  We propose a PDE-ODE model for tissue regeneration, obtained by parabolic
upscaling from kinetic transport equations written for the mesoscopic densities
of mesenchymal stem cells and chondrocytes which evolve in an artificial
scaffold impregnated with hyaluron. Due to the simple chosen turning kernels,
the effective equations obtained on the macroscopic level are of the usual
reaction-diffusion-taxis type. We prove global existence of solutions to the
coupled macroscopic system and perform a stability and bifurcation analysis,
which shows that the observed patterns are driven by taxis. Numerical
simulations illustrate the model behavior for various tactic sensitivities and
initial conditions.
