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Data-Driven Computational Simulation in Bone Mechanics

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Abstract

The data-driven approach was formally introduced in the field of computational mechanics just a few years ago, but it has gained increasing interest and application as disruptive technology in many other fields of physics and engineering. Although the fundamental bases of the method have been already settled, there are still many challenges to solve, which are often inherently linked to the problem at hand. In this paper, the data-driven methodology is applied to a particular problem in tissue biomechanics, a context where this approach is particularly suitable due to the difficulty in establishing accurate and general constitutive models, due to the intrinsic intra and inter-individual variability of the microstructure and associated mechanical properties of biological tissues. The problem addressed here corresponds to the characterization and mechanical simulation of a piece of cortical bone tissue. Cortical horse bone tissue was mechanically tested using a biaxial machine. The displacement field was obtained by means of digital image correlation and then transformed into strains by approximating the displacement derivatives in the bone virtual geometric image. These results, together with the approximated stress state, assumed as uniform in the small pieces tested, were used as input in the flowchart of the data-driven methodology to solve several numerical examples, which were compared with the corresponding classical model-based fitted solution. From these results, we conclude that the data-driven methodology is a useful tool to directly simulate problems of biomechanical interest without the imposition (model-free) of complex spatial and individually-varying constitutive laws. The presented data-driven approach recovers the natural spatial variation of the solution, resulting from the complex structure of bone tissue, i.e. heterogeneity, microstructural hierarchy and multifactorial architecture, making it possible to add the intrinsic stochasticity of biological tissues into the data set and into the numerical approach.

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Acknowledgments

The authors gratefully acknowledge the Spanish Ministry of Economy and Competitiveness (PGC2018-097257-B-C31, DPI2017-82501-P, MAT2016-76039-C4-4-R, AEI/FEDER, UE) and Andalusian Office of Economy and Science (US-1261691, FEDER, UE) for research funding.

Conflict of interest

The authors declare that they have no conflict of interest.

Human and Animal Participants

The experiment was conducted on cadaveric animal (horse) tissue. The horse femur was obtained via a butcher’s service (La Pañoleta, Seville - Spain), and tested in the biomechanics research laboratory of the Department of Mechanical Engineering of the University of Seville. Then, the animal was not sacrificed for the purposes of the present study.

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Authors and Affiliations

  1. School of Engineering, University of Seville, Camino de los descubrimientos s/n, 41092, Seville, Spain

    J. A. Sanz-Herrera, E. Reina-Romo & J. Domínguez

  2. University of Huelva, Huelva, Spain

    J. Mora-Macías

  3. Mechanical Engineering Department, Aragón Institute of Engineering Research (I3A), Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), University of Zaragoza, Zaragoza, Spain

    J. Ayensa-Jiménez, M. H. Doweidar & M. Doblaré

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  1. J. A. Sanz-Herrera
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Correspondence to J. A. Sanz-Herrera.

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Associate Editor Elena S. Di Martino oversaw the review of this article.

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Sanz-Herrera, J.A., Mora-Macías, J., Ayensa-Jiménez, J. et al. Data-Driven Computational Simulation in Bone Mechanics. Ann Biomed Eng 49, 407–419 (2021). https://doi.org/10.1007/s10439-020-02550-9

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