Model for direct bone apposition on pre-existing surfaces, during peri-implant osseointegration

In the present paper, a model for the early stages of peri-implant bone regeneration is developed. This model is able to capture some important characteristics of endosseous healing, which were not incorporated in the existing models. It is a well known fact, that during peri-implant osseointegration, bone forms only by apposition on the pre-existing rigid surface, which initially consists of the implant surface and the old bone surface. In order to track the movement of the front of the newly formed bone, a moving boundary problem is formulated. Another important feature of the current model, is that the cell differentiation is considered as a gradual process, evolving in time and being influenced by the presence of growth factors. Hence, the evolution of cell differentiation level is captured in the present approach. Numerical methods, used to solve the set of partial differential equations with hyperbolic terms, defined within the domain with the moving boundary, are described.