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Med. Biol."],"published-print":{"date-parts":[[2026,5,14]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    <jats:italic>Objective.<\/jats:italic>\n                    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.\n                    <jats:italic>Approach.<\/jats:italic>\n                    Beam profiles for the quasi-monoenergetic 17.5 MeV electron beam from the 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 radiation was modelled as a Gaussian source and the electron distribution in the patient was modelled using classical observations with continuous slowing down approximation (CSDA). 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 (UHDR), a proton arc, and a robotic photon treatment.\n                    <jats:italic>Main results.<\/jats:italic>\n                    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 \u00b1 0.13 versus 1.54 \u00b1 0.13 and 1.35 \u00b1 0.26 respectively; median \u00b1 hemi-range; p &lt; 0.05). Brain V\n                    <jats:sub>12Gy<\/jats:sub>\n                    and skin dose were acceptable for all treatments.\n                    <jats:italic>Significance.<\/jats:italic>\n                    The dose calculation provides a fast and efficient method for inverse planning in the potential clinical application of a scanned electron beam at UHDR. The results show that such an approach could be useful in the treatment of superficial target volumes.\n                  <\/jats:p>","DOI":"10.1088\/1361-6560\/ae6225","type":"journal-article","created":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:55:33Z","timestamp":1776725733000},"page":"095014","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["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"],"prefix":"10.1088","volume":"71","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-5265-5927","authenticated-orcid":true,"given":"J","family":"Bedford","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4457-8897","authenticated-orcid":false,"given":"M","family":"Gross","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-8637-9564","authenticated-orcid":false,"given":"F","family":"Riemer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3808-9576","authenticated-orcid":false,"given":"Z","family":"Amirkhanyan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5654-1250","authenticated-orcid":false,"given":"F","family":"Stephan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2309-0814","authenticated-orcid":false,"given":"U","family":"Oelfke","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2026,5,6]]},"reference":[{"key":"pmbae6225bib1","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1016\/S0168-9002(03)01368-8","type":"journal-article","article-title":"Geant4\u2014a simulation toolkit","volume":"506","author":"Agostinelli","year":"2003","journal-title":"Nucl. 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