{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T19:06:07Z","timestamp":1779908767176,"version":"3.53.1"},"reference-count":18,"publisher":"IOP Publishing","issue":"10","license":[{"start":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T00:00:00Z","timestamp":1779840000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T00:00:00Z","timestamp":1779840000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100003706","name":"Korea Research Institute of Standards and Science","doi-asserted-by":"crossref","award":["GP2025-0008-01"],"award-info":[{"award-number":["GP2025-0008-01"]}],"id":[{"id":"10.13039\/501100003706","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100008783","name":"National Research Council of Science & Technology","doi-asserted-by":"crossref","award":["CAP22041-100"],"award-info":[{"award-number":["CAP22041-100"]}],"id":[{"id":"10.13039\/501100008783","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Phys. Med. Biol."],"published-print":{"date-parts":[[2026,5,28]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    <jats:italic>Objective.<\/jats:italic>\n                    The conventional linear-quadratic (LQ) model is the standard tool for radiotherapy but lacks dose-rate dependence, limiting its application in ultra-high dose rate (UHDR) regimes. This study proposes the radical-mediated linear-exponential (RMLE) model to quantitatively describe biological effects as a function of dose rate and oxygen concentration, aiming to model the FLASH sparing effect and identify underlying physicochemical mechanisms.\n                    <jats:italic>Approach.<\/jats:italic>\n                    The RMLE model formulates cell survival as a function of dose, dose rate, and oxygen partial pressure. It incorporates a saturation term for lethal damage at high doses, alongside a dose-rate dependent radical survival probability (\n                    <jats:italic>P<\/jats:italic>\n                    <jats:sub>s<\/jats:sub>\n                    ) and an oxygen-dependent damage fixation probability (\n                    <jats:italic>P<\/jats:italic>\n                    <jats:sub>x<\/jats:sub>\n                    ). The model was validated using\n                    <jats:italic>in vitro<\/jats:italic>\n                    prostate cancer cell survival under varying dose rates (FLASH vs CONV) and oxygenation conditions (normoxia vs hypoxia). A hierarchical regression strategy was employed to decouple\n                    <jats:italic>P<\/jats:italic>\n                    <jats:sub>s<\/jats:sub>\n                    and\n                    <jats:italic>P<\/jats:italic>\n                    <jats:sub>x<\/jats:sub>\n                    , and physical feasibility was evaluated using track\u2013track interaction simulations.\n                    <jats:italic>Main results.<\/jats:italic>\n                    The RMLE model successfully reproduced the dose-response curves across all experimental conditions, resolving the high-dose overestimation issue of the standard LQ model. Analysis indicated that the FLASH sparing effect\u2014notably more pronounced under hypoxic conditions\u2014cannot be explained by oxygen depletion alone. Instead, the present analysis supports a synergistic interaction between radical recombination (reduced\n                    <jats:italic>P<\/jats:italic>\n                    <jats:sub>s<\/jats:sub>\n                    ) and oxygen depletion (reduced\n                    <jats:italic>P<\/jats:italic>\n                    <jats:sub>x<\/jats:sub>\n                    ). Furthermore, track structure simulations revealed that achieving necessary physical recombination at 600 Gy s\n                    <jats:sup>\u22121<\/jats:sup>\n                    requires a microsecond-scale interaction time (\n                    <jats:italic>\u03c4<\/jats:italic>\n                    \u223c10\u2013100\n                    <jats:italic>\u03bc<\/jats:italic>\n                    s), suggesting mediation by long-lived secondary chemical species.\n                    <jats:italic>Significance.<\/jats:italic>\n                    The RMLE model provides a mathematically tractable diagnostic framework to evaluate biological responses in the UHDR regime. The results suggest that the\n                    <jats:italic>in vitro<\/jats:italic>\n                    FLASH phenomenon arises from the interplay of microsecond-scale physical track overlap and chemical oxygen depletion. This model serves as a potential tool for exploring the fundamental mechanisms and informing future investigations into clinical FLASH protocols.\n                  <\/jats:p>","DOI":"10.1088\/1361-6560\/ae6c92","type":"journal-article","created":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T22:55:35Z","timestamp":1778626535000},"page":"105018","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["The radical-mediated linear-exponential (RMLE) model: integrating radical recombination and oxygen depletion for FLASH radiotherapy"],"prefix":"10.1088","volume":"71","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9161-6318","authenticated-orcid":true,"given":"In Jung","family":"Kim","sequence":"first","affiliation":[{"name":"Korea Research Institute of Standards and Science (KRISS)"},{"name":"University Science and Technology (UST)"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jong In","family":"Park","sequence":"additional","affiliation":[{"name":"Korea Research Institute of Standards and Science (KRISS)"},{"name":"University Science and Technology (UST)"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Seongmoon","family":"Jung","sequence":"additional","affiliation":[{"name":"Korea Research Institute of Standards and Science (KRISS)"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chul-Young","family":"Yi","sequence":"additional","affiliation":[{"name":"Korea Research Institute of Standards and Science (KRISS)"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yunho","family":"Kim","sequence":"additional","affiliation":[{"name":"Korea Research Institute of Standards and Science (KRISS)"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Young-Min","family":"Seong","sequence":"additional","affiliation":[{"name":"Korea Research Institute of Standards and Science (KRISS)"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2026,5,27]]},"reference":[{"key":"pmbae6c92bib1","doi-asserted-by":"publisher","DOI":"10.1259\/bjr.20190702","type":"journal-article","article-title":"The FLASH effect depends on oxygen concentration","volume":"93","author":"Adrian","year":"2020","journal-title":"Br. 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Published on behalf of Institute of Physics and Engineering in Medicine by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2026-01-01","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2026-05-12","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2026-05-27","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}