  In this paper we present an individual-based mechanical model that describes
the dynamics of two contiguous cell populations with different proliferative
and mechanical characteristics. An off-lattice modelling approach is considered
whereby: (i) every cell is identified by the position of its centre; (ii)
mechanical interactions between cells are described via generic nonlinear force
laws; and (iii) cell proliferation is contact inhibited. We formally show that
the continuum counterpart of this discrete model is given by a free-boundary
problem for the cell densities. The results of the derivation demonstrate how
the parameters of continuum mechanical models of multicellular systems can be
related to biophysical cell properties. We prove an existence result for the
free-boundary problem and construct travelling-wave solutions. Numerical
simulations are performed in the case where the cellular interaction forces are
described by the celebrated Johnson-Kendall-Roberts model of elastic contact,
which has been previously used to model cell-cell interactions. The results
obtained indicate excellent agreement between the simulation results for the
individual-based model, the numerical solutions of the corresponding
free-boundary problem and the travelling-wave analysis.
