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Artificial Neural Network analysis for modeling fibril structure in bone

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Abstract

The bone as seen hierarchically is a structured material with mechanical properties depending on several scales. We will focus our study here on the fibril scale which is formed essentially by collagen and mineral. In order to find the macroscopic properties of the fibril we have proposed a multiscale approach. From finite element simulation performed on a unit cell, an Artificial Neural Network (ANN) model is developed in order to identify the material properties of the fibril. The advantage of this method is that it can be used to define the equivalent properties of a class of parameterized unit cells.

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Abbreviations

NN:

Neural Network

RVE:

Representative Volume Element

BP:

Back-propagation

DOE:

Design Of Experiments

FEM:

Finite Element Method

References

  1. Dorozhkin, S. V., “Nanosized and Nanocrystalline Calcium Orthophosphates,” Acta Biomaterialia, Vol. 6, No. 3, pp. 715–734, 2010.

    Article  Google Scholar 

  2. Barkaoui, A. and Hambli, R., “Finite Element 3D Modeling of Mechanical Behavior of Mineralized Collagen Microfibrils,” Journal of Applied Biomaterials & Biomechanics, Vol. 9, No. 3, pp. 207–213, 2011.

    Google Scholar 

  3. Hambli, R., Katerchi, H., and Benhamou, C. L., “Multiscale Methodology for Bone Remodelling Simulation using Coupled Finite Element and Neural Network Computation,” Biomechanics and Modeling in Mechanobiology, Vol. 10, No. 1, pp. 133–145, 2011.

    Article  Google Scholar 

  4. Martinez-Reina, J., Garcia-Aznar, J., Dominguez, J., and Doblaré, M., “A Bone Remodelling Model Including the Directional Activity of BMUs,” Biomechanics and Modeling in Mechanobiology, Vol. 8, No. 2, pp. 111–127, 2009.

    Article  Google Scholar 

  5. Hamed, E., Lee, Y., and Jasiuk, I., “Multiscale Modeling of Elastic Properties of Cortical Bone,” Acta Mechanica, Vol. 213, No. 1–2, pp. 131–154, 2010.

    Article  MATH  Google Scholar 

  6. Hamed, E., Jasiuk, I., Yoo, A., Lee, Y., and Liszka, T., “Multi-Scale Modelling of Elastic Moduli of Trabecular Bone,” Journal of The Royal Society Interface, Vol. 9, No. 72, pp. 1654–1673, 2012.

    Article  Google Scholar 

  7. Hamed, E. and Jasiuk, I., “Multiscale Damage and Strength of Lamellar Bone Modeled by Cohesive Finite Elements,” Journal of the Mechanical Behavior of Biomedical Materials, Vol. 28, pp. 94–110, 2013.

    Article  Google Scholar 

  8. Khaterchi, H., Chamekh, A., and Belhadjsalah, H., “Multi-Scale Modelling of Orthotropic Properties of Trabecular Bone in Nanoscale,” Design and Modeling of Mechanical Systems, pp. 557–566, 2013.

    Chapter  Google Scholar 

  9. Khaterchi, H. and Belhadjsalah, H., “A Three-Scale Identification of Orthotropic Properties of Trabecular Bone,” Computer Methods in Biomechanics and Biomedical Engineering, Vol. 16, No. Suppl. 1, pp. 272–274, 2013.

    Article  Google Scholar 

  10. Barkaoui, A. and Hambli, R., “Finite Element 3D Modeling of Mechanical Behavior of Mineralized Collagen Microfibrils,” Journal of Applied Biomaterials & Biomechanics, Vol. 9, No. 3, pp. 207–213, 2011.

    Google Scholar 

  11. Rho, J. Y., Kuhn-Spearing, L., and Zioupos, P., “Mechanical Properties and the Hierarchical Structure of Bone,” Medical Engineering & Physics, Vol. 20, No. 2, pp. 92–102, 1998.

    Article  Google Scholar 

  12. Reilly, D. T., Burstein, A. H., and Frankel, V. H., “The Elastic Modulus for Bone,” Journal of Biomechanics, Vol. 7, No. 3, pp. 271–275, 1974.

    Article  Google Scholar 

  13. Choi, K., Kuhn, J. L., Ciarelli, M. J., and Goldstein, S. A., “The Elastic Moduli of Human Subchondral, Trabecular, and Cortical Bone Tissue and the Size-Dependency of Cortical Bone Modulus,” Journal of Biomechanics, Vol. 23, No. 11, pp. 1103–1113, 1990.

    Article  Google Scholar 

  14. Zhang, J., Niebur, G. L., and Ovaert, T. C., “Mechanical Property Determination of Bone through Nano-and Micro-Indentation Testing and Finite Element Simulation,” Journal of Biomechanics, Vol. 41, No. 2, pp. 267–275, 2008.

    Article  Google Scholar 

  15. Barkaoui, A., Chamekh, A., Merzouki, T., Hambli, R., and Mkaddem, A., “Multiscale Approach Including Microfibril Scale to Assess Elastic Constants of Cortical Bone based on Neural Network Computation and Homogenization Method,” International Journal for Numerical Methods in Biomedical Engineering, Vol. 30, No. 3, pp. 318–338, 2014.

    Article  MathSciNet  Google Scholar 

  16. Martínez-Reina, J., Domínguez, J., and García-Aznar, J., “Effect of Porosity and Mineral Content on the Elastic Constants of Cortical Bone: A Multiscale Approach,” Biomechanics and Modeling in Mechanobiology, Vol. 10, No. 3, pp. 309–322, 2011.

    Article  Google Scholar 

  17. Fritsch, A. and Hellmich, C., “‘Universal Microstructural Patterns in Cortical and Trabecular, Extracellular and Extravascular Bone Materials: Micromechanics-based Prediction of Anisotropic Elasticity,” Journal of Theoretical Biology, Vol. 244, No. 4, pp. 597–620, 2007.

    Article  Google Scholar 

  18. Sansalone, V., Lemaire, T., and Naili, S., “Variational Homogenization for Modeling Fibrillar Structures in Bone,” Mechanics Research Communications, Vol. 36, No. 2, pp. 265–273, 2009.

    Article  MATH  Google Scholar 

  19. Ghanbari, J. and Naghdabadi, R., “Nonlinear Hierarchical Multiscale Modeling of Cortical Bone Considering Its Nanoscale Microstructure,” Journal of Biomechanics, Vol. 42, No. 10, pp. 1560–1565, 2009.

    Article  Google Scholar 

  20. Currey, J. D., “Bones: Structure and Mechanics,” Princeton University Press, pp. 1–380, 2002.

    Google Scholar 

  21. Jäger, I. and Fratzl, P., “Mineralized Collagen Fibrils: A Mechanical Model with a Staggered Arrangement of Mineral Particles,” Biophysical Journal, Vol. 79, No. 4, pp. 1737–1746, 2000.

    Article  Google Scholar 

  22. Kotha, S. P. and Guzelsu, N., “Tensile Behavior of Cortical Bone: Dependence of Organic Matrix Material Properties on Bone Mineral Content,” Journal of Biomechanics, Vol. 40, No. 1, pp. 36–45, 2007.

    Article  Google Scholar 

  23. Currey, J. D., “The Effect of Porosity and Mineral Content on the Young's Modulus of Elasticity of Compact Bone,” Journal of Biomechanics, Vol. 21, No. 2, pp. 131–139, 1988.

    Article  Google Scholar 

  24. Lees, S., “Considerations Regarding the Structure of the Mammalian Mineralized Osteoid from Viewpoint of the Generalized Packing Model,” Connective Tissue Research, Vol. 16, No. 4, pp. 281–303, 1987.

    Article  Google Scholar 

  25. Landis, W., “The Strength of a Calcified Tissue Depends in Part on the Molecular Structure and Organization of Its Constituent Mineral Crystals in their Organic Matrix,” Bone, Vol. 16, No. 5, pp. 533–544, 1995.

    Article  Google Scholar 

  26. Hellmich, C., Ulm, F. J., and Dormieux, L., “Can the Diverse Elastic Properties of Trabecular and Cortical Bone be Attributed to Only a Few Tissue-Independent Phase Properties and their Interactions?” Biomechanics and Modeling in Mechanobiology, Vol. 2, No. 4, pp. 219–238, 2004.

    Article  Google Scholar 

  27. Chamekh, A., Salah, H. B. H., and Hambli, R., “Inverse Technique Identification of Material Parameters using Finite Element and Neural Network Computation,” The International Journal of Advanced Manufacturing Technology, Vol. 44, No. 1–2, pp. 173–179, 2009.

    Article  Google Scholar 

  28. Halpin, J. C. and Kardos, J. L., “The Halpin-Tsai Equations: A Review,” Polymer Engineering & Science, Vol. 16, No. 5, pp. 344–352, 1976.

    Article  Google Scholar 

  29. Porter, D., “Pragmatic Multiscale Modelling of Bone as a Natural Hybrid Nanocomposite,” Materials Science and Engineering: A, Vol. 365, No. 1, pp. 38–45, 2004.

    Article  Google Scholar 

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Correspondence to Houda Khaterchi.

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Khaterchi, H., Chamekh, A. & BelHadjSalah, H. Artificial Neural Network analysis for modeling fibril structure in bone. Int. J. Precis. Eng. Manuf. 16, 581–587 (2015). https://doi.org/10.1007/s12541-015-0078-1

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  • DOI: https://doi.org/10.1007/s12541-015-0078-1

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