{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T08:28:31Z","timestamp":1787041711315,"version":"build-2736575974"},"reference-count":32,"publisher":"IOP Publishing","issue":"16","license":[{"start":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T00:00:00Z","timestamp":1787011200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T00:00:00Z","timestamp":1787011200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"},{"start":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T00:00:00Z","timestamp":1787011200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/questions\/alternative-author-rights-policies\/"},{"start":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T00:00:00Z","timestamp":1787011200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/questions\/alternative-author-rights-policies\/"}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Phys. Med. Biol."],"published-print":{"date-parts":[[2026,8,28]]},"abstract":"Abstract<\/jats:title>\n \n Objective.<\/jats:italic>\n FLASH radiotherapy introduces beam temporal structure at the pulse and sub-pulse scale, whereas most tumor control probability (TCP) models are formulated at the fraction or treatment-course scale. This study developed\n \n \n \n <\/jats:tex-math>\n \n \n \n TC<\/mml:mtext>\n <\/mml:mrow>\n \n \n \n P<\/mml:mtext>\n <\/mml:mrow>\n \n \n LRF<\/mml:mtext>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n , a pulse-resolved extension of the published Lee\u2013Rosen time-dependent TCP formulation, here denoted\n \n \n \n <\/jats:tex-math>\n \n \n \n TC<\/mml:mtext>\n <\/mml:mrow>\n \n \n \n P<\/mml:mtext>\n <\/mml:mrow>\n \n \n LR<\/mml:mtext>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n , to connect FLASH beam microstructure, oxygen\/radical kinetics, biological repair, and treatment-course repopulation.\n Approach.<\/jats:italic>\n TCP\n LR<\/jats:sub>\n was used as the parent treatment-course TCP model because it accommodates variable interfraction timing and kick-off-time-dependent accelerated repopulation. Its conventional cumulative survival term was replaced by a FLASH-aware survival term derived from a reduced-order oxygen\/radical ordinary differential equation kernel. Each FLASH fraction was represented as a pulse train. The same oxygen\/radical kinetics, lesion-yield calculation, and post-fraction repair layer were also implemented for standard-dose-rate continuous delivery to provide an internal comparator. The implementation was verified against uniform-dose benchmarks reported in the original Lee\u2013Rosen publication describing\n \n \n \n <\/jats:tex-math>\n \n \n \n TC<\/mml:mtext>\n <\/mml:mrow>\n \n \n \n P<\/mml:mtext>\n <\/mml:mrow>\n \n \n LR<\/mml:mtext>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n and then evaluated using exploratory FLASH, repair, pulse-structure, and standard-dose-rate scenarios.\n Main results.<\/jats:italic>\n Conventional verification reproduced published benchmark trends, with maximum absolute differences of 1.44, 1.21, and 3.48 percentage points for head-and-neck, breast, and prostate cases, respectively. In a 3 \u00d7 8 Gy starter case, calibrated null-FLASH TCP was 0.790. Moderate chemistry and strong radical recombination yielded TCP values of 0.713 and 0.703, respectively, whereas mild oxygen limitation reduced TCP to 0.276. Standard-dose-rate continuous delivery produced negligible oxygen depletion under null and moderate chemistry assumptions, while deliberately oxygen-limited standard-dose-rate cases showed reduced TCP.\n Significance.<\/jats:italic>\n This exploratory framework provides a mechanistic treatment-course TCP platform for hypothesis testing in FLASH radiotherapy. It demonstrates how pulse microstructure and continuous standard-dose-rate delivery can be evaluated within the same published variable-time\n \n \n \n <\/jats:tex-math>\n \n \n \n TC<\/mml:mtext>\n <\/mml:mrow>\n \n \n \n P<\/mml:mtext>\n <\/mml:mrow>\n \n \n LR<\/mml:mtext>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n formulation, while showing that FLASH TCP behavior depends on oxygen\/radical kinetic assumptions, pulse structure, repair, and oxygen availability rather than being universally preserved or reduced.\n <\/jats:p>","DOI":"10.1088\/1361-6560\/ae944e","type":"journal-article","created":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T22:58:23Z","timestamp":1785797903000},"page":"165003","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Pulse-resolved tumor control probability modeling for FLASH radiotherapy using a variable-time treatment-course framework"],"prefix":"10.1088","volume":"71","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0218-4942","authenticated-orcid":true,"given":"Tae Kyu","family":"Lee","sequence":"first","affiliation":[{"name":"Indiana University Health Arnett"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2026,8,18]]},"reference":[{"key":"pmbae944ebib1","doi-asserted-by":"publisher","DOI":"10.3389\/fphy.2023.1215422","type":"journal-article","article-title":"Intertrack interaction at ultra-high dose rates and its role in the FLASH effect","volume":"11","author":"Baikalov","year":"2023","journal-title":"Front. 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All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2026-06-04","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2026-08-03","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2026-08-18","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}