultra-high dose rate. The results show that such an approach could be useful in the treatment of superficial target volumes.