Sensitivity analysis and parametric study of elastic properties of an unidirectional mineralized bone fibril-array using mean field methods

Biomechanics and Modeling in Mechanobiology

Volumn 9, Issue 5, 2010, Pages 499-510

  Reisinger, Andreas G ^a   Pahr, Dieter H ^a   Zysset, Philippe K ^a  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Bone; Elastic constants; Fibril array; Mean field method; Micromechanical model; Sensitivity analysis

Indexed keywords

BONE; COLLAGEN; ELASTIC CONSTANTS; ELASTICITY; MINERALOGY; STIFFNESS; STIFFNESS MATRIX;

ELASTIC PROPERTIES; FIBRIL ARRAY; KEYS PARAMETERS; MATRIX; MEAN FIELD METHODS; MICROMECHANICAL MODELLING; MINERALISATION; MINERALIZED BONE; PARAMETRIC STUDY; STRAIN RATIOS;

SENSITIVITY ANALYSIS;

ARTICLE; BIOLOGICAL MODEL; BONE; BONE MINERALIZATION; ELASTICITY; HISTOLOGY;

BONE AND BONES; CALCIFICATION, PHYSIOLOGIC; ELASTICITY; MODELS, BIOLOGICAL;

EID: 77958101171     PISSN: 16177959     EISSN: 16822978     Source Type: Journal    
DOI: 10.1007/s10237-010-0190-1     Document Type: Article

References (57)

1. U Akiva H Wagner S Weiner 1998 Modelling the three-dimensional elastic constants of parallel-fibred and lamellar bone J Mater Sci 33 6 1497 1509 10.1023/A:1004303926771
2. O Akkus 2005 Elastic deformation of mineralized collagen fibrils: an equivalent inclusion based composite model J Biomech Eng 127 3 383 390 10.1115/1.1894204
3. Y Benveniste 1987 A new approach to the application of mori-tanaka's theory in composite materials Mech Mater 6 147 157 10.1016/0167-6636(87)90005-6
4. D Birk E Zycband S Woodruff D Winkelmann R Trelstad 1997 Collagen fibrillogenesis in situ: fibril segments become long fibrils as the developing tendon matures Dev Dyn 208 3 291 298 10.1002/(SICI)1097-0177(199703)208: 3<291::AID-AJA1>3.0.CO;2-D
5. A Cribb J Scott 1995 Tendon response to tensile stress: an ultrastructural investigation of collagen:proteoglycan interactions in stressed tendon J Anat 187 Pt.2 423 428
6. J Currey 1969 The mechanical consequences of variation in the mineral content of bone J Biomech 2 1 1 11 10.1016/0021-9290(69)90036-0
7. J Currey 2004 Tensile yield in compact bone is determined by strain, post-yield behaviour by mineral content J Biomech 37 4 549 556 10.1016/j.jbiomech.2003.08.008
8. S Cusack A Miller 1979 Determination of the elastic constants of collagen by brillouin light scattering J Mol Biol 135 1 39 51 10.1016/0022-2836(79) 90339-5
9. D Ebenstein L Pruitt 2006 Nanoindentation of biological materials Nano Today 1 3 26 33 10.1016/S1748-0132(06)70077-9
10. S Eppell W Tong J Katz L Kuhn M Glimcher 2001 Shape and size of isolated bone mineralites measured using atomic force microscopy J Orthop Res 19 6 1027 1034 10.1016/S0736-0266(01)00034-1
11. J Eshelby 1957 The determination of the elastic field of an ellipsoidal inclusion, and related problems Proc R Soc Lond A Math Phys Sci 241 1226 376 396 10.1098/rspa.1957.0133 87326 0079.39606
12. G Fantner J Adams P Turner P Thurner L Fisher P Hansma 2007 Nanoscale ion mediated networks in bone: osteopontin can repeatedly dissipate large amounts of energy Nano Lett 7 8 2491 2498 10.1021/nl0712769
13. P Fratzl R Weinkamer 2007 Nature's hierarchical materials Prog Mater Sci 52 8 1263 1334 10.1016/j.pmatsci.2007.06.001
14. P Fratzl H Gupta E Paschalis P Roschger 2004 Structure and mechanical quality of the collagen-mineral nano-composite in bone J Mater Chem 14 2115 2123 10.1039/b402005g
15. A Fritsch 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 4 597 620 10.1016/j.jtbi.2006.09.013
16. A Fritsch C Hellmich L Dormieux 2009 Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: experimentally supported micromechanical explanation of bone strength J Theor Biol 260 2 230 252 10.1016/j.jtbi.2009.05.021
17. M Giraud-Guille 1988 Twisted plywood architecture of collagen fibrils in human compact bone osteons Calcif Tissue Int 42 3 167 180 10.1007/BF02556330
18. H Gupta W Wagermaier G Zickler D Raz-BenAroush S Funari P Roschger H Wagner P Fratzl 2005 Nanoscale deformation mechanisms in bone Nano Lett 5 10 2108 2111 10.1021/nl051584b
19. H Gupta J Seto W Wagermaier P Zaslansky P Boesecke P Fratzl 2006 Cooperative deformation of mineral and collagen in bone at the nanoscale Proc Natl Acad Sci USA 103 47 17,741 17,746 10.1073/pnas.0604237103
20. PK Hansma GE Fantner JH Kindt PJ Thurner G Schitter PJ Turner SF Udwin MM Finch 2005 Sacrificial bonds in the interfibrillar matrix of bone J Musculoskelet Neuronal Interact 5 4 313 315
21. C Hellmich F Ulm 2002 Micromechanical model for ultrastructural stiffness of mineralized tissues J Engrg Mech 128 8 898 908 10.1061/(ASCE)0733-9399(2002) 128:8(898)
22. C Hellmich J Barthlmy L Dormieux 2004 Mineral-collagen interactions in elasticity of bone ultrastructure-a continuum micromechanics approach Eur J Mech A/Solids 23 5 783 810 10.1016/j.euromechsol.2004.05.004 1058.74584
23. S Hengsberger A Kulik P Zysset 2002 Nanoindentation discriminates the elastic properties of individual human bone lamellae under dry and physiological conditions Bone 30 1 178 184 10.1016/S8756-3282(01)00624-X
24. S Hengsberger J Enstroem F Peyrin P Zysset 2003 How is the indentation modulus of bone tissue related to its macroscopic elastic response? a validation study Journal of Biomechanics 36 10 1503 1509 10.1016/S0021-9290(03)00131-3
25. T Hofmann F Heyroth H Meinhard W Frnzel K Raum 2006 Assessment of composition and anisotropic elastic properties of secondary osteon lamellae J Biomech 39 12 2282 2294 10.1016/j.jbiomech.2005.07.009
26. I Jaeger P Fratzl 2000 Mineralized collagen fibrils: a mechanical model with a staggered arrangement of mineral particles Biophys J 79 4 1737 1746 10.1016/S0006-3495(00)76426-5
27. B Ji H Gao 2004 Mechanical properties of nanostructure of biological materials J Mech Phys Solids 52 9 1963 1990 10.1016/j.jmps.2004.03.006 1115.74348
28. JL Katz A Meunier 1993 Scanning acoustic microscope studies of the elastic properties of osteons and osteon lamellae J Biomech Eng 115 4B 543 548 10.1115/1.2895537
29. SP Kotha S Kotha N Guzelsu 2000 A shear-lag model to account for interaction effects between inclusions in composites reinforced with rectangular platelets Compos Sci Technol 60 11 2147 2158 10.1016/S0266-3538(00)00114-7
30. W Landis F Silver 2002 The structure and function of normally mineralizing avian tendons Comp Biochem Physiol A Mol Integr Physiol 133 4 1135 1157 10.1016/S1095-6433(02)00248-9
31. S Lees 1979 A model for the distribution of hap crystallites in bonean hypothesis Calcif Tissue Int 27 1 53 56 10.1007/BF02441161
32. S Lees 1987 Considerations regarding the structure of the mammalian mineralized osteoid from viewpoint of the generalized packing model Connect Tissue Res 16 4 281 303 10.3109/03008208709005616
33. S Lees KS Prostak VK Ingle K Kjoller 1994 The loci of mineral in turkey leg tendon as seen by atomic force microscope and electron microscopy Calcif Tissue Int 55 3 180 189 10.1007/BF00425873
34. T Mori 1973 Average stress in matrix and average elastic energy of materials with misfitting inclusions Acta Met 21 5 571 574 10.1016/0001-6160(73) 90064-3
35. S Nikolov D Raabe 2008 Hierarchical modeling of the elastic properties of bone at submicron scales: the role of extrafibrillar mineralization Biophys J 94 11 4220 4232 10.1529/biophysj.107.125567
36. J Orgel T Irving A Miller T Wess 2006 Microfibrillar structure of type i collagen in situ Proc Natl Acad Sci U S A 103 24 9001 9005 10.1073/pnas. 0502718103
37. KS Prostak S Lees 1996 Visualization of crystal-matrix structure. In situ demineralization of mineralized turkey leg tendon and bone Calcif Tissue Int 59 6 474 479
38. M Raspanti T Congiu S Guizzardi 2002 Structural aspects of the extracellular matrix of the tendon : an atomic force and scanning electron microscopy study Arch Histol Cytol 65 1 37 43 10.1679/aohc.65.37
39. J Rho L Kuhn-Spearing P Zioupos 1998 Mechanical properties and the hierarchical structure of bone Med Eng Phys 20 2 92 102 10.1016/S1350-4533(98) 00007-1
40. JY Rho TY Tsui GM Pharr 1997 Elastic properties of human cortical and trabecular lamellar bone measured by nanoindentation Biomaterials 18 20 1325 1330 10.1016/S0142-9612(97)00073-2
41. J van der Rijt K van der Werf M Bennink P Dijkstra J Feijen 2006 Micromechanical testing of individual collagen fibrils Macromol Biosci 6 9 697 702 10.1002/mabi.200600063
42. R Roessle 1927 Untersuchungen ueber knochenhaerte Beitr Pathol Anat 77 174 208
43. N Sasaki S Odajima 1996 Elongation mechanism of collagen fibrils and force-strain relations of tendon at each level of structural hierarchy J Biomech 29 9 1131 1136 10.1016/0021-9290(96)00024-3
44. N Sasaki A Tagami T Goto M Taniguchi M Nakata 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 3 333 337 10.1023/A:1014079421895
45. F Silver J Freeman G Seehra 2003 Collagen self-assembly and the development of tendon mechanical properties J Biomech 36 10 1529 1553 10.1016/S0021-9290(03)00135-0
46. X Su K Sun FZ Cui WJ Landis 2003 Organization of apatite crystals in human woven bone Bone 32 2 150 162 10.1016/S8756-3282(02)00945-6
47. J Swadener G Pharr 2001 Indentation of elastically anisotropic half-spaces by cones and parabolae of revolution Philos Mag A 81 20 447 466 10.1080/01418610108214314
48. GP Tandon GJ Weng 1984 The effect of aspect ratio of inclusions on the elastic properties of unidirectionally aligned composites Pol Compos 5 4 327 333 10.1002/pc.750050413
49. W Wagermaier HS Gupta A Gourrier M Burghammer P Roschger P Fratzl 2006 Spiral twisting of fiber orientation inside bone lamellae Biointerphases 1 1 1 5 10.1116/1.2178386
50. S Weiner W Traub 1992 Bone structure: from angstroms to microns FASEB J 6 3 879 885
51. S Weiner H Wagner 1998 The material bone: structure-mechanical function relations Annu Rev Mater Sci 28 1 271 298 10.1146/annurev.matsci.28.1.271
52. S Weiner T Arad I Sabanay W Traub 1997 Rotated plywood structure of primary lamellar bone in the rat: orientations of the collagen fibril arrays Bone 20 6 509 514 10.1016/S8756-3282(97)00053-7
53. S Weiner W Traub H Wagner 1999 Lamellar bone: structure-function relations J Struct Biol 126 3 241 255 10.1006/jsbi.1999.4107
54. PJ Withers 1989 The determination of the elastic field of an ellipsoidal inclusion in a transversely isotropic medium, and its relevance to composite materials Philos Mag A 59 4 759 781 10.1080/01418618908209819
55. H Yao L Ouyang W Ching 2007 Ab initio calculation of elastic constants of ceramic crystals J Am Ceram Soc 90 10 3194 3204 10.1111/j.1551-2916.2007.01931. x
56. Y Yoon S Cowin 2008 The estimated elastic constants for a single bone osteonal lamella Biomech Model Mechanobiol 7 1 1 11 10.1007/s10237-006-0072-8
57. P Zysset X Guo C Hoffler K Moore S Goldstein 1999 Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur J Biomech 32 10 1005 1012 10.1016/S0021-9290(99)00111-6