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Predictions of the elastic modulus of trabecular bone in the femoral head and the intertrochanter: a solitary wave-based approach

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Abstract

This paper deals with the numerical prediction of the elastic modulus of trabecular bone in the femoral head (FH) and the intertrochanteric (IT) region via site-specific bone quality assessment using solitary waves in a one-dimensional granular chain. For accurate evaluation of bone quality, high-resolution finite element models of bone microstructures in both FH and IT are generated using a topology optimization-based bone microstructure reconstruction scheme. A hybrid discrete element/finite element (DE/FE) model is then developed to study the interaction of highly nonlinear solitary waves in a granular chain with the generated bone microstructures. For more robust and reliable prediction of the bone’s mechanical properties, a face sheet is placed at the interface between the last chain particle and the bone microstructure, allowing more bone volume to be engaged in the dynamic deformation during interaction with the solitary wave. The hybrid DE/FE model was used to predict the elastic modulus of the IT and FH by analysing the characteristic features of the two primary reflected solitary waves. It was found that the solitary wave interaction is highly sensitive to the elastic modulus of the bone microstructure and can be used to identify differences in bone density. Moreover, it was found that the use of a relatively stiff face sheet significantly reduces the sensitivity of the wave interaction to local stiffness variations across the test surface of the bone, thereby enhancing the robustness and reliability of the proposed method. We also studied the effect of the face sheet thickness on the characteristics of the reflected solitary waves and found that the optimal thickness that minimizes the error in the modulus predictions is 4 mm for the FH and 2 mm for the IT, if the primary reflected solitary wave is considered in the evaluation process. We envisage that the proposed diagnostic scheme, in conjunction with 3D-printed high-resolution bone models of an actual patient, could provide a viable solution to current limitations in site-specific bone quality assessment.

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Acknowledgements

The Authors gratefully appreciate the financial support from the Abu Dhabi Department of Education and Knowledge (ADEK) through the Award for Research Excellence (AARE) 2017 [Grant Number AARE17-069] and Khalifa University Competitive Internal Research Award Program (CIRA) [Grant Number CIRA-2019-009].

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Authors and Affiliations

  1. Department of Civil Infrastructure and Environmental Engineering, Khalifa University of Science and Technology, Abu Dhabi, 127788, UAE

    Sangyoung Yoon & Tae-Yeon Kim

  2. Department of Mechanical Engineering, Khalifa University of Science and Technology, Abu Dhabi, 127788, UAE

    Andreas Schiffer

  3. The Cho Chun Shik Graduate School of Green Transportation, Korea Advanced Institute of Science and Technology, Daejeon, 34051, Republic of Korea

    In Gwun Jang

  4. Department of Biomedical Engineering, Khalifa University of Science and Technology, Abu Dhabi, 127788, UAE

    Sungmun Lee

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  1. Sangyoung Yoon
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  2. Andreas Schiffer
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  3. In Gwun Jang
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  4. Sungmun Lee
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  5. Tae-Yeon Kim
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Correspondence to Andreas Schiffer or Tae-Yeon Kim.

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Yoon, S., Schiffer, A., Jang, I.G. et al. Predictions of the elastic modulus of trabecular bone in the femoral head and the intertrochanter: a solitary wave-based approach. Biomech Model Mechanobiol 20, 1733–1749 (2021). https://doi.org/10.1007/s10237-021-01473-1

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  • DOI: https://doi.org/10.1007/s10237-021-01473-1

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