Nature's hierarchical materials

Progress in Materials Science

Volumn 52, Issue 8, 2007, Pages 1263-1334

  Fratzl, Peter ^a   Weinkamer, Richard ^a  

^a MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

FIBER REINFORCED MATERIALS; HIERARCHICAL SYSTEMS; WOOD;

FUNCTIONAL ADAPTATION; HIERARCHICAL STRUCTURE;

BONE;

FIBERS; HIERARCHICAL SYSTEMS; WOOD;

EID: 34548501731     PISSN: 00796425     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.pmatsci.2007.06.001     Document Type: Review

References (352)

1. Aksay I.A., and Weiner S. Biomaterials - is this really a field of research?. Curr Opin Solid State Mater Sci 3 (1998) 219-220
2. Schwendener S. Das mechanische Prinzip im anatomischen Bau der Monocotylen mit vergleichenden Ausblicken auf die übrigen Pflanzenklassen (1874), Leipzig, Engelmann Verlag
3. Thompson AW. On growth and form - the complete revised edition (unaltered republication of Cambridge Univ. Press, 1942) ed. (1992), Dover Publications
4. Mattheck C., and Kubler H. The internal optimization of trees (1995), Springer Verlag, Berlin
5. Jeronimidis G. In: Elices M. (Ed). Structural biological materials, design and structure-property relationships (2000), Pergamon, Amsterdam 3-29 [chapters 1 and 2]
6. Currey J.D. Bones - structure and mechanics (2002), Princeton University Press, Princeton p. 436
7. Cowin S.Ce. Bone mechanics handbook (2001), CRC Press, Boca Raton
8. Vincent J.F.V. Structural biomaterials. revised ed. (1990), Princeton University Press, Princeton
9. Wainwright S.A., Biggs W.D., Currey J.D., and Gosline J.M. Mechanical design in organisms (1982), Princeton University Press p. 423
10. Niklas K.J. Plant biomechanics: an engineering approach to plant form and function (1992), University of Chicago Press, Chicago p. 607
11. Niklas K.J., Spatz H.C., and Vincent J. Plant biomechanics: an overview and prospectus. Am J Bot 93 (2006) 1369-1378
12. Mattheck C. Design in nature: learning from trees (1998), Springer-Verlag, Berlin, New York p. xiv, 276 p
13. Collins M.W., Hunt G.D., and Atherton M.Ae. Optimisation mechanics in Nature (2004), Wit Press, Southampton, Boston
14. Gibson L.J., and Ashby M.F. Cellular solids, structure and properties. 2nd ed. (1999), Cambridge University Press, Cambridge p. 510
15. Hull D., and Clyne T.W. An introduction to composite materials. 2nd ed. (1996), Cambridge University Press, Cambridge, UK
16. Torquato S. Random heterogeneous materials: microstructure and macroscopic properties (2002), Springer, New York p. xxi, 701 p
17. Tirrell D.A. Hierarchical structures in biology as a guide for new materials technology (1994), National Academy Press, Washington p. 130
18. Sanchez C. Biomimétisme et Matériaux (2001), OFTA, Paris
19. Sarikaya M. Biomimetics: materials fabrication through biology. Proc Natl Acad Sci USA 96 (1999) 14183-14185
20. Vincent J.F.V., Bogatyreva O.A., Bogatyrev N.R., Bowyer A., and Pahl A.-K. Biomimetics: its practice and theory. J R Soc Interface 3 (2006) 471-482
21. Vincent J.F.V., and Mann D.L. Systematic technology transfer from biology to engineering. Philos Trans R Soc London Ser A - Math Phys Eng Sci 360 (2002) 159-173
22. Fratzl P. Biomimetic materials research - what can we really learn from Nature's structural materials?. J R Soc Interface 4 (2007) 637-642
23. Lipowsky R. The physics of bio-systems. From molecules to network. Biophys Rev Lett 1 (2006) 223-230
24. Nachtigall W. Bionik - Grundlagen und Beispiele für Ingenieure und Naturwissenschaftler (1998), Springer-Verlag, Berlin p. 350
25. French M. Invention and evolution - design in Nature and engineering. 2nd ed. (1994), Cambridge University Press, Cambridge p. 367
26. Mann S. Biomineralization - principles and concepts in bioinorganic chemistry (2001), Oxford University Press p. 198
27. Ashby M.F., Gibson L.J., Wegst U., and Olive R. The mechanical-properties of natural materials. 1. Material property charts. Proc R Soc London Ser A - Math Phys Sci 450 (1995) 123-140
28. Gibson L.J., Ashby M.F., Karam G.N., Wegst U., and Shercliff H.R. The mechanical-properties of natural materials. 2. Microstructures for mechanical efficiency. Proc R Soc London Ser A - Math Phys Sci 450 (1995) 141-162
29. Wegst U.G.K., and Ashby M.F. The mechanical efficiency of natural materials. Philos Mag 84 (2004) 2167-2181
30. Mattheck C., and Bethge K. The structural optimization of trees. Naturwissenschaften 85 (1998) 1-10
31. Meyers MA, Chen, P-Y, Lin AYM, Yasuaki Seki Y. Biological Materials: structure and mechanical properties. Progr Mater Sci, this issue. doi:10.1016/j.pmatsci.2007.05.002.
32. Fengel D., and Wegener G. Wood: chemistry, ultrastructure, reactions (1989), de Gruyter, Berlin
33. Fratzl P. Cellulose and collagen: from fibres to tissues. Curr Opin Colloid Interface Sci 8 (2003) 32-39
34. Lichtenegger H., Muller M., Paris O., Riekel C., and Fratzl P. Imaging of the helical arrangement of cellulose fibrils in wood by synchrotron X-ray microdiffraction. J Appl Crystallogr 32 (1999) 1127-1133
35. Fahlen J., and Salmen L. On the lamellar structure of the tracheid cell wall. Plant Biol 4 (2002) 339-345
36. Fahlen J., and Salmen L. Pore and matrix distribution in the fiber wall revealed by atomic force microscopy and image analysis. Biomacromolecules 6 (2005) 433-438
37. Lichtenegger H, Reiterer A, Tschegg SE, Müller M, Riekel C, Paris O, et al. In: Spatz HC, Speck T, Thieme G, editors. Microfibril angle determined by X-ray scattering and the correlation with the mechanical properties of wood. Plant Biomechanics 2000, Stuttgart, 2000.
38. Jakob H.F., Fratzl P., and Tschegg S.E. Size and arrangement of elementary cellulose fibrils in wood cells - a small-angle X-ray-scattering study of Picea abies. J Struct Biol 113 (1994) 13-22
39. Jakob H.F., Fengel D., Tschegg S.E., and Fratzl P. The elementary cellulose fibril in Picea abies: comparison of transmission electron microscopy, small-angle X-ray scattering, and wide-angle X-ray scattering results. Macromolecules 28 (1995) 8782-8787
40. Zimmermann T., Thommen V., Reimann P., and Hug H. Ultrastructural appearance of embedded and polished wood cell walls as revealed by atomic force microscopy. J Struct Biol 156 (2006) 363-369
41. Jakob H.F., Tschegg S.E., and Fratzl P. Hydration dependence of the wood-cell wall structure in Picea abies. A small-angle X-ray scattering study. Macromolecules 29 (1996) 8435-8440
42. Fratzl P., Jakob H.F., Rinnerthaler S., Roschger P., and Klaushofer K. Position-resolved small-angle X-ray scattering of complex biological materials. J Appl Crystallogr 30 (1997) 765-769
43. Bergander A., and Salmen L. Variations in transverse fibre wall properties: relations between elastic properties and structure. Holzforschung 54 (2000) 654-660
44. Bergander A., and Salmen L. Cell wall properties and their effects on the mechanical properties of fibers. J Mater Sci 37 (2002) 151-156
45. Keckes J., Burgert I., Fruhmann K., Muller M., Kolln K., Hamilton M., et al. Cell-wall recovery after irreversible deformation of wood. Nat Mater 2 (2003) 810-814
46. Weiner S., and Wagner H.D. The material bone: structure mechanical function relations. Ann Rev Mater Sci 28 (1998) 271-298
47. Rho J.Y., Kuhn-Spearing L., and Zioupos P. Mechanical properties and the hierarchical structure of bone. Med Eng Phys 20 (1998) 92-102
48. Fratzl P., Gupta H.S., Paschalis E.P., and Roschger P. Structure and mechanical quality of the collagen-mineral nano-composite in bone. J Mater Chem 14 (2004) 2115-2123
49. Roschger P., Fratzl P., Eschberger J., and Klaushofer K. Validation of quantitative backscattered electron imaging for the measurement of mineral density distribution in human bone biopsies. Bone 23 (1998) 319-326
50. Roschger P., Gupta H.S., Berzanovich A., Ittner G., Dempster D.W., Fratzl P., et al. Constant mineralization density distribution in cancellous human bone. Bone 32 (2003) 316-323
51. Weiner S., Arad T., Sabanay I., and Traub W. Rotated plywood structure of primary lamellar bone in the rat: orientations of the collagen fibril arrays. Bone 20 (1997) 509-514
52. Weiner S., Traub W., and Wagner H.D. Lamellar bone: structure-function relations. J Struct Biol 126 (1999) 241-255
53. Ascenzi A., Bonucci E., Generali P., Ripamonti A., and Roveri N. Orientation of apatite in single osteon samples as studied by pole figures. Calcified Tissue Int 29 (1979) 101-105
54. Rho J.Y., Zioupos P., Currey J.D., and Pharr G.M. Variations in the individual thick lamellar properties within osteons by nanoindentation. Bone 25 (1999) 295-300
55. Martin R., Farjanel J., Eichenberger D., Colige A., Kessler E., Hulmes D.J.S., et al. Liquid crystalline ordering of procollagen as a determinant of three-dimensional extracellular matrix architecture. J Mol Biol 301 (2000) 11-17
56. Hulmes D.J.S. Building collagen molecules, fibrils, and suprafibrillar structures. J Struct Biol 137 (2002) 2-10
57. Giraud-Guille M.M. Twisted plywood architecture of collagen fibrils in human compact-bone osteons. Calcified Tissue Int 42 (1988) 167-180
58. Bigi A., Burghammer M., Falconi R., Koch M.H.J., Panzavolta S., and Riekel C. Twisted plywood pattern of collagen fibrils in teleost scales: an X-ray diffraction investigation. J Struct Biol 136 (2001) 137-143
59. Jaschouz D., Paris O., Roschger P., Hwang H.S., and Fratzl P. Pole figure analysis of mineral nanoparticle orientation in individual trabecula of human vertebral bone. J Appl Crystallogr 36 (2003) 494-498
60. Rinnerthaler S., Roschger P., Jakob H.F., Nader A., Klaushofer K., and Fratzl P. Scanning small angle X-ray scattering analysis of human bone sections. Calcified Tissue Int 64 (1999) 422-429
61. Camacho N.P., Rinnerthaler S., Paschalis E.P., Mendelsohn R., Boskey A.L., and Fratzl P. Complementary information on bone ultrastructure from scanning small angle X-ray scattering and Fourier-transform infrared microspectroscopy. Bone 25 (1999) 287-293
62. Roschger P., Grabner B.M., Rinnerthaler S., Tesch W., Kneissel M., Berzlanovich A., et al. Structural development of the mineralized tissue in the human L4 vertebral body. J Struct Biol 136 (2001) 126-136
63. Termine J.D., and Robey P.G. Bone matrix proteins and the mineralization process. In: Favus M.J. (Ed). Primer on the metabolic bone diseases and disorders of mineral metabolism. 3rd ed. (1996), An Official Publication of the American Society for Bone and Mineral Research, Lippincott-Raven Publishers
64. Hodge A.J., and Petruska J.A. Aspects of protein structure. In: Ramachandran G.N. (Ed) (1963), Academic Press, New York 289-300
65. Landis W.J., Hodgens K.J., Arena J., Song M.J., and McEwen B.F. Structural relations between collagen and mineral in bone as determined by high voltage electron microscopic tomography. Microsc Res Tech 33 (1996) 192-202
66. White S.W., Hulmes D.J.S., Miller A., and Timmins P.A. Collagen-mineral axial relationship in calcified Turkey leg tendon by X-ray and neutron-diffraction. Nature 266 (1977) 421-425
67. Landis W.J. Mineral characterization in calcifying tissues: atomic, molecular and macromolecular perspectives. Connect Tissue Res 35 (1996) 1-8
68. Hassenkam T., Fantner G.E., Cutroni J.A., Weaver J.C., Morse D.E., and Hansma P.K. High-resolution AFM imaging of intact and fractured trabecular bone. Bone 35 (2004) 4-10
69. Sodek J., Ganss B., and McKee M.D. Osteopontin. Crit Rev Oral Biol Med 11 (2000) 279-303
70. Landis W.J., Hodgens K.J., Song M.J., Arena J., Kiyonaga S., Marko M., et al. Mineralization of collagen may occur on fibril surfaces: evidence from conventional and high-voltage electron microscopy and three-dimensional imaging. J Struct Biol 117 (1996) 24
71. Traub W., Arad T., and Weiner S. Origin of mineral crystal-growth in collagen fibrils. Matrix 12 (1992) 251-255
72. Fratzl P., Fratzl-Zelman N., Klaushofer K., Vogl G., and Koller K. Nucleation and growth of mineral crystals in bone studied by small-angle X-ray-scattering. Calcified Tissue Int 48 (1991) 407-413
73. Glimcher M.J. Recent studies of the mineral phase in bone and its possible linkage to the organic matrix by protein-bound phosphate bonds. Philos Trans R Soc London Ser B - Biol Sci 304 (1984) 479-508
74. Grynpas M., Bonar L.C., and Glimcher M.J. X-ray diffraction radial distribution function studies on bone mineral and synthetic calcium phosphates. J Mater Sci (1985) 19
75. Posner A.S. The mineral of bone. Clinal Orthopaedics and Related Research 200 (1985) 87-98
76. Rubin M.A., Rubin J., and Jasiuk W. SEM and TEM study of the hierarchical structure of C57BL/6J and C3H/HeJ mice trabecular bone. Bone 35 (2004) 11-20
77. Fratzl P., Groschner M., Vogl G., Plenk H., Eschberger J., Fratzl-Zelman N., et al. Mineral crystals in calcified tissues - a comparative-study by SAXS. J Bone Min Res 7 (1992) 329-334
78. Weiner S., and Traub W. Bone-structure - from angstroms to microns. FASEB J 6 (1992) 879-885
79. Fratzl P., Fratzl-Zelman N., and Klaushofer K. Collagen packing and mineralization - an X-ray-scattering investigation of Turkey leg tendon. Biophys J 64 (1993) 260-266
80. Fratzl P. Small-angle scattering in materials science: a short review of applications in alloys, ceramics and composite materials. J Appl Crystallogr 36 (2003) 397-404
81. Paris O., Zizak I., Lichtenegger H., Roschger P., Klaushofer K., and Fratzl P. Analysis of the hierarchical structure of biological tissues by scanning X-ray scattering using a micro-beam. Cell Mol Biol 46 (2000) 993-1004
82. Fantner G.E., Hassenkam T., Kindt J.H., Weaver J.C., Birkedal H., Pechenik L., et al. Sacrificial bonds and hidden length dissipate energy as mineralized fibrils separate during bone fracture. Nat Mater 4 (2005) 612-616
83. Landis W.J., Song M.J., Leith A., Mcewen L., and Mcewen B.F. Mineral and organic matrix interaction in normally calcifying tendon visualized in 3 dimensions by high-voltage electron-microscopic tomography and graphic image-reconstruction. J Struct Biol 110 (1993) 39-54
84. Lees S., and Mook H.A. Equatorial diffraction spacing as a function of water-content in fully mineralized cow bone determined by neutron-diffraction. Calcified Tissue Int 39 (1986) 291-292
85. Canty E.G., and Kadler K.E. Collagen fibril biosynthesis in tendon: a review and recent insights. Comp Biochem Physiol A - Mol Integr Physiol 133 (2002) 979-985
86. Kadler K.E., Holmes D.F.T., and Chapman J.A. Collagen fibril formation. Biochem J 316 (1996) 1-11
87. Veis A. Collagen fibrillar structure in mineralized and nonmineralized tissues. Curr Opin Solid State Mater Sci 2 (1997) 370-378
88. Wess T.J. Collagen fibrillar form and function. In: Parry D., and Squire J. (Eds). Fibrous proteins: coiled-coils, collagen and elastomers vol. 70 (2005), Elsevier Inc., Burlington 341-374
89. Knott L., and Bailey A.J. Collagen cross-links in mineralizing tissues: a review of their chemistry, function, and clinical relevance. Bone 22 (1998) 181-187
90. Prockop D.J., and Kivirikko K.I. Heritable diseases of collagen. N Engl J Med 311 (1984) 376-396
91. Yamauchi M. Collagen: the major matrix molecule in mineralized tissues. In: Anderson J.J.B., and Garner S.C. (Eds). Calcium Phosphorus Health Dis (1996), CRC Press, New York 127-141
92. Prockop D.J., and Kivirikko K.I. Collagens: molecular biology, diseases, and potentials for therapy [review]. Ann Rev Biochem 64 (1995) 403-434
93. Levi C., Barton J.L., Guillemet C., Le Bras E., and Lehuede P. A remarkably strong natural glassy rod: the anchoring spicule of the Monorhaphis sponge. J Mater Sci Lett 8 (1989) 337-339
94. Hamm C.E., Merkel R., Springer O., Jurkojc P., Maier C., Prechtel K., et al. Architecture and material properties of diatom shells provide effective mechanical protection. Nature 421 (2003) 841-843
95. Sarikaya M., Fong H., Sunderland N., Flinn B.D., Mayer G., Mescher A., et al. Biomimetic model of a sponge-spicular optical fiber - mechanical properties and structure. J Mater Res 16 (2001) 1420-1428
96. Woesz A., Weaver J.C., Kazanci M., Dauphin Y., Aizenberg J., Morse D.E., et al. Micromechanical properties of biological silica in skeletons of deep-sea sponges. J Mater Res 21 (2006) 2068-2078
97. Aizenberg J., Weaver J.C., Thanawala M.S., Sundar V.C., Morse D.E., and Fratzl P. Skeleton of Euplectella sp.: structural hierarchy from the nanoscale to the macroscale. Science 309 (2005) 275-278
98. Aizenberg J., Sundar V.C., Yablon A.D., Weaver J.C., and Chen G. Biological glass fibers: correlation between optical and structural properties. Proc Natl Acad Sci USA 101 (2004) 3358-3363
99. Sundar V.C., Yablon A.D., Grazul J.L., Ilan M., and Aizenberg J. Fibre-optical features of a glass sponge - some superior technological secrets have come to light from a deep-sea organism. Nature 424 (2003) 899-900
100. Saito T., Uchida I., and Takeda M. Skeletal growth of the deep-sea hexactinellid sponge Euplectella oweni, and host selection by the symbiotic shrimp Spongicola japonica (Crustacea:Decapoda:Spongicolidae). J Zool 258 (2002) 521-529
101. Weaver J.C., Aizenberg J., Fantner G.E., Kisailus D., Woesz A., Allen P., et al. Hierarchical assembly of the siliceous skeletal lattice of the Hexactinellid Sponge Euplactella aspergillum. J Struct Biol 158 (2007) 93-106
102. Heaney R.P. Is the paradigm shifting?. Bone 33 (2003) 457-465
103. Woesz A., Stampfl J., and Fratzl P. Cellular solids beyond the apparent density - an experimental assessment of mechanical properties. Adv Eng Mater 6 (2004) 134-138
104. Banhart J. Aluminum foams: on the road to real applications. Mrs Bull 28 (2003) 290-295
105. Green D.J., and Colombo R. Cellular ceramics: intriguing structures, novel properties, and innovative applications. Mrs Bull 28 (2003) 296-300
106. Roberts A.P., and Garboczi E.J. Elastic properties of model random three-dimensional open-cell solids. J Mech Phys Solids 50 (2002) 33-55
107. Huiskes R. If bone is the answer, then what is the question?. J Anat 197 (2000) 145-156
108. Cowin S.C. The false premise of Wolff's law. Forma 12 (1997) 247-262
109. Thurner P.J., Wyss P., Voide R., Stauber M., Stampanoni M., Sennhauser U., et al. Time-lapsed investigation of three-dimensional failure and damage accumulation in trabecular bone using synchrotron light. Bone 39 (2006) 289-299
110. Homminga J., Van-Rietbergen B., Lochmuller E.M., Weinans H., Eckstein F., and Huiskes R. The osteoporotic vertebral structure is well adapted to the loads of daily life, but not to infrequent "error" loads. Bone 34 (2004) 510-516
111. Gibson L.J. Biomechanics of cellular solids. J Biomech 38 (2005) 377-399
112. Greenhill G. Determination of the greatest height consistent with stability that a vertical pole or mast can be made, and the greatest height to which a tree of given proportions can grow. Proc Cambridge Philos Soc 4 (1881) 65-73
113. McMahon T. Size and shape in biology. Science 179 (1973) 1201-1204
114. Landau L.D., and Lifshitz E.M. Theory of elasticity. 3rd English ed. (1986), Butterworth-Heinemann p. viii, 187 p
115. Ashby M.F. The mechanical-properties of cellular solids. Metall Trans A - Phys Metall Mater Sci 14 (1983) 1755-1769
116. Lichtenegger H., Reiterer A., Stanzl-Tschegg S.E., and Fratzl P. Variation of cellulose microfibril angles in softwoods and hardwoods - a possible strategy of mechanical optimization. J Struct Biol 128 (1999) 257-269
117. Ashby M.F. Materials selection in mechanical design. 2nd ed. (1999), Butterworth-Heinemann, Oxford
118. Morgan E.F., Yeh O.C., Chang W.C., and Keaveny T.W. Nonlinear behavior of trabecular bone at small strains. J Biomech Eng - Trans ASME 123 (2001) 1-9
119. van Rietbergen B., and Huiskes R. Elastic constants of cancellous bone. In: Cowin S.C. (Ed). Bone mechanics handbook (2001), CRC Press, Boca Raton
120. van Lenthe G.H., Stauber M., and Muller R. Specimen-specific beam models for fast and accurate prediction of human trabecular bone mechanical properties. Bone 39 (2006) 1182-1189
121. Harrigan T.P., Jasty M., Mann R.W., and Harris W.H. Limitations of the continuum assumption in cancellous bone. J Biomech 21 (1988) 269-275
122. Yang G.Y., Kabel J., Van Rietbergen B., Odgaard A., Huiskes R., and Cowin S.C. The anisotropic Hooke's law for cancellous bone and wood. J Elasticity 53 (1999) 125-146
123. Morgan E.F., Bayraktar H.H., and Keaveny T.M. Trabecular bone modulus-density relationships depend on anatomic site. J Biomech 36 (2003) 897-904
124. Odgaard A. Three-dimensional methods for quantification of cancellous bone architecture. Bone 20 (1997) 315-328
125. Odgaard A. Quantification of cancellous bone architecture. In: Cowin S.C. (Ed). Bone mechanics handbook (2001), CRC Press, Boca Raton
126. Odgaard A., Kabel J., vanRietbergen B., Dalstra M., and Huiskes R. Fabric and elastic principal directions of cancellous bone are closely related. J Biomech 30 (1997) 487-495
127. Cowin S.C. The relationship between the elasticity tensor and the fabric tensor. Mech Mater 4 (1985) 137-147
128. Zysset P.K. A review of morphology-elasticity relationships in human trabecular bone: theories and experiments. J Biomech 36 (2003) 1469-1485
129. Kinney J.H., and Ladd A.J.C. The relationship between three-dimensional connectivity and the elastic properties of trabecular bone. J Bone Min Res 13 (1998) 839-845
130. Kabel J., Odgaard A., van Rietbergen B., and Huiskes R. Connectivity and the elastic properties of cancellous bone. Bone 24 (1999) 115-120
131. Deshpande V.S., Ashby M.F., and Fleck N.A. Foam topology bending versus stretching dominated architectures. Acta Mater 49 (2001) 1035-1040
132. Fyhrie D.P., and Schaffler M.B. Failure mechanisms in human vertebral cancellous bone. Bone 15 (1994) 105-109
133. Keaveny T.M. Strength of trabecular bone. In: Cowin S.C. (Ed). Bone mechanics handbook (2001), CRC Press, Boca Raton
134. Mosekilde L., Mosekilde L., and Danielsen C.C. Biomechanical competence of vertebral trabecular bone in relation to ash density and age in normal individuals. Bone 8 (1987) 79-85
135. Hernandez C.J., and Keaveny T.M. A biomechanical perspective on bone quality. Bone 39 (2006) 1173-1181
136. Nazarian A., and Muller R. Time-lapsed microstructural imaging of bone failure behavior. J Biomech 37 (2004) 55-65
137. Kopperdahl D.L., and Keaveny T.M. Yield strain behavior of trabecular bone. J Biomech 31 (1998) 601-608
138. Keaveny T.M., Morgan E.F., Niebur G.L., and Yeh O.C. Biomechanics of trabecular bone. Ann Rev Biomed Eng 3 (2001) 307-333
139. Bayraktar H.H., and Keaveny T.M. Mechanisms of uniformity of yield strains for trabecular bone. J Biomech 37 (2004) 1671-1678
140. Silva M.J., and Gibson L.J. Modeling the mechanical behavior of vertebral trabecular bone: effects of age-related changes in microstructure. Bone 21 (1997) 191-199
141. Vajjhala S., Kraynik A.M., and Gibson L.J. A cellular solid model for modulus reduction due to resorption of trabeculae in bone. J Biomech Eng - Trans ASME 122 (2000) 511-515
142. Guo X.E., and Kim C.H. Mechanical consequence of trabecular bone loss and its treatment: a three-dimensional model simulation. Bone 30 (2002) 404-411
143. Davy D.T., and Jepsen K.J. Bone damage mechanics. In: Cowin S.C. (Ed). Bone mechanics handbook (2001), CRC Press, Boca Raton
144. Zysset P.K., and Curnier A. A 3D damage model for trabecular bone based on fabric tensors. J Biomech 29 (1996) 1549-1558
145. Wachtel E.F., and Keaveny T.M. Dependence of trabecular damage on mechanical strain. J Orthopaed Res 15 (1997) 781-787
146. Sahar N.D., Hong S.I., and Kohn D.H. Micro- and nano-structural analyses of damage in bone. Micron 36 (2005) 617-629
147. Lee T.C., Mohsin S., Taylor D., Parkesh R., Gunnlaugsson T., O'Brien F.J., et al. Detecting microdamage in bone. J Anat 203 (2003) 161-172
148. Haddock S.M., Yeh O.C., Mummaneni P.V., Rosenberg W.S., and Keaveny T.M. Similarity in the fatigue behavior of trabecular bone across site and species. J Biomech 37 (2004) 181-187
149. Haddock S.M., Yeh O.C., Mummaneni P.V., Rosenberg W.S., and Keaveny T.M. Similarity in the fatigue behavior of trabecular bone across site and species (vol. 37, p. 181, 2004). J Biomech 39 (2006) 593
150. Rapillard L., Charlebois M., and Zysset P.K. Compressive fatigue behavior of human vertebral trabecular bone. J Biomech 39 (2006) 2133-2139
151. Vollrath F., and Knight D.P. Liquid crystalline spinning of spider silk. Nature 410 (2001) 541-548
152. Gosline J.M., Demont M.E., and Denny M.W. The structure and properties of spider silk. Endeavour 10 (1986) 37-43
153. Landis W.J. A study of calcification in the leg tendons from the domestic Turkey. J Ultrastruct Mol Struct Res 94 (1986) 217-238
154. Landis W.J., and Silver F.H. The structure and function of normally mineralizing avian tendons. Comp Biochem Physiol A - Mol Integr Physiol 133 (2002) 1135-1157
155. Gupta H.S., Roschger P., Zizak I., Fratzl-Zelman N., Nader A., Klaushofer K., et al. Mineralized microstructure of calcified avian tendons: a scanning small angle X-ray scattering study. Calcified Tissue Int 72 (2003) 567-576
156. Gupta H.S., Messmer P., Roschger P., Bernstorff S., Klaushofer K., and Fratzl P. Synchrotron diffraction study of deformation mechanisms in mineralized tendon. Phys Rev Lett 93 (2004) 158101
157. Hulmes D.J.S., Wess T.J., Prockop D.J., and Fratzl P. Radial packing, order, and disorder in collagen fibrils. Biophys J 68 (1995) 1661-1670
158. Orgel J., Miller A., Irving T.C., Fischetti R.F., Hammersley A.P., and Wess T.J. The in situ supermolecular structure of type I collagen. Structure 9 (2001) 1061-1069
159. Ottani V., Raspanti M., and Ruggeri A. Collagen structure and functional implications. Micron 32 (2001) 251-260
160. Baer E., Cassidy J.J., and Hiltner A. Hierarchical structure of collagen composite systems - lessons from biology. Pure Appl Chem 63 (1991) 961-973
161. Baer E., Hiltner A., and Jarus D. Relationship of hierarchical structure to mechanical properties. Macromol Symp 147 (1999) 37-61
162. Diamant J., Arridge R.G.C., Baer E., Litt M., and Keller A. Collagen - ultrastructure and its relation to mechanical properties as a function of aging. Proc R Soc London Ser B - Biol Sci 180 (1972) 293
163. Misof K., Rapp G., and Fratzl P. A new molecular model for collagen elasticity based on synchrotron X-ray scattering evidence. Biophys J 72 (1997) 1376-1381
164. Folkhard W., Geercken W., Knorzer E., Mosler E., Nemetschekgansler H., Nemetschek T., et al. Structural dynamic of native tendon collagen. J Mol Biol 193 (1987) 405-407
165. Folkhard W., Mosler E., Geercken W., Knorzer E., Nemetschekgansler H., Nemetschek T., et al. Quantitative-analysis of the molecular sliding mechanism in native tendon collagen - time-resolved dynamic studies using synchrotron radiation. Int J Biol Macromol 9 (1987) 169-175
166. Fratzl P., Misof K., Zizak I., Rapp G., Amenitsch H., and Bernstorff S. Fibrillar structure and mechanical properties of collagen. J Struct Biol 122 (1998) 119-122
167. Mosler E., Folkhard W., Knorzer E., Nemetschekgansler H., Nemetschek T., and Koch M.H.J. Stress-induced molecular rearrangement in tendon collagen. J Mol Biol 182 (1985) 589-596
168. Sasaki N., and Odajima S. Elongation mechanism of collagen fibrils and force-strain relations of tendon at each level of structural hierarchy. J Biomech 29 (1996) 1131-1136
169. Sasaki N., and Odajima S. Stress-strain curve and Young's modulus of a collagen molecule as determined by the X-ray diffraction technique. J Biomech 29 (1996) 655-658
170. Sasaki N., Shukunami N., Matsushima N., and Izumi Y. Time-resolved X-ray diffraction from tendon collagen during creep using synchrotron radiation. J Biomech 32 (1999) 285-292
171. Puxkandl R., Zizak I., Paris O., Keckes J., Tesch W., Bernstorff S., et al. Viscoelastic properties of collagen: synchrotron radiation investigations and structural model. Philos Trans R Soc London Ser B - Biol Sci 357 (2002) 191-197
172. Cribb A.M., and Scott J.E. Tendon response to tensile-stress - an ultrastructural investigation of collagen-proteoglycan interactions in stressed tendon. J Anat 187 (1995) 423-428
173. Light N.D., and Bailey A.J. Covalent cross-links in collagen. Methods Enzymol 82A (1982) 360-372
174. Bailey A.J., Paul R.G., and Knott L. Mechanisms of maturation and ageing of collagen. Mech Ageing Dev 106 (1998) 1-56
175. Davison P.F. The contribution of labile crosslinks to the tensile behavior of tendons. Connect Tissue Res 18 (1989) 293-305
176. Eyre D.R., Paz M.A., and Gallop P.M. Cross-linking in collagen and elastin. Ann Rev Biochem 53 (1984) 717-748
177. Lees S., Eyre D.R., and Barnard S.M. BAPN dose dependence of mature crosslinking in bone matrix collagen of rabbit compact bone: corresponding variation of sonic velocity and equatorial diffraction spacing. Connect Tissue Res 24 (1990) 95-105
178. Kastelic J., Galeski A., and Baer E. Multicomposite structure of tendon. Connect Tissue Res 6 (1978) 11-23
179. Buehler M.J. Nature designs tough collagen: explaining the nanostructure of collagen fibrils. Proc Natl Acad Sci USA 103 (2006) 12285-12290
180. Bozec L., and Horton M. Topography and mechanical properties of single molecules of type I collagen using atomic force microscopy. Biophys J 88 (2005) 4223-4231
181. Bozec L., van der Heijden G., and Horton M. Collagen fibrils: nanoscale ropes. Biophys J 92 (2007) 70-75
182. Sun Y.L., Luo Z.P., Fertala A., and An K.N. Direct quantification of the flexibility of type I collagen monomer. Biochem Biophys Res Commun 295 (2002) 382-386
183. Bustamante C., Marko J.F., Siggia E.D., and Smith S. Entropic elasticity of lambda-phage DNA. Science 265 (1994) 1599-1600
184. Buehler M.J. Atomistic and continuum modeling of mechanical properties of collagen: elasticity, fracture, and self-assembly. J Mater Res 21 (2006) 1947-1961
185. Fratzl P., and Gupta H.S. Nanoscale mechanisms of bone deformation and fracture. In: Bäuerlein E. (Ed). Handbook of biomineralization vol. 1 (2007), Wiley-VCH Verlag GmbH, Weinheim 397-414
186. Gebhardt W. Regarding the functionally important assembly techniques of the small scale and large scale building blocks of the vertebral bone II: special part: the building of the Haversian lamellar system and its functional meaning. Arch Entwickl Mech Org 20 (1906) 187-322
187. Boyde A., Bianco P., Barbos M.P., and Ascenzi A. Collagen orientation in compact-bone. 1. A new method for the determination of the proportion of collagen parallel to the plane of compact-bone sections. Metab Bone Dis Relat Res 5 (1984) 299-307
188. Barbos M.P., Bianco P., Ascenzi A., and Boyde A. Collagen orientation in compact-bone. 2. Distribution of lamellae in the whole of the human femoral-shaft with reference to its mechanical-properties. Metab Bone Dis Relat Res 5 (1984) 309-315
189. Ascenzi A., Bonucci E., and Bocciare Ds. An electron microscope study of osteon calcification. J Ultrastruct Res 12 (1965) 287
190. Marotti G., Muglia M.A., and Palumbo C. Structure and function of lamellar bone. Clin Rheumatol 13 (1994) 63-68
191. Wagermaier W., Gupta H.S., Gourrier A., Burghammer M., Roschger P., and Fratzl P. Spiral twisting of fiber orientation inside bone lamellae. Biointerphases 1 (2006) 1-5
192. Wagermaier W., Gupta H.S., Gourrier A., Paris O., Roschger P., Burghammer M., et al. Scanning texture analysis of lamellar bone using microbeam synchrotron X-ray radiation. J Appl Crystallogr 40 (2007) 115-120
193. Neville A.C. Biology of fibrous composites: development beyond the cell membrane (1993), Cambridge University Press, New York, NY
194. Zioupos P. On microcracks, microcracking, in vivo, in vitro, in situ and other issues. J Biomech 32 (1999) 209-211
195. Gupta H.S., Stachewicz U., Wagermaier W., Roschger P., Wagner H.D., and Fratzl P. Mechanical modulation at the lamellar level in osteonal bone. J Mater Res 21 (2006) 1913-1921
196. Qiu S.J., Rao D.S., Fyhrie D.P., Palnitkar S., and Parfitt A.M. The morphological association between microcracks and osteocyte lacunae in human cortical bone. Bone 37 (2005) 10-15
197. Suresh S., Sugimura Y., and Ogawa T. Fatigue cracking in materials with brittle surface-coatings. Scripta Metall Mater 29 (1993) 237-242
198. Simha N.K., Fischer F.D., Kolednik O., and Chen C.R. Inhomogeneity effects on the crack driving force in elastic and elastic-plastic materials. J Mech Phys Solids 51 (2003) 209-240
199. Kolednik O. The yield stress gradient effect in inhomogeneous materials. Int J Solids Struct 37 (2000) 781-808
200. Reiterer A., Lichtenegger H., Fratzl P., and Stanzl-Tschegg S.E. Deformation and energy absorption of wood cell walls with different nanostructure under tensile loading. J Mater Sci 36 (2001) 4681-4686
201. Reiterer A., Lichtenegger H., Tschegg S., and Fratzl P. Experimental evidence for a mechanical function of the cellulose microfibril angle in wood cell walls. Philos Mag A - Phys Condens Matter Struct Defects Mech Prop 79 (1999) 2173-2184
202. Wimmer R., Downes G.M., and Evans R. Temporal variation of microfibril angle in Eucalyptus nitens grown in different irrigation regimes (vol. 22, p. 449, 2002). Tree Physiol 22 (2002) 817
203. Lindstrom H., Evans J.W., and Verrill S.P. Influence of cambial age and growth conditions on microfibril angle in young Norway spruce (Picea abies [L.] Karst.). Holzforschung 52 (1998) 573-581
204. Evans R., Stringer S., and Kibblewhite R.P. Variation of microfibril angle, density and fibre orientation in twenty-nine Eucalyptus nitens trees. Appita J 53 (2000) 450-457
205. Kibblewhite R.P., Evans R., Riddell M.J.C., and Shelbourne C.J.A. Changes in density and wood-fibre properties with height position in 15/16-year-old Eucalyptus nitens and E-fastigata. Appita J 57 (2004) 240-247
206. Kibblewhite R.P., Evans R., Grace J.C., and Riddell M.J.C. Fibre length, microfibril angle and wood colour variation and interrelationships for two radiata pine trees with mild and severe compression wood. Appita J 58 (2005) 316-322
207. Bonham V.A., and Barnett J.R. Fibre length and microfibril angle in silver birch (Betula pendula Roth). Holzforschung 55 (2001) 159-162
208. Mosbrugger V. The tree habit in land plants: a functional comparison of trunk constructions with a brief introduction into the biomechanics of trees (1990), Springer-Verlag, Berlin, New York p. 161
209. Astley O.M., and Donald A.M. A small-angle X-ray scattering study of the effect of hydration on the microstructure of flax fibers. Biomacromolecules 2 (2001) 672-680
210. Yamamoto H., and Kojima Y. Properties of cell wall constituents in relation to longitudinal elasticity of wood - Part 1. Formulation of the longitudinal elasticity of an isolated wood fiber. Wood Sci Technol 36 (2002) 55-74
211. Yamamoto H., Kojima Y., Okuyama T., Abasolo W.P., and Gril J. Origin of the biomechanical properties of wood related to the fine structure of the multi-layered cell wall. J Biomech Eng - Trans ASME 124 (2002) 432-440
212. Yamamoto H., Yoshida M., and Okuyama T. Growth stress controls negative gravitropism in woody plant stems. Planta 216 (2002) 280-292
213. Brown R.M. Cellulose structure and biosynthesis. Pure Appl Chem 71 (1999) 767-775
214. Ferl R., Wheeler R., Levine H.G., and Paul A.L. Plants in space. Curr Opin Plant Biol 5 (2002) 258-263
215. Brett CT. Cellulose microfibrils in plants: biosynthesis, deposition, and integration into the cell wall. In: International review of cytology - a survey of cell biology, vol. 199, 2000; vol. 199, p. 161-99.
216. Kimura S., and Kondo T. Recent progress in cellulose biosynthesis. J Plant Res 115 (2002) 297-302
217. Nishiyama Y., Langan P., and Chanzy H. Crystal structure and hydrogen-bonding system in cellulose 1 beta from synchrotron X-ray and neutron fiber diffraction. J Am Chem Soc 124 (2002) 9074-9082
218. Baker A.A., Helbert W., Sugiyama J., and Miles M.J. New insight into cellulose structure by atomic force microscopy shows the I-alpha crystal phase at near-atomic resolution. Biophys J 79 (2000) 1139-1145
219. Kondo T., Togawa E., and Brown R.M. Nematic ordered cellulose: a concept of glucan chain association. Biomacromolecules 2 (2001) 1324-1330
220. Somerville C., Bauer S., Brininstool G., Facette M., Hamann T., Milne J., et al. Toward a systems approach to understanding plant-cell walls. Science 306 (2004) 2206-2211
221. Baskin T.I. On the alignment of cellulose microfibrils by cortical microtubules: a review and a model. Protoplasma 215 (2001) 150-171
222. Funada R., Miura H., Shibagaki M., Furusawa O., Miura T., Fukatsu E., et al. Involvement of localized cortical microtubules in the formation of a modified structure of wood. J Plant Res 114 (2001) 491-497
223. Paredez A.R., Somerville C.R., and Ehrhardt D.W. Visualization of cellulose synthase demonstrates functional association with microtubules. Science 312 (2006) 1491-1495
224. Emons A.M.C., and Mulder B.M. How the deposition of cellulose microfibrils builds cell wall architecture. Trends Plant Sci 5 (2000) 35-40
225. Gassan J., Chate A., and Bledzki A.K. Calculation of elastic properties of natural fibers. J Mater Sci 36 (2001) 3715-3720
226. Spatz H.C., Köhler L., and Niklas K.J. Mechanical behaviour of plant tissues: composite materials or structures?. J Exp Biol 202 (1999) 3269-3272
227. Köhler L., and Spatz H.C. Micromechanics of plant tissues beyond the linear-elastic range. Planta 215 (2002) 33-40
228. Burgert I., Keckes J., Fruhmann K., Fratzl P., and Tschegg S.E. A comparison of two techniques for wood fibre isolation evaluation by tensile tests on single fibres with different microfibril angle. Plant Biol 4 (2002) 9-12
229. Fratzl P. Hierarchical structure and mechanical adaptation of biological materials. In: Reis R.L., and Weiner S. (Eds). Learning from Nature - how to design new implantable biomaterials. NATO science series - II vol. 171 (2004), Kluwer Academic Publishers. 15-34
230. Fratzl P., Burgert I., and Keckes J. Mechanical model for the deformation of the wood cell wall. Z Metallkd 95 (2004) 579-584
231. Fratzl P., Burgert I., and Gupta H.S. On the role of interface polymers for the mechanics of natural polymeric composites. Phys Chem Chem Phys 6 (2004) 5575-5579
232. Currey J.D. The design of mineralised hard tissues for their mechanical functions. J Exp Biol 202 (1999) 3285-3294
233. Currey J.D. How well are bones designed to resist fracture?. J Bone Min Res 18 (2003) 591-598
234. Peterlik H., Roschger P., Klaushofer K., and Fratzl P. From brittle to ductile fracture of bone. Nat Mater 5 (2006) 52-55
235. Zioupos P., and Currey J.D. The extent of microcracking and the morphology of microcracks in damaged bone. J Mater Sci 29 (1994) 978-986
236. Vashishth D., Tanner K.E., and Bonfield W. Experimental validation of a microcracking-based toughening mechanism for cortical bone. J Biomech 36 (2003) 121-124
237. Liu D.M., Weiner S., and Wagner H.D. Anisotropic mechanical properties of lamellar bone using miniature cantilever bending specimens. J Biomech 32 (1999) 647-654
238. Nalla R.K., Kruzic J.J., and Ritchie R.O. On the origin of the toughness of mineralized tissue: microcracking or crack bridging?. Bone 34 (2004) 790-798
239. Nalla R.K., Kinney J.H., and Ritchie R.O. Mechanistic fracture criteria for the failure of human cortical bone. Nat Mater 2 (2003) 164-168
240. Nalla R.K., Kruzic J.J., Kinney J.H., and Ritchie R.O. Mechanistic aspects of fracture and R-curve behavior in human cortical bone. Biomaterials 26 (2005) 217-231
241. 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 (1995) 533-544
242. Zioupos P., and Currey J.D. Changes in the stiffness, strength, and toughness of human cortical bone with age. Bone 22 (1998) 57-66
243. Zioupos P., Currey J.D., and Hamer A.J. The role of collagen in the declining mechanical properties of aging human cortical bone. J Biomed Mater Res 45 (1999) 108-116
244. Zioupos P. Ageing human bone: factors affecting its biomechanical properties and the role of collagen. J Biomater Appl 15 (2001) 187-229
245. Wang X.D., Bank R.A., TeKoppele J.M., and Agrawal C.M. The role of collagen in determining bone mechanical properties. J Orthopaed Res 19 (2001) 1021-1026
246. Wang X., Shen X., Li X., and Agrawal C.M. Age-related changes in the collagen network and toughness of bone. Bone 31 (2002) 1-7
247. Landis W.J., Librizzi J.J., Dunn M.G., and Silver F.H. A study of the relationship between mineral-content and mechanical-properties of Turkey gastrocnemius tendon. J Bone Min Res 10 (1995) 859-867
248. Gupta H.S., Seto J., Wagermaier W., Zaslansky P., Boesecke P., and Fratzl P. Cooperative deformation of mineral and collagen in bone at the nanoscale. Proc Natl Acad Sci USA 103 (2006) 17741-17746
249. Braidotti P., Bemporad E., D'Alessio T., Sciuto S.A., and Stagni L. Tensile experiments and SEM fractography on bovine subchondral bone. J Biomech 33 (2000) 1153-1157
250. Craig A.S., Birtles M.J., Conway J.F., and Parry D.A.D. An estimate of the mean length of collagen fibrils in rat tail-tendon as a function of age. Connect Tissue Res 19 (1989) 51-62
251. Gupta H.S., Wagermaier W., Zickler G.A., Aroush D.R.B., Funari S.S., Roschger P., et al. Nanoscale deformation mechanisms in bone. Nano Lett 5 (2005) 2108-2111
252. Thompson J.B., Kindt J.H., Drake B., Hansma H.G., Morse D.E., and Hansma P.K. Bone indentation recovery time correlates with bond reforming time. Nature 414 (2001) 773-776
253. Bonar L.C., Lees S., and Mook H.A. Neutron-diffraction studies of collagen in fully mineralized bone. J Mol Biol 181 (1985) 265-270
254. Tai K., Ulm F.J., and Ortiz C. Nanogranular origins of the strength of bone. Nano Lett 6 (2006) 2520-2525
255. Gupta H.S., Fratzl P., Kerschnitzki M., Benecke G., Wagermaier W., and Kirchner H.O.K. Evidence for an elementary process in bone plasticity with an activation enthalpy of 1 eV. J R Soc Interface 4 (2007) 277-282
256. Fantner G.E., Oroudjev E., Schitter G., Golde L.S., Thurner P., Finch M.M., et al. Sacrificial bonds and hidden length: unraveling molecular mesostructures in tough materials. Biophys J 90 (2006) 1411-1418
257. Heiss A., DuChesne A., Denecke B., Grotzinger J., Yamamoto K., Renne T., et al. Structural basis of calcification inhibition by alpha(2)-HS glycoprotein/fetuin-A - formation of colloidal calciprotein particles. J Biol Chem 278 (2003) 13333-13341
258. Scott J.E., and Parry D.A.D. Control of collagen fibril diameters in tissues. Int J Biol Macromol 14 (1992) 292-293
259. Leporatti S., Gao C., Voigt A., Donath E., and Mohwald H. Shrinking of ultrathin polyelectrolyte multilayer capsules upon annealing: a confocal laser scanning microscopy and scanning force microscopy study. Euro Phys J E 5 (2001) 13-20
260. Burr D.B., Milgrom C., Fyhrie D., Forwood M., Nyska M., Finestone A., et al. In vivo measurement of human tibial strains during vigorous activity. Bone 18 (1996) 405-410
261. Smith B.L., Schaffer T.E., Viani M., Thompson J.B., Frederick N.A., Kindt J., et al. Molecular mechanistic origin of the toughness of natural adhesives, fibres and composites. Nature 399 (1999) 761-763
262. Gutsmann T., Hassenkam T., Cutroni J.A., and Hansma P.K. Sacrificial bonds in polymer brushes from rat tail tendon functioning as nanoscale velcro. Biophys J 89 (2005) 536-542
263. Fantner G., Hassenkam T., Kindt J.H., Weaver J.C., Birkedal H., Pechenik L., et al. Sacrificial bonds and hidden length dissipate energy as mineralized fibrils separate during bone fracture. Nat Mater 4 (2005) 612-616
264. Jager I., and Fratzl P. Mineralized collagen fibrils: a mechanical model with a staggered arrangement of mineral particles. Biophys J 79 (2000) 1737-1746
265. Gao H.J., Ji B.H., Jager I.L., Arzt E., and Fratzl P. Materials become insensitive to flaws at nanoscale: lessons from nature. Proc Natl Acad Sci USA 100 (2003) 5597-5600
266. Gupta H.S., Schratter S., Tesch W., Roschger P., Berzlanovich A., Schoeberl T., et al. Two different correlations between nanoindentation modulus and mineral content in the bone-cartilage interface. J Struct Biol 149 (2005) 138-148
267. Gao H.J. Application of fracture mechanics concepts to hierarchical biomechanics of bone and bone-like materials. Int J Fract 138 (2006) 101-137
268. Mosekilde L., Ebbesen E.N., Tornvig L., and Thomsen J.S. Trabecular bone structure and strength - remodelling and repair. J Musculoskel Neuron Interact 1 (2000) 25-30
269. Chalmers J., and Ray R.D. The growth of transplanted foetal bones in different immunological environments. J Bone Joint Surg Br Vol 44 (1962) 149-164
270. Goodship A.E., and Cunningham J.L. Pathophysiology of functional adaptation of bone in remodeling and repair in vivo. In: Cowin S.C. (Ed). Bone mechanics handbook (2001), CRC Press, Boca Raton
271. Farber J., Lichtenegger H.C., Reiterer A., Stanzl-Tschegg S., and Fratzl P. Cellulose microfibril angles in a spruce branch and mechanical implications. J Mater Sci 36 (2001) 5087-5092
272. Huiskes R., Ruimerman R., van Lenthe G.H., and Janssen J.D. Effects of mechanical forces on maintenance and adaptation of form in trabecular bone. Nature 405 (2000) 704-706
273. Weinans H., and Odgaard A. Bone structure & remodeling: an introduction. In: Odgaard A., and Weinans H. (Eds). Bone structure and remodeling (1995), World Scientific, Singapore
274. Jee W.S.S. Integrated bone tissue physiology: anatomy and physiology. In: Cowin S.C. (Ed). Bone mechanics handbook (2001), CRC Press, Boca Raton
275. Ruffoni D., Fratzl P., Roschger P., Klaushofer K., and Weinkamer R. The bone mineralization density distribution as a fingerprint of the mineralization process. Bone 40 (2007) 1308-1319
276. Parfitt A.M. Misconceptions (2): turnover is always higher in cancellous than in cortical bone. Bone 30 (2002) 807-809
277. Frost H.M. Bone mass and the mechanostat - a proposal. Anat Rec 219 (1987) 1-9
278. Frost H.M. Bone's mechanostat: a 2003 update. Anat Rec Part A - Disc Mol Cell Evolut Biol 275A (2003) 1081-1101
279. Robling A.G., Castillo A.B., and Turner C.H. Biomechanical and molecular regulation of bone remodeling. Ann Rev Biomed Eng 8 (2006) 455-498
280. Pearson O.M., and Lieberman D.E. The aging of Wolff's "law: ontogeny and responses to mechanical loading cortical bone. Am J Phys Anthropol (2004) 63-99
281. Bertram J.E.A., and Swartz S.M. The law of bone transformation - a case of crying Wolff. Biol Rev Cambridge Philos Soc 66 (1991) 245-273
282. Johnson K.A., Muir P., Nicoll R.G., and Roush J.K. Asymmetric adaptive modeling of central tarsal bones in racing greyhounds. Bone 27 (2000) 257-263
283. Nikander R., Sievanen H., Heinonen A., and Kannus P. Femoral neck structure in adult female athletes subjected to different loading modalities. J Bone Min Res 20 (2005) 520-528
284. Heinonen A., Sievanen H., Kyrolainen H., Perttunen J., and Kannus P. Mineral mass, size, and estimated mechanical strength of triple jumpers' lower limb. Bone 29 (2001) 279-285
285. Goodship A.E., Lanyon L.E., and Mcfie H. Functional adaptation of bone to increased stress - experimental-study. J Bone Joint Surg Am Vol 61 (1979) 539-546
286. Rubin C.T., and Lanyon L.E. Regulation of bone-formation by applied dynamic loads. J Bone Joint Surg Am Vol 66A (1984) 397-402
287. Lanyon L.E., and Rubin C.T. Static vs dynamic loads as an influence on bone remodeling. J Biomech 17 (1984) 897-905
288. Mosley J.R., and Lanyon L.E. Strain rate as a controlling influence on adaptive modeling in response to dynamic loading of the ulna in growing male rats. Bone 23 (1998) 313-318
289. Rubin C., Turner A.S., Bain S., Mallinckrodt C., and McLeod K. Anabolism - low mechanical signals strengthen long bones. Nature 412 (2001) 603-604
290. Turner C.H., Takano Y., and Owan I. Aging changes mechanical loading thresholds for bone-formation in rats. J Bone Min Res 10 (1995) 1544-1549
291. De Souza R.L., Matsuura M., Eckstein F., Rawlinson S.C.F., Lanyon L.E., and Pitsillides A.A. Non-invasive axial loading of mouse tibiae increases cortical bone fori-nation and modifies trabecular organization: a new model to study cortical and cancellous compartments in a single loaded element. Bone 37 (2005) 810-818
292. Vico L., Collet P., Guignandon A., Lafage-Proust M.H., Thomas T., Rehailia M., et al. Effects of long-term microgravity exposure on cancellous and cortical weight-bearing bones of cosmonauts. Lancet 355 (2000) 1607-1611
293. Rittweger J., Frost H.M., Schiessl H., Ohshima H., Alkner B., Tesch P., et al. Muscle atrophy and bone loss after 90 days' bed rest and the effects of flywheel resistive exercise and pamidronate: results from the LTBR study. Bone 36 (2005) 1019-1029
294. Ehrlich P.J., and Lanyon L.E. Mechanical strain and bone cell function: a review. Osteoporosis Int 13 (2002) 688-700
295. Burger E.H. Experiments on cell mechanosensitvity: bone cells as mechanical engineers. In: Cowin S.C. (Ed). Bone mechanics handbook (2001), CRC Press, Boca Raton
296. Burger E.H., and Klein-Nulend J. Mechanotransduction in bone - role of the lacuno-canalicular network. FASEB J 13 (1999) S101-S112
297. Kleinnulend J., Vanderplas A., Semeins C.M., Ajubi N.E., Frangos J.A., Nijweide P.J., et al. Sensitivity of osteocytes to biomechanical stress in-vitro. FASEB J 9 (1995) 441-445
298. Jacobs C.R., Yellowley C.E., Davis B.R., Zhou Z., Cimbala J.M., and Donahue H.J. Differential effect of steady versus oscillating flow on bone cells. J Biomech 31 (1998) 969-976
299. Hughes-Fulford M. Signal transduction and mechanical stress. Science's STKE 249 (2004) re12
300. Burr D.B. Targeted and nontargeted remodeling. Bone 30 (2002) 2-4
301. Verborgt O., Gibson G.J., and Schaffler M.B. Loss of osteocyte integrity in association with microdamage and bone remodeling after fatigue in vivo. J Bone Min Res 15 (2000) 60-67
302. Cowin S.C. Bone stress-adaptation models. J Biomech Eng - Trans ASME 115 (1993) 528-533
303. Huiskes R., Weinans H., and Vanrietbergen B. The relationship between stress shielding and bone-resorption around total hip stems and the effects of flexible materials. Clin Orthopaed Relat Res (1992) 124-134
304. Pettermann H.E., Reiter T.J., and Rammerstorfer F.G. Computational simulation of internal bone remodeling. Arch Comput Methods Eng 4 (1997) 295-323
305. Huiskes R. The law of adaptive bone remodeling: a case for crying Newton?. In: Odgaard A., and Weinans H. (Eds). Bone structure and remodeling (1995), World Scientific, Singapore
306. Hegedus D.H., and Cowin S.C. Bone remodeling-II - small strain adaptive elasticity. J Elasticity 6 (1976) 337-352
307. Hart R.T. Bone modeling and remodeling: theories and computation. In: Cowin S.C. (Ed). Bone mechanics handbook (2001), CRC Press, Boca Raton
308. Hernandez C.J., Beaupre G.S., and Carter D.R. A model of mechanobiologic and metabolic influences on bone adaptation. J Rehab Res Dev 37 (2000) 235-244
309. Weinkamer R., Hartmann M.A., Brechet Y., and Fratzl P. Stochastic lattice model for bone remodeling and aging. Phys Rev Lett 93 (2004) 228102
310. Ruimerman R., Hilbers P., van Rietbergen B., and Huiskes R. A theoretical framework for strain-related trabecular bone maintenance and adaptation. J Biomech 38 (2005) 931-941
311. Carter D.R., Orr T.E., and Fyhrie D.P. Relationships between loading history and femoral cancellous bone architecture. J Biomech 22 (1989) 231-244
312. Currey J.D. The validation of algorithms used to explain adaptive bone remodeling in bone. In: Odgaard A., and Weinans H. (Eds). Bone structure and remodeling (1995), World Scientific, Singapore
313. Ruimerman R., van Rietbergen B., Hilbers P., and Huiskes R. The effects of trabecular-bone loading variables on the surface signaling potential for bone remodeling and adaptation. Ann Biomed Eng 33 (2005) 71-78
314. Prendergast P.J., and Taylor D. Prediction of bone adaptation using damage accumulation. J Biomech 27 (1994) 1067-1076
315. Mullender M.G., and Huiskes R. Proposal for the regulatory mechanism of Wolffs law. J Orthopaed Res 13 (1995) 503-512
316. Tsubota K., and Adachi T. Spatial and temporal regulation of cancellous bone structure: characterization of a rate equation of trabecular surface remodeling. Med Eng Phys 27 (2005) 305-311
317. Tanck E., Ruimerman R., and Huiskes R. Trabecular architecture can remain intact for both disuse and overload enhanced resorption characteristics. J Biomech 39 (2006) 2631-2637
318. Hartmann MA. Lattice models in materials science. PhD thesis. Humboldt University, Berlin, 2006.
319. Alvarado A.S. Regeneration in the metazoans: why does it happen?. Bioessays 22 (2000) 578-590
320. Gerstenfeld L.C., Cullinane D.M., Barnes G.L., Graves D.T., and Einhorn T.A. Fracture healing as a post-natal developmental process: molecular, spatial, and temporal aspects of its regulation. J Cell Biochem 88 (2003) 873-884
321. Einhorn T.A. The cell and molecular biology of fracture healing. Clin Orthopaed Relat Res (1998) S7-S21
322. Prendergast P.J., and Van der Meulen M.C.H. Mechanics of bone regeneration. In: Cowin S.C. (Ed). Bone mechanics handbook (2001), CRC Press, Boca Raton
323. Carter D.R., and Beaupré G.S. Skeletal function and form, mechanobiology of skeletal development, aging, and regeneration (2001), Cambridge University Press, Cambridge
324. McKibbin B. Biology of fracture healing in long bones. J Bone Joint Surg Br Vol 60 (1978) 150-162
325. Li R., Ahmad T., Spetea M., Ahmed M., and Kreicbergs A. Bone reinnervation after fracture: a study in the rat. J Bone Min Res 16 (2001) 1505-1510
326. Claes L., Augat P., Suger G., and Wilke H.J. Influence of size and stability of the osteotomy gap on the success of fracture healing. J Orthopaed Res 15 (1997) 577-584
327. Goodship A.E., Watkins P.E., Rigby H.S., and Kenwright J. The role of fixator frame stiffness in the control of fracture-healing - an experimental-study. J Biomech 26 (1993) 1027-1035
328. Claes L.E., Heigele C.A., Neidlinger-Wilke C., Kaspar D., Seidl W., Margevicius K.J., et al. Effects of mechanical factors on the fracture healing process. Clin Orthopaed Relat Res (1998) S132-S147
329. Epari D.R., Schell H., Bail H.J., and Duda G.N. Instability prolongs the chondral phase during bone healing in sheep. Bone 38 (2006) 864-870
330. Seebeck P., Thompson M.S., Parwani A., Taylor W.R., Schell H., and Duda G.N. Gait evaluation: a tool to monitor bone healing?. Clin Biomech 20 (2005) 883-891
331. Kassi J.P., Hoffmann J.E., Heller M., Raschke M., and Duda G.N. Assessment of the stability of fracture fixation systems: mechanical device to investigate the 3-D stiffness in vitro. Biomed Tech 46 (2001) 247-252
332. Goodship A.E., Cunningham J.L., and Kenwright J. Strain rate and timing of stimulation in mechanical modulation of fracture healing. Clin Orthopaed Relat Res (1998) S105-S115
333. Roux W. Gesammelte Abhandlungen über Entwicklungsmechanik der Organismen (1895), Wilhelm Engelmann's Verlag, Leipzig p. 436
334. Perren S.M., and Cordey J. The concept of interfragmentary strain. In: Uhthoff H.K. (Ed). Current concepts of internal fixation of fractures (1980), Springer, Berlin 63-77
335. Pauwels F. Grundriss einer Biomechanik der Frakturheilung. Verhandlungen der Deutschen Orthopädischen Gesellschaft (1941), Ferdinand Enke Verlag, Stuttgart 62-108 Translated in: Biomechanics of fracture healing, in: Biomechanics of the locomotor apparatus, Springer-Verlag, Berlin, 1980
336. Weinans H., and Prendergast P.J. Tissue adaptation as a dynamical process far from equilibrium. Bone 19 (1996) 143-149
337. Carter D.R., Blenman P.R., and Beaupre G.S. Correlations between mechanical-stress history and tissue differentiation in initial fracture-healing. J Orthopaed Res 6 (1988) 736-748
338. Giori N.J., Beaupre G.S., and Carter D.R. Cellular-shape and pressure may mediate mechanical control of tissue composition in tendons. J Orthopaed Res 11 (1993) 581-591
339. Claes L.E., and Heigele C.A. Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing. J Biomech 32 (1999) 255-266
340. Cowin S.C. Bone poroelasticity. J Biomech 32 (1999) 217-238
341. Prendergast P.J., Huiskes R., and Soballe K. Biophysical stimuli on cells during tissue differentiation at implant interfaces. J Biomech 30 (1997) 539-548
342. Lacroix D., and Prendergast P.J. A mechano-regulation model for tissue differentiation during fracture healing: analysis of gap size and loading. J Biomech 35 (2002) 1163-1171
343. Lacroix D., Prendergast P.J., Li G., and Marsh D. Biomechanical model to simulate tissue differentiation and bone regeneration: application to fracture healing. Med Biol Eng Comput 40 (2002) 14-21
344. Isaksson H., Wilson W., van Donkelaar C.C., Huiskes R., and Ito K. Comparison of biophysical stimuli for mechano-regulation of tissue differentiation during fracture healing. J Biomech 39 (2006) 1507-1516
345. Isaksson H., Van Donkelaar C.C., Huiskes R., and Ito K. Corroboration of mechanoregulatory algorithms for tissue differentiation during fracture healing: comparison with in vivo results. J Orthopaed Res 24 (2006) 898-907
346. Canalis E., Economides A.N., and Gazzerro E. Bone morphogenetic proteins, their antagonists, and the skeleton. Endocrine Rev 24 (2003) 218-235
347. Groeneveld E.H.J., and Burger E.H. Bone morphogenetic proteins in human bone regeneration. Euro J Endocrinol 142 (2000) 9-21
348. Bailon-Plaza A., and van der Meulen M.C.H. A mathematical framework to study the effects of growth factor influences on fracture healing. J Theor Biol 212 (2001) 191-209
349. Bailon-Plaza A., and van der Meulen M.C.H. Beneficial effects of moderate, early loading and adverse effects of delayed or excessive loading on bone healing. J Biomech 36 (2003) 1069-1077
350. Iqbal J., and Zaidi M. Molecular regulation of mechanotransduction. Biochem Biophys Res Commun 328 (2005) 751-755
351. De Jong H. Modeling and simulation of genetic regulatory systems: a literature review. J Comput Biol 9 (2002) 67-103
352. Vogel S. Cats' paws and catapults: mechanical worlds of Nature and people (2000), W.W. Norton & Company p. 384