A Suite of Mathematical Models for Bone Ingrowth, Bone Fracture Healing and Intra-Osseous Wound Healing

In this paper, some modeling aspects with respect to bone ingrowth, frac- ture healing and intra-osseous wound healing are described. We consider a finite el- ement method for a model of bone ingrowth into a prosthesis. Such a model can be used as a tool for a surgeon to investigate the bone ingrowth kinetics when position- ing a prosthesis. The overall model consists of two coupled models: the biological part that consists of non-linear diffusion-reaction equations for the various cell den- sities and the mechanical part that contains the equations for poro-elasticity. The two models are coupled and in this paper the model is presented with some preliminary academic results. The model is used to carry out a parameter sensitivity analysis of ingrowth kinetics with respect to the parameters involved. Further, we consider a Finite Element model due to Bailon-Plaza and Van der Meulen for fracture heal- ing in bone. This model is based on a set of coupled convection-diffusion-reaction equations and mechanical issues have not been incorporated. A parameter sensitiv- ity analysis has been carried out. Finally, we consider a simplified model due to Adam to simulate intra-osseous wound healing. This model treats the wound edge as a moving boundary. To solve the moving boundary problem, the level set method is used. For the mesh points in the vicinity of the wound edge, a local adaptive mesh refinement is applied.