Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-25T15:53:32.054Z Has data issue: false hasContentIssue false

Universal Microstructural Patterns in Bone: Micromechanics-Based Prediction of Anisotropic Material Behavior

Published online by Cambridge University Press:  26 February 2011

Andreas Fritsch
Affiliation:
[email protected], Vienna University of Technology, Institute for Mechanics of Materials and Structures, Karlsplatz 13/202, Vienna (Wien), A-1040, Austria
Christian Hellmich
Affiliation:
[email protected], Vienna University of Technology (TU Wien), Vienna, A-1040, Austria
Get access

Abstract

Bone materials are characterized by an astonishing variability and diversity. Still, because of ‘architectural constraints’, their fundamental hierarchical organization or basic building plans remain largely unchanged during biological evolution. These building plans govern the mechanical interaction of the elementary components of bone (hydroxyapatite, collagen, water; with directly measurable tissue-independent elastic properties), which are here quantified through a multiscale homogenization scheme delivering effective elastic properties of bone materials: At a scale of 10 nm, long cylindrical collagen molecules, attached to each other at their ends by ∼1.5 nm long crosslinks and hosting intermolecular water inbetween, form a contiguous matrix called wet collagen. At a scale of several hundred nanometers, wet collagen and mineral crystal agglomerations interpenetrate each other, forming the mineralized fibril. At a scale of 5 microns, the solid bone matrix is represented as collagen fibril inclusions embedded in a foam of largely disordered (extrafibrillar) mineral crystals. Remarkably, needle and sphere type representations of disordered minerals deliver quasi-identical mechanical behavior of such extrafibrillar porous polycrystals. At a scale above the ultrastructure lacunae are embedded in extracellular bone matrix, forming the extravascular bone material. Model estimates predicted from tissue-specific composition data agree remarkably well with corresponding stiffness experiments across cortical and trabecular materials, which opens new possibilities in the exploitation of computer tomographic data for nano-to-macro mechanics of bone organs, especially in combination with currently investigated extensions towards damage and failure.

Type
Research Article
Copyright
Copyright © Materials Research Society 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Seilacher, A., Lethaia 3, 393396 (1970).Google Scholar
2. Gould, S. and Lewontin, R., Proceedings of the Royal Society of London, Series B 205 (1161), 581598 (1979).Google Scholar
3. Katz, J.L., Yoon, H.S., Lipson, S., Maharidge, R., Meunier, A., and Christel, P., Calcified Tissue International 36, S31–S36 (1984).Google Scholar
4. Currey, J., Journal of Biomechanics 2, 477480 (1969).Google Scholar
5. Katz, J., Nature 283, 106107 (1980).Google Scholar
6. Crolet, J., Aoubiza, B., and Meunier, A., Journal of Biomechanics 26, 677687 (1993).Google Scholar
7. Hellmich, Ch. and Ulm, F.-J., Journal of Biomechanics 35, 11991212 (2002).Google Scholar
8. Zaoui, A., Journal of Engineering Mechanics (ASCE) 128 (8), 808816 (2002).Google Scholar
9. Eshelby, J., Proceedings of the Royal Society London, Series A 241, 376396 (1957).Google Scholar
10. Laws, N., Journal of Elasticity 7 (1), 9197 (1977).Google Scholar
11. Hellmich, Ch., in Applied Micromechanics of Porous Media, ed. L., Dormieux, F.-J., Ulm (CISM Courses and lectures 480, Springer, Wien - New York, 2005) pp. 289332.Google Scholar
12. Fritsch, A. and Hellmich, Ch., Journal of Theoretical Biology, in print, available online at www.sciencedirect.com, doi:10.1016/j.jtbi.2006.09.013.Google Scholar
13. Katz, J. and Ukraincik, K., Journal of Biomechanics 4, 221227 (1971).Google Scholar
14. Cusack, S. and Miller, A., Journal of Molecular Biology 135, 3951 (1979).Google Scholar
15. Lees, S., Heeley, J., and Claery, P., Calcified Tissue International 29, 107117 (1979).Google Scholar
16. Lees, S., Ahern, J., and Leonard, M., Journal of the Acoustical Society of America 74 (1), 2833 (1983).Google Scholar
17. Lees, S., Connective Tissue Research 16, 281303 (1987).Google Scholar
18. Hellmich, Ch. and Ulm, F.-J., Biomechanics and Modeling in Mechanobiology 2, 2136 (2003).Google Scholar
19. Lees, S., Hanson, D., Page, E., and Mook, H., Journal of Bone and Mineral Research 9 (9), 13771389 (1994).Google Scholar
20. Ashman, R., Cowin, S., van Buskirk, W., and Rice, J., Journal of Biomechanics 17, 349361 (1984).Google Scholar
21. Ashman, R. and Rho, J., Journal of Biomechanics 21, 177181 (1988).Google Scholar
22. McCarthy, R., Jeffcott, L., and McCartney, R., Journal of Biomechanics 23, 11391143 (1990).Google Scholar
23. Fritsch, A., Dormieux, L., and Hellmich, Ch., Comptes Rendus Mecanique 334, 151157 (2006).Google Scholar
24. Hellmich, Ch., BarthÈlÈmy, J.-F., and Dormieux, L., European Journal of Mechanics A/Solids 23, 783810 (2004).Google Scholar
25. Eppell, S.J., Tong, W., Katz, J.L., Kuhn, L., and Glimcher, M.J., Journal of Orthopaedic Research 19, 10271034 (2001).Google Scholar
26. Weiner, S. and Wagner, H.D., Annual Review of Materials Science 28, 271298 (1998).Google Scholar
27. Rosen, V. Benzra, Hobbs, L.W., and Spector, M., Biomaterials 23, 921928 (2002).Google Scholar
28. Landis, W.J., Song, M.J., Leith, A., McEwen, L., and McEwen, B.F., Journal of Structural Biology 110, 3954 (1993).Google Scholar
29. Zylberberg, L., Traub, W., de Buffrenil, V., Allizard, F., Arad, T., and Weiner, S., Bone 23, 241247 (1998).Google Scholar
30. Torabia, S. and Hellmich, Ch., in Proceedings of the 16th International Bone Densitometry Workshop, ed. P., Laugier, D., Hans (Annecy, France, 2004).Google Scholar