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Derivation and application of effective interface conditions for continuum mechanical models of cell invasion through thin membranes

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Author(s)

Mark Andrew Joseph Chaplain, Chiara Giverso, Tommaso Lorenzi, Luigi Preziosi

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Abstract

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.
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Original languageEnglish
Pages (from-to)2011–2031
Number of pages21
JournalSIAM Journal of of Applied Mathematics
Volume79
Issue number5
Early online date22 Oct 2019
DOIs
Publication statusPublished - 2019

    Research areas

  • Continuum mechanics, Thin membranes, Effective interface conditions, Cell invasion, Basement membrane, Ovarian cancer

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