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Med. Biol."],"published-print":{"date-parts":[[2026,10,14]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    <jats:italic>Objective.<\/jats:italic>\n                    Radiotherapy remains one of the most widely used cancer treatments. However, optimizing its effectiveness requires a deeper understanding of the tumor architecture and its influence on radiation response. Three-dimensional spheroid cultures offer a more physiologically relevant model than traditional 2D assays, and their integration with\n                    <jats:italic>in silico<\/jats:italic>\n                    techniques enable the simulation of both growth dynamics and radiobiological response across multiple scales.\n                    <jats:italic>Approach.<\/jats:italic>\n                    In this study, we developed a multi-scale\n                    <jats:italic>in silico<\/jats:italic>\n                    framework capable of simulating tumor spheroid growth, using a cellular potts model, and transferring that information to OpenTOPAS to simulate irradiation with any given particle type, where in this work we apply it specifically to a 6 MV photon beam. The dose deposited at each cell was used to determine cell fate via a two-lesion kinetic model (TLKM), which accounts for cellular oxygen concentration, the number of radiation-induced double-strand breaks, their type (simple or complex), and their origin (direct or indirect). The model was applied to two rectal cancer cell lines (SW837 and SW1463) subjected to a short-course radiotherapy regimen of 5 Gy\/fraction over 5 consecutive days, replicating the fractionation schedule used in short-course radiotherapy for rectal cancer patients.\n                    <jats:italic>Main results.<\/jats:italic>\n                    The calibrated model reproduces experimental spheroid growth and viability data across fractionated treatment, with oxygen dynamics and hypoxic and necrotic zonation behaving as expected under the model\u2019s consumption\u2013diffusion coupling, consistent with, though not independently validated, against spatially-resolved measurements. To our knowledge, this is also the first practical application of the oxygen fixation parameter within the TLKM.\n                    <jats:italic>Significance.<\/jats:italic>\n                    This framework provides a flexible platform for investigating alternative treatment regimens, combination therapies, and particle-based modalities. Expanding the experimental dataset, particularly with spatially resolved measurements of proliferative, hypoxic, and necrotic zones, will be essential to further constrain and validate the model. Incorporating subcellular damage mechanisms and explicit dose-rate effects into the TLKM formulation represents key directions for future development.\n                  <\/jats:p>","DOI":"10.1088\/1361-6560\/aeafa3","type":"journal-article","created":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T22:53:03Z","timestamp":1790981583000},"page":"195040","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["<i>In silico<\/i>\n                    modeling of radiobiological effects using tumor spheroids"],"prefix":"10.1088","volume":"71","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0860-594X","authenticated-orcid":true,"given":"Tiago A","family":"Azevedo","sequence":"first","affiliation":[{"name":"University of Coimbra"},{"name":"Institute of Biophysics, University of Coimbra"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6457-2356","authenticated-orcid":true,"given":"Diogo","family":"Est\u00eav\u00e3o","sequence":"additional","affiliation":[{"name":"i3S Institute for Research & Innovation in Health, University of Porto"},{"name":"P.CCC- Porto Comprehensive Cancer Center Raquel Seruca"},{"name":"ICBAS\u2014School of Medicine and Biomedical Sciences, University of Porto"},{"name":"Ghent University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4185-7871","authenticated-orcid":false,"given":"Ana M","family":"Abrantes","sequence":"additional","affiliation":[{"name":"Institute of Biophysics, University of Coimbra"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6078-0721","authenticated-orcid":true,"given":"Rui D","family":"Travasso","sequence":"additional","affiliation":[{"name":"University of Coimbra"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7051-040X","authenticated-orcid":false,"given":"T\u00e2nia","family":"Cruz","sequence":"additional","affiliation":[{"name":"i3S Institute for Research & Innovation in Health, University of Porto"},{"name":"P.CCC- Porto Comprehensive Cancer Center Raquel Seruca"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0724-0272","authenticated-orcid":false,"given":"Maria Jos\u00e9","family":"Oliveira","sequence":"additional","affiliation":[{"name":"i3S Institute for Research & Innovation in Health, University of Porto"},{"name":"P.CCC- Porto Comprehensive Cancer Center Raquel Seruca"},{"name":"ICBAS\u2014School of Medicine and Biomedical Sciences, University of Porto"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3015-7821","authenticated-orcid":false,"given":"Jo\u00e3o","family":"Carvalho","sequence":"additional","affiliation":[{"name":"University of Coimbra"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2026,10,13]]},"reference":[{"key":"pmbaeafa3bib1","doi-asserted-by":"publisher","first-page":"2623","DOI":"10.1145\/3292500.3330701","type":"conference-proceedings","article-title":"Optuna: a next-generation hyperparameter optimization framework","author":"Akiba","year":"2019"},{"key":"pmbaeafa3bib2","doi-asserted-by":"publisher","DOI":"10.1177\/15330338251350909","type":"journal-article","article-title":"Radiobiological modeling with Monte Carlo tools\u2014simulating cellular responses to ionizing radiation","volume":"24","author":"Azevedo","year":"2025","journal-title":"Technol. 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