References
- Ambardar , A. and Ferris , C.D. 1978 . Compact anisotropic bone: elastic constants, in vitro aging effects and numerical results of a mathematical model . Acta Biologica Academiae Scientiarum Hungaricae , 29 ( 1 ) : 81 – 94 .
- Aoubiza , B. , Crolet , J.M. and Meunier , A. 1996 . On the mechanical characterization of compact bone structure using the homogenization theory . J. Biomech. , 29 ( 12 ) : 1539 – 1547 .
- Ashman , R.B. , Cowin , S.C. , van Buskirk , W.C. and Rice , J.C. 1984 . A continuous wave technique for the measurement of the elastic properties of cortical bone . J. Biomech. , 17 ( 5 ) : 349 – 361 .
- Bousson , V. , Meunier , A. , Bergot , C. , Vicaut , E. , Rocha , M.A. , Morais , M.H. , Laval-Jeantet , A.M. and Laredo , J.D. 2001 . Distribution of intracortical porosity in human midfemoral cortex by age and gender . J. Bone Miner. Res. , 16 : 1308 – 1317 .
- Broz , J.J. , Simske , S.J. and Greenberg , A.R. 1995 . Material and compositional properties of selectively demineralized cortical bone . J. Biomech. , 28 ( 11 ) : 1357 – 1368 .
- Cowin , S.C. 1999 . Bone poroelasticity . J. Biomech. , 32 ( 3 ) : 217 – 238 .
- Cowin , S.C. 2001 . Bone Mechanics Handbook , 2nd ed. , Edited by: Cowin , S.C. Vol. 1 , Boca Raton, FL : CRC Press .
- Crolet , J.M. , Aoubiza , B. and Meunier , A. 1993 . Compact bone: numerical simulation of mechanical characteristics . J. Biomech. , 26 ( 6 ) : 677 – 687 .
- Currey , J.D. 2002 . Bones: Structure and Mechanics , Princeton, NJ : Academic Press .
- Currey , J.D. and Zioupos , P. 2001 . The effect of porous microstructure on the anisotropy of bone-like tissue: a counterexample . J. Biomech. , 34 ( 5 ) : 707 – 710 .
- Dong , N.X. and Guo , E.X. 2004 . The dependence of transversely isotropic elasticity of human femoral cortical bone on porosity . J. Biomech. , 37 ( 8 ) : 1281 – 1287 .
- Eringen , A.C. 1967 . Mechanics of Continua , New York : Wiley & Sons Inc. .
- François , M. , Geymonat , G. and Berthaud , Y. 1998 . Determination of the symmetries of an experimentally determined stiffness tensor: application to acoustic measurements . Int. J. Solids Struct. , 35 ( 31–32 ) : 4091 – 4106 .
- Harrigan , T.P. , Jasty , M. , Mann , R.W. and Harris , W.H. 1988 . Limitations of the continuum assumption in cancellous bone . J. Biomech. , 21 ( 4 ) : 269 – 275 .
- Hellmich , C. 2005 . “ Microelasticity of bone ” . In Applied Micromechanics of Porous Media , Edited by: Dormieux , L. and Ulm , F.-J. 289 – 332 . New York : Springer .
- Hellmich , C. and Ulm , F.J. 2002 . Micromechanical model for ultrastructural stiffness of mineralized tissues . J. Eng. Mech. , 128 ( 8 ) : 898 – 908 .
- Hellmich , C. and Ulm , F.J. 2004 . Can the diverse elastic properties of trabecular and cortical bone be attributed to only a few tissue-independant phase properties and their interactions? . Biomech. Model. Mechanobiol. , 2 : 219 – 238 .
- Hellmich , C. , Barthelemy , J.-F. and Dormieux , L. 2004 . Mineral-collagen interactions in elasticity of bone ultrastructure—a continuum micromechanics approach . Eur. J. Mech. A/Solids , 23 ( 5 ) : 783 – 810 .
- Helnwein , P. 2001 . Some remarks on the compressed matrix representation of symmetric second-order and fourth-order tensors . Comput. Methods Appl. Mech. Eng. , 190 ( 22–23 ) : 2753 – 2770 .
- Hoc , T. , Henry , L. , Verdier , M. , Aubry , D. , Sedel , L. and Meunier , A. 2006 . Effect of microstructure on the mechanical properties of Haversian cortical bone . Bone , 38 ( 4 ) : 466 – 474 .
- Hofmann , T. , Heyroth , F. , Meinhard , H. , Franzel , W. and Raum , K. 2006 . Assessment of composition and anisotropic elastic properties of secondary osteon lamellae . J. Biomech. , 39 ( 12 ) : 2282 – 2294 .
- Hollister , S.J. and Kikuchi , N. 1992 . A comparison of homogenization and standard mechanics analyses for periodic porous composites . Comput. Mech. , 10 : 73 – 95 .
- Hollister , S.J. , Fyhrie , D.P. , Jepsen , K.J. and Goldstein , S.A. 1991 . Application of homogenization theory to the study of trabecular bone mechanics . J. Biomech. , 24 ( 9 ) : 825 – 839 .
- Hollister , S.J. , Brennan , J.M. and Kikuchi , N. 1994 . A homogenization sampling procedure for calculating trabecular bone effective stiffness and tissue level stress . J. Biomech. , 27 ( 4 ) : 433 – 444 .
- Kabel , J. , van Rietbergen , B. , Dalstra , M. , Odgaard , A. and Huiskes , R. 1999 . The role of an effective isotropic tissue modulus in the elastic properties of cancellous bone . J. Biomech. , 32 ( 7 ) : 673 – 680 .
- Kachanov , M. and Sevostianov , I. 2001 . Authors' response . J. Biomech. , 34 ( 5 ) : 709 – 710 .
- Katz , J.L. and Meunier , A. 1997 . Scanning acoustic microscopy of human and canine cortical bone microstructure at high frequencies . Stud. Health Technol. Inform. , 40 : 123 – 137 .
- Katz , J.L. and Yoon , H.S. 1984 . The structure and anisotropic mechanical properties of bone . IEEE Trans. Biomed. Eng. , 31 ( 12 ) : 878 – 884 .
- Lide , R. , ed. 1993 . Handbook of Chemistry and Physics , 74th ed. , Boca Raton : CRC Press .
- Lucchinetti , E. 2001 . “ Composite models of bone properties ” . In Bone Mechanics Handbook , Edited by: Cowin , S.C. Boca Raton, FL : CRC Press .
- Martin , R.B. , Burr , D.B. and Sharkey , N.A. 1998 . Skeletal Tissue Mechanics , 1st ed. , Vol. 1 , New York : Springer .
- Pithioux , M. , Lasaygues , P. and Chabrand , P. 2002 . An alternative ultrasonic method for measuring the elastic properties of cortical bone . J. Biomech. , 35 : 961 – 968 .
- Racila , M. and Crolet , J.M. 2006 . Multi physic and multi scale aspects in human cortical bone . Rom. J. Phys. , 51 ( 5–6 ) : 1157 – 1161 .
- Raum , K. , Jenderka , K.V. , Klemenz , A. and Brandt , J. 2003 . Multilayer analysis: quantitative scanning acoustic microscopy for tissue characterization at a microscopic scale . IEEE Trans. Ultrason. Ferroelect. Freq. Contr. , 50 ( 5 ) : 507 – 516 .
- Raum , K. , Reisshauer , J. and Brandt , J. 2004 . Frequency and resolution dependence of the anisotropic impedance estimation in cortical bone using time-resolved scanning acoustic microscopy . J. Biomed. Mater. Res. , 71A ( 3 ) : 430 – 438 .
- Raum , K. , Leguerney , I. , Chandelier , F. , Bossy , E. , Talmant , M. , Saied , A. , Peyrin , F. and Laugier , P. 2005 . Bone microstructure and elastic tissue properties are reflected in qus axial transmission measurements . Ultrasound Med. Biol. , 31 ( 9 ) : 1225 – 1235 .
- Raum , K. , Cleveland , R.O. , Peyrin , F. and Laugier , P. 2006 . Derivation of elastic stiffness from site-matched mineral density and acoustic impedance maps . Phys. Med. Biol. , 51 ( 3 ) : 747 – 758 .
- Reilly , D.T. and Burstein , A.H. 1975 . The elastic and ultimate properties of compact bone tissue . J. Biomech. , 8 ( 2 ) : 393 – 405 .
- Rho , J.Y. 1996 . An ultrasonic method for measuring the elastic properties of human tibial cortical and cancellous bone . Ultrasonics , 34 ( 8 ) : 777 – 783 .
- Rho , J.Y. , Zioupos , P. , Currey , J.D. and Pharr , G.M. 2002 . Microstructural elasticity and regional heterogeneity in human femoral bone of various ages examined by nano-indentation . J. Biomech. , 35 ( 2 ) : 189 – 198 .
- Royer , D. and Dieulesaint , E. 1999 . Elastic Waves in Solids. 1. Free and Guided Propagation , Vol. 1 , New York : Springer Verlag .
- Sanchez-Hubert , J. and Sanchez-Palencia , E. 1992 . Introduction aux méthodes asymptotiques et à l'homogénéisation , Paris : Masson .
- Sevostianov , I. and Kachanov , M. 1998 . On the relationship between microstructure of the cortical bone and its overall elastic properties . Int. J. Fract. , 92 ( 1 ) : 1 – 8 .
- Sevostianov , I. and Kachanov , M. 2000 . Impact of the porous microstructure on the overall elastic properties of the osteonal cortical bone . J. Biomech. , 33 ( 7 ) : 881 – 888 .
- Stoneham , M.A. and Harding , J.H. 2003 . Not too big, not too small: the appropriate scale . Nat. Mater. , 2 : 77 – 83 .
- Takano , Y. , Turner , C.H. and Burr , D.B. 1996 . Mineral anisotropy in mineralized tissues is similar among species and mineral growth occurs independently of collagen orientation in rats: results from acoustic velocity measurements . J. Bone Miner. Res. , 11 ( 9 ) : 1292 – 1301 .
- Taylor , W.R. , Roland , E. , Ploeg , H. , Hertig , D. , Klabunde , R. , Warner , M.D. , Hobatho , M.C. , Rakotomanana , L. and Clift , S.E. 2002 . Determination of orthotropic bone elastic constants using fea and modal analysis . J. Biomech. , 35 ( 6 ) : 767 – 773 .
- Torquato , S. 2002 . “ Random heterogeneous materials ” . In Interdisciplinary Applied Mathematics; Mechanics and Materials , Edited by: Antman , S.S. New York : Springer .
- van Buskirk , W.C. , Cowin , S.C. and Ward , R.N. 1981 . Ultrasonic measurements of orthotropic elastic constants of bovine femoral bone . J. Biomech. Eng.-T ASME , 103 : 67 – 71 .
- van Rietbergen , B. , Weinans , H. , Huiskes , R. and Odgaard , A. 1995 . A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models . J. Biomech. , 28 ( 1 ) : 69 – 81 .
- van Rietbergen , B. , Odgaard , A. , Kabel , J. and Huiskes , R. 1996 . Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture . J. Biomech. , 29 ( 12 ) : 1653 – 1657 .
- Watzky , A. and Naili , S. 2004 . Orthotropic bone remodeling: case of plane stresses . Mech. Res. Commun. , 31 ( 5 ) : 617 – 625 .
- Weiner , S. and Traub , W. 1986 . Organization of hydroxyapatite crystals within collagen fibrils . FEBS Lett. , 206 ( 2 ) : 262 – 266 .
- Weiner , S. , Traub , W. and Wagner , H.D. 1999 . Lamellar bone: structure–function relations . J. Struct. Biol. , 126 ( 3 ) : 241 – 255 .
- Yoon , H.S. and Katz , J.L. 1976a . Ultrasonic wave propagation in human cortical bone. I: theoretical considerations for hexagonal symmetry . J. Biomech. , 9 : 407 – 412 .
- Yoon , H.S. and Katz , J.L. 1976b . Ultrasonic wave propagation in human cortical bone. II: measurements of elastic properties and microhardness . J. Biomech. , 9 ( 7 ) : 459 – 464 .
- Zaoui , A. 2002 . Continuum micromechanics . J. Eng. Mech. , 128 : 808 – 816 .
- Zohdi , T.I. and Wriggers , P. 2005 . Introduction to Computational Micromechanics , Edited by: Pfeiffer , F. and Wriggers , P. Berlin : Springer . Lecture Notes in Applied Computational Mechanics
- Zysset , P.K. , Guo , X.E. , Hoffler , C.E. , Moore , K.E. and Goldstein , S.A. 1999 . Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur . J. Biomech. , 32 ( 10 ) : 1005 – 1012 .