Hierarchical modeling of the elastic properties of bone at submicron scales: The role of extrafibrillar mineralization

Biophysical Journal

Volumn 94, Issue 11, 2008, Pages 4220-4232

  Nikolov, Svetoslav ^a   Raabe, Dierk ^a  

^a MAX PLANCK INSTITUT FÜR EISENFORSCHUNG GMBH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

FIBRILLAR COLLAGEN;

ANISOTROPY; ARTICLE; BIOLOGICAL MODEL; BONE; BONE MINERALIZATION; COMPUTER SIMULATION; ELASTICITY; MECHANICAL STRESS; PHYSIOLOGY; SHEAR STRENGTH; ULTRASTRUCTURE;

ANISOTROPY; BONE AND BONES; CALCIFICATION, PHYSIOLOGIC; COMPUTER SIMULATION; ELASTICITY; FIBRILLAR COLLAGENS; MODELS, BIOLOGICAL; SHEAR STRENGTH; STRESS, MECHANICAL;

EID: 44849089062     PISSN: 00063495     EISSN: 15420086     Source Type: Journal    
DOI: 10.1529/biophysj.107.125567     Document Type: Article

References (48)

1. Werner, S., and H. D. Wagner. 1998. The material bone: structure-mechanical function relations. Annu. Rev. Mater. Sci. 28:271-298.
2. Rho, J.-Y., L. Kuhn-Spearing, and P. Zioupos. 1998. Mechanical properties and the hierarchical structure of bone. Med. Eng. Phys. 20:92-102.
3. Jager, I., and P. Fratzl. 2000. Mineralized collagen fibrils: a mechanical model with a staggered arrangement of mineral particles. Biophys. J. 79: 1737-1746.
4. Vesentini, S., C. F. C. Fitie, F. M. Montevecchi, and A. Redaelli. 2005. Molecular assessment of the elastic properties of collagen-like homo-trimer sequences. Biomech. Model. Mechanobiol. 3:224-234.
5. Fantner, G. E., T. Hassenkam, J. H. Kindt, J. C. Weaver, H. Birkedal, L. Pechenik, J. A. Cutroni, G. A. G. Cidade, G. Stucky, D. E. Morse, and P. K. Hansma. 2005. Sacrificial bonds and hidden length dissipate energy as mineralized fibrils separate during bone fracture. Nat. Mater. 4:612-616.
6. Fratzl, P., H. S. Gupta, E. P. Paschalis, and P. Roschger. 2004. Structure and mechanical quality of the collagen-mineral nano-composite in bone. J. Mater. Chem. 14:2115-2123.
7. Rubin, M. A., I. Jasiuk, J. Taylor, J. Rubin, T. Ganey, and R. P. Apkarian. 2003. TEM analysis of the nanostructure of normal and osteoporotic human trabecular bone. Bone. 33:270-282.
8. Sasaki, N., A. Tagami, T. Goto, M. Taniguchi, M. Nakata, and K. Hikichi. 2002. Atomic force microscopic studies on the structure of bovine femoral cortical bone at the collagen fibril-mineral level. J. Mater. Sci. Mater. Med. 13:333-337.
9. Hassenkam, T., G. E. Fantner, J. A. Cutroni, J. C. Weaver, D. E. Morse, and P. K. Hansma. 2004. High-resolution AFM imaging of intact and fractured trabecular bone. Bone. 35:4-10.
10. Kindt, J. H., P. J. Thurner, M. E. Lauer, B. L. Bosma, G. Schitter, G. E. Fantner, M. Izumi, J.C. Weaver, D. E. Morse, and P. K. Hansma. 2007. In situ observation of fluoride-ion-induced hydroxyapatite-collagen detachment on bone fracture surfaces by atomic force microscopy. Nanotechnology. 18:135102-1-8.
11. Akiva, U., H. D. Wagner, and S. Weiner. 1998. Modeling the three- dimensional elastic constants of parallel-fibered and lamellar bone. J. Mater. Sci. 33:1497-1509.
12. Akkus, O. 2005. Elastic deformation of mineralized collagen fibrils: an equivalent inclusion based composite model. Trans. ASME. 127:383-390.
13. Fritsch, A., and C. Hellmich. 2007. "Universal" microstructural patterns in cortical and trabecular, extracellular and extravascular bone materials: micromechanics-based prediction of anisotropic elasticity. J. Theor. Biol. 244:597-620.
14. Bhowmik, R., K. S. Katti, and D. R. Katti. 2007. Mechanics of molecular collagen is influenced by hydroxyapatite in natural bone. J. Mater. Sci. 42:8795-8803.
15. Broedling, N. C., A. Hartmaier, M. J. Buehler, and H. Gao. 2007. The strength limit in a bio-inspired metallic nanocomposite. J. Mech. Phys. Solids. In press. 10.1016/jmps.2007.06.006.
16. Eshelby, J. 1957. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. Lond. A. 241:376-396.
17. Lebensohn, R. A., and C. N. Tomé. 2003. VPSC6. Los Alamos National Laboratory, Los Alamos, New Mexico.
18. Hodge, A. J., and J. A. Petruska. 1963. Recent studies with the electron microscope on ordered aggregates of the tropocollagen macromolecule. In Aspects of Protein Structure. G. N. Ramachandran, editor. Academic Press, New York.
19. Miller, A. 1984. Collagen: the organic matrix of bone. Phil. Trans. R. Soc. London B. 304:455-477.
20. Torquato, S. 1998. Effective stiffness tensor of composite media: II. Applications to isotropic dispersions. J. Mech. Phys. Solids. 35:1411-1440.
21. McPhedran, R. C., and G. W. Milton. 1981. Bounds and exact theories for the transport properties of inhomogeneous media. Appl. Phys. A. 26:207-220.
22. Eischen, J. W., and S. Torquato. 1993. Determining elastic behavior of composites by the boundary elementmethod. J. Appl. Phys. 74:159-170.
23. Hill, R. 1964. Theory of mechanical properties of fiber-strengthened materials: I. Elastic behavior. J. Mech. Phys. Solids. 12:199-212.
24. Mori, T., and K. Tanaka. 1973. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 21:571-574.
25. Benveniste, Y. 1987. A new approach to the application of Mori- Tanaka's theory in composite materials. Mech. Mater. 6:147-157.
26. Lees, S. 2003. Mineralization of type I collagen. Biophys. J. 85:204-207.
27. Zhang, W., S. S. Liao, and F. Z. Cui. 2003. Hierarchical self-assembly of nano-fibrils in mineralized collagen. Chem. Mater. 15:3221-3226.
28. Piez, K. A., and A. Miller. 1974. The structure of collagen fibrils. J. Supramol. Struct. 2:121-137.
29. Andrianov, I. V., V. V. Danishevs'kyy, and D. Weichert. 2002. Asymptotic determination of effective elastic properties of composite materials with fibrous square-shaped inclusions. Eur. J. Mech. A Solids. 21:1019-1036.
30. Gupta, H. S., J. Seto, W. Wagermaier, P. Zaslansky, P. Boesecke, and P. Fratzl. 2006. Cooperative deformation of mineral and collagen in bone at the nanoscale. Proc. Natl. Acad. Sci. USA. 103:17741-17746.
31. Doghri, I. 2000. Mechanics of Deformable Solids: Linear and Nonlinear, Analytical and Computational Aspects. Springer, Berlin, Germany.
32. Gommers, B., I. Verpoest, and P. Van Houtte. 1998. The Mori-Tanaka method applied to textile composite materials. Acta Mater. 46:2223-2235.
33. Hofmann, H., T. Voss, K. Kuhn, and J. Engel. 1984. Localization of flexible sites in thread-like molecules from electron micrographs. Comparison of interstitial, basement membrane and intima collagens. J. Mol. Biol. 172:325-343.
34. Sasaki, N., and S. Odajima. 1996. Stress-strain curve and Young's modulus of a collagen molecule as determined by the x-ray diffraction technique. J. Biomech. 29:655-658.
35. Katz, J. L. 1971. Hard tissue as a composite material. I. Bounds on the elastic behavior. J. Biomech. 4:455-473.
36. Martin, R. I., and P. W. Brown. 1995. Mechanical properties of hydroxyapatite formed at physiological temperature. J. Mat. Science. Mat. Med. 6:138-143.
37. Snyders, R., D. Music, D. Sigumonrong, B. Schelnberger, J. Jensen, and J. M. Schneider. 2007. Experimental and ab initio study of the mechanical properties of hydroxyapatite. Appl. Phys. Lett. 90:193902-1-13.
38. Gilmore, R. S., and J. L. Katz. 1982. Elastic properties of apatites. J. Mater. Sci. 17:1131-1141.
39. Currey, J. D. 1999. What determines the bending strength of compact bone? J. Exp. Biol. 202:2495-2503.
40. Katz, E. P., and S. Li. 1973. Structure and function of bone collagen fibrils. J. Mol. Biol. 80:1-5.
41. Sasaki, N., and Y. Sudoh. 1997. X-ray pole figure analysis of apatite crystals and collagen molecules in bone. Calcif. Tissue Int. 60:361-367.
42. Lees, S., K. S. Prostak, V. K. Ingle, and K. Kjoller. 1994. The loci of mineral in turkey leg tendon as seen by atomic force microscope and electron microscopy. Calcif. Tissue Int. 55:180-189.
43. Espinoza Orías, A. A. 2005. The relationship between the mechanical anisotropy of human cortical bone tissue and its microstructure. PhD thesis. University of Notre Dame, Notre Dame, Indiana.
44. Hengsberger, S., A. Kulik, and P. Zysset. 2001. A combined atomic force microscopy and nanoindentation technique to investigate the elastic properties of bone structural units. Eur. Cell. Mater. 1:12-17.
45. Swadener, J. G., J.-Y. Rho, and G. M. Pharr. 2001. Effects of anisotropy on elastic moduli measured by nanoindentation in human tibial cortical bone. J. Biomed. Mater. Res. 57:108-112.
46. Reference deleted in proof.
47. Van Buskirk, W. C., S. C. Cowin, and R. N. Ward. 1981. Ultrasonic measurements of orthotropic elastic constants of bovine femoral bone. Trans. ASME J. Biomech. Eng. 103:67-72.
48. Ashman, R. B., S. C. Cowin, W. C. Van Buskirk, and J. C. Rice. 1984. A continuous wave technique for the measurement of the elastic properties of cortical bone. J. Biomech. 17:349-361.