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Bone density growth and the biomechanics of healthy and prosthetic femur

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Abstract

The development of computational models to describe bone behavior when prosthetic devices are used has gained tremendous importance. In particular, computational modeling for bone growth and resorption processes can be a useful tool to determine the implant success or failure. We present a model for investigating bone density growth for healthy and prosthetic femur with a total hip arthroplasty. The model, which is based on a continuum theory for density growth and remodeling in biological materials that accounts for the coupling between biological and mechanical effects, is implemented in COMSOL Multiphysics and two simulation examples are presented. In the first example, where mechanical loads due to daily physical activities are considered, it is shown that higher stress zones (in prosthetic femur mid-diaphysis of about 46 MPa) and lower stress zones (in prosthetic femur neck of about 28 MPa) are candidates for bone growth and resorption zones, respectively. In addition, it is shown that higher and lower stress levels in these zones may lead to possible periprosthetic fractures (bone mid-diaphysis overloaded in 7–10 MPa post-operatively) and eventually to implant aseptic loosening due to resorption (bone femoral neck unloaded in 13–17 MPa post-operatively). In the second example, where the mechanical load corresponds to the average of the loads considered previously, the obtained results for bone density are in good agreement with real bone density distribution in the proximal femur, which illustrates the model capability to locate bone density growth zones (of about 1615 \(\mathrm {kg/{m}^{3}}\) in the mid-diaphysis) and bone density resorption zones (of about 1259 \(\mathrm {kg/{m}^{3}}\) in the neck) due to mechanical loads for the femur post-operative condition after a total hip arthroplasty surgical procedure.

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Notes

  1. Lagrangian quadratic: \(Lag_{k}(\text {T})\), \(k=2\), being k the polynomial degree of the element shape function and \(\text {T}\) the mesh type: triangular in this case [17]

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Acknowledgements

The authors gratefully acknowledge the financial support provided by CNPQ under Grant (870068/1997.0) and CAPES PNPD (31001017030D4).

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Authors and Affiliations

  1. Department of Mechanical Engineering, PEM/COPPE, Federal University of Rio de Janeiro, UFRJ, PO Box 68503, Rio de Janeiro, RJ, 21945-970, Brazil

    Joan O’Connor, Lavinia A. Borges & Fernando P. Duda

  2. Department of Nanotechnology Engineering Program, PENt/COPPE, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, RJ, 21941-972, Brazil

    Fernando P. Duda

  3. Faculty of Mechanical Engineering, ITEC, Federal University of Pará, PO Box 8619, Belém, PA, 66.075-900, Brazil

    Antônio G. B. da Cruz

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  1. Joan O’Connor
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  2. Lavinia A. Borges
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Correspondence to Joan O’Connor.

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Technical Editor: Estevam Barbosa Las Casas.

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O’Connor, J., Borges, L.A., Duda, F.P. et al. Bone density growth and the biomechanics of healthy and prosthetic femur. J Braz. Soc. Mech. Sci. Eng. 39, 3743–3756 (2017). https://doi.org/10.1007/s40430-017-0874-x

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