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A Suite of Mathematical Models for Bone Ingrowth, Bone Fracture Healing and Intra-Osseous Wound Healing

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Advanced Computational Methods in Science and Engineering

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 71))

Abstract

In this paper, some modeling aspects with respect to bone ingrowth, fracture healing and intra-osseous wound healing are described.We consider a finite element method for a model of bone ingrowth into a prosthesis. Such a model can be used as a tool for a surgeon to investigate the bone ingrowth kinetics when positioning a prosthesis. The overall model consists of two coupled models: the biological part that consists of non-linear diffusion-reaction equations for the various cell densities and themechanical part that contains the equations for poro-elasticity. The two models are coupled and in this paper the model is presented with some preliminary academic results. The model is used to carry out a parameter sensitivity analysis of ingrowth kinetics with respect to the parameters involved. Further, we consider a Finite Element model due to Bailon-Plaza and Van der Meulen for fracture healing in bone. This model is based on a set of coupled convection-diffusion-reaction equations and mechanical issues have not been incorporated. A parameter sensitivity analysis has been carried out. Finally, we consider a simplified model due to Adam to simulate intra-osseous wound healing. This model treats the wound edge as a moving boundary. To solve the moving boundary problem, the level set method is used. For the mesh points in the vicinity of the wound edge, a local adaptive mesh refinement is applied.

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Authors and Affiliations

  1. Delft Institute of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands

    F. J. Vermolen, E. M. van Aken & E. Javierre

  2. Mechanical, Maritime and Materials Engineering, Delft University of Technology, Mekelweg 2, 2628 CD, Delft, The Netherlands

    A. Andreykiv, J. C. van der Linden & A. van Keulen

Authors
  1. F. J. Vermolen
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  2. A. Andreykiv
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  3. E. M. van Aken
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  4. J. C. van der Linden
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  5. E. Javierre
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  6. A. van Keulen
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Corresponding author

Correspondence to F. J. Vermolen .

Editor information

Editors and Affiliations

  1. Scientific Computing &, Centrum Wiskunde & Informatica, Science Park 123, Amsterdam, 1098 XG, Netherlands

    Barry Koren

  2. Inst. Applied Mathematics, Delft University of Technology, Mekelweg 4, Delft, 2628 CD, Netherlands

    Kees Vuik

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© 2009 Springer-Verlag Berlin Heidelberg

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Vermolen, F.J., Andreykiv, A., van Aken, E.M., Linden, J.C.v., Javierre, E., van Keulen, A. (2009). A Suite of Mathematical Models for Bone Ingrowth, Bone Fracture Healing and Intra-Osseous Wound Healing. In: Koren, B., Vuik, K. (eds) Advanced Computational Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03344-5_10

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