{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,27]],"date-time":"2026-09-27T10:29:32Z","timestamp":1790504972520,"version":"4.1.0"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,3,1]],"date-time":"2020-03-01T00:00:00Z","timestamp":1583020800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,3,1]],"date-time":"2020-03-01T00:00:00Z","timestamp":1583020800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000054","name":"National Cancer Institute","doi-asserted-by":"publisher","award":["U54CA193489"],"award-info":[{"award-number":["U54CA193489"]}],"id":[{"id":"10.13039\/100000054","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000837","name":"University of Nottingham","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000837","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Bull Math Biol"],"published-print":{"date-parts":[[2020,3]]},"DOI":"10.1007\/s11538-020-00718-x","type":"journal-article","created":{"date-parts":[[2020,3,16]],"date-time":"2020-03-16T11:06:57Z","timestamp":1584356817000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Speed Switch in Glioblastoma Growth Rate due to Enhanced Hypoxia-Induced Migration"],"prefix":"10.1007","volume":"82","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4083-3803","authenticated-orcid":false,"given":"Lee","family":"Curtin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6391-4155","authenticated-orcid":false,"given":"Andrea","family":"Hawkins-Daarud","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6830-8031","authenticated-orcid":false,"given":"Kristoffer G.","family":"van der Zee","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2464-6119","authenticated-orcid":false,"given":"Kristin R.","family":"Swanson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3028-9138","authenticated-orcid":false,"given":"Markus R.","family":"Owen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2020,3,16]]},"reference":[{"issue":"9","key":"718_CR1","doi-asserted-by":"publisher","first-page":"4082","DOI":"10.1172\/JCI76739","volume":"124","author":"JE Adair","year":"2014","unstructured":"Adair JE, Johnston SK, Mrugala MM, Beard BC, Guyman LA, Baldock AL, Bridge CA, Hawkins-Daarud A, Gori JL, Born DE et al (2014) Gene therapy enhances chemotherapy tolerance and efficacy in glioblastoma patients. J Clin Investig 124(9):4082\u20134092","journal-title":"J Clin Investig"},{"issue":"10","key":"718_CR2","doi-asserted-by":"publisher","first-page":"e99057","DOI":"10.1371\/journal.pone.0099057","volume":"9","author":"AL Baldock","year":"2014","unstructured":"Baldock AL, Sunyoung A, Russell R, Johnston SK, Neal M, David C, Kamala C-S, Greg S, Trister AD, Malone H et al (2014a) Patient-specific metrics of invasiveness reveal significant prognostic benefit of resection in a predictable subset of gliomas. PLoS ONE 9(10):e99057","journal-title":"PLoS ONE"},{"issue":"6","key":"718_CR3","doi-asserted-by":"publisher","first-page":"779","DOI":"10.1093\/neuonc\/nou027","volume":"16","author":"AL Baldock","year":"2014","unstructured":"Baldock AL, Yagle K, Born DE, Ahn S, Trister AD, Neal M, Johnston SK, Bridge CA, Basanta D, Scott J et al (2014b) Invasion and proliferation kinetics in enhancing gliomas predict IDH1 mutation status. Neuro-oncology 16(6):779\u2013786","journal-title":"Neuro-oncology"},{"key":"718_CR4","doi-asserted-by":"crossref","unstructured":"Bell C, Dowson N, Fay M, Thomas P, Puttick S, Gal Y, Rose S (2015) Hypoxia imaging in gliomas with 18f-fluoromisonidazole pet: toward clinical translation. In: Seminars in nuclear medicine, vol\u00a045. Elsevier, pp 136\u2013150","DOI":"10.1053\/j.semnuclmed.2014.10.001"},{"issue":"3","key":"718_CR5","doi-asserted-by":"publisher","first-page":"920","DOI":"10.1158\/0008-5472.CAN-03-2073","volume":"64","author":"DJ Brat","year":"2004","unstructured":"Brat DJ, Castellano-Sanchez AA, Hunter SB, Pecot M, Cohen C, Hammond EH, Devi SN, Kaur B, Van Meir EG (2004) Pseudopalisades in glioblastoma are hypoxic, express extracellular matrix proteases, and are formed by an actively migrating cell population. Cancer Res 64(3):920\u2013927","journal-title":"Cancer Res"},{"issue":"4","key":"718_CR6","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1111\/j.1469-1809.1937.tb02153.x","volume":"7","author":"RA Fisher","year":"1937","unstructured":"Fisher RA (1937) The wave of advance of advantageous genes. Ann Eugen 7(4):355\u2013369","journal-title":"Ann Eugen"},{"issue":"8","key":"718_CR7","doi-asserted-by":"publisher","first-page":"1624","DOI":"10.1200\/JCO.2003.05.063","volume":"21","author":"A Giese","year":"2003","unstructured":"Giese A, Bjerkvig R, Berens ME, Westphal M (2003) Cost of migration: invasion of malignant gliomas and implications for treatment. J Clin Oncol 21(8):1624\u20131636","journal-title":"J Clin Oncol"},{"issue":"1","key":"718_CR8","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/j.gde.2006.12.006","volume":"17","author":"JD Gordan","year":"2007","unstructured":"Gordan JD, Simon MC (2007) Hypoxia-inducible factors: central regulators of the tumor phenotype. Curr Opin Genet Dev 17(1):71\u201377","journal-title":"Curr Opin Genet Dev"},{"issue":"1","key":"718_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1097\/nen.0b013e31802d9000","volume":"66","author":"HLP Harpold","year":"2007","unstructured":"Harpold HLP, Alvord EC, Swanson KR (2007) The evolution of mathematical modeling of glioma proliferation and invasion. J Neuropathol Exp Neurol 66(1):1\u20139","journal-title":"J Neuropathol Exp Neurol"},{"key":"718_CR10","doi-asserted-by":"publisher","first-page":"66","DOI":"10.3389\/fonc.2013.00066","volume":"3","author":"A Hawkins-Daarud","year":"2013","unstructured":"Hawkins-Daarud A, Rockne RC, Anderson ARA, Swanson KR (2013) Modeling tumor-associated edema in gliomas during anti-angiogenic therapy and its impact on imageable tumor. Front Oncol 3:66","journal-title":"Front Oncol"},{"issue":"109","key":"718_CR11","doi-asserted-by":"publisher","first-page":"20150388","DOI":"10.1098\/rsif.2015.0388","volume":"12","author":"A Hawkins-Daarud","year":"2015","unstructured":"Hawkins-Daarud A, Rockne R, Corwin D, Anderson ARA, Kinahan P, Swanson KR (2015) In silico analysis suggests differential response to bevacizumab and radiation combination therapy in newly diagnosed glioblastoma. J R Soc Interface 12(109):20150388","journal-title":"J R Soc Interface"},{"issue":"9","key":"718_CR12","doi-asserted-by":"publisher","first-page":"3749","DOI":"10.1073\/pnas.1014480108","volume":"108","author":"O Keunen","year":"2011","unstructured":"Keunen O, Johansson M, Oudin A, Sanzey M, Rahim SAA, Fack F, Thorsen F, Taxt T, Bartos M, Jirik R et al (2011) Anti-VEGF treatment reduces blood supply and increases tumor cell invasion in glioblastoma. Proc Natl Acad Sci 108(9):3749\u20133754","journal-title":"Proc Natl Acad Sci"},{"issue":"3","key":"718_CR13","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1111\/j.1365-2990.2003.00535.x","volume":"30","author":"P Korkolopoulou","year":"2004","unstructured":"Korkolopoulou P, Patsouris E, Konstantinidou AE, Pavlopoulos PM, Kavantzas N, Boviatsis E, Thymara I, Perdiki M, Thomas-Tsagli E, Angelidakis D et al (2004) Hypoxia-inducible factor 1$$\\alpha $$\/vascular endothelial growth factor axis in astrocytomas. associations with microvessel morphometry, proliferation and prognosis. Neuropathol Appl Neurobiol 30(3):267\u2013278","journal-title":"Neuropathol Appl Neurobiol"},{"key":"718_CR14","volume-title":"WHO classification of tumours of the central nervous system","author":"D Louis","year":"2016","unstructured":"Louis D, Ohgaki H, Wiestler O, Cavenee W (2016) WHO classification of tumours of the central nervous system, 4th edn. International Agency for Research on Cancer, Lyon","edition":"4"},{"issue":"12","key":"718_CR15","doi-asserted-by":"publisher","first-page":"2875","DOI":"10.1007\/s11538-012-9786-1","volume":"74","author":"A Mart\u00ednez-Gonz\u00e1lez","year":"2012","unstructured":"Mart\u00ednez-Gonz\u00e1lez A, Calvo GF, Romasanta LAP, P\u00e9rez-Garc\u00eda VM (2012) Hypoxic cell waves around necrotic cores in glioblastoma: a biomathematical model and its therapeutic implications. Bull Math Biol 74(12):2875\u20132896","journal-title":"Bull Math Biol"},{"issue":"73","key":"718_CR16","doi-asserted-by":"publisher","first-page":"1757","DOI":"10.1098\/rsif.2012.0030","volume":"9","author":"SC Massey","year":"2012","unstructured":"Massey SC, Assanah MC, Lopez KA, Canoll P, Swanson KR (2012) Glial progenitor cell recruitment drives aggressive glioma growth: mathematical and experimental modelling. J R Soc Interface 9(73):1757\u20131766","journal-title":"J R Soc Interface"},{"issue":"1","key":"718_CR17","doi-asserted-by":"publisher","first-page":"e51951","DOI":"10.1371\/journal.pone.0051951","volume":"8","author":"ML Neal","year":"2013","unstructured":"Neal ML, Trister AD, Cloke T, Sodt R, Ahn S, Baldock AL, Bridge CA, Lai A, Cloughesy TF, Mrugala MM et al (2013a) Discriminating survival outcomes in patients with glioblastoma using a simulation-based, patient-specific response metric. PloS ONE 8(1):e51951","journal-title":"PloS ONE"},{"issue":"10","key":"718_CR18","doi-asserted-by":"publisher","first-page":"2976","DOI":"10.1158\/0008-5472.CAN-12-3588","volume":"73","author":"ML Neal","year":"2013","unstructured":"Neal ML, Trister AD, Ahn S, Baldock A, Bridge CA, Guyman L, Lange J, Sodt R, Cloke T, Lai A et al (2013b) Response classification based on a minimal model of glioblastoma growth is prognostic for clinical outcomes and distinguishes progression from pseudoprogression. Cancer Res 73(10):2976\u20132986","journal-title":"Cancer Res"},{"issue":"1","key":"718_CR19","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1097\/00006123-200207000-00002","volume":"51","author":"SM Raza","year":"2002","unstructured":"Raza SM, Lang FF, Aggarwal BB, Fuller GN, Wildrick DM, Sawaya R (2002) Necrosis and glioblastoma: a friend or a foe? A review and a hypothesis. Neurosurgery 51(1):2\u201313","journal-title":"Neurosurgery"},{"key":"718_CR20","unstructured":"Roniotis A, Sakkalis V, Tzamali E, Tzedakis G, Zervakis M, Marias K (2012) Solving the pihna model while accounting for radiotherapy. In: Advanced research workshop on in silico oncology and cancer investigation\u2014The TUMOR project workshop (IARWISOCI), 2012 5th International. IEEE, pp 1\u20134"},{"issue":"3","key":"718_CR21","doi-asserted-by":"publisher","first-page":"525","DOI":"10.3171\/jns.1997.86.3.0525","volume":"86","author":"DL Silbergeld","year":"1997","unstructured":"Silbergeld DL, Chicoine MR (1997) Isolation and characterization of human malignant glioma cells from histologically normal brain. J Neurosurg 86(3):525\u2013531","journal-title":"J Neurosurg"},{"key":"718_CR22","doi-asserted-by":"crossref","unstructured":"Singleton KW, Porter AB, Hu LS, Johnston SK, Bond KM, Rickertsen CR, De\u00a0Leon G, Whitmire SA, Clark-Swanson KR, Mrugala MM et\u00a0al (2019) Days gained response discriminates treatment response in patients with recurrent glioblastoma receiving bevacizumab-based therapies. bioRxiv, p 752402","DOI":"10.1101\/752402"},{"issue":"9","key":"718_CR23","doi-asserted-by":"publisher","first-page":"2623","DOI":"10.1158\/1078-0432.CCR-07-4995","volume":"14","author":"AM Spence","year":"2008","unstructured":"Spence AM, Muzi M, Swanson KR, O\u2019Sullivan F, Rockhill JK, Rajendran JG, Adamsen TCH, Link JM, Swanson PE, Yagle KJ et al (2008) Regional hypoxia in glioblastoma multiforme quantified with [18f] fluoromisonidazole positron emission tomography before radiotherapy: correlation with time to progression and survival. Clin Cancer Res 14(9):2623\u20132630","journal-title":"Clin Cancer Res"},{"issue":"10","key":"718_CR24","doi-asserted-by":"publisher","first-page":"987","DOI":"10.1056\/NEJMoa043330","volume":"352","author":"R Stupp","year":"2005","unstructured":"Stupp R, Mason WP, Van Den Bent MJ, Weller M, Fisher B, Taphoorn MJB, Belanger K, Brandes AA, Marosi C, Bogdahn U et al (2005) Radiotherapy plus concomitant and adjuvant temozolomide for glioblastoma. N Engl J Med 352(10):987\u2013996","journal-title":"N Engl J Med"},{"issue":"5","key":"718_CR25","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1016\/S1470-2045(09)70025-7","volume":"10","author":"R Stupp","year":"2009","unstructured":"Stupp R, Hegi ME, Mason WP, van den Bent MJ, Taphoorn MJB, Janzer RC, Ludwin SK, Allgeier A, Fisher B, Belanger K et al (2009) Effects of radiotherapy with concomitant and adjuvant temozolomide versus radiotherapy alone on survival in glioblastoma in a randomised phase III study: 5-year analysis of the eortc-ncic trial. Lancet Oncol 10(5):459\u2013466","journal-title":"Lancet Oncol"},{"issue":"5","key":"718_CR26","doi-asserted-by":"publisher","first-page":"1259","DOI":"10.1007\/s11538-017-0271-8","volume":"80","author":"A Swan","year":"2018","unstructured":"Swan A, Hillen T, Bowman JC, Murtha AD (2018) A patient-specific anisotropic diffusion model for brain tumour spread. Bull Math Biol 80(5):1259\u20131291","journal-title":"Bull Math Biol"},{"key":"718_CR27","volume-title":"Mathematical modeling of the growth and control of tumors","author":"KR Swanson","year":"1999","unstructured":"Swanson KR (1999) Mathematical modeling of the growth and control of tumors. University of Washington, Seattle, WA"},{"issue":"5","key":"718_CR28","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1046\/j.1365-2184.2000.00177.x","volume":"33","author":"KR Swanson","year":"2000","unstructured":"Swanson KR, Alvord EC Jr, Murray JD (2000) A quantitative model for differential motility of gliomas in grey and white matter. Cell Prolif 33(5):317\u201329","journal-title":"Cell Prolif"},{"issue":"1","key":"718_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jns.2003.06.001","volume":"216","author":"KR Swanson","year":"2003","unstructured":"Swanson KR, Bridge C, Murray JD, Alvord EC (2003a) Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion. J Neurol Sci 216(1):1\u201310","journal-title":"J Neurol Sci"},{"issue":"1","key":"718_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jns.2003.06.001","volume":"216","author":"KR Swanson","year":"2003","unstructured":"Swanson KR, Bridge C, Murray JD, Alvord EC Jr (2003b) Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion. J Neurol Sci 216(1):1\u201310","journal-title":"J Neurol Sci"},{"issue":"1","key":"718_CR31","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1038\/sj.bjc.6604125","volume":"98","author":"KR Swanson","year":"2008","unstructured":"Swanson KR, Rostomily RC, Alvord EC Jr (2008) A mathematical modelling tool for predicting survival of individual patients following resection of glioblastoma: a proof of principle. Br J Cancer 98(1):113\u2013119","journal-title":"Br J Cancer"},{"issue":"24","key":"718_CR32","doi-asserted-by":"publisher","first-page":"7366","DOI":"10.1158\/0008-5472.CAN-11-1399","volume":"71","author":"KR Swanson","year":"2011","unstructured":"Swanson KR, Rockne RC, Claridge J, Chaplain MAJ, Alvord EC, Anderson ARA (2011) Quantifying the role of angiogenesis in malignant progression of gliomas: in silico modeling integrates imaging and histology. Cancer Res 71(24):7366\u20137375","journal-title":"Cancer Res"},{"issue":"23","key":"718_CR33","doi-asserted-by":"publisher","first-page":"9133","DOI":"10.1158\/0008-5472.CAN-08-3863","volume":"69","author":"CH Wang","year":"2009","unstructured":"Wang CH, Rockhill JK, Mrugala M, Peacock DL, Lai A, Jusenius K, Wardlaw JM, Cloughesy T, Spence AM, Rockne R et al (2009) Prognostic significance of growth kinetics in newly diagnosed glioblastomas revealed by combining serial imaging with a novel biomathematical model. Cancer Res 69(23):9133\u20139140","journal-title":"Cancer Res"},{"issue":"6","key":"718_CR34","doi-asserted-by":"publisher","first-page":"1220","DOI":"10.1161\/01.STR.17.6.1220","volume":"17","author":"T Yamaguchi","year":"1986","unstructured":"Yamaguchi T, Kanno I, Uemura K, Fumjo Shishido A, Inugami TO, Murakami M, Suzuki K (1986) Reduction in regional cerebral metabolic rate of oxygen during human aging. Stroke 17(6):1220\u20131228","journal-title":"Stroke"},{"issue":"7","key":"718_CR35","doi-asserted-by":"publisher","first-page":"e723","DOI":"10.1038\/cddis.2013.232","volume":"4","author":"Y Yang","year":"2013","unstructured":"Yang Y, Lin Hou Y, Li JN, Liu L (2013) Neuronal necrosis and spreading death in a drosophila genetic model. Cell Death Dis 4(7):e723","journal-title":"Cell Death Dis"},{"issue":"11","key":"718_CR36","doi-asserted-by":"publisher","first-page":"2606","DOI":"10.1002\/1097-0142(20000601)88:11<2606::AID-CNCR25>3.0.CO;2-W","volume":"88","author":"D Zagzag","year":"2000","unstructured":"Zagzag D, Zhong H, Scalzitti JM, Laughner E, Simons JW, Semenza GL (2000) Expression of hypoxia-inducible factor 1$$\\alpha $$ in brain tumors. Cancer 88(11):2606\u20132618","journal-title":"Cancer"},{"issue":"12","key":"718_CR37","doi-asserted-by":"publisher","first-page":"1221","DOI":"10.1038\/labinvest.3700482","volume":"86","author":"D Zagzag","year":"2006","unstructured":"Zagzag D, Lukyanov Y, Li Lan M, Ali A, Esencay M, Mendez O, Yee H, Voura EB, Newcomb EW (2006) Hypoxia-inducible factor 1 and vegf upregulate cxcr4 in glioblastoma: implications for angiogenesis and glioma cell invasion. Lab Investig 86(12):1221","journal-title":"Lab Investig"}],"container-title":["Bulletin of Mathematical Biology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11538-020-00718-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11538-020-00718-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11538-020-00718-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,15]],"date-time":"2021-03-15T20:58:17Z","timestamp":1615841897000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11538-020-00718-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3]]},"references-count":37,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["718"],"URL":"https:\/\/doi.org\/10.1007\/s11538-020-00718-x","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/862920","asserted-by":"object"}]},"ISSN":["0092-8240","1522-9602"],"issn-type":[{"value":"0092-8240","type":"print"},{"value":"1522-9602","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3]]},"assertion":[{"value":"4 September 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 March 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 March 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"43"}}