Derivation and application of effective interface conditions for continuum mechanical models of cell invasion through thin membranes
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We 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.
Chaplain , 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 on Applied Mathematics , vol. 79 , no. 5 , pp. 2011–2031 . https://doi.org/10.1137/19M124263X
SIAM Journal on Applied Mathematics
© 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 https://doi.org/10.1137/19M124263X
DescriptionFunding: UK EPSRC grant no. EP/N014642/1.
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