Abstract
In this work, we study a bone remodeling model used to reproduce the phenomenon of osseointegration around endosseous implants. The biological problem is written in terms of the densities of platelets, osteogenic cells, and osteoblasts and the concentrations of two growth factors. Its variational formulation leads to a strongly coupled nonlinear system of parabolic variational equations. An existence and uniqueness result of this variational form is stated. Then, a fully discrete approximation of the problem is introduced by using the finite element method and a semi-implicit Euler scheme. A priori error estimates are obtained, and the linear convergence of the algorithm is derived under some suitable regularity conditions and tested with a numerical example. Finally, one- and two-dimensional numerical results are presented to demonstrate the accuracy of the algorithm and the behavior of the solution.
Highlights
The study of the phenomenon of osseointegration in endosseous implants is a very interesting issue because of the increasing use of many types of implants in clinical practice
Dental implantation stands out as the area that has benefited the most from the innovation and continuous development of bone implants in the last few years. This is probably due to the outstanding clinical results. These dental implants are artificial systems that consist of an endosteal component, which is completely inside the mandible, and an abutment that connects the endosseous component with the oral cavity, in order to replace a missing tooth [2]
One- and two-dimensional numerical simulations are presented in Section 4, where we show the accuracy of the numerical resolution and the behavior of the solution
Summary
The study of the phenomenon of osseointegration in endosseous implants is a very interesting issue because of the increasing use of many types of implants in clinical practice. Dental implantation stands out as the area that has benefited the most from the innovation and continuous development of bone implants in the last few years. This is probably due to the outstanding clinical results (see, e.g., [1]). The number of papers dealing with the numerical simulation of the behavior and stability of dental implants is huge (see, for instance, [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]). One- and two-dimensional numerical simulations are presented in Section 4, where we show the accuracy of the numerical resolution and the behavior of the solution
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