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Mathematical modelling of the degradation behaviour of biodegradable metals

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Abstract

A mathematical model for the biodegradation of magnesium is developed in this study to inspect the corrosion behaviour of biodegradable implants. The aim of this study was to provide a suitable framework for the assessment of the corrosion rate of magnesium which includes the process of formation/dissolution of the protective film. The model is intended to aid the design of implants with suitable geometries. The level-set method is used to follow the changing geometry of the implants during the corrosion process. A system of partial differential equations is formulated based on the physical and chemical processes that occur at the implant-medium boundary in order to simulate the effect of the formation of a protective film on the degradation rate. The experimental data from the literature on the corrosion of a high-purity magnesium sample immersed in simulated body fluid is used to calibrate the model. The model is then used to predict the degradation behaviour of a porous orthopaedic implant. The model successfully reproduces the precipitation of the corrosion products on the magnesium surface and the effect on the degradation rate. It can be used to simulate the implant degradation and the formation of the corrosion products on the surface of biodegradable magnesium implants with complex geometries.

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Funding

V. Manhas and Y. Guyot are funded by Belgian National Fund for Scientific Research (FNRS) grant FRFC 2.4564.12. The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007–2013)/ERC Grant Agreement No. 279100. The nano-CT images were generated using the X-ray computed tomography facilities of the Department of Materials Engineering of the KU Leuven, financed by the Hercules Foundation (Project AKUL 09/001: Micro- and nano-CT for the hierarchical analysis of materials).

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Authors and Affiliations

  1. Christ Church, University of Oxford, Oxford, OX1 1DP, UK

    P. Bajger

  2. Department of Engineering Science, University of Oxford, Oxford, OX1 3PJ, UK

    J. M. A. Ashbourn

  3. Biomechanics Research Unit, University of Liège, Liège, Belgium

    V. Manhas, Y. Guyot & L. Geris

  4. Prometheus, R&D Division of Skeletal Tissue Engineering, KU Leuven, Leuven, Belgium

    V. Manhas, Y. Guyot & L. Geris

  5. Biomechanics Section, KU Leuven, Leuven, Belgium

    V. Manhas & L. Geris

  6. Department of Materials Engineering, KU Leuven, Leuven, Belgium

    K. Lietaert

  7. College of Inter-Faculty Individual Studies in Mathematics and Natural Sciences, University of Warsaw, Warsaw, Poland

    P. Bajger

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  1. P. Bajger
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  2. J. M. A. Ashbourn
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  3. V. Manhas
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  4. Y. Guyot
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  5. K. Lietaert
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  6. L. Geris
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Correspondence to P. Bajger.

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Bajger, P., Ashbourn, J.M.A., Manhas, V. et al. Mathematical modelling of the degradation behaviour of biodegradable metals. Biomech Model Mechanobiol 16, 227–238 (2017). https://doi.org/10.1007/s10237-016-0812-3

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  • DOI: https://doi.org/10.1007/s10237-016-0812-3

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