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 beamof 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 solverfor such an accelerator and then applies the method to treatment planning for superficial brainmetastases. Approach. Beam profiles for the quasi-monoenergetic 17.5 MeV electron beam fromthe Photo Injector Test facility at Deutsches Elektronen-Synchrotron laboratory in Zeuthen (PITZ)were measured at various depths in a water tank using radiochromic film. The incident radiationwas modelled as a Gaussian source and the electron distribution in the patient was modelled usingclassical observations with continuous slowing down approximation (CSDA). This distributionthen 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 brainmetastases. The dose due to scanned electrons was compared with that from a single passivelyscattered proton beam at ultra-high dose rate (UHDR), a proton arc, and a robotic photon treatment. Main results. The calculated dose distribution in a homogeneous water phantom agreedwith the measured data to within the 3% experimental uncertainty at all depths. Scanned electronbeams were able to provide dose distributions for superficial brain metastases that had a betterconformity index than either passively scattered protons or robotic photon treatment (1.02 ± 0.13versus 1.54 ± 0.13 and 1.35 ± 0.26 respectively; median ± hemi-range; p < 0.05). Brain V12Gy andskin dose were acceptable for all treatments. Significance. The dose calculation provides a fast andefficient method for inverse planning in the potential clinical application of a scanned electronbeam at UHDR.Theresults show that such an approach could be useful in the treatment of superficial target volumes.