Bone ingrowth on the surface of endosseous implants. Part 2: Theoretical and numerical analysis

The study of osseointegration of endosseous implants is a matter of great interest, mostly due to the increase in the use of many types of implants in clinical practice. Bone ingrowth results from a complex process, in which mechanics and biology play a major role. A wide variety of diverse factors can affect the development of the process, such as the properties or geometry of the implant surface, the mechanical stimulation or the initial cell conditions. In the first part of this article [Moreo, P., García-Aznar, J.M., Doblaré, M., 2008. Bone ingrowth on the surface of endosseous implants. Part 1: mathematical model. J. Theor. Biol., in press] a model composed of a set of reaction-diffusion equations was proposed to simulate the formation of bone around implants, specially focused on the early stages of bone healing, that was able to contemplate the effects of surface microtopography. The goal of this second part is to use the model to analyse the effect of factors such as cell stimulation, the initial cell concentration in the host bone and the geometry of the implant. For this purpose, two different simplified versions of the model are here analysed theoretically and further insight is gained from the study of the stability of fixed points and existence of travelling waves. Additionally, numerical simulations by means of the finite element method have been performed to examine the osseointegration of a dental implant with grooves at the surface of the threads. Results obtained from the analysis and simulations show that the model can reproduce some features of peri-implant bone ingrowth.