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Numerical Analysis of an Osseointegration Model

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jacobo Baldonedo & José R. Fernández & Abraham Segade, 2020. "Numerical Analysis of an Osseointegration Model," Mathematics, MDPI, vol. 8(1), pages 1-20, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:87-:d:305314
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    References listed on IDEAS

    as
    1. Yun He & Istabrak Hasan & Ludger Keilig & Dominik Fischer & Luisa Ziegler & Marcus Abboud & Gerhard Wahl & Christoph Bourauel, 2018. "Numerical investigation of bone remodelling around immediately loaded dental implants using sika deer (Cervus nippon) antlers as implant bed," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 21(4), pages 359-369, March.
    2. Bruno Salles Sotto-Maior & Emílio Graciliano Ferreira Mercuri & Plinio Mendes Senna & Neuza Maria Souza Picorelli Assis & Carlos Eduardo Francischone & Altair Antoninha Del Bel Cury, 2016. "Evaluation of bone remodeling around single dental implants of different lengths: a mechanobiological numerical simulation and validation using clinical data," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 19(7), pages 699-706, May.
    3. Istabrak Hasan & Alireza Rahimi & Ludger Keilig & Kai-Thomas Brinkmann & Christoph Bourauel, 2012. "Computational simulation of internal bone remodelling around dental implants: a sensitivity analysis," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 15(8), pages 807-814.
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