Mathematical analysis of trabecular 'trajectories' in apparent trajectorial structures: The unfortunate historical emphasis on the human proximal femur

Journal of Theoretical Biology

Volumn 244, Issue 1, 2007, Pages 15-45

  Skedros, John G ^a,b   Baucom, Sidney L ^b  

^a UNIVERSITY OF UTAH SCHOOL OF MEDICINE   (United States)

^b Utah Bone & Joint Center   (United States)

Author keywords

Cancellous bone adaptation; Cancellous bone anisotropy; Stress trajectories; Trabecular bone; Trajectory hypothesis; Wolff's law

Indexed keywords

ADAPTATION; ANISOTROPY; BONE; HUMAN EVOLUTION; MATHEMATICAL ANALYSIS; STRESS; TRAJECTORY;

ARTICLE; CALCANEUS; CHIMPANZEE; FEMUR; MATHEMATICAL ANALYSIS; PREDICTION; PRIORITY JOURNAL; STRESS FRACTURE; TRABECULAR BONE;

ADAPTATION, PHYSIOLOGICAL; ADULT; ANIMALS; ANISOTROPY; CALCANEUS; CARTILAGE, ARTICULAR; DEER; FEMALE; FEMUR NECK; HUMANS; MALE; MIDDLE AGED; MODELS, BIOLOGICAL; PAN TROGLODYTES; SHEEP, DOMESTIC; SPECIES SPECIFICITY; STRESS, MECHANICAL; WEIGHT-BEARING;

ARTIODACTYLA; AXIS (DEER); CERVIDAE; OVIS ARIES; PAN; PAN TROGLODYTES;

EID: 33751021119     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2006.06.029     Document Type: Article

References (271)

1. Aamodt A., Lund-Larsen J., Eine J., Andersen E., Benum P., and Schnell Husby O. In vivo measurements show tensile axial strain in the proximal lateral aspect of the human femur. J Orthop Res 15 (1997) 927-931
2. Akeson W.H., Amiel D., Kwan M., Abitbol J.J., and Garfin S.R. Stress dependence of synovial joints. In: Hall B.K. (Ed). Bone: Fracture Repair and Regeneration (1992), CRC Press, Boca Raton 33-60
3. Albert E. Die architectur der tibia. Wiener Med Wochenscrift (4, 5, & 6) (1900) 161-164 219-224, 265-273
4. Albert, E., 1900b. Einführung in das studium der architektur der röhrenknochen. Alfred Hölder. Vienna, Austria.
5. Alexander R.M. Bipedal animals, and their differences from humans. J Anat 204 (2004) 321-330
6. Arem A.J., and Madden J.W. Is there a Wolff's law for connective tissue?. Sur. Forum 25 (1974) 512-514
7. Ascenzi A., and Bell G.H. Bones as a mechanical engineering problem. In: Bourne G.H. (Ed). The Biochemistry and Physiology of Bone (1972), Academic Press Inc., New York 311-352
8. Backman S. The proximal end of the femur: investigations with special reference to the etiology of femoral neck fractures; anatomical studies; roentgen projections; theoretical stress calculations; experimental production of fractures. Acta Radiol 146 (1957) 1-166
9. Bacon G.E., Bacon P.J., and Griffiths R.K. A neutron diffraction study of the bones of the foot. J. Anat. 139 (1984) 265-273
10. Bagi C.M., Wilkie D., Georgelos K., Williams D., and Bertolini D. Morphological and structural characteristics of the proximal femur in human and rat. Bone 21 (1997) 261-267
11. Bähr F. Beöbachtungen über die statischen Beziehungen des beckens zur uteren extremität. Deutsche. Ztschr. Orthop. Chir. 55 (1899) 52-59
12. Barbieri L., and Buoncristiani I. Considerations on some problems of osseous physiopathology in relation to a photoelastic study of the femur. Chir. Organ. Mov 62 (1975) 201-208
13. Baumgaertner M., and Higgins T. Femoral neck fractures. In: Bucholz R., and Heckman J. (Eds). Rockwood and Green's Fractures in Adults (2002), Lippincott Williams and Wilkins, Philadelphia, PA 1579-1634
14. Bay B.K., Yerby S.A., McLain R.F., and Toh E. Measurement of strain distributions within vertebral body sections by texture correlation. Spine 24 (1999) 10-17
15. Bayraktar H.H., and Keaveny T.M. Mechanisms of uniformity of yield strains for trabecular bone. J. Biomech. 37 (2004) 1671-1678
16. Beaupré G.S., Orr T.E., and Carter D.R. An approach for time-dependent bone modeling and remodeling-theoretical development. J. Orthop. Res. 8 (1990) 651-661
17. Beck T.J., Ruff C.B., Warden K.E., Scott W.W., and Gopala U. Predicting femoral neck strength from bone mineral data: a structural approach. Invest. Radiol. 25 (1990) 6-18
18. Bergmann G., Graichen F., and Rohlmann A. Hip joint loading during walking and running, measured in two patients. J. Biomech. 26 (1993) 969-990
19. Bergmann G., Deuretzbacher G., Heller M., Graichen F., Rohlmann A., Strauss J., and Duda G.N. Hip contact forces and gait patterns from routine activities. J. Biomech. 34 (2001) 859-871
20. Berquist T.H., and Coventry M.B. The pelvis and hips. In: Berquist T.H. (Ed). Imaging of Orthopedic Trauma (1992), W.B. Saunders Co, Philadelphia, PA 207-310
21. Bertram J.E., and Swartz S.M. The 'law of bone transformation': a case of crying Wolff?. Biol. Rev. Camb. Philos. Soc. 66 (1991) 245-273
22. Biewener A.A., Swartz S.M., and Bertram J.E.A. Bone modeling during growth: dynamic strain equilibrium in the chick tibiotarsus. Calcif Tissue Int. 39 (1986) 390-395
23. Biewener A.A., Fazzalari N.L., Konieczynski D.D., and Baudinette R.V. Adaptive changes in trabecular architecture in relation to functional strain patterns and disuse. Bone 19 (1996) 1-8
24. Biewener A.A., Thomason J., Goodship A., and Lanyon L.E. Bone stress in the horse forelimb during locomotion at different gaits: a comparison of two experimental methods. J. Biomech. 16 (1983) 565-576
25. Black M.D. Correspondence of trabecular and cortical geometries: a natural test of Wolff's Law. Am J Phys Anthrop. Suppl 38 (2004) 63
26. Bloebaum R.D., Lauritzen R.S., Skedros J.G., Smith E.F., Thomas K.A., Bennett J.T., and Hofmann A.A. Roentgenographic procedure for selecting proximal femur allograft for use in revision arthroplasty. J. Arthroplasty. 8 (1993) 347-360
27. Bousson V., Peyrin F., Bergot C., Hausard M., Sautet A., and Laredo J.D. Cortical bone in the human femoral neck: three-dimensional appearance and porosity using synchrotron radiation. J. Bone Miner Res. 19 (2004) 794-801
28. Bouvier M. Application of in vivo bone strain measurement techniques to problems of skeletal adaptations. Yearbook of Physical Anthropology 28 (1985) 237-248
29. Brand R.A., Stanford C.M., and Swan C.C. How do tissues respond and adapt to stresses around a prosthesis? A primer on finite element stress analysis for orthopaedic surgeons. Iowa Orthop. J. 23 (2003) 13-22
30. Brickley-Parsons D., and Glimcher M.J. Is the chemistry of collagen in intervertebral discs an expression of Wolff's Law? A study of the human lumbar spine. Spine 9 (1984) 148-163
31. Bromage T.G., Goldman H.M., McFarlin S.C., Warshaw J., Boyde A., and Riggs C.M. Circularly polarized light standards for investigations of collagen fiber orientation in bone. Anat. Rec. B. New Anat. 274 (2003) 157-168
32. Brown T.D., and DiGioia A.M. A contact-couples finite element analysis of the natural adult hip. J. Biomech. 17 (1984) 437-448
33. Büdinger K. Der spongiosabau der oberen extremität. Ztschr. Heilkunde XXIV (1903) 1-82
34. Bullough P.G., and Vigorita V.J. Atlas of Orthopaedic Pathology with Clinical and Radiologic Correlations (1984), J.B. Lippincott Co, Baltimore, MD
35. Burger E., Klein-Nulend J., and Smit T. Strain-derived canalicular fluid flow regulates osteoclast activity in a remodelling osteon-a proposal. J. Biomech. 36 (2003) 1453-1459
36. Carey E.J. Studies in the dynamics of histogenesis. Radiology 13 (1929) 127-168
37. Carter D.R., and Beaupré G.S. Skeletal Function and Form (2001), Cambridge University Press, Cambridge, UK pp. 138-160
38. Carter D.R., and Wong M. Mechanical stresses and endochondral ossification in the chondroepiphysis. J. Orthop. Res. 6 (1988) 148-154
39. 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
40. Chapman M.W., and Zickel R.E. Subtrochanteric Fractures of the Femur (1988), J. B. Lippincott Pub Co, New York pp. 361-372
41. Cheal E.J., Hayes W.C., Snyder B.D., and Nunamaker D.M. Trabecular bone remodeling around smooth and porous implants in an equine patellar model. J. Biomech. 20 (1987) 1121-1134
42. Chung S.M., Batterman S.C., and Brighton C.T. Shear strength of the human femoral capital epiphyseal plate. J. Bone Joint Surg. 58-A (1976) 94-103
43. Cohen B., Chorney G.S., Phillips D.P., Dick H.M., Buckwalter J.A., Ratcliffe A., and Mow V.C. The microstructural tensile properties and biochemical composition of the bovine distal femoral growth plate. J. Orthop. Res. 10 (1992) 263-275
44. Cowin S.C. Mechanical modeling of the stress adaptation process in bone. Calcif Tissue Int 36 (1984) S98-S103
45. Cowin S.C. Wolff's law of trabecular architecture at remodeling equilibrium. J. Biomech. Eng. 108 (1986) 83-88
46. Cowin S.C. Mechanical properties of cancellous bone tissues. In: Cowin S.C. (Ed). Bone Mechanics (1989), CRC Press, Boca Raton, FL 129-157
47. Cowin S.C. A resolution restriction for Wolff's law of trabecular architecture. Bull. Hosp. Joint Dis. Orthop. Inst. 49 (1989) 205-212
48. Cowin S.C. A resolution restriction for Wolff's law of trabecular architecture. Bull Hosp. Joint Dis. 49 (1989) 205-212
49. Cowin S.C. The false premise of Wolff's law. Forma 12 (1997) 247-262
50. Cowin S.C. The false premise in Wolff's law. In: Cowin S.C. (Ed). Bone Mechanics Handbook (2001), CRC Press, Boca Raton, FL pp. 30-1-30-15
51. Cristofolini L., Viceconti M., Cappello A., and Toni A. Mechanical validation of whole bone composite femur models. J. Biomech. 29 (1996) 525-535
52. Culmann K. Die Graphische Statik (1866), Verlag Von Meyer & Zeller, Zurich, Switzerland p. 633
53. Currey J.D. The Mechanical Adaptations of Bone (1984), Princeton University Press, Englewood Cliff, NJ 294
54. Currey J.D. Was Wolff correct?. Forma 12 (1997) 263-266
55. D'Aout K., Vereecke E., Schoonaert K., De Clercq D., Van Elsacker L., and Aerts P. Locomotion in bonobos (Pan paniscus): differences and similarities between bipedal and quadrupedal terrestrial walking, and a comparison with other locomotor modes. J. Anat. 204 (2004) 353-361
56. Davy D.T., Kotzar G.M., Brown R.H., Heiple K.G., Goldberg V.M., Heiple Jr. K.G., Berilla J., and Burstein A.H. Telemetric force measurements across the hip after total arthroplasty. J. Bone Joint Surg. 70-A (1988) 45-50
57. Demes B., Jungers W.L., and Walker C. Cortical bone distribution in the femoral neck of strepsirhine primates. J. Hum. Evol. 39 (2000) 367-379
58. Dibbets J.M.H. One century of Wolff's law. In: Carlson D.S., and Goldstein S.A. (Eds). Bone Biodynamics in Orthodontic and Orthopedic Treatment (1992), University of Michigan, Ann Arbor, MI 1-13
59. Ding M., Odgaard A., Danielsen C.C., and Hvid I. Mutual associations among microstructural, physical and mechanical properties of human cancellous bone. J. Bone Joint Surg. 84-B (2002) 900-907
60. Elftman H., and Manter J. Chimpanzee and human feet in bipedal walking. Am. J. Phys. Anthrop. 20 (1935) 69-79
61. Elke R.P., Cheal R.J., Simmons C., and Poss R. Three-dimensional anatomy of the cancellous structures within the proximal femur from computed tomography data. J. Orthop. Res. 13 (1995) 513-523
62. Fajardo R.J., and Muller R. Three-dimensional analysis of nonhuman primate trabecular architecture using micro-computed tomography. Am. J. Phys. Anthropol. 115 (2001) 327-336
63. Farkas A., Milton M.J., and Hayner J.C. An anatomical study of the mechanics, pathology, and healing of fracture of the femoral neck. J. Bone Joint Surg. 30-A (1948) 53-69
64. Fazzalari N.L., Crisp D.J., and Vernon-Roberts B. Mathematical modeling of trabecular bone structure: the evaluation of analytical and quantified surface to volume relationships in the femoral head and iliac crest. J. Biomech. 22 (1989) 901-910
65. Fernandes P., Rodrigues H., and Jacobs C. A model of bone adaptation using a global optimisation criterion based on the trajectorial theory of Wolff. Comput. Methods Biomech. Biomed. Eng. 2 (1999) 125-138
66. Field R.E., and Kenyon C.M. A mathematical analysis for the modeling of trabecular bone. J. Biomed. Eng. 11 (1989) 384-389
67. Finlay J.B., Chess D.G., Hardie W.R., Rorabeck C.H., and Bourne R.B. An evaluation of three loading configurations for the in vitro testing of femoral strains in total hip arthroplasty. J. Orthop. Res. 9 (1991) 749-759
68. Ford C.M., and Keaveny T.M. The dependence of shear failure properties of trabecular bone on apparent density and trabecular orientation. J. Biomech. 29 (1996) 1309-1317
69. Forrester J.C., Zederfeldt B., Hayes T.L., and Hunt T.K. Wolff's law in relation to the healing skin wound. J. Trauma 10 (1970) 770-779
70. Fox, J.C., 2003. Biomechanics of the proximal femur: role of bone distribution and architecture. Mechanical Engineering, University of California at Berkeley. PhD Thesis, p. 151.
71. Francillon-Vieillot H., de Buffrénil V., Castanet J., Géraudie J., Meunier F., Sire J., Zylberberg L., and de Ricqlès A. Microstructure and mineralization of vertebrate skeletal tissues. In: Carter J. (Ed). Skeletal Biomineralization: Patterns, Processes and Evolutionary Trends (1990), Van Nostrand Reinhold, New York 471-530
72. Frankel V.H. The Femoral Neck: Function, Fracture Mechanisms, Internal Fixation: An Experimental Study (1960), Charles C. Thomas, Springfield, IL p. 120
73. Freiberg A.H. Wolff's law and the functional pathogenesis of deformity. Am. J. Med. Sci. 124 (1902) 956-972
74. Frost H.M. The Laws of Bone Structure (1964), Thomas, Springfield, IL p. 167
75. Frost H.M. Intermediary Organization of the Skeleton I and II (1986), CRC Press Inc, Boca Raton, FL
76. Frost H.M. Structural adaptations to mechanical usage. A proposed "three-way rule" for bone modeling. Part I. Vet. Compar. Orthop. Traumatol. 1 (1988) 7-17
77. Frost H.M. Structural adaptations to mechanical usage. A proposed "three-way rule" for bone modeling. Part II. Vet. Compar. Orthop. Traumatol. 2 (1988) 80-85
78. Frost H.M. Skeletal structural adaptations to mechanical usage (SATMU): 3. The hyaline cartilage modeling problem. Anat. Rec. 226 (1990) 423-432
79. Fung Y.C. Biomechanical Aspects of Growth and Tissue Engineering (1990), Springer, New York pp. 499-546
80. Ganey T.M., and Ogden J.A. Pre- and post-natal development of the hip. In: Callaghan J.J., Rosenbery A.G., and Rubash H.E. (Eds). The Adult Hip (1998), Lippincott-Raven Publishers, Philadelphia, PA 39-55
81. Garden R.S. The structure and function of the proximal end of the femur. J. Bone Joint Surg. 43-B (1961) 576-589
82. Gibson L.J., and Ashby M.F. Cancellous bone. In: Ward I.M. (Ed). Cellular Solids: Structure and Properties (1997), Cambridge University Press, Cambridge, UK 429-452
83. Greenspan A. Orthopaedic Radiology: A Practical Approach (1988), JB Lippincott, Philadelphia, PA pp. 5.19-5.20
84. Greenspan S.L., Myers E.R., Kiel D.P., Parker R.A., Hayes W.C., and Resnick N.M. Fall direction, bone mineral density, and function: risk factors for hip fracture in frail nursing home elderly. Am. J. Med. 104 (1998) 539-545
85. Hall B.K. Introduction. In: Murray P.D.F. (Ed). Bones (1985), Cambridge University Press, New York xi-xxxii
86. Hamrick M.W. A chondral modeling theory revisited. J. Theor. Biol. 201 (1999) 201-208
87. 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
88. Harty M. The Anatomy of the Hip Joint (1984), Springer, New York, NY pp. 45-74
89. Hayes W.C., and Snyder B. Toward a quantitative formulation of Wolff's law in trabecular bone. In: Cowin S.C. (Ed). Mechanical Properties of Bone (1981), The American Society of Mechanical Engineers, New York 43-68
90. Herrera M., Panchon A., and Perez-Bacete M. Trabecular trajectory in the articular process of the human fourth cervical vertebrae. J. Anat. 199 (2001) 345-348
91. Heřt J. A new explanation of the cancellous bone architecture. Funct. Dev. Morphol. 2 (1992) 17-24
92. Heřt J. A new attempt at the interpretation of the functional architecture of the cancellous bone. J. Biomech. 27 (1994) 239-242
93. Heřt J., Fiala P., and Jirova J. Mechanical loading of the human femoral neck. Acta. Chir. Orthop. Traumatol. Cech. 68 (2001) 222-229
94. Hodge W.A., Fijan R.S., Carlson K.L., Burgess R.G., Harris W.H., and Mann R.W. Contact pressures in the human hip joint measured in vivo. Proc. Natl. Acad. Sci. USA 83 (1986) 2879-2883
95. Holt B.M., Ruff C.B., and Trinkaus E. The Wolff's law debate: throwing water out, but keeping the baby. Am. J. Phys. Anthrop. Suppl. 38 (2004) 115-116
96. Huiskes R. If bone is the answer, then what is the question?. J. Anat. 197 (2000) 145-156
97. Huiskes R., Janssen J.D., and Slooff T.J. A detailed comparison of experimental and theoretical stress-analyses of a human femur. In: Cowin S.C. (Ed). Mechanical Properties of Bone (1981), The American Society of Mechanical Engineers, New York 211-234
98. Huiskes R., Weinans H., Grootenboer H.J., Dalstra M., Fudala B., and Slooff T.J. Adaptive bone-remodeling theory applied to prosthetic-design analysis. J. Biomech. 20 (1987) 1135-1150
99. 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
100. Inman V. Functional aspects of the abductor muscles of the hip. J. Bone Joint Surg. 29-A (1947) 607-619
101. Issever A.S., Walsh A., Lu Y., Burghardt A., Lotz J.C., and Majumdar S. Micro-computed tomography evaluation of trabecular bone structure on loaded mice tail vertebrae. Spine 28 (2003) 123-128
102. Jacobs C.R., Simo J.C., Beaupre G.S., and Carter D.H. Adaptive bone remodeling incorporating simultaneous density and anisotropy considerations. J. Biomech. 30 (1997) 603-613
103. Jansen M. On Bone Formation: Its Relation to Tension and Pressure (1920), Manchester University Press, Longmans, Green and Co, London, UK p. 114
104. Jee W.S.S., Li X.J., and Ke H.Z. The skeletal adaptation to mechanical usage in the rat. Cells Mater. 1 (1991) 131-142
105. Jenkins Jr. F.A. Chimpanzee bipedalism: cineradiographic analysis and implications for the evolution of gait. Science 178 (1972) 877-879
106. Joshi M.G., Advani S.G., Miller F., and Santare M.H. Analysis of a femoral hip prosthesis designed to reduce stress shielding. J. Biomech. 33 (2000) 1655-1662
107. Judex S., Gross T.S., Bray R.C., and Zernicke R.F. Adaptation of bone to physiological stimuli. J. Biomech. 30 (1997) 421-429
108. Kachigan S.K. Statistical Analysis (1986), Radius Press, New York, NY p. 589
109. Kalmey J.K., and Lovejoy C.O. Collagen fiber orientation in the femoral necks of apes and humans: do their histological structures reflect differences in locomotor loading?. Bone 31 (2002) 327-332
110. Kapandji I. The Physiology of Joints: Lower Limb 2 (1987), Churchill Livingstone, Edinburgh, UK p. 219
111. Kawashima T., and Uhthoff H.K. Pattern of bone loss of the proximal femur: a radiologic, densitometric, and histomorphometric study. J. Orthop. Res. 9 (1991) 634-640
112. Keaveny T.M. Strength of trabecular bone. In: Cowin S.C. (Ed). Bone Mechanics Handbook (2001), CRC Press, Boca Raton, FL pp. 16-1-16-42
113. Keaveny T.M., and Hayes W.C. Mechanical properties of cortical and trabecular bone. In: Hall B.K. (Ed). Bone (1993), CRC Press, Boca Raton, FL 285-344
114. Keaveny T.M., Wachtel E.F., Cutler M.J., and Pinilla T.P. Yield strains for bovine trabecular bone are isotropic but asymmetric. Trans. Orthop. Res. Soc. 19 (1994) 428
115. Keaveny T.M., Wachtel E.F., Zadesky S.P., and Arramon Y.P. Application of the Tsai-Wu quadratic multiaxial failure criterion to bovine trabecular bone. J. Biomech. Eng. 121 (1999) 99-107
116. Keaveny T.M., Morgan E.F., Niebur G.L., and Yeh O.C. Biomechanics of trabecular bone. Annu. Rev. Biomed. Eng. 3 (2001) 307-333
117. Keith A. Menders of the Maimed: The Anatomical and Physiological Principles Underlying the Treatment of Injuries to Muscles, Nerves, Bones, and Joints (1919), J.B. Lippincott Company, Philadelphia, PA p. 335
118. Kennedy K.A.R. Skeletal markers of occupational stress. In: İşcan M.Y., and Kennedy K.A.R. (Eds). Reconstruction of Life from the Skeleton (1989), Alan R. Liss, Inc, New York 129-160
119. Kerr W.C., and Bishop A.R. Dynamics of structural phase transitions in highly anisotropic systems. Phys. Rev. B. Condens. Matter 34 (1986) 6295-6314
120. Kerr R., Resnick D., Sartoris D.J., Kursunoglu S., Pineda C., Haghighi P., Greenway G., and Guerra Jr. J. Computerized tomography of proximal femoral trabecular patterns. J. Orthop. Res. 4 (1986) 45-56
121. Knothe Tate M.L. "Whither flows the fluid in bone?" An osteocyte's perspective. J. Biomech. 36 (2003) 1409-1424
122. Kobayashi S., Takahashi H.E., Ito A., Saito N., Nawata M., Horiuchi H., Ohta H., Iorio R., Yamamoto N., and Takaoka K. Trabecular minimodeling in human iliac bone. Bone 32 (2003) 163-169
123. Koch J.C. The laws of bone architecture. Am. J. Anat. 21 (1917) 177-298
124. Kothari M., Keaveny T.M., Lin J.C., Newitt D.C., Genant H.K., and Majumdar S. Impact of spatial resolution on the prediction of trabecular architecture parameters. Bone 22 (1998) 437-443
125. Koval K.J., and Zuckerman J.D. Handbook of Fractures (2002), Lippincott Williams & Wilkins, Philadelphia, PA p. 466
126. Kriz M.A. The surface anatomy, internal structure, and external morphology of the mammalian proximal femur with special reference to its developmental biology. Anthropology, Kent State, Kent Ohio. Masters of Arts, 89 (2002)
127. Kriz M.A., Reno P.L., and Lovejoy C.O. Morphometric variation in proximal femoral development in primates and mammals. Am. J. Phys. Anthrop. Suppl 34 (2002) 97
128. Kumaresan S., Yoganandan N., Pintar F.A., Maiman D.J., and Goel V.K. Contribution of disc degeneration to osteophyte formation in the cervical spine: a biomechanical investigation. J. Orthop. Res. 19 (2001) 977-984
129. Kummer B. Bauprinzipien des Säugerskeletes Georg Thieme Verlag (1959), Stuttgart, Germany p. 235
130. Kuo T., Skedros J.G., and Bloebaum R.D. Comparison of human, primate and canine femora: Implications for biomaterials testing in total hip replacement. J. Biomed. Mater Res. 40 (1998) 475-489
131. Kuo T., Skedros J.G., and Bloebaum R.D. Measurement of the femoral anteversion by biplane radiography and ct imaging; comparison with an anatomic reference. Invest. Radiol. 38 (2003) 221-229
132. Kyle R. Fractures of the proximal part of the femur. J. Bone Joint Surg. 76-A (1994) 924-951
133. Lanyon L.D. Analysis of surface bone strain in the calcaneus of sheep during normal locomotion. J. Biomech. 6 (1973) 41-49
134. Lanyon L.E. Experimental support for the trajectorial theory of bone structure. J. Bone Joint Surg. 56-B (1974) 160-166
135. Lanyon L.E., and Rubin C.T. Functional adaptation in skeletal structures. In: Hildebrand M., Bramble D.M., Liem K.F., and Wake D.B. (Eds). Functional Vertebrate Morphology (1985), The Belkap Press of Harvard University Press, Cambridge, MA 1-25
136. Laroche M., Ludot I., Thiechart M., Arlet J., Pieraggi M., Chiron P., Moulinier L., Cantagrel A., Puget J., Utheza G., and Mazieres B. Study of the interosseous vessels of the femoral head in patients with fractures of the femoral neck or osteoarthritis of the hip. Osteop. Int. 5 (1995) 213-217
137. Laros G. Intertrochanteric fractures. In: McCollister E. (Ed). Surgery of the Musculoskeletal System (1990), Churchill Livingstone, New York 2613-2639
138. Lee T.C., and Taylor D. Bone remodeling: should we cry Wolff?. Ir. J. Med. Sc. 168 (1999) 102-105
139. Lim L.-A., Carmichael S.W., and Cabanela M.E. Biomechanics of total hip arthroplasty. Anat. Rec. 257 (1999) 110-116
140. Löer F., and Weigmann R. Julius Wolff and Friedrich Pauwels: Wolff's concept of a causal therapy of orthopaedic diseases using biological adaptation phenomena and its realization by Friedrich Pauwels. In: Regling G. (Ed). Wolff's Law and Connective Tissue Regulation (1992), Walter de Gruyter, New York 23-30
141. Lotz J.C., Cheal E.J., and Hayes W.C. Stress distributions within the proximal femur during gait and falls: implications for osteoporotic fracture. Osteop. Int. 5 (1995) 252-261
142. Lovejoy C.O. The natural history of human gait and posture. Part 2. Hip and thigh. Gait Posture 21 (2005) 113-124
143. Lovejoy C.O., Heiple K.G., Meindl R.S., Ohman J.C., and White T.D. The Maka femur and its bearing on the antiquity of human walking: applying contemporary concepts of morphogenesis to the human fossil record. Am. J. Phys. Anthropol. 119 (2002) 97-133
144. Lovejoy C.O., McCollum M.A., Reno P.L., and Rosenman B.A. Developmental biology and human evolution. Annu. Rev. Anthropol. 32 (2003) 85-109
145. Macchiarelli R., Bondioli L., Galichon V., and Tobias P. Hip bone trabecular architecture shows uniquely distinctive locomotor behaviour in South African australopithecines. J. Hum. Evol. 36 (1999) 211-232
146. Maquet P.J. Biomechanics of the Hip: As Applied to Osteoarthritis and Related Conditions (1985), Springer, New York p. 309
147. Markolf K.L. Biomechanics of the hip. In: Amstutz H.C. (Ed). Hip Arthroplasty (1991), Churchill Livingstone, New York 15-23
148. Martin R.B., Burr D.B., and Sharkey N.A. Skeletal Tissue Mechanics (1998), Springer, New York p. 392
149. Martini F.H. Fundamentals of Anatomy and Physiology (1995), Prentice Hall, Upper Saddle River, NJ p. 1144
150. Martinón-Torres M. Quantifying trabecular orientation in the pelvic cancellous bone of modern humans, chimpanzees, and the Kebara 2 Neanderthal. Am. J. Hum. Biol. 15 (2003) 647-661
151. Mason M.W., Skedros J.G., and Bloebaum R.D. Evidence of strain-mode-related cortical adaptation in the diaphysis of the horse radius. Bone 17 (1995) 229-237
152. Mayhew P.M., Thomas C.D., Clement J.G., Loveridge N., Beck T.J., Bonfield W., Burgoyne C.J., and Reeve J. Relation between age, femoral neck cortical stability, and hip fracture risk. Lancet 366 (2005) 129-135
153. McHenry H.M. The ischium and hip extensor mechanism in human evolution. Am. J. Phys. Anthropol. 43 (1975) 39-46
154. Mehlman C.T., Araghi A., and Roy D.R. Hyphenated history: the Hueter-Volkmann law. Am. J. Orthop. 26 (1997) 798-800
155. Meislin R.J., Zuckerman J.D., Kummer F.J., and Frankel V.H. A biomechanical analysis of the sliding hip screw: the question of plate angle. J. Orthop. Trauma. 4 (1990) 106-130
156. Miller M.D. Review of Orthopaedics (1996), W.B. Saunders Company, Philadelphia, PA p. 510
157. Miller Z., Fuchs M.B., and Arcan M. Trabecular bone adaptation with an orthotropic material model. J. Biomech. 35 (2002) 247-256
158. Moen C.T., and Pelker R.R. Biomechanical and histological correlations in growth plate failure. J. Pediatr. Orthop. 4 (1984) 180-184
159. Moore K.L. Clinically Oriented Anatomy (1985), Williams and Wilkins, Baltimore, MD p. 1101
160. Morris J.M. Biomechanical aspects of the hip joint. Orthop. Clin. North Am. 2 (1971) 33-54
161. Möser M., and Hein W. Krafte an der hufte-das Unteergurtmodell. Beitr Orthop Traumatol 34 (1987) 83-92 179-189
162. Moss-Salentijn L. Long bone growth. In: Hall B.K. (Ed). Bone (1992), CRC Press, Boca Raton, FL 6 Bone growth-A, pp. 185-208
163. Mourtada F.A., Beck T.J., Hauser D.L., Ruff C.B., and Bao G. Curved beam model of the proximal femur for estimating stress using dual-energy X-ray absorptiometry derived structural geometry. J. Orthop. Res. 14 (1996) 483-492
164. Murray P.D.F. Bones: A Study of the Development and Structure of the Vertebrate Skeleton (1936), Cambridge University Press, Cambridge, UK p. 203
165. Myers E.R., and Wilson S.E. Biomechanics of osteoporosis and vertebral fracture. Spine 22 (1997) 25S-31S
166. Neville A.C. Biology of Fibrous Composites: Development Beyond the Cell Membrane (1993), Cambridge University Press, New York p. 214
167. Nuzzo S., Meneghini C., Braillon P., Bouvier R., Mobilio S., and Peyrin F. Microarchitectural and physical changes during fetal growth in human vertebral bone. J. Bone Miner Res. 18 (2003) 760-768
168. Oatis C. Structure and function of the bones and noncontractile elements of the hip. Kinesiology: The Mechanics and Pathomechanics of Human Movement (2004), Lippincott Williams and Wilkins, Philadelphia, PA 663-678
169. Odgaard A. Quantification of cancellous bone architecture. In: Cowin S.C. (Ed). Bone Mechanics Handbook (2001), CRC Press, Boca Raton, FL pp. 14-1-14-19
170. Ogden J.A. Hip development and vascularity: relationship to chondro-osseous trauma in the growing child. In: Ogden J.A. (Ed). The Hip (1981), CV Mosby, St. Louis, Mo
171. Ogden J.A. Femur. In: Ogden J.A. (Ed). Skeletal Injury in the Child (1990), W.B. Saunders Co., Philadelphia, PA 683-744
172. Oh I., and Harris W.H. Proximal strain distribution in the loaded femur. An in vitro comparison of the distributions in the intact femur and after insertion of different hip-replacement femoral components. J. Bone Joint Surg. 60-A (1978) 75-85
173. Osborne D., Effmann E., Broda K., and Harrelson J. The development of the upper end of the femur, with special reference to its internal architecture. Radiology 137 (1980) 71-76
174. Oxnard C.E., and Yang H.C.L. Beyond biometrics: studies of complex biological patterns. In: Ashton E.H., and Holmes R.L. (Eds). Perspectives in Primate Biology (The Proceedings of a Symposium Held at the Zoological Society of London 31 May and 1 June 1979) (1981), Academic Press, London, UK 127-167
175. Parfitt A.M., Mundy G.R., Roodman G.D., Hughes D.E., and Boyce B.F. A new model for the regulation of bone resorption, with particular reference to the effects of bisphosphonates. J. Bone Miner Res. 11 (1996) 150-159
176. Parkinson I.H., and Fazzalari N.L. Interrelationships between structural parameters of cancellous bone reveal accelerated structural change at low bone volume. J. Bone Miner Res. 18 (2003) 2200-2205
177. Pauwels F. Biomechanics of the Normal and Diseased Hip: Theoretical Foundation, Technique, and Results of Treatment (1976), Springer, New York p. 276
178. Pedersen D.R., Brand R.A., and Davy D.T. Pelvic muscle and acetabular contact forces during gait. J. Biomech. 30 (1997) 959-965
179. Phillips J.R., Williams J.F., and Melick R.A. Prediction of the strength of the neck of femur from its radiological appearance. Biomed. Eng. 10 (1975) 367-372
180. Pidaparti R.M.V., and Turner C.H. Cancellous bone architecture: advantages of nonorthogonal trabecular alignment under multidirectional loading. J. Biomech. 30 (1997) 979-983
181. Pinilla T.P., Boardman K.C., Bouxsein M.L., Myers E.R., and Hayes W.C. Impact direction from a fall influences the failure load of the proximal femur as much as age-related bone loss. Calcif. Tissue Int. 58 (1996) 231-235
182. Pontzer H., Lieberman D.E., Momin E., Devlin M.J., Polk J.D., Hallgrimsson B., and Cooper D.M. Trabecular bone in the bird knee responds with high sensitivity to changes in load orientation. J. Exp. Biol. 209 (2006) 57-65
183. Radin E.L., Blaha J.D., Rose R.M., and Litsky A.A. Practical Biomechanics for the Orthopaedic Surgeon (1992), Churchill Livingstone, New York p. 216
184. Rasch P.J., and Burke R.K. Kinesiology and Applied Anatomy (1978), Lea & Febiger, Philadelphia, PA p. 496
185. Reddy M.S., Geurs N.C., Wang I.C., Liu P.R., Hsu Y.T., Jeffcoat R.L., and Jeffcoat M.K. Mandibular growth following implant restoration: does Wolff's law apply to residual ridge resorption?. Int. J. Periodont. Restor. Dent. 22 (2002) 315-321
186. Reno P.L., Kriz M.A., McCollum M.A., and Lovejoy C.O. Scanning electron microscopic analysis of regional histomorphological variations within the physis of the primate proximal femur. Am. J. Phys. Anthrop. Suppl 34 (2002) 130
187. Resnick D., and Niwayama G. Osteoporosis. In: Resnick D., and Niwayama G. (Eds). Diagnosis of Bone and Joint Disorders (1988), WB Saunders Co, Philadelphia, PA 2022-2085
188. Rice J.C., Cowin S.C., and Bowman J.A. On the dependence of the elasticity and strength of cancellous bone on apparent density. J. Biomech. 21 (1988) 155-168
189. Richmond B.G., Nakatsukasa R., Ketcham R., and Hirakawa T. Trabecular bone structure in human and chimpanzee knee joints. Am. J. Phys. Anthrop. Suppl 38 (2004) 167
190. Roesler H. Some historical remarks of the theory of cancellous bone structure (Wolff's Law). In: Cowin S.C. (Ed). Mechanical Properties of Bone (1981), The American Society of Mechanical Engineers, New York 27-42
191. Roesler H. The history of some fundamental concepts in bone biomechanics. J. Biomech. 20 (1987) 1025-1034
192. Rook L., Bondioli L., Kohler M., Moya-Sola S., and Macchiarelli R. Oreopithecus was a bipedal ape after all: evidence from the iliac cancellous architecture. Proc. Natl. Acad. Sci. USA. 96 (1999) 8795-8799
193. Rosenthal D.I., and Scott J.A. Biomechanics important to interpret radiographs of the hip. Skel. Radiol. 9 (1983) 185-188
194. Rubin C.T. Response of bone to mechanical stimulation. In: Dee R. (Ed). Principles of Orthopaedic Practice (1988), McGraw-Hill Book Company, New York 79-89
195. Rubin C.T., and Hausman M.R. The cellular basis of Wolff's law. Transduction of physical stimuli to skeletal adaptation. Rheum. Dis. Clin. North Am. 14 (1988) 503-517
196. Rubin C.T., and McLeod K.J. Inhibition of osteopenia by biophysical intervention. In: Marcus R., Feldman D., and Kelsey J. (Eds). Osteoporosis (1996), Academic Press, New York 351-371
197. Rubin C., Gross T., Qin Y.X., Fritton S., Guilak F., and McLeod K. Differentiation of the bone-tissue remodeling response to axial and torsional loading in the turkey ulna. J. Bone Joint Surg. 78-A (1996) 1523-1533
198. Rubin C., Turner A.S., Bain S., Mallinckrodt C., and McLeod K. Low mechanical signals strengthen long bones. Nature 412 (2001) 603-604
199. Ruff C.B., and Hayes W.C. Cross-sectional geometry of Pecos Pueblo femora and tibiae-A biomechanical investigation: 1. Method and general patterns of variation. Am. J. Phys. Anthrop. 60 (1983) 359-381
200. Ruff C.B., and Hayes W.C. Bone-mineral content in lower limb. Relationship to cross-sectional geometry. J. Bone Joint Surg. 66-A (1984) 1024-1031
201. Ruff C., Holt B., and Trinkaus E. Who's afraid of the big bad Wolff?: "Wolff's law" and bone functional adaptation. Am. J. Phys. Anthropol. 129 (2006) 484-498
202. Rüttimann B. A noteworthy meeting of the society for nature research in Zurich: Two important precursors of Julius Wolff: Carl Culmann and Hermann von Meyer. In: Regling G. (Ed). Wolff's Law and Connective Tissue Regulation (1992), Walter de Gruyter, New York 13-22
203. Ryan T.M., and Ketcham R.A. Angular orientation of trabecular bone in the femoral head and its relationships to hip joint loads in leaping primates. J. Morphol. 265 (2005) 249-263
204. Ryan T.M., and Ketcham R.A. Angular orientation of trabecular bone in the femoral head and its relationships to hip joint loads in leaping primates. J. Morphol. 265 (2005) 249-263
205. Rydell N.W. Forces acting on the femoral head-prosthesis. A study on strain gauge supplied prostheses in living persons. Acta Orthop. Scand. 37 Suppl 88 (1966) 1-132
206. Sabry F.F., Ebraheim N.A., and Rezcallah A.T. Internal architecture of the calcaneus: implications for calcaneus fractures. Foot Ankle Int 21 (2000) 114-118
207. Schatzker J. Subtrochanteric fractures of the femur. The Rationale of Operative Fracture Care (1984), Springer, Berlin, Germany 217-234
208. Schatzker J. Screws and plates and their application. In: Müller M.E., Allgöwer M., Schneider R., and Willenegger H. (Eds). Manual of Internal Fixation-Techniques Recommended by the AO-ASIF Group (1991), Springer, New York 179-290
209. Schmitt D. Insights into the evolution of human bipedalism from experimental studies of humans and other primates. J. Exp. Biol. 206 (2003) 1437-1448
210. Siffert R.S. Patterns of deformity of the developing hip. In: Katz J.F., and Siffert R.S. (Eds). Management of Hip Disorders in Children (1983), J.B. Lippincott Co, Philadelphia, PA 73-91
211. Sim E., Freimuller W., and Reiter T.J. Finite element analysis of the stress distributions in the proximal end of the femur after stabilization of a pertrochanteric model fracture: a comparison of two implants. Injury 26 (1995) 445-449
212. Sinclair D., and Dangerfield P. Human Growth After Birth (1998), Oxford University Press, New York p. 71
213. Singh M., Nagrath A.R., and Maini P.S. Changes in trabecular pattern of the upper end of the femur as an index of osteoporosis. J. Bone Joint Surg. 52-A (1970) 457-467
214. Skedros J.G. Collagen fiber orientation: a characteristic of strain-mode-related regional adaptation in cortical bone. Bone 28 (2001) S110-S111
215. Skedros J.G., and Bloebaum R.D. Geometric analysis of a tension/compression system: implications for femoral neck modeling. Trans. Orthop. Res. Soc. 37th Annual Meeting (1991) 421
216. Skedros J.G., and Brady J.H. Ontogeny of cancellous bone anisotropy in a natural "trajectorial structure": genetics or epigenetics. J. Bone Miner. Res. Suppl. 1 (2001) S331
217. Skedros J.G., Bloebaum R.D., Mason M.W., and Bramble D.M. Analysis of a tension/compression skeletal system: possible strain-specific differences in the hierarchical organization of bone. Anat. Rec. 239 (1994) 396-404
218. Skedros J.G., Hughes D.E., Nelson K., and Winet H. Collagen fiber orientation in the proximal femur: challenging Wolff's tension/compression interpretation. J. Bone Miner Res. 14 (1999) S441
219. Skedros J.G., Brady J., and Sybrowsky C.L. Mathematical analysis of trabecular trajectories in apparent trajectorial structures: the unfortunate historical emphasis on the human proximal femur. Am. J. Phys. Anthropol. 33 (2002) 142
220. Skedros J.G., Hunt K.J., and Bloebaum R.D. Relationships of loading history and structural and material characteristics of bone: development of the mule deer calcaneus. J. Morphol. 259 (2004) 281-307
221. Skerry T. Biomechanical influences on skeletal growth and development. In: O'Higgins P., and Cohn M.J. (Eds). Development, Growth, and Evolution: Implications for the Study of the Homonid Skeleton (2000), Academic Press, San Diego, CA 30-39
222. Skerry T.M., and Lanyon L.E. Interruption of disuse by short duration walking exercise does not prevent bone loss in the sheep calcaneus. Bone 16 (1995) 269-274
223. Smith J.W. The relationship of epiphysial plates to stress in some bones of the lower limb. J. Anat. London 96 (1962) 58-78
224. Smith J.W. The structure and stress relations of fibrous epiphysial plates. J. Anat. London 96 (1962) 209-225
225. Solger B. Der gegenwärtige stand der lehre von der knochen-aechitecur. Moleschott's Untersuchungen zur Naturlehre des Menschen und der Thiere XVI: (1899) 187-219
226. Stanford C.M., and Brand R.A. Toward an understanding of implant occlusion and strain adaptive bone modeling and remodeling. J. Prosthet. Dent. 81 (1999) 553-561
227. Stanford C.M., and Schneider G.B. Functional behaviour of bone around dental implants. Gerodontology 21 (2004) 71-77
228. Stauber M., Rapillard L., Van Lenthe G.H., Zysset P., and Muller R. Important of individual rods and plates in the assessment of bone quality and their contribution to bone stiffness. J. Bone Miner. Res. 21 (2006) 586-595
229. Stephen L., and Lee S. William Fairbairn. The Dictionary of National Biography (1964), Oxford University Press, Oxford, UK 987-989
230. Su S.C. Microstructure and Mineral Content Correlations to Strain Parameters in Cortical Bone of the Artiodactyl Calcaneus (1998), University of Utah, Salt Lake City, UT p. 64
231. Su S.C., Skedros J.G., Bachus K.N., and Bloebaum R.D. Loading conditions and cortical bone construction of an artiodactyl calcaneus. J. Exp. Biol. 202 (1999) 3239-3254
232. Swartz S., Parker A., and Huo C. Theoretical and empirical scaling patterns and topological homology in bone trabeculae. J. Exp. Biol. 201 (1998) 573-590
233. Tachdjian M.O. Developmental coxa vara. Pediatric orthopedics (1990), WB Saunders Co, Philadelphia, PA 585
234. Tanck E., Hannink G., Ruimerman R., Buma P., Burger E., and Huiskes R. Cortical development under the growth plate is regulated by mechanical load transfer. J. Anat. 208 (2006) 73-79
235. Teng S., and Herring S.W. A stereological study of trabecular architecture in the mandibular condyle of the pig. Arch. Oral. Biol. 40 (1995) 299-310
236. Thompson A. The relation of structure and function as illustrated by the form of the lower epiphysial suture of the femur. J. Anat. London 36 (1902) 95-105
237. Thompson D.W. On Growth and Form (1917), Cambridge University Press, Cambridge, UK p. 793
238. Thompson D.W. On form and mechanical efficiency. On Growth and Form (1943), MacMillan Company, New York 958-1005
239. Thomason J.J. To what extent can the mechanical environment of a bone be inferred from its internal architecture?. In: Thomason J.J. (Ed). Functional Vertebrate Morphology in Vertebrate Paleontology (1995), Cambridge University Press, Cambridge, UK 249-277
240. Thorpe S.K., Crompton R.H., Gunther M.M., Ker R.F., and McNeill Alexander R. Dimensions and moment arms of the hind- and forelimb muscles of common chimpanzees (Pan troglodytes). Am. J. Phys. Anthropol. 110 (1999) 179-199
241. Tillman B., Bartz B., and Schleider A. Stress in the human ankle joint: a brief review. Arch. Orthop. Trauma Surg. 103 (1985) 385-391
242. Tobin W. The internal architecture of the femur and its clinical significance. J. Bone Joint Surg. 37-A (1955) 57-71
243. Tobin W. An atlas of the comparative anatomy of the upper end of the femur. Clin. Orthop. Rel. Res. 56 (1968) 83-103
244. Treharne R.W. Review of Wolff's law and its proposed means of operation. Orthop. Rev. 10 (1981) 35-47
245. Triepel H. Die Architektur der knochenspongiosa in neuer Auffassung. Z. Knostitutionslehre 8 (1922) 269-311
246. Trueta J. Studies of the Development and Decay of the Human Frame (1968), W.B. Saunders Co., Philadelphia, PA p. 389
247. Tsubota K., Adachi T., and Tomita Y. Functional adaptation of cancellous bone in human proximal femur predicted by trabecular surface remodeling simulation toward uniform stress state. J. Biomech. 35 (2002) 1541-1551
248. Turner C.H. On Wolff's law of trabecular architecture. J. Biomech. 25 (1992) 1-9
249. Turner C.H., Owan I., and Takano Y. Mechanotransduction in bone: role of strain rate. Am. J. Physiol. 269 (1995) E438-E442
250. Van Audekercke R., and Van der Perre G. The effect of osteoporosis on the mechanical properties of bone structures. Clin Rheumatol. Suppl (1994) 38-44
251. Van Rietbergen B., Huiskes R., Eckstein F., and Ruegsegger P. Trabecular bone tissue strains in the healthy and osteoporotic human femur. J. Bone Miner Res. 18 (2003) 1781-1788
252. Vander Sloten J., and Van der Perre G. Trabecular structure compared to stress trajectories in the proximal femur and the calcaneus. J. Biomed. Eng. 11 (1989) 203-208
253. Venieratos D., Papadopoulos N.J., Anastassiou J., and Katritsis E.D. A quantitative Estimation of the divergence between the trabecular system and the stress trajectories in the upper end of the human femoral bone. Anat. Anz. 163 (1987) 301-310
254. Viola, T., 2002. Locomotion dependent variation in the proximal femoral trabecular pattern in primates. Institute of Anthropology, University of Vienna, Austria. Ph.D. Thesis, 123.
255. von Meyer G.H. Die Architekur der Spongiosa. Arch. Anat. Physiol. Wissenschaf. Med. 34 (1867) 615-628
256. Wang X., and Niebur G.L. Microdamage propagation in trabecular bone due to changes in loading mode. J. Biomech. 39 (2006) 781-790
257. Ward S., and Sussman R. Correlates between locomotor anatomy and behavior in two sympatric species of Lemur. Am. J. Phys. Anthropol. 50 (1979) 575-590
258. Whedon G.D., and Heaney R.P. Effects of physical inactivity, paralysis, and weightlessness on bone growth. In: Hall B.K. (Ed). Bone: Bone Growth vol. 7 (1993), CRC Press, Boca Raton, FL 57-78
259. Williams J.L., Do P.D., Eick J.D., and Schmidt T.L. Tensile properties of the physis vary with anatomic location, thickness, strain rate and age. J. Orthop. Res. 19 (2001) 1043-1048
260. Williams J.L., Vani J.N., Eick J.D., Petersen E.C., and Schmidt T.L. Shear strength of the physis varies with anatomic location and is a function of modulus, inclination, and thickness. J. Orthop. Res. 17 (1999) 214-222
261. Wolff J. Uber die bedeutung der architektur der spongiösen substanz für die frage vom knochenwachsthum. Central. Med. Wissenschaf.: VII Jahrgang 54 (1869) 849-851
262. Wolff J. Uber die innere architektur der knochen und ihre bedeutung für die frage vom knochenwachstum. Arch. Pathol. Anat. Physiol. Klin. Med. 50 (1870) 389-453
263. Wolff J. Beiträge zur lehre von der heilung der fracturen. Arch. Klin. Chirurgie 14 (1872) 270-312
264. Wolff J. Zur Knochenwachsthumsfrage. Arch. Pathol. Anat. Physiol. Klin. Med. 61 (1874) 417-456
265. Wolff J. Das Gesetz der Transformation der Knochen (1892), Springer, Berlin, Germany p. 126
266. Wolff J. The Law of Bone Remodeling (1986), Springer, Berlin, Germany p. 126
267. Woo S.L., Kuei S.C., Amiel D., Gomez M.A., Hayes W.C., White F.C., and Akeson W.H. The effect of prolonged physical training on the properties of long bone: a study of Wolff's Law. J. Bone Joint Surg. 63-A (1981) 780-787
268. Yamada H. Strength of Biological Materials (1970), Williams and Wilkins Co., Baltimore, MD pp. 23-30
269. Zippel H. Julius Wolff and the law of bone remodeling. In: Regling G. (Ed). Wolff's Law and Connective Tissue Regulation (1992), Walter de Gruyter, New York 1-12
270. Zschokke E. Weitere Untersuchungen uber das Verhaltniss der Knochenbildung zur Statik und Mechanik des Vertebraten-Skelettes (1892), Zurich, Switzerland p. 102
271. Zylstra M. Trabecular architecture of metacarpal heads in catarrhines: a preliminary report. Am. J. Phys. Anthropol. 30 (2000) 331