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Maximum effect of the heterogeneity of tissue mineralization on the effective cortical bone elastic properties

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Abstract

The mineralization level is heterogeneous in cortical bone extracellular matrix as a consequence of remodeling. Models of the effective elastic properties at the millimeter scale have been developed based on idealizations of the vascular pore network and matrix properties. Some popular models do not take into account the heterogeneity of the matrix. However, the errors on the predicted elasticity when the difference in elastic properties between osteonal and interstitial tissues is not modeled have not been quantified. This work provides an estimation of the maximum error. We compare the effective elasticity of a representative volume element (RVE) assuming (1) different elastic properties in osteonal and interstitial tissues vs. (2) average matrix properties. In order to account for the variability of bone microstructure, we use a collection of high resolution images of the pore network to build RVEs. In each RVE we assumed a constant osteonal wall thickness and we artificially varied this thickness between 35 and 140 \(\upmu\)m to create RVEs with different amounts of osteonal tissue. The homogenization problem was solved with a fast Fourier transform (FFT)-based numerical scheme. We found that the error depends on pore volume fraction and varies on average from 1 to \(7\%\) depending on the assumed diameter of the osteons. The results suggest that matrix heterogeneity may be disregarded in cortical bone models in most practical cases.

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Acknowledgements

The authors would like to thank ESRF for the access of beamline at ID 19 and 17 and the help from Cécile Olivier and Françoise Peyrin (CREATIS, CNRS 5220, INSERM U1206, Lyon) for performing SR-\(\mu\)CT experiments. This work has received financial support from Engineering Department of Sorbonne Université (UFR 919).

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Authors and Affiliations

  1. Sorbonne Université, INSERM, CNRS, Laboratoire d’Imagerie Biomédicale, 75006, Paris, France

    Luc Brémaud, Xiran Cai & Quentin Grimal

  2. Sorbonne Université, CNRS, Institut Jean Le Rond d’Alembert, 75005, Paris, France

    Luc Brémaud & Renald Brenner

  3. School of Information Science and Technology, ShanghaiTech University, Pudong District, 201210, Shanghai, China

    Xiran Cai

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  1. Luc Brémaud
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Correspondence to Quentin Grimal.

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Brémaud, L., Cai, X., Brenner, R. et al. Maximum effect of the heterogeneity of tissue mineralization on the effective cortical bone elastic properties. Biomech Model Mechanobiol 20, 1509–1518 (2021). https://doi.org/10.1007/s10237-021-01459-z

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