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Estimation of the effective yield properties of human trabecular bone using nonlinear micro-finite element analyses

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Abstract

Micro-finite element (\(\upmu \)FE) analyses are often used to determine the apparent mechanical properties of trabecular bone volumes. Yet, these apparent properties depend strongly on the applied boundary conditions (BCs) for the limited size of volumes that can be obtained from human bones. To attenuate the influence of the BCs, we computed the yield properties of samples loaded via a surrounding layer of trabecular bone (“embedded configuration”). Thirteen cubic volumes (10.6 mm side length) were collected from \(\upmu \)CT reconstructions of human vertebrae and femora and converted into \(\upmu \)FE models. An isotropic elasto-plastic material model was chosen for bone tissue, and nonlinear \(\upmu \)FE analyses of six uniaxial, shear, and multi-axial load cases were simulated to determine the yield properties of a subregion (5.3 mm side length) of each volume. Three BCs were tested. Kinematic uniform BCs (KUBCs: each boundary node is constrained with uniform displacements) and periodicity-compatible mixed uniform BCs (PMUBCs: each boundary node is constrained with a uniform combination of displacements and tractions mimicking the periodic BCs for an orthotropic material) were directly applied to the subregions, while the embedded configuration was achieved by applying PMUBCs on the larger volumes instead. Yield stresses and strains, and element damage at yield were finally compared across BCs. Our findings indicate that yield strains do not depend on the BCs. However, KUBCs significantly overestimate yield stresses obtained in the embedded configuration (+43.1 ± 27.9%). PMUBCs underestimate (−10.0 ± 11.2%), but not significantly, yield stresses in the embedded situation. Similarly, KUBCs lead to higher damage levels than PMUBCs (+51.0 ± 16.9%) and embedded configurations (+48.4 ± 15.0%). PMUBCs are better suited for reproducing the loading conditions in subregions of the trabecular bone and deliver a fair estimation of their effective (asymptotic) yield properties.

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Acknowledgements

The authors thank Bert van Rietbergen (Eindhoven University of Technology, Netherlands) for providing the \(\upmu \)CT data and Karol Daszkiewicz (Gdansk, University of Technology, Poland) for his support. This work was funded by the Gebert Rüf Foundation (GRS-079/14) and the Swiss National Science Foundation (Grant no. 143769).

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Authors and Affiliations

  1. Institute for Surgical Technology and Biomechanics, University of Bern, Bern, Switzerland

    Patrik Wili, Ghislain Maquer, Jarunan Panyasantisuk & Philippe K. Zysset

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  1. Patrik Wili
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  2. Ghislain Maquer
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  3. Jarunan Panyasantisuk
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  4. Philippe K. Zysset
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Correspondence to Ghislain Maquer.

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Wili, P., Maquer, G., Panyasantisuk, J. et al. Estimation of the effective yield properties of human trabecular bone using nonlinear micro-finite element analyses. Biomech Model Mechanobiol 16, 1925–1936 (2017). https://doi.org/10.1007/s10237-017-0928-0

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