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We consider a continuum mechanical model for the migration of multiple cellpopulations through parts of tissue separated by thin membranes. In this model,cells belonging to different populations may be characterised by differentproliferative abilities and mobility, which may vary from part to part of thetissue, as well as by different invasion potentials within the membranes. Theoriginal transmission problem, consisting of a set of mass balance equationsfor the volume fraction of cells of every population complemented withcontinuity of stresses and mass flux across the surfaces of the membranes, isthen reduced to a limiting transmission problem whereby each thin membrane isreplaced by an effective interface. In order to close the limiting problem, aset of biophysically-consistent transmission conditions is derived through aformal asymptotic method. Models based on such a limiting transmission problemmay find fruitful application in a variety of research areas in the biologicaland medical sciences, including developmental biology, immunology and cancergrowth and invasion.

Effective interface conditions for continuum mechanical models describing the invasion of multiple cell populations through thin membranes