{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T22:16:47Z","timestamp":1783117007826,"version":"3.54.6"},"reference-count":14,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T00:00:00Z","timestamp":1775174400000},"content-version":"vor","delay-in-days":2,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["aapm.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Medical Physics"],"published-print":{"date-parts":[[2026,4]]},"abstract":"Abstract<\/jats:title>\n \n Background<\/jats:title>\n The shape of cell survival curves at the tissue level remains an open question in radiobiology. While homogeneous cell populations (so\u2010called single cells) typically exhibit an exponential decrease in survival with increasing dose, it is unclear whether this behavior persists in multicellular systems, where oxygen and nutrient gradients introduce additional complexity.<\/jats:p>\n <\/jats:sec>\n \n Purpose<\/jats:title>\n This study investigates how oxygen diffusion and consumption in tumor spheroids modify the aggregate radiation response and whether the resulting survival curves follow a purely exponential or a linear\u2013quadratic (LQ) form on the logarithmic scale.<\/jats:p>\n <\/jats:sec>\n \n Methods<\/jats:title>\n \n WiDr human colon adenocarcinoma cells were modeled using the track\u2010event theory of cell survival. The parameters\n p<\/jats:italic>\n \u00a0=\u00a00.04\u00a0Gy\n \u22121<\/jats:sup>\n ,\n q<\/jats:italic>\n \u00a0=\u00a00.70\u00a0Gy\n \u22121<\/jats:sup>\n , and\n \n OER\n max<\/jats:sub>\n <\/jats:italic>\n \u00a0=\u00a03.44 were obtained by fitting oxic and anoxic single\u2010cell data from West et\u00a0al. Oxygen tension profiles\n pO2(r)<\/jats:italic>\n in spheroids were calculated according to the diffusion\u2013consumption model of\n Grimes et\u00a0al.<\/jats:italic>\n using\n \n p\n 0<\/jats:sub>\n <\/jats:italic>\n \u00a0=\u00a0150\u00a0Torr,\n \n r\n l<\/jats:sub>\n <\/jats:italic>\n \u00a0=\u00a0216\u00a0\u00b5m, and\n a<\/jats:italic>\n \u00a0=\u00a01.27\u00d710\n \u22126<\/jats:sup>\n \u00a0m\n 3<\/jats:sup>\n \u00a0kg\u00a0s\n \u22121<\/jats:sup>\n . Oxygen\u2010dependent, location\u2010specific cellular radiosensitivity was modeled via the oxygen enhancement ratio (\n OER<\/jats:italic>\n ), and the overall spheroid survival fraction was obtained by integrating survival over the viable spheroid volume, using both numerical calculation and a closed\u2010form analytical approximation.\n <\/jats:p>\n <\/jats:sec>\n \n Results<\/jats:title>\n \n Both the mechanistic oxygen\u2013diffusion\u2013based numerical survival model and the simplified approximation reproduced experimental survival data for WiDr spheroids of diameters 100\u20131200\u00a0\u00b5m reported by Buffa et\u00a0al. and West et\u00a0al. The predicted survival curves become progressively less steep as spheroid size increases, reflecting the larger hypoxic fraction. For large spheroids, both model and data exhibit a distinct\n upward curvature<\/jats:italic>\n of the survival curve at high doses, deviating from both exponential and downward\u2010bending LQ behavior. This effect arises from dose\u2010dependent weighting of oxic and hypoxic cell subpopulations within the heterogeneous spheroid.\n <\/jats:p>\n <\/jats:sec>\n \n Conclusions<\/jats:title>\n The results support the hypothesis that oxygen heterogeneity fundamentally alters the apparent dose\u2013response relationship in multicellular systems. The transition from single\u2010cell to spheroid\u2010level behavior introduces non\u2010linear averaging effects that produce survival curves not captured by standard exponential or LQ models. These findings provide a mechanistic bridge between cellular radiobiology and tissue\u2010scale dose\u2013response modeling.<\/jats:p>\n <\/jats:sec>","DOI":"10.1002\/mp.70425","type":"journal-article","created":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T03:08:16Z","timestamp":1775272096000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the shape of the radiation survival curve in tumor spheroids: The role of oxygen heterogeneity"],"prefix":"10.1002","volume":"53","author":[{"given":"Uwe","family":"Schneider","sequence":"first","affiliation":[{"name":"Department of Physics Science Faculty University of Z\u00fcrich Z\u00fcrich Switzerland"},{"name":"Radiotherapy Hirslanden Z\u00fcrich Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ning","family":"Liang","sequence":"additional","affiliation":[{"name":"Department of Physics Science Faculty University of Z\u00fcrich Z\u00fcrich Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00fcrgen","family":"Besserer","sequence":"additional","affiliation":[{"name":"Department of Physics Science Faculty University of Z\u00fcrich Z\u00fcrich Switzerland"},{"name":"Radiotherapy Hirslanden Z\u00fcrich Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,4,3]]},"reference":[{"key":"e_1_2_8_2_1","volume-title":"Radiobiology for the Radiologist","author":"Hall 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