Numerical Analysis of an Osseointegration Model

Jacobo Baldonedo, José R. Fernández and Abraham Segade
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Jacobo Baldonedo: Department of Mechanical Engineering, School of Industrial Engineering, University of Vigo, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain
José R. Fernández: Department of Applied Mathematics I, Telecomunication Engineering School, University of Vigo, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain
Abraham Segade: Department of Mechanical Engineering, School of Industrial Engineering, University of Vigo, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain

Mathematics, 2020, vol. 8, issue 1, 1-20

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.

Keywords: bone remodeling; bone cells; finite elements; a priori error estimates; numerical simulations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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