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Different parameters of the model are modified to identify key biological factors relevant to the behavior of angiogenesis. The results show that in the presence of a stronger flux, angiogenesis occurs later owing to the chemical flux that creates a more uniform and homogeneous matrix, decreasing the pronunciation of the gradient and reducing the potential of chemotaxis.<\/jats:p>","DOI":"10.1002\/qub2.70009","type":"journal-article","created":{"date-parts":[[2025,6,13]],"date-time":"2025-06-13T03:19:37Z","timestamp":1749784777000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Modeling angiogenesis under Robin boundary conditions"],"prefix":"10.1002","volume":"13","author":[{"given":"Pablo","family":"\u00c1lvarez\u2010Caudevilla","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas Universidad Carlos III de Madrid  Legan\u00e9s Madrid Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cristina","family":"Br\u00e4ndle","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas Universidad Carlos III de Madrid  Legan\u00e9s Madrid Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Elena","family":"Encinas","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas Universidad Carlos III de Madrid  Legan\u00e9s Madrid Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,6,13]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1056\/NEJM197111182852108"},{"key":"e_1_2_8_3_1","first-page":"1110","article-title":"A review on angiogenesis and its assays","volume":"15","author":"Tahergorabi Z","year":"2012","journal-title":"Iran J Basic Med Sci"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-003-0262-2"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-5193(71)90050-6"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-34646-3_5"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/mana.200310430"},{"issue":"2","key":"e_1_2_8_8_1","first-page":"5338","article-title":"Global existence for a kinetic model of pattern formation with density\u2010suppressed motilities","volume":"269","author":"Fujie K","year":"2020","journal-title":"J Math Biol"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1006\/bulm.1998.0042"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.1111\/sapm.12625"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2007.12.007"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1142\/S021820251640008X"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202519500398"},{"key":"e_1_2_8_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2020.06.041"},{"key":"e_1_2_8_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.anihpc.2016.08.003"},{"key":"e_1_2_8_16_1","doi-asserted-by":"publisher","DOI":"10.1006\/bulm.2001.0240"},{"key":"e_1_2_8_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2018.10.007"},{"key":"e_1_2_8_18_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.4923066"},{"key":"e_1_2_8_19_1","doi-asserted-by":"publisher","DOI":"10.4064\/am2301-2-2017"},{"key":"e_1_2_8_20_1","doi-asserted-by":"publisher","DOI":"10.4064\/am42-2-1"},{"key":"e_1_2_8_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/S1567-5769(02)00271-0"},{"key":"e_1_2_8_22_1","first-page":"125","volume-title":"Conservative numerical schemes for the Keller\u2010Segel system and numerical results","author":"Saito N","year":"2009"}],"container-title":["Quantitative Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/qub2.70009","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T04:55:22Z","timestamp":1758344122000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/qub2.70009"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,13]]},"references-count":21,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["10.1002\/qub2.70009"],"URL":"https:\/\/doi.org\/10.1002\/qub2.70009","archive":["Portico"],"relation":{},"ISSN":["2095-4689","2095-4697"],"issn-type":[{"type":"print","value":"2095-4689"},{"type":"electronic","value":"2095-4697"}],"subject":[],"published":{"date-parts":[[2025,6,13]]},"assertion":[{"value":"2024-11-13","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-05-02","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-06-13","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70009"}}