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We consider a continuum mechanical model of cell invasion through thinmembranes. The model consists of a transmission problem for cell volumefraction complemented with continuity of stresses and mass flux across thesurfaces of the membranes. We reduce the original problem to a limitingtransmission problem whereby each thin membrane is replaced by an effectiveinterface, and we develop a formal asymptotic method that enables thederivation of a set of biophysically consistent transmission conditions toclose the limiting problem. The formal results obtained are validated vianumerical simulations showing that the relative error between the solutions tothe original transmission problem and the solutions to the limiting problemvanishes when the thickness of the membranes tends to zero. In order to showpotential applications of our effective interface conditions, we employ thelimiting transmission problem to model cancer cell invasion through thebasement membrane and the metastatic spread of ovarian carcinoma.

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