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dc.contributor.authorKatsaounis, Dimitrios
dc.contributor.authorChaplain, Mark Andrew Joseph
dc.contributor.authorSfakianakis, Nikolaos
dc.identifier.citationKatsaounis , D , Chaplain , M A J & Sfakianakis , N 2023 , ' Stochastic differential equation modelling of cancer cell migration and tissue invasion ' , Journal of Mathematical Biology , vol. 87 , 8 .
dc.identifier.otherPURE: 286024315
dc.identifier.otherPURE UUID: f4b46fca-7812-49fd-a182-66f682189b20
dc.identifier.otherScopus: 85162010961
dc.identifier.otherORCID: /0000-0001-5727-2160/work/137914897
dc.identifier.otherORCID: /0000-0002-2675-6338/work/137915595
dc.identifier.otherORCID: /0009-0002-7918-9805/work/137915716
dc.descriptionFunding: Engineering and Physical Sciences Research Council (EPSRC) EP/S030875/1).en
dc.description.abstractInvasion of the surrounding tissue is a key aspect of cancer growth and spread involving a coordinated effort between cell migration and matrix degradation, and has been the subject of mathematical modelling for almost 30 years. In this current paper we address a long-standing question in the field of cancer cell migration modelling. Namely, identify the migratory pattern and spread of individual cancer cells, or small clusters of cancer cells, when the macroscopic evolution of the cancer cell colony is dictated by a specific partial differential equation (PDE). We show that the usual heuristic understanding of the diffusion and advection terms of the PDE being one-to-one responsible for the random and biased motion of the solitary cancer cells, respectively, is not precise. On the contrary, we show that the drift term of the correct stochastic differential equation scheme that dictates the individual cancer cell migration, should account also for the divergence of the diffusion of the PDE. We support our claims with a number of numerical experiments and computational simulations.
dc.relation.ispartofJournal of Mathematical Biologyen
dc.rights© The Author(s) 2023. This open access article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material.en
dc.subjectCancer invasionen
dc.subjectMultiscale modellingen
dc.subjectHybrid continuum-discreteen
dc.subjectCoupled partial and stochastic partial differential equationsen
dc.subjectQA Mathematicsen
dc.subjectQH301 Biologyen
dc.subjectRC0254 Neoplasms. Tumors. Oncology (including Cancer)en
dc.subjectSDG 3 - Good Health and Well-beingen
dc.titleStochastic differential equation modelling of cancer cell migration and tissue invasionen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. School of Mathematics and Statisticsen
dc.contributor.institutionUniversity of St Andrews. Applied Mathematicsen
dc.description.statusPeer revieweden

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