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Nanoscale heterogeneity promotes energy dissipation in bone

Nature Materials volume 6, pages 454–462 (2007)Cite this article

Abstract

Nanomechanical heterogeneity is expected to influence elasticity, damage, fracture and remodelling of bone. Here, the spatial distribution of nanomechanical properties of bone is quantified at the length scale of individual collagen fibrils. Our results show elaborate patterns of stiffness ranging from ∼2 to 30 GPa, which do not correlate directly with topographical features and hence are attributed to underlying local structural and compositional variations. We propose a new energy-dissipation mechanism arising from nanomechanical heterogeneity, which offers a means for ductility enhancement, damage evolution and toughening. This hypothesis is supported by computational simulations that incorporate the nanoscale experimental results. These simulations predict that non-uniform inelastic deformation over larger areas and increased energy dissipation arising from nanoscale heterogeneity lead to markedly different biomechanical properties compared with a uniform material. The fundamental concepts discovered here are applicable to a broad class of biological materials and may serve as a design consideration for biologically inspired materials technologies.

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Figure 1: Schematic diagram of experiment used to quantify nanomechanical heterogeneity in bone.
Figure 2: The ultrastructure and nanomechanical spatial heterogeneity of bone stiffness.
Figure 3: Quantitative analysis of nanomechanical-property maps using discrete wavelet transform.
Figure 4: FEA simulations of the effect of nanomechanical spatial heterogeneity on larger-scale biomechanical properties.
Figure 5: FEA simulations of the effect of nanomechanical spatial heterogeneity on larger-scale compressive loading.
Figure 6: Wavelet decomposition of a 2D image47.

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References

  1. Weiner, S. & Wagner, H. D. The material bone: Structure–mechanical function relations. Annu. Rev. Mater. Sci. 28, 271–298 (1998).

    Article  CAS  Google Scholar 

  2. Currey, J. Structural heterogeneity in bone: Good or bad? J. Musculoskelet. Neuronal Interact. 5, 317 (2005).

    CAS  Google Scholar 

  3. Lakes, R. S. Materials with structural hierarchy. Nature 361, 511–515 (1993).

    Article  Google Scholar 

  4. Morgan, E. F., Bayraktar, H. H. & Keaveny, T. M. Trabecular bone modulus–density relationships depend on anatomic site. J. Biomech. 36, 897–904 (2003).

    Article  Google Scholar 

  5. Pope, M. H. & Outwater, J. O. Mechanical properties of bone as a function of position and orientation. J. Biomech. 7, 61–66 (1974).

    Article  CAS  Google Scholar 

  6. Skedros, J. G., Sorenson, S. M., Takano, Y. & Turner, C. H. Dissociation of mineral and collagen orientations may differentially adapt compact bone for regional loading environments: Results from acoustic velocity measurements in deer calcanei. Bone 39, 143–151 (2006).

    Article  CAS  Google Scholar 

  7. Rho, J. Y., Roy, M. E., Tsui, T. Y. & Pharr, G. M. Elastic properties of microstructural components of human bone tissue as measured by nanoindentation. J. Biomed. Mater. Res. 45, 48–54 (1999).

    Article  CAS  Google Scholar 

  8. Gupta, H. S. et al. Mechanical modulation at the lamellar level in osteonal bone. J. Mater. Res. 21, 1913–1921 (2006).

    Article  CAS  Google Scholar 

  9. Martin, R. B. & Burr, D. B. Structure, Function and Adaptation of Compact Bone (Raven, New York, 1989).

    Google Scholar 

  10. Rho, J. Y., Zioupos, P., Currey, J. D. & Pharr, G. M. Microstructural elasticity and regional heterogeneity in human femoral bone of various ages examined by nano-indentation. J. Biomech. 35, 189–198 (2002).

    Article  CAS  Google Scholar 

  11. Balooch, G. et al. TGF-beta regulates the mechanical properties and composition of bone matrix. Proc. Natl Acad. Sci. 102, 18813–18818 (2005).

    Article  CAS  Google Scholar 

  12. Zysset, P. K., Guo, X. E., Hoffler, C. E., Moore, K. E. & Goldstein, S. A. Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur. J. Biomech. 32, 1005–1012 (1999).

    Article  CAS  Google Scholar 

  13. Catanese, J. 3rd, Iverson, E. P., Ng, R. K. & Keaveny, T. M. Heterogeneity of the mechanical properties of demineralized bone. J. Biomech. 32, 1365–1369 (1999).

    Article  Google Scholar 

  14. Peterlik, H., Roschger, P., Klaushofer, K. & Fratzl, P. From brittle to ductile fracture of bone. Nature Mater. 5, 52–55 (2006).

    Article  CAS  Google Scholar 

  15. Phelps, J. B., Hubbard, G. B., Wang, X. & Agrawal, C. M. Microstructural heterogeneity and the fracture toughness of bone. J. Biomed. Mater. Res. 51, 735–741 (2000).

    Article  CAS  Google Scholar 

  16. Jaasma, M. J., Bayraktar, H. H., Niebur, G. L. & Keaveny, T. M. Biomechanical effects of intraspecimen variations in tissue modulus for trabecular bone. J. Biomech. 35, 237–246 (2002).

    Article  Google Scholar 

  17. Fantner, G. E. et al. Sacrificial bonds and hidden length dissipate energy as mineralized fibrils separate during bone fracture. Nature Mater. 4, 612–616 (2005).

    Article  CAS  Google Scholar 

  18. Gao, H., Ji, B., Jager, I. L., Arzt, E. & Fratzl, P. Materials become insensitive to flaws at nanoscale: Lessons from nature. Proc. Natl Acad. Sci. USA 100, 5597–5600 (2003).

    Article  CAS  Google Scholar 

  19. Gupta, H. S. et al. Nanoscale deformation mechanisms in bone. Nano Lett. 5, 2108–2111 (2005).

    Article  CAS  Google Scholar 

  20. Tai, K., Ulm, F.-J. & Ortiz, C. Nanogranular origins of the strength of bone. Nano Lett. 6, 2520–2525 (2006).

    Article  CAS  Google Scholar 

  21. Currey, J. D. Effects of differences in mineralization on the mechanical properties of bone. Phil. Trans. R. Soc. Long B 304, 509–518 (1984).

    Article  CAS  Google Scholar 

  22. Currey, J. D. The effect of porosity and mineral content on the Young’s modulus elasticity of compact bone. J. Biomech. 21, 131–139 (1988).

    Article  CAS  Google Scholar 

  23. You, L. D., Weinbaum, S., Cowin, S. C. & Schaffler, M. B. Ultrastructure of the osteocyte process and its pericellular matrix. Anat. Rec. A Discov. Mol. Cell Evol. Biol. 278, 505–513 (2004).

    Article  Google Scholar 

  24. Tai, K., Qi, H. J. & Ortiz, C. Effect of mineral content on the nanoindentation properties and nanoscale deformation mechanisms of bovine tibial cortical bone. J. Mater. Sci.- Mater. Med. 16, 947–959 (2005).

    Article  CAS  Google Scholar 

  25. Oliver, W. C. & Pharr, G. M. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564–1583 (1992).

    Article  CAS  Google Scholar 

  26. Giraudguille, M. M. Twisted plywood architecture of collagen fibrils in human compact-bone osteons. Calcif. Tissue Int. 42, 167–180 (1988).

    Article  CAS  Google Scholar 

  27. Hofmann, T., Heyroth, F., Meinhard, H., Franzel, W. & Raum, K. Assessment of composition and anisotropic elastic properties of secondary osteon lamellae. J. Biomech. 39, 2282–2294 (2006).

    Article  Google Scholar 

  28. Kazanci, M., Roschger, P., Paschalis, E. P., Klaushofer, K. & Fratzl, P. Bone osteonal tissues by Raman spectral mapping: Orientation-composition. J. Struct. Biol. 156, 489–496 (2006).

    Article  CAS  Google Scholar 

  29. Wagermaier, W. et al. Spiral twisting of fiber orientation inside bone lamellae. Biointerphases 1, 1–5 (2006).

    Article  CAS  Google Scholar 

  30. Ardizzoni, A. Osteocyte lacunar size–lamellar thickness relationships in human secondary osteons. Bone 28, 215–219 (2001).

    Article  CAS  Google Scholar 

  31. Mallat, S. A Wavelet Tour of Signal Processing (Academic, San Diego, 1998).

    Google Scholar 

  32. Donnelly, E., Baker, S. P., Boskey, A. L. & van der Meulen, M. C. H. Effects of surface roughness and maximum load on the mechanical properties of cancellous bone measured by nanoindentation. J. Biomed. Mater. Res. A 77, 426–435 (2006).

    Article  Google Scholar 

  33. Nalla, R. K., Kinney, J. H. & Ritchie, R. O. Mechanistic fracture criteria for the failure of human cortical bone. Nature Mater. 2, 164–168 (2003).

    Article  CAS  Google Scholar 

  34. Currey, J. D. Tensile yield in compact bone is determined by strain, post-yield behaviour by mineral content. J. Biomech. 37, 549–556 (2004).

    Article  Google Scholar 

  35. Rho, J. Y. Ultrasonic method for measuring elastic properties of human tibial cortical and cancellous bone. Ultrasonics 34, 777–783 (1996).

    Article  CAS  Google Scholar 

  36. Böhm, H. J. & Han, W. Comparisons between three-dimensional and two-dimensional multi-particle unit cell models for particle reinforced metal matrix composites. Modell. Simul. Mater. Sci. Eng. 9, 47–65 (2001).

    Article  Google Scholar 

  37. Shen, H. & Lissenden, C. J. 3D finite element analysis of particle-reinforced aluminum. Mater. Sci. Eng. A 338, 271–281 (2002).

    Article  Google Scholar 

  38. Nakamura, T. & Suresh, S. Effects of thermal residual-stresses and fiber packing on deformation of metal-matrix composites. Acta. Metal. Mater. 41, 1665–1681 (1993).

    Article  CAS  Google Scholar 

  39. Ehrlich, P. J. & Lanyon, L. E. Mechanical strain and bone cell function: A review. Osteoporos. Int. 13, 688–700 (2002).

    Article  CAS  Google Scholar 

  40. You, L., Cowin, S. C., Schaffler, M. B. & Weinbaum, S. A model for strain amplification in the actin cytoskeleton of osteocytes due to fluid drag on pericellular matrix. J. Biomech. 34, 1375–1386 (2001).

    Article  CAS  Google Scholar 

  41. Burger, E. H. & Klein-Nulend, J. Mechanotransduction in bone—role of the lacuno-canalicular network. FASEB J. 13 (suppl), S101–S112 (1999).

    Article  CAS  Google Scholar 

  42. Vesenka, J., Manne, S., Giberson, R., Marsh, T. & Henderson, E. Colloidal gold particles as an incompressible atomic force microscope imaging standard for assessing the compressibility of biomolecules. Biophys. J. 65, 992–997 (1993).

    Article  CAS  Google Scholar 

  43. Seog, J. et al. Direct measurement of glycosamnoglycan intermolecular interactions via high-resolution force spectroscopy. Macromolecules 35, 5601–5615 (2002).

    Article  CAS  Google Scholar 

  44. Oliver, W. C. & Pharr, G. M. Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19, 3–20 (2004).

    Article  CAS  Google Scholar 

  45. Pharr, W. C. O. Indentation of an elastic planar substrate by solid. J. Mater. Res. 7, 1564 (1992).

    Article  Google Scholar 

  46. Strang, G. & Nguyen, T. Wavelets and Filter Banks (Wellesley-Cambridge, Wellesley, MA, 1996).

    Google Scholar 

  47. Tsai, D. M. & Hsiao, B. Automatic surface inspection using wavelet reconstruction. Pattern Recognition 34, 1285–1305 (2001).

    Article  Google Scholar 

  48. Dao, M., Chollacoop, N., Van Vliet, K. J., Venkatesh, T. A. & Suresh, S. Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater. 49, 3899–3918 (2001).

    Article  CAS  Google Scholar 

  49. Gouldstone, A. et al. Indentation across size scales and disciplines: Recent developments in experimentation and modeling. Acta Mater. 55, (2007, doi:10.1016/j.actamat.2006.08.044).

    Article  CAS  Google Scholar 

  50. Thurner, P. et al. High-speed photography of compressed human trabecular bone correlates whitening to microscopic damage. Eng. Fracture Mech. 74, 1928–1941 (2007).

    Article  Google Scholar 

  51. Landis, W. J. 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 16, 533–544 (1995).

    Article  CAS  Google Scholar 

  52. Wachtel, E. & Weiner, S. Small-angle X-ray scattering study of dispersed crystals from bone and tendon. J. Bone Miner. Res. 9, 1651–1655 (1994).

    Article  CAS  Google Scholar 

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Acknowledgements

The authors thank the MIT Department of Materials Science and Engineering Nanomechanical Testing Facility, The Whitaker Foundation and the US Army through the MIT Institute for Soldier Nanotechnologies (contract number DAAD-19-02-D0002), and the NIH grant 1-R01-GM076689-01 on multiscale modelling for funding. M.D. and S.S. also acknowledge partial support from the United States Army Research Office and the Joint Improvised Explosive Devices Defeat Organization under contract number W911NF-07-1-0035. The content does not necessarily reflect the position of the government and no official endorsement should be inferred. The authors would also like to thank graphic artist Beryl Simon for preparation of Fig. 2g.

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  1. Kuangshin Tai and Ming Dao: These authors contributed equally to this work

Authors and Affiliations

  1. Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA

    Kuangshin Tai, Ming Dao, Subra Suresh & Christine Ortiz

  2. Division of Biological Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA

    Subra Suresh

  3. Department of Chemical Engineering and Materials Science, University of California, One Shields Avenue, Davis, California 95616, USA

    Ahmet Palazoglu

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  1. Kuangshin Tai
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Correspondence to Christine Ortiz.

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Tai, K., Dao, M., Suresh, S. et al. Nanoscale heterogeneity promotes energy dissipation in bone. Nature Mater 6, 454–462 (2007). https://doi.org/10.1038/nmat1911

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