Stability analysis for a peri-implant osseointegration model

We investigate stability of the solution of the equations proposed in [Moreo, 2008], which model peri-implant osseointegration process. For certain parameter values, the solution has a ’wave-like’ profile, which appears in the distribution of osteogenic cells, osteoblasts, growth factor and bone matrix. That is in contradiction with experimental observations. In our study we investigate the conditions, under which such profile appears in the solution. Those conditions are determined in terms of model parameters, by means of linear stability analysis, carried out at one of the homogeneous steady-state solutions of the simplified system. The analysis is validated with finite element simulations. The simulations show, that stability of the homogeneous steady-state could determine the behavior of the solution of the whole system, when certain initial conditions are considered.
Electrical Engineering, Mathematics and Computer Science