Elastic deformation of mineralized collagen fibrils: An equivalent inclusion based composite model

Journal of Biomechanical Engineering

Volumn 127, Issue 3, 2005, Pages 383-390

  Akkus, Ozan ^a  

^a The University of Toledo   (United States)

Author keywords

Apatite Crystals; Collagen Fibrils; Mineralization; Modulus; Nanocomposites; Poisson's Ratio

Indexed keywords

ASPECT RATIO; CELLS; CRYSTALS; DEFORMATION; ELASTICITY; FIBERS; MINERALS; POISSON RATIO; STRESSES; TISSUE;

BIOMINERALIZATION; COLLAGEN FIBRILS; ELASTIC DEFORMATION; SUPRAMOLECULAR LEVEL;

COLLAGEN;

COLLAGEN FIBRIL; MINERAL;

ARTICLE; MATHEMATICAL ANALYSIS; MINERALIZATION; MOLECULAR MODEL; POISSON DISTRIBUTION; RIGIDITY; SHEAR STRESS; TENSILE STRENGTH; WEIGHT BEARING; YOUNG MODULUS;

ANIMALS; BONE AND BONES; CALCIFICATION, PHYSIOLOGIC; ELASTICITY; FIBRILLAR COLLAGENS; HUMANS; MODELS, BIOLOGICAL; MODELS, CHEMICAL; MOLECULAR CONFORMATION; PHASE TRANSITION; STRESS, MECHANICAL; WEIGHT-BEARING;

EID: 21144453883     PISSN: 01480731     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1894204     Document Type: Article

References (52)

1. Landis, W. J., 1995, "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 (N.Y.) 16, pp. 533-544.
2. Lees, S. 1987, "Considerations Regarding the structure of the Mammalian Mineralized Osteoid From Viewpoint of the Generalized Packing Model," Connect. Tissue Res., 16, 281-303.
3. Lees, S., and Prostak, K., 1988, "The Locus of Mineral Crystallites in Bone," Connect. Tissue Res., 18, 41-54.
4. Lees, S., Prostak, K. S., Ingle, V. K., and Kjoller, K., 1994, "The Loci of Mineral in Turkey Leg Tendon as Seen by Atomic Force Microscope and Electron Microscopy," Calcif. Tissue Int., 55, 180-189.
5. Landis, W. J., Hodgens, K. J., Song, M. J., J. Arena, S. Kiyonaga, M. Marko, C. Owen, and B. F. McEwen, 1996, "Mineralization of Collagen May Occur on Fibril Surfaces: Evidence From Conventional and High-Voltage Electron Microscopy and Three-Dimensional Imaging," J. Struct. Biol., 117, 24-35.
6. Fratzl, P., N. Fratzl-Zelman, K. Klaushofer, G. Vogl, and K. Koller, 1991, "Nucleation and Growth of Mineral Crystals in Bone studied by Small-Angle X-Ray Scattering," Calcif. Tissue Int., 48, 407-413.
7. Handschin, R. G., and W. B. Stern, 1994, "Crystallographic and Chemical Analysis of Human Bone Apatite (Crista Iliaca)," Clin. Rheumatol., 13 Suppl 1, 75-90.
8. Knott, L., and A. J. Bailey, 1998, "Collagen Cross-Links in Mineralizing Tissues: A Review of Their Chemistry, Function, and Clinical Relevance," Bone (N.Y.), 22, 181-187.
9. Eyre, D. R., 1981, "Crosslink Maturation in Bone Collagen," in The Chemistry and Biology of Mineralized Connective Tissues, A. Veiss, ed., Elsevier North-Holland, NY. pp. 51-55.
10. Heywood, B. R., N. H. Sparks, R. P. Shellis, S. Weiner, and S. Mann, 1990, "Ultrastructure, Morphology and Crystal Growth of Biogenic and Synthetic Apatites," Connect. Tissue Res., 25, 103-119.
11. Mueller, K. H., A. Trias, and R. D. Ray, 1966, Bone Density and Compostiton. Age-Related and Pathological Changes in Water and Mineral Content," J. Bone Jt. Surg., Am. Vol., 48, 140-148.
12. Quarles, L. D., and M. K. Drezner, 2001, "Pathophysiology of X-Linked Hypophosphatemia, Tumor-Induced Osteomalacia, and Autosomal Dominant Hypophosphatemia: A PerPHEXing Problem," J. Clin. Endocrinol. Metab., 86, 494-496.
13. Roschger, P., P. Fratzl, J. Eschberger, and K. Klaushofer, 1998, "Validation of quantitative Backscattered Electron Imaging for the Measurement of Mineral Density Distribution in Human Bone Biopsies," Bone (N. Y.), 23, 319-326.
14. Boskey, A. L., 1989, "Noncollagenous Matrix Proteins and Their Role in Mineralization," Bone Miner., 6, 111-123.
15. Eanes, E. D., and A. W. Hailer, 1998, "The Effect of Fluoride on the Size and Morphology of Apatite Crystals Grown From Physiologic Solutions," Calcif. Tissue Int., 63, 250-257.
16. Fratzl, P., S. Schreiber, P. Roschger, M. H. Lafage, G. Rodan, and K. Klaushofer, 1996, Effects of Sodium Fluoride and Alendronate on the Bone Mineral in Minipigs: A Small-Angle X-Ray Scattering and Backscattered Electron Imaging Study," J. Bone Miner. Res., 11, 248-253.
17. Freeman, J. J., B. Wopenka, M. J. Silva, and J. D. Pasteris, 2001, "Raman Spectroscopic Detection of Changes in Bioapatite in Mouse Femora as a Function of Age and In Vitro Fluoride Treatment," Calcif. Tissue Int., 68, 156-162.
18. Katz, J. L., 1971, "Hard Tissue as a Composite Material. I. Bounds on the Elastic Behavior," J. Biomech., 4, 455-473.
19. Wagner, H. D., and S. Weiner, 1992, "On the Relationship Between the MicroStructure of Bone and Its Mechanical Stiffness. J. Biomech., 25, 1311-1320.
20. Kotha, S. P., S. Kotha, and N. Guzelsu, 2000, "A Shear-Lag Model to Account for Interaction Effects Between Inclusions in Composites Reinforced With Rectangular Platelets," Compos. Sci. Technol., 60, 2147-2158.
21. Jäger, I., and P. Fratzl, 2000, "Mineralized Collagen Fibrils: A Mechanical Model With a Staggered Arrangement of Mineral Particles," Biophys. J., 79, 1737-1746.
22. Petruska, J. A., and A. J. Hodge, 1964, "A Subunit Model for the Tropocollagen Macromolecule," Proc. Natl. Acad. Sci. U.S.A., 51, 871-876.
23. Gilmore, R. S., and J. L. Katz, 1982, "Elastic Properties of Apatites," J. Mater. Sci., 17, 1131-1141.
24. Rey, C., B. Collins, T. Goehl, I. R. Dickson, and M. J. Glimcher, 1989, "The Carbonate Environment in Bone Mineral: A Resolution-Enhanced Fourier TransForm Infrared Spectroscopy Study," Calcif. Tissue Int., 45, 157-164.
25. Rey, C., V. Renugopalakrishnan, B. Collins, and M. J. Glimcher, 1991, "Fourier Transform Infrared Spectroscopic Study of the Carbonate Ions in Bone Mineral During Aging," Calcif. Tissue Int., 49, 251-258.
26. 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.
27. Eshelby, J. D., 1957, "The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems," Proc. R. Soc. London, Ser. A, A241, 376-396.
28. Pedersen, O. B., 1983, "Thermoelasticity and Plasticity of Composites -I. Mean Field Theory," Acta Metall., 31, 1795-1808.
29. Mammone, J. F., and S. M. Hudson, 1993, "Micromechanics of Bone Strength and Fracture," J. Biomech., 26, 439-446.
30. Zioupos, P., J. D. Currey, and A. J. Hamer, 1999, "The Role of Collagen in the Declining Mechanical Properties of Aging Human Cortical Bone," J. Biomed. Mater. Res., 45, 108-116.
31. Wang, X., X. Shen, X. Li, and C. M. Agrawal, 2002, "Age-Related Changes in the Collagen Network and Toughness of Bone," Bone (N.Y.), 31, 1-7.
32. Fratzl, P., N. Fratzl-Zelman, and K. Klaushofer, 1993, "Collagen Packing and Mineralization. An X-Ray Scattering Investigation of Turkey Leg Tendon," Biophys. J., 64, 260-266.
33. Chapman, G. E., and K. A. McLauchlan, 1969, "The Hydration Structure of Collagen," Proc. R. Soc. London, Ser. B, 173, 223-234.
34. Pineri, M. H., M. Escoubes, and G. Roche, 1978, "Water-Collagen Interactions: Calorimetric and Mechanical Experiments," Biopolymers, 17, 2799-2815.
35. Berendsen, H. J., and C. Migchelsen, 1966, "Hydration Structure of Collagen and Influence of Salts," Fed. Proc., 25, 998-1002.
36. 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.
37. Rho, J. Y., T. Y. Tsui, and G. M. Pharr, 1997, "Elastic Properties of Human Cortical and Trabecular Lamellar Bone Measured by Nanoindentation, " Biomaterials, 18, 1325-1330.
38. 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. Cells Mater, 1, 12-17.
39. Boskey, A., M. Maresca, and J. Appel, 1989, "The Effects of Noncollagenous Matrix Proteins on Hydroxyapatite Formation and Proliferation in a Collagen Gel System," Calcif. Tissue Res., 21, 171-176; discussion 177-178.
40. Takano, Y., C. H. Turner, I. Owan, R. B. Martin, S. T. Lau, M. R. Forwood, and D. B. Burr, 1999, "Elastic Anisotropy and Collagen Orientation of Osteonal Bone are Dependent on the Mechanical Strain Distribution," J. Orthop. Res., 17, 59-66.
41. Martin, R. B., and D. L. Boardman, 1993, "The Effects of Collagen Fiber Orientation, Porosity, Density, and Mineralization on Bovine Cortical Bone Bending Properties," J. Biomech., 26, 1047-1054.
42. Martin, R. B., and J. Ishida, 1989, "The Relative Effects of Collagen Fiber Orientation, Porosity, Density, and Mineralization on Bone Strength," J. Biomech., 22, 419-426.
43. Martin, R. B., S. T. Lau, P. V. Mathews, V. A. Gibson, and S. M. Stover, 1996, "Collagen Fiber Organization is Related to Mechanical Properties and Remodeling in Equine Bone. A Comparison of Two Methods," J. Biomech., 29, 1515-1521.
44. Borsato, K. S., and N. Sasaki, 1997, "Measurement of partition of stress between mineral and collagen phases in bone using X-ray diffraction techniques," J. Biomech., 30, 955-957.
45. Traub, W., T. Arad, and S. Weiner, 1992, "Growth of Mineral Crystals in Turkey Tendon Collagen Fibers," Connect. Tissue Res., 28, 99-111.
46. Eppell, S. J., W. Tong, J. L. Katz, L. Kuhn, and M. J. Glimcher, 2001, "Shape and Size of Isolated Bone Mineralites Measured Using Atomic Force Micrscopy," J. Orthop. Res., 19, 1027-1034.
47. Kim, H. M., C. Rey, and M. J. Glimcher, 1995, "Isolation of Calcium-Phosphate Crystals of Bone by Non-Aqueous Methods at Low Temperature," J. Bone Miner. Res., 10, 1589-1601.
48. Erts, D., L. J. Gathercole, and E. D. T. Atkins, 1994, "Scanning Probe Microscopy of Intrafibrillar Crystallites in Calcified Collagen," J. Mater. Sci.: Mater. Med., 5, 200-206.
49. Reilly, D. T., and A. H. Burstein, 1975, "The Elastic and Ultimate Properties of Compact Bone Tissue," J. Biomech., 8, 393-405.
50. Knets, I., and Malmeisters, A., 1977, "Deformabiliry and Strength of Human Compact Bone Tissue," Mechanics of Biological Solids: Proc. Euromech. Colloquium 68. G. Brankov, ed., Bulgarian Academy of Sciences, Sofia.
51. 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.
52. Clyne, T. W., and Withers, P. J., 1993, An Introduction to Metal Matrix Composites, Cambridge University Press, Cambridge, UK.