Show simple item record

Files in this item


Item metadata

dc.contributor.authorChaplain, Mark Andrew Joseph
dc.contributor.authorGiverso, Chiara
dc.contributor.authorLorenzi, Tommaso
dc.contributor.authorPreziosi, Luigi
dc.identifier.citationChaplain , M A J , Giverso , C , Lorenzi , T & Preziosi , L 2019 , ' Derivation and application of effective interface conditions for continuum mechanical models of cell invasion through thin membranes ' , SIAM Journal of of Applied Mathematics , vol. 79 , no. 5 , pp. 2011–2031 .
dc.identifier.otherPURE: 260335515
dc.identifier.otherPURE UUID: 3fc2d092-d39b-43c0-9ff1-5de0195bf863
dc.identifier.otherORCID: /0000-0001-5727-2160/work/63716860
dc.identifier.otherScopus: 85077400155
dc.identifier.otherWOS: 000493900600017
dc.descriptionFunding: UK EPSRC grant no. EP/N014642/1.en
dc.description.abstractWe consider a continuum mechanical model of cell invasion through thin membranes. The model consists of a transmission problem for cell volume fraction complemented with continuity of stresses and mass flux across the surfaces of the membranes. We reduce the original problem to a limiting transmission problem whereby each thin membrane is replaced by an effective interface, and we develop a formal asymptotic method that enables the derivation of a set of biophysically consistent transmission conditions to close the limiting problem. The formal results obtained are validated via numerical simulations showing that the relative error between the solutions to the original transmission problem and the solutions to the limiting problem vanishes when the thickness of the membranes tends to zero. In order to show potential applications of our effective interface conditions, we employ the limiting transmission problem to model cancer cell invasion through the basement membrane and the metastatic spread of ovarian carcinoma.
dc.relation.ispartofSIAM Journal of of Applied Mathematicsen
dc.rights© 2019, Society for Industrial and Applied Mathematics. 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 as such may differ slightly from the final published version. The final published version of this work is available at
dc.subjectContinuum mechanicsen
dc.subjectThin membranesen
dc.subjectEffective interface conditionsen
dc.subjectCell invasionen
dc.subjectBasement membraneen
dc.subjectOvarian canceren
dc.subjectQA Mathematicsen
dc.subjectQH301 Biologyen
dc.subjectRC0254 Neoplasms. Tumors. Oncology (including Cancer)en
dc.titleDerivation and application of effective interface conditions for continuum mechanical models of cell invasion through thin membranesen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews.School of Mathematics and Statisticsen
dc.contributor.institutionUniversity of St Andrews.Applied Mathematicsen
dc.description.statusPeer revieweden

This item appears in the following Collection(s)

Show simple item record