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dc.contributor.authorHodgkinson, Arran
dc.contributor.authorChaplain, Mark Andrew Joseph
dc.contributor.authorDomschke, Pia
dc.contributor.authorTrucu, Dumitru
dc.identifier.citationHodgkinson , A , Chaplain , M A J , Domschke , P & Trucu , D 2018 , ' Computational approaches and analysis for a spatio-structural-temporal invasive carcinoma model ' , Bulletin of Mathematical Biology , vol. 80 , no. 4 , pp. 701-737 .
dc.identifier.otherPURE: 252047094
dc.identifier.otherPURE UUID: 48269cba-73ff-4b4c-aa49-64ea839d6560
dc.identifier.otherScopus: 85044341233
dc.identifier.otherORCID: /0000-0001-5727-2160/work/55378859
dc.identifier.otherWOS: 000428067300001
dc.description.abstractSpatio-temporal models have long been used to describe biological systems of cancer, but it has not been until very recently that increased attention has been paid to structural dynamics of the interaction between cancer populations and the molecular mechanisms associated with local invasion. One system that is of particular interest is that of the urokinase plasminogen activator (uPA) wherein uPA binds uPA receptors on the cancer cell surface, allowing plasminogen to be cleaved into plasmin, which degrades the extracellular matrix and this way leads to enhanced cancer cell migration. In this paper, we develop a novel numerical approach and associated analysis for spatio-structuro-temporal modelling of the uPA system for up to two-spatial and two-structural dimensions. This is accompanied by analytical exploration of the numerical techniques used in simulating this system, with special consideration being given to the proof of stability within numerical regimes encapsulating a central differences approach to approximating numerical gradients. The stability analysis performed here reveals instabilities induced by the coupling of the structural binding and proliferative processes. The numerical results expound how the uPA system aids the tumour in invading the local stroma, whilst the inhibitor to this system may impede this behaviour and encourage a more sporadic pattern of invasion.
dc.relation.ispartofBulletin of Mathematical Biologyen
dc.rights© 2018, Society for Mathematical Biology. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at
dc.subjectCancer invasionen
dc.subjectStructured cell population dynamicsen
dc.subjectComputational modellingen
dc.subjectQA Mathematicsen
dc.subjectQH301 Biologyen
dc.subjectRC0254 Neoplasms. Tumors. Oncology (including Cancer)en
dc.titleComputational approaches and analysis for a spatio-structural-temporal invasive carcinoma modelen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Applied Mathematicsen
dc.description.statusPeer revieweden

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