  We consider a continuum mechanical model for the migration of multiple cell
populations through parts of tissue separated by thin membranes. In this model,
cells belonging to different populations may be characterised by different
proliferative abilities and mobility, which may vary from part to part of the
tissue, as well as by different invasion potentials within the membranes. The
original transmission problem, consisting of a set of mass balance equations
for the volume fraction of cells of every population complemented with
continuity of stresses and mass flux across the surfaces of the membranes, is
then reduced to a limiting transmission problem whereby each thin membrane is
replaced by an effective interface. In order to close the limiting problem, a
set of biophysically consistent transmission conditions is derived through a
formal asymptotic method. Models based on such a limiting transmission problem
may find fruitful application in a variety of research areas in the biological
and medical sciences, including developmental biology, immunology and cancer
growth and invasion.
