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Open AccessArticle

Numerical Analysis of an Osseointegration Model

1
Department of Mechanical Engineering, School of Industrial Engineering, University of Vigo, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain
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Department of Applied Mathematics I, Telecomunication Engineering School, University of Vigo, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 87; https://doi.org/10.3390/math8010087
Received: 5 December 2019 / Revised: 26 December 2019 / Accepted: 30 December 2019 / Published: 5 January 2020
(This article belongs to the Special Issue Finite Element Analysis)
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. View Full-Text
Keywords: bone remodeling; bone cells; finite elements; a priori error estimates; numerical simulations bone remodeling; bone cells; finite elements; a priori error estimates; numerical simulations
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MDPI and ACS Style

Baldonedo, J.; Fernández, J.R.; Segade, A. Numerical Analysis of an Osseointegration Model. Mathematics 2020, 8, 87.

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