A new method for quantitative ultrasound measurements at multiple skeletal sites: First results of precision and fracture discrimination, Clinical Densitometry, vol.3, issue.10, pp.1-7, 2000. ,
Bone microstructure and elastic tissue properties are reflected in QUS axial transmission measurements, Ultrasound Med. Biol, vol.31, pp.1225-1235, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00443425
Comparison of three ultrasonic axial transmission methods for bone assessment, Ultrasound in Medicine & Biology, vol.31, issue.5, pp.633-642, 2005. ,
DOI : 10.1016/j.ultrasmedbio.2005.02.001
Thickness sensitivity of ultrasound velocity in long bone phantoms, Ultrasound in Medicine & Biology, vol.30, issue.11, pp.1517-1521, 2004. ,
DOI : 10.1016/j.ultrasmedbio.2004.08.017
The dependence of transversely isotropic elasticity of human femoral cortical bone on porosity, Journal of Biomechanics, vol.37, issue.8, pp.1281-1287, 2004. ,
DOI : 10.1016/j.jbiomech.2003.12.011
Impact of the porous microstructure on the overall elastic properties of the osteonal cortical bone The compressive behaviour of bone as a two phase porous material, J. Biomech. J. Bone Jt. Surg., Am, vol.33, issue.59, pp.881-888, 1977. ,
The effect of porosity and mineral content on the Young's modulus of elasticity of compact bone Young's modulus, bending strength, and tissue physical properties of human compact bone, J. Biomech. J. Orthop . Res, vol.21, issue.8, pp.131-139, 1988. ,
Transmission scanning acoustic imaging of human cortical bone and relation with the microstructure, Tane, O. Hirotsugu, M. Hirao, T. Ikeda, and H. Nakajima, pp.639-647, 2002. ,
DOI : 10.1016/j.clinbiomech.2004.02.009
A synchrotron radiation microtomography system for the analysis of trabecular bone samples, Medical Physics, vol.8, issue.2, pp.2194-2204, 1999. ,
DOI : 10.1002/jbmr.5650100213
Derivation of elastic stiffness from site-matched mineral density and acoustic impedance maps, Physics in Medicine and Biology, vol.51, issue.3, pp.747-758, 2005. ,
DOI : 10.1088/0031-9155/51/3/018
URL : https://hal.archives-ouvertes.fr/hal-00443423
wave propagation in heterogeneous media: Velocity???stress finite???difference method, GEOPHYSICS, vol.51, issue.4, pp.889-901, 1986. ,
DOI : 10.1190/1.1442147
Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media, GEOPHYSICS, vol.66, issue.1, pp.294-307, 2001. ,
DOI : 10.1190/1.1444908
A continuous wave technique for the measurement of the elastic properties of cortical bone, Journal of Biomechanics, vol.17, issue.5, pp.349-361, 1984. ,
DOI : 10.1016/0021-9290(84)90029-0
Acoustic Fields and Waves in Solids, 1973. ,
On the anisotropic elastic properties of hydroxyapatite, Journal of Biomechanics, vol.4, issue.3, pp.221-227, 1971. ,
DOI : 10.1016/0021-9290(71)90007-8
Ultrasonic wave propagation in human cortical bone???II. Measurements of elastic properties and microhardness, Journal of Biomechanics, vol.9, issue.7, pp.459-462, 1976. ,
DOI : 10.1016/0021-9290(76)90089-0
Anisotropy of Young's modulus of bone, Nature, vol.21, issue.5742, pp.106-107, 1980. ,
DOI : 10.1115/1.3629590
An alternative ultrasonic method for measuring the elastic properties of cortical bone, Journal of Biomechanics, vol.35, issue.7, pp.961-968, 2002. ,
DOI : 10.1016/S0021-9290(02)00027-1
URL : https://hal.archives-ouvertes.fr/hal-00008733
Ultrasonic Measurement of Orthotropic Elastic Constants of Bovine Femoral Bone, Journal of Biomechanical Engineering, vol.103, issue.2, pp.67-71, 1981. ,
DOI : 10.1115/1.3138262
The effects of remodeling on the elastic properties of bone, Calcified Tissue International, vol.14, issue.S1, pp.31-36 ,
DOI : 10.1097/00003086-197003000-00034
An ultrasonic method for measuring the elastic properties of human tibial cortical and cancellous bone, Ultrasonics, vol.34, issue.8, pp.717-783, 1996. ,
DOI : 10.1016/S0041-624X(96)00078-9
Contribution of collagen and mineral to the elastic anisotropy of bone, Calcified Tissue International, vol.4, issue.5, pp.381-386, 1994. ,
DOI : 10.1007/BF00299319
Assessment of composition and anisotropic elastic properties of secondary osteon lamellae, Journal of Biomechanics, vol.39, issue.12, pp.2282-2294, 2006. ,
DOI : 10.1016/j.jbiomech.2005.07.009
The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques, Journal of Biomechanics, vol.32, issue.4, pp.437-441, 1999. ,
DOI : 10.1016/S0021-9290(98)00177-8
Microstructural elasticity and regional heterogeneity in human femoral bone of various ages examined by nano-indentation, Journal of Biomechanics, vol.35, issue.2, pp.189-198, 2002. ,
DOI : 10.1016/S0021-9290(01)00199-3
An Application of Nanoindentation Technique to Measure Bone Tissue Lamellae Properties, Journal of Biomechanical Engineering, vol.120, issue.7, pp.1046-1053, 2005. ,
DOI : 10.1016/0021-9290(75)90075-5
Comparison of Microcomputed Tomographic and Microradiographic Measurements of Cortical Bone Porosity, Calcified Tissue International, vol.74, issue.5, pp.437-447, 2004. ,
DOI : 10.1007/s00223-003-0071-z
Quantitative 3D analysis of the canal network in cortical bone by microcomputed tomography, Anat. Rec, vol.274, pp.169-179, 2003. ,
The elastic and ultimate properties of compact bone tissue, Journal of Biomechanics, vol.8, issue.6, pp.393-405, 1975. ,
DOI : 10.1016/0021-9290(75)90075-5
Compact anisotropic bone: Elastic constants , in vitro aging effects and numerical results of a mathematical model, Acta Biol. Acad. Sci. Hung, vol.29, pp.81-941978 ,
The relationship between elastic properties and microstructure of bovine cortical bone, Journal of Biomechanics, vol.17, issue.4, pp.231-240, 1984. ,
DOI : 10.1016/0021-9290(84)90134-9
Anisotropic Poisson's ratio and compression modulus of cortical bone determined by speckle interferometry, Journal of Biomechanics, vol.40, issue.2, pp.252-264, 2007. ,
DOI : 10.1016/j.jbiomech.2006.01.021
Effect of Voxel Size on 3D Micro-CT Analysis of Cortical Bone Porosity, Calcified Tissue International, vol.47, issue.3, pp.211-219, 2007. ,
DOI : 10.1007/s00223-005-0274-6
Int???gration par s???ries des ???quations diff???rentielles lin???aires, Mathematische Annalen, vol.32, issue.3, pp.450-456, 1888. ,
DOI : 10.1007/BF01443609
Methods of Matrix Algebra Academic, 1965. ,
Theoretical similarities of Rayleigh and Lamb modes of vibration, The Journal of the Acoustical Society of America, vol.60, issue.2, pp.374-377, 1976. ,
DOI : 10.1121/1.381092
On wave propagating along the plane surface of an elastic solid, Proc. London Math. Soc, pp.1-17 ,
The Mechanical Properties of Cortical Bone, The Journal of Bone & Joint Surgery, vol.56, issue.5, pp.1001-1022, 1974. ,
DOI : 10.2106/00004623-197456050-00012
An ultrasonic method for measuring the elastic properties of human tibial cortical and cancellous bone, Ultrasonics, vol.34, issue.8, pp.777-783, 1996. ,
DOI : 10.1016/S0041-624X(96)00078-9
Stable recursive algorithm for elastic wave propagation in layered anisotropic media: Stiffness matrix method, The Journal of the Acoustical Society of America, vol.112, issue.3, pp.822-834, 2002. ,
DOI : 10.1121/1.1497365
A Baseline and Vision of Ultrasonic Guided Wave Inspection Potential, Journal of Pressure Vessel Technology, vol.46, issue.3, pp.273-282, 2002. ,
DOI : 10.1109/58.764852
A sextic formalism for three-dimensional elastodynamics of cylindrically anisotropic radially inhomogeneous materials, Proc. R. Soc. London, pp.1611-1639, 2003. ,
DOI : 10.1098/rspa.2002.1075
Long-wavelength dispersion of acoustic waves in transversely inhomogeneous anisotropic plates, Wave Motion, vol.42, issue.4, pp.367-382, 2005. ,
DOI : 10.1016/j.wavemoti.2005.04.005
Steady State Problems in Anisotropic Elasticity, Journal of Mathematics and Physics, vol.35, issue.1-4, pp.77-103, 1962. ,
DOI : 10.1002/sapm1956351323
Transmission of Elastic Waves through a Stratified Solid Medium, Journal of Applied Physics, vol.20, issue.2, pp.89-93, 1950. ,
DOI : 10.1063/1.1698236
Guided modes in a plane elastic layer with gradually continuous acoustic properties, NDT & E International, vol.37, issue.8, pp.633-644, 2004. ,
DOI : 10.1016/j.ndteint.2004.04.003
Stable reformulation of transfer matrix method for wave propagation in layered anisotropic media, Ultrasonics, vol.39, issue.6, pp.413-424, 2001. ,
DOI : 10.1016/S0041-624X(01)00082-8
Experimental Confirmation of Lamb Waves at Megacycle Frequencies, Journal of Applied Physics, vol.90, issue.6, pp.967-971, 1961. ,
DOI : 10.1121/1.1916293
Picard iteration algorithm combined with Gauss???Seidel technique for initial value problems, Applied Mathematics and Computation, vol.190, issue.1, pp.345-355, 2007. ,
DOI : 10.1016/j.amc.2007.01.058
Guided waves in fluid-filled pipes surrounded by different fluids, Ultrasonics, vol.39, issue.5, pp.367-375, 2001. ,
DOI : 10.1016/S0041-624X(01)00064-6
Acoustic Fields and Waves in Solids, 1973. ,
Le dTveloppement en sTrie de Peano du matricant pour l'Ttude de la propagation d'ondes en milieux continvment variables ? Peano expansion of the matricant to study elastic wave propagation in continuously heterogeneous media, 2005. ,
Propagation of elastic waves in a fluid-loaded anisotropic functionally graded waveguide: Application to ultrasound characterization, The Journal of the Acoustical Society of America, vol.127, issue.3, pp.1307-1317, 2010. ,
DOI : 10.1121/1.3292949
URL : https://hal.archives-ouvertes.fr/hal-00711941
Impact of localized inhomogeneity on the surface-wave velocity and bulk-wave reflection in solids, Ultrasonics, vol.46, issue.1, pp.1-12, 2007. ,
DOI : 10.1016/j.ultras.2006.09.001
Effect of porosity on effective diagonal stiffness coefficients (cii) and elastic anisotropy of cortical bone at 1MHz: A finite-difference time domain study, The Journal of the Acoustical Society of America, vol.122, issue.3, pp.1810-1817, 2007. ,
DOI : 10.1121/1.2759165
Transmission scanning acoustic imaging of human cortical bone and relation with the microstructure, Clinical Biomechanics, vol.19, issue.6, pp.639-647, 2004. ,
DOI : 10.1016/j.clinbiomech.2004.02.009
Distribution of intracortical porosity in human midfemoral cortex by age and gender, Journal of Bone and Mineral Research, vol.16, pp.1308-1317, 2001. ,
The dependence of transversely isotropic elasticity of human femoral cortical bone on porosity, Journal of Biomechanics, vol.37, issue.8, pp.1281-1287, 2004. ,
DOI : 10.1016/j.jbiomech.2003.12.011
Polynomial method applied to acoustic waves in inhomogeneous cylinders, IEEE Symposium on Ultrasonics, 2003, 2003. ,
DOI : 10.1109/ULTSYM.2003.1293165
URL : https://hal.archives-ouvertes.fr/hal-00145983
Acoustical Guided Waves in Inhomogeneous Cylindrical Materials, Ferroelectrics, vol.2, issue.1, pp.115-123, 2008. ,
DOI : 10.1016/j.wavemoti.2005.01.005
URL : https://hal.archives-ouvertes.fr/hal-00284506
Guided waves in radially graded cylinders: a polynomial approach, NDT & E International, vol.38, issue.5, pp.344-353, 2005. ,
DOI : 10.1016/j.ndteint.2004.10.004
URL : https://hal.archives-ouvertes.fr/hal-00125131
Three???Dimensional Investigation of the Propagation of Waves in Hollow Circular Cylinders. I. Analytical Foundation, The Journal of the Acoustical Society of America, vol.31, issue.5, pp.568-573, 1959. ,
DOI : 10.1121/1.1907753
Bone mass and architecture determination: state of the art, Best Practice & Research Clinical Endocrinology & Metabolism, vol.22, issue.5, pp.737-764, 2008. ,
DOI : 10.1016/j.beem.2008.07.003
Influence of a gradient of material properties on ultrasonic wave propagation in cortical bone: Application to axial transmission, The Journal of the Acoustical Society of America, vol.125, issue.6, pp.4043-4052, 2009. ,
DOI : 10.1121/1.3117445
URL : https://hal.archives-ouvertes.fr/hal-00711923
Characteristics of waves in a functionally graded cylinder, International Journal for Numerical Methods in Engineering, vol.38, issue.3, pp.653-676, 2002. ,
DOI : 10.1016/S0020-7683(00)00219-5
The dispersion of surface waves on multilayered media, Bulletin of the Seismological Society of America, vol.43, pp.377-393, 1953. ,
DOI : 10.1029/SP030p0086
Design optimization of functionally graded dental implant, Bio-Medical Materials and Engineering, vol.14, pp.133-143, 2004. ,
Wave propagation in transversely isotropic cylinders, International Journal of Solids and Structures, vol.44, issue.16, pp.5236-5246, 2007. ,
DOI : 10.1016/j.ijsolstr.2006.12.029
Surface impedance matrices to model the propagation in multilayered media, Ultrasonics, vol.41, issue.7, pp.501-507, 2003. ,
DOI : 10.1016/S0041-624X(03)00167-7
A propagator matrix method for periodically stratified media, Journal of Acoustical Society of America, vol.73, issue.1, pp.137-142, 1982. ,
On Waves in an Elastic Plate, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.93, issue.648, pp.114-128, 1917. ,
DOI : 10.1098/rspa.1917.0008
Ultrasonic Method for Measuring Elastic Coefficients of Bone and Results on Fresh and Dried Bovine Bones, IEEE Transactions on Biomedical Engineering, vol.17, issue.2, 1970. ,
DOI : 10.1109/TBME.1970.4502706
Development of a new ultrasonic technique for bone and biomaterials in vitro characterization, Journal of Biomedical Material Research Part B, pp.63-441, 2002. ,
Design optimization of functionally graded dental implant for bone remodeling, Composites Part B: Engineering, vol.40, issue.7, pp.668-675, 2009. ,
DOI : 10.1016/j.compositesb.2009.04.015
A robust transfer matrix formulation for the ultrasonic response of multilayered absorbing media, The Journal of the Acoustical Society of America, vol.92, issue.1, pp.452-467, 1992. ,
DOI : 10.1121/1.404256
Mode Coupling Occurring in the Propagation of Elastic Pulses in Wires, The Journal of the Acoustical Society of America, vol.33, issue.4, pp.435-445, 1961. ,
DOI : 10.1121/1.1908685
Axisymmetric Vibrations of Orthotropic Cylinders, The Journal of the Acoustical Society of America, vol.36, issue.11, pp.2106-2112, 1964. ,
DOI : 10.1121/1.1919329
Wave Propagation in Transversely Isotropic Circular Cylinders Part I: Theory, The Journal of the Acoustical Society of America, vol.37, issue.6, pp.1016-1026, 1965. ,
DOI : 10.1121/1.1909508
Modeling the impact of soft tissue on axial transmission measurements of ultrasonic guided waves in human radius, The Journal of the Acoustical Society of America, vol.124, issue.4, pp.2364-2373, 2008. ,
DOI : 10.1121/1.2973228
Vibrations and waves in laminated orthotropic circular cylinders, Journal of Sound and Vibration, vol.18, issue.3, pp.429-444, 1971. ,
DOI : 10.1016/0022-460X(71)90714-0
application, Physiological Measurement, vol.23, issue.4, pp.755-768, 2002. ,
DOI : 10.1088/0967-3334/23/4/313
URL : https://hal.archives-ouvertes.fr/hal-00902380
Modal Analysis of Hollow Cylindrical Guided Waves and Applications, Japanese Journal of Applied Physics, vol.40, issue.Part 1, No. 1, pp.364-370, 2001. ,
DOI : 10.1143/JJAP.40.364
An alternative ultrasonic method for measuring the elastic properties of cortical bone, Journal of Biomechanics, vol.35, issue.7, pp.961-968, 2002. ,
DOI : 10.1016/S0021-9290(02)00027-1
URL : https://hal.archives-ouvertes.fr/hal-00008733
Axisymmetric wave propagation in fluid???loaded cylindrical shells. II: Theory versus experiment, The Journal of the Acoustical Society of America, vol.92, issue.2, pp.1144-1155, 1992. ,
DOI : 10.1121/1.404041
Guided ultrasound wave propagation in intact and healing long bones, Ultrasound in Medicine & Biology, vol.32, issue.5, pp.693-708, 2006. ,
DOI : 10.1016/j.ultrasmedbio.2006.02.001
Three-dimensional finite element modeling of guided ultrasound wave propagation in intact and healing long bones, The Journal of the Acoustical Society of America, vol.121, issue.6, pp.3907-3921, 2007. ,
DOI : 10.1121/1.2354067
On wave propagating along the plane surface of an elastic solid, Proceedings of the London Mathematical Society, vol.7, pp.4-11, 1885. ,
Spatial distribution of anisotropic acoustic impedance assessed by time-resolved 50-MHz scanning acoustic microscopy and its relation to porosity in human cortical bone, Bone, vol.43, pp.187-194, 2008. ,
A sextic formalism for three-dimensional elastodynamics of cylindrically anisotropic radially inhomogeneous materials, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.459, issue.2035, pp.1611-1639, 2003. ,
DOI : 10.1098/rspa.2002.1075
Wave propagation in anisotropic laminated hollow cylinders of infinite extent, The Journal of the Acoustical Society of America, vol.96, issue.6, pp.3744-3752, 1994. ,
DOI : 10.1121/1.410564
Steady State Problems in Anisotropic Elasticity, Journal of Mathematics and Physics, vol.35, issue.1-4, pp.77-103, 1962. ,
DOI : 10.1002/sapm1956351323
Transmission of Elastic Waves through a Stratified Solid Medium, Journal of Applied Physics, vol.20, issue.2, pp.89-93, 1950. ,
DOI : 10.1063/1.1698236
Stable reformulation of transfer matrix method for wave propagation in layered anisotropic media, Ultrasonics, vol.39, issue.6, pp.413-424, 2001. ,
DOI : 10.1016/S0041-624X(01)00082-8
Biocompatibility of materials and development to functionally graded implant for bio-medical application, Composites Science and Technology, vol.64, issue.6, pp.893-908, 2004. ,
DOI : 10.1016/j.compscitech.2003.09.005
Picard iteration algorithm combined with Gauss???Seidel technique for initial value problems, Applied Mathematics and Computation, vol.190, issue.1, pp.345-355, 2007. ,
DOI : 10.1016/j.amc.2007.01.058
An Experimental and Theoretical Investigation of Elastic Wave Propagation in a Cylinder, The Journal of the Acoustical Society of America, vol.51, issue.1B, pp.265-283, 1972. ,
DOI : 10.1121/1.1912838
Bone strength and its determinants, Osteoporosis International, vol.18, issue.S3, pp.13-18, 2003. ,
DOI : 10.1002/jor.1100180315
Prediction of fracture load at different skeletal sites by geometric properties of the cortical shell, Journal of Bone and Mineral Research, vol.5, issue.9, pp.1356-1363, 1996. ,
DOI : 10.1097/00004424-199328090-00006
The role of cortical bone and its microstructure in bone strength, Age and Ageing, vol.35, issue.suppl_2, pp.27-31, 2006. ,
DOI : 10.1093/ageing/afl081
Le d eveloppement en s erie de Peano du matricant pour l' etude de la propagation d'ondes en milieux contin^ ument variables?Peano expansion of the matricant to study elastic wave propagation in continuously heterogeneous media, 2005. ,
Propagation of elastic waves in an anisotropic functionally graded hollow cylinder in vacuum, Ultrasonics, vol.51, issue.2, pp.123-130, 2011. ,
DOI : 10.1016/j.ultras.2010.07.001
Propagation of elastic waves in a fluid-loaded anisotropic functionally graded waveguide: Application to ultrasound characterization, The Journal of the Acoustical Society of America, vol.127, issue.3, pp.1307-1317, 2010. ,
DOI : 10.1121/1.3292949
URL : https://hal.archives-ouvertes.fr/hal-00711941
Effect of porosity on effective diagonal stiffness coefficients (cii) and elastic anisotropy of cortical bone at 1MHz: A finite-difference time domain study, The Journal of the Acoustical Society of America, vol.122, issue.3, pp.1810-1817, 2007. ,
DOI : 10.1121/1.2759165
Three-dimensional simulations of ultrasonic axial transmission velocity measurement on cortical bone models, The Journal of the Acoustical Society of America, vol.115, issue.5 ,
DOI : 10.1121/1.1689960
URL : https://hal.archives-ouvertes.fr/hal-00109676
CT of the Middiaphyseal Femur: Cortical Bone Mineral Density and Relation to Porosity, Radiology, vol.217, issue.1, pp.179-187, 2000. ,
DOI : 10.1148/radiology.217.1.r00se11179
Distribution of Intracortical Porosity in Human Midfemoral Cortex by Age and Gender, Journal of Bone and Mineral Research, vol.26, issue.7, pp.1308-1317, 2001. ,
DOI : 10.1148/radiology.217.1.r00se11179
Mechanical factors in bone growth and development, Bone, vol.18, issue.1, pp.5-10, 1996. ,
DOI : 10.1016/8756-3282(95)00373-8
Incidence of clinically diagnosed vertebral fractures: A population-based study in, J Bone Miner Res, vol.87, pp.221-227, 1985. ,
Bone density and risk of hip fracture in men and women: cross sectional analysis, BMJ, vol.315, issue.7102, pp.221-225, 1997. ,
DOI : 10.1136/bmj.315.7102.221
The dependence of transversely isotropic elasticity of human femoral cortical bone on porosity, Journal of Biomechanics, vol.37, issue.8, pp.1281-1287, 2004. ,
DOI : 10.1016/j.jbiomech.2003.12.011
Bone Matters: Are Density Increases Necessary to Reduce Fracture Risk?, Journal of Bone and Mineral Research, vol.6, issue.6, pp.183-187, 2000. ,
DOI : 10.7326/0003-4819-117-1-1
URL : http://onlinelibrary.wiley.com/doi/10.1359/jbmr.2000.15.2.183/pdf
Age trends in remodeling of the femoral midshaft differ between the sexes, Journal of Orthopaedic Research, vol.145, issue.4, pp.590-597, 2005. ,
DOI : 10.1042/cs0820429
Three???Dimensional Investigation of the Propagation of Waves in Hollow Circular Cylinders. I. Analytical Foundation, The Journal of the Acoustical Society of America, vol.31, issue.5, pp.568-573, 1959. ,
DOI : 10.1121/1.1907753
Femoral geometry as a risk factor for osteoporotic hip fracture in men and women, Medical Engineering & Physics, vol.30, issue.10, pp.1275-1286, 2008. ,
DOI : 10.1016/j.medengphy.2008.09.002
A determination of the minimum sizes of representative volume elements for the prediction of cortical bone elastic properties, Biomechanics and Modeling in Mechanobiology, vol.23, issue.2???3, pp.1-13, 2011. ,
DOI : 10.1007/978-3-540-32360-0
Influence of a gradient of material properties on ultrasonic wave propagation in cortical bone: Application to axial transmission, The Journal of the Acoustical Society of America, vol.125, issue.6, pp.4043-4052, 2009. ,
DOI : 10.1121/1.3117445
The dispersion of surface waves on multilayered media, Bull Seismol Soc Am, vol.43, pp.377-393, 1953. ,
DOI : 10.1029/SP030p0086
Hip Fractures and the Contribution of Cortical Versus Trabecular Bone to Femoral Neck Strength, Journal of Bone and Mineral Research, vol.24, issue.3, pp.468-474, 2009. ,
DOI : 10.1359/jbmr.081108
Surface impedance matrices to model the propagation in multilayered media, Ultrasonics, vol.41, issue.7, pp.501-507, 2003. ,
DOI : 10.1016/S0041-624X(03)00167-7
Age and bone mass as predictors of fracture in a prospective study., Journal of Clinical Investigation, vol.81, issue.6, pp.1804-1809, 1988. ,
DOI : 10.1172/JCI113523
FRAX??? and the assessment of fracture probability in men and women from the UK, Osteoporosis International, vol.17, issue.Suppl 2, pp.385-397, 2008. ,
DOI : 10.1093/qjmed/hci029
A propagator matrix method for periodically stratified media, J Acoust Soc Am, vol.731, pp.137-142, 1982. ,
Assessment of Anisotropic Tissue Elasticity of Cortical Bone from High-Resolution, Angular Acoustic Measurements, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.54, issue.8, pp.1560-1570, 2007. ,
DOI : 10.1109/TUFFC.2007.426
On Waves in an Elastic Plate, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.93, issue.648, pp.114-128, 1917. ,
DOI : 10.1098/rspa.1917.0008
Development of a new ultrasonic technique for bone and biomaterialsin vitro characterization, Journal of Biomedical Materials Research, vol.34, issue.4, pp.441-446, 2002. ,
DOI : 10.1016/S0041-624X(96)00078-9
A robust transfer matrix simulation for ultrasonic response of multilayered absorbing media, J Acoust Soc Am, vol.92, pp.452-467, 1992. ,
Cortical and trabecular bone in the femoral neck both contribute to proximal femur failure load prediction, Osteoporosis International, vol.22, issue.3, pp.445-453, 2009. ,
DOI : 10.4135/9781412985604
Meta-analysis of how well measures of bone mineral density predict occurrence of osteoporotic fractures, BMJ, vol.312, issue.7041, pp.1254-1259, 1996. ,
DOI : 10.1136/bmj.312.7041.1254
Cross-Sectional Versus Longitudinal Evaluation of Bone Loss in Men and Women, Osteoporosis International, vol.11, issue.7, pp.592-599, 2000. ,
DOI : 10.1007/s001980070080
Axisymmetric Vibrations of Orthotropic Cylinders, The Journal of the Acoustical Society of America, vol.36, issue.11, pp.2106-2112, 1964. ,
DOI : 10.1121/1.1919329
Assessment of the cortical bone thickness using ultrasonic guided waves: Modelling and in vitro study, Ultrasound in Medicine & Biology, vol.33, issue.2, pp.254-262, 2007. ,
DOI : 10.1016/j.ultrasmedbio.2006.07.038
Modeling the impact of soft tissue on axial transmission measurements of ultrasonic guided waves in human radius, The Journal of the Acoustical Society of America, vol.124, issue.4, pp.2364-2373, 2008. ,
DOI : 10.1121/1.2973228
Comparison of three ultrasonic axial transmission methods for bone assessment, Ultrasound in Medicine & Biology, vol.31, issue.5, pp.633-642, 2005. ,
DOI : 10.1016/j.ultrasmedbio.2005.02.001
Vibrations and waves in laminated orthotropic circular cylinders, Journal of Sound and Vibration, vol.18, issue.3, pp.429-444, 1971. ,
DOI : 10.1016/0022-460X(71)90714-0
Modal Analysis of Hollow Cylindrical Guided Waves and Applications, Japanese Journal of Applied Physics, vol.40, issue.Part 1, No. 1, pp.364-370, 2001. ,
DOI : 10.1143/JJAP.40.364
Assessment of bone status using speed of sound at multiple anatomical sites, Ultrasound in Medicine & Biology, vol.27, issue.10, pp.1337-1345, 2001. ,
DOI : 10.1016/S0301-5629(01)00437-9
Guided ultrasound wave propagation in intact and healing long bones, Ultrasound in Medicine & Biology, vol.32, issue.5, pp.693-708, 2006. ,
DOI : 10.1016/j.ultrasmedbio.2006.02.001
Three-dimensional finite element modeling of guided ultrasound wave propagation in intact and healing long bones, The Journal of the Acoustical Society of America, vol.121, issue.6 ,
DOI : 10.1121/1.2354067
The Mechanical Properties of Cortical Bone, The Journal of Bone & Joint Surgery, vol.56, issue.5, pp.1001-1022, 1974. ,
DOI : 10.2106/00004623-197456050-00012
Risk factors for hip fracture in women with high BMD: EPIDOS study, Osteoporosis International, vol.65, issue.2, pp.149-154, 2005. ,
DOI : 10.1007/s00198-004-1661-y
A sextic formalism for three-dimensional elastodynamics of cylindrically anisotropic radially inhomogeneous materials, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.459, issue.2035 ,
DOI : 10.1098/rspa.2002.1075
Wave propagation in anisotropic laminated hollow cylinders of infinite extent, The Journal of the Acoustical Society of America, vol.96, issue.6, pp.3744-3752, 1994. ,
DOI : 10.1121/1.410564
Steady State Problems in Anisotropic Elasticity, Journal of Mathematics and Physics, vol.35, issue.1-4, pp.77-103, 1962. ,
DOI : 10.1002/sapm1956351323
Use of multiple acoustic wave modes for assessment of long bones: Model study, Ultrasonics, vol.43, issue.8, pp.672-680, 2005. ,
DOI : 10.1016/j.ultras.2005.03.004
Transmission of Elastic Waves through a Stratified Solid Medium, Journal of Applied Physics, vol.20, issue.2, pp.89-93, 1950. ,
DOI : 10.1063/1.1698236
A Comparison of Bone Mineral Density between Caucasian, Asian and Afro-Caribbean Women, Clinical Science, vol.87, issue.5, pp.587-591, 1994. ,
DOI : 10.1042/cs0870587
High resolution cortical bone thickness measurement from clinical CT data, Medical Image Analysis, vol.14, issue.3, pp.276-290, 2010. ,
DOI : 10.1016/j.media.2010.01.003
URL : https://doi.org/10.1016/j.media.2010.01.003
Stable reformulation of transfer matrix method for wave propagation in layered anisotropic media, Ultrasonics, vol.39, issue.6, pp.413-424, 2001. ,
DOI : 10.1016/S0041-624X(01)00082-8
Bone Mineral Density Differences at the Femoral Neck and Ward's Triangle: A Comparison Study on the Reference Data Between Chinese and Caucasian Women, Calcified Tissue International, vol.67, issue.3, pp.195-198, 2000. ,
DOI : 10.1007/s002230001139
The Response of Pediatric Ribs to Quasi-static Loading: Mechanical Properties and Microstructure, Annals of Biomedical Engineering, vol.120, issue.398???419, 2013. ,
DOI : 10.1115/1.2834288
Design and validation of bending test method for characterization of miniature pediatric cortical bone specimens, Proc. Inst, pp.105-113, 2013. ,
DOI : 10.1016/S8756-3282(00)00269-6
Reduced diaphyseal strength associated with high intracortical vascular porosity within long bones of children with osteogenesis imperfecta, Bone, vol.66, pp.121-130, 2014. ,
DOI : 10.1016/j.bone.2014.05.022
Bone properties by nanoindentation in mild and severe osteogenesis imperfecta, Clinical Biomechanics, vol.28, issue.1, pp.110-116, 2013. ,
DOI : 10.1016/j.clinbiomech.2012.10.003
A continuous wave technique for the measurement of the elastic properties of cortical bone, Journal of Biomechanics, vol.17, issue.5, pp.349-3610021, 1984. ,
DOI : 10.1016/0021-9290(84)90029-0
The relative influence of apatite crystal orientations and intracortical porosity on the elastic anisotropy of human cortical bone, Journal of Biomechanics, vol.45, issue.16, pp.2743-2749, 2012. ,
DOI : 10.1016/j.jbiomech.2012.09.011
Spatial distribution of acoustic and elastic properties of human femoral cortical bone, Journal of Biomechanics, vol.37, issue.4, pp.503-510, 2004. ,
DOI : 10.1016/j.jbiomech.2003.09.013
URL : https://hal.archives-ouvertes.fr/hal-00023425
Accurate measurement of cortical bone elasticity tensor with resonant ultrasound spectroscopy, Journal of the Mechanical Behavior of Biomedical Materials, vol.18, 2013. ,
DOI : 10.1016/j.jmbbm.2012.09.017
In vitro ultrasonic and mechanic characterization of the modulus of elasticity of children cortical bone, Ultrasonics, vol.54, issue.5, 2013. ,
DOI : 10.1016/j.ultras.2013.09.014
URL : https://hal.archives-ouvertes.fr/hal-00937888
Computed tomography, histological and ultrasonic measurements of adolescent scoliotic rib hump geometrical and material properties, Journal of Biomechanics, vol.45, issue.14, pp.2467-2471, 2012. ,
DOI : 10.1016/j.jbiomech.2012.07.002
URL : https://hal.archives-ouvertes.fr/hal-01278231
The role of mineralization and organic matrix in the microhardness of bone tissue from controls and osteoporotic patients, Bone, vol.43, issue.3, pp.532-538, 2008. ,
DOI : 10.1016/j.bone.2008.05.024
Delayed puberty and peak bone mass, European Journal of Endocrinology, vol.139, issue.3, pp.257-259, 1998. ,
DOI : 10.1530/eje.0.1390257
URL : http://www.eje-online.org/content/139/3/257.full.pdf
Peak bone mineral density, lean body mass and fractures, Bone, vol.46, issue.2, pp.336-341, 2010. ,
DOI : 10.1016/j.bone.2009.10.003
The contribution of the organic matrix to bone???s material properties, Bone, vol.31, issue.1, pp.8-11, 2002. ,
DOI : 10.1016/S8756-3282(02)00815-3
The elastic moduli of human subchondral, trabecular, and cortical bone tissue and the size-dependency of cortical bone modulus, Journal of Biomechanics, vol.23, issue.11, pp.1103-1113, 1990. ,
DOI : 10.1016/0021-9290(90)90003-L
The longitudinal Young's modulus of cortical bone in the midshaft of human femur and its correlation with CT scanning data, 2004. ,
Role of collagen and other organics in the mechanical properties of bone, Osteoporos. Int, vol.14, pp.29-36, 2003. ,
The mechanical properties of bone tissue in children, The Journal of Bone & Joint Surgery, vol.57, issue.6, pp.810-814, 1975. ,
DOI : 10.2106/00004623-197557060-00015
The mechanical and morphological properties of 6 year-old cranial bone, Journal of Biomechanics, vol.45, issue.15, pp.2493-2498, 2012. ,
DOI : 10.1016/j.jbiomech.2012.07.001
Skeletal status in males aged 7?80???years assessed by quantitative ultrasound at the hand phalanges, Osteoporosis International, vol.14, issue.4, pp.295-300, 2003. ,
DOI : 10.1007/s00198-002-1355-2
Anatomic variation in the elastic anisotropy of cortical bone tissue in the human femur, Journal of the Mechanical Behavior of Biomedical Materials, vol.2, issue.3, pp.255-263, 2009. ,
DOI : 10.1016/j.jmbbm.2008.08.005
Mechanical properties of OI type III bone tissue measured by nanoindentation, Journal of Biomedical Materials Research Part A, vol.29, issue.1, pp.71-77, 2006. ,
DOI : 10.1097/01241398-198507000-00014
The degree of mineralization is a determinant of bone strength: a study on human calcanei, Bone, vol.34, issue.5, 2004. ,
DOI : 10.1016/j.bone.2003.12.012
URL : https://hal.archives-ouvertes.fr/inserm-00557244
Assessment of cortical bone elasticity and strength: Mechanical testing and ultrasound provide complementary data, Medical Engineering & Physics, vol.31, issue.9, pp.1140-1147, 2009. ,
DOI : 10.1016/j.medengphy.2009.07.011
Influence of a gradient of material properties on ultrasonic wave propagation in cortical bone: Application to axial transmission, The Journal of the Acoustical Society of America, vol.125, issue.6, pp.4043-4052, 2009. ,
DOI : 10.1121/1.3117445
Contribution of collagen and mineral to the elastic anisotropy of bone, Calcified Tissue International, vol.4, issue.5, 1994. ,
DOI : 10.1007/BF00299319
Atlas of mechanical properties of human cortical and cancellous bone, 1991. ,
Anisotropy of Young's modulus of human tibial cortical bone, Medical & Biological Engineering & Computing, vol.9, issue.2938, 2000. ,
DOI : 10.1002/j.1538-7305.1943.tb01304.x
Mechanical and mineral properties of osteogenesis imperfecta human bones at the tissue level, Bone, vol.65, pp.18-24, 2014. ,
DOI : 10.1016/j.bone.2014.04.030
P020 Bending properties of cranial bone segments of new-born children, S65, pp.21-9290, 1998. ,
DOI : 10.1016/S0021-9290(98)80132-2
The effects of remodeling on the elastic properties of bone, Calcified Tissue International, vol.14, issue.S1, pp.31-36, 1984. ,
DOI : 10.1097/00003086-197003000-00034
Young's modulus, bending strength, and tissue physical properties of human compact bone, Journal of Orthopaedic Research, vol.14, issue.4, pp.592-603, 1990. ,
DOI : 10.3109/ort.1965.36.suppl-83.01
Elastic Coefficients of Animal Bone, Science, vol.165, issue.3890, pp.287-288, 1969. ,
DOI : 10.1126/science.165.3890.287
Ultrasonic characterization of orthotropic elastic bovine bones, Ultrasonics, vol.39, issue.8, pp.567-573, 2002. ,
DOI : 10.1016/S0041-624X(02)00261-5
URL : https://hal.archives-ouvertes.fr/hal-01438705
A study of some properties of a sample of bovine cortical bone using ultrasound, Calcified Tissue International, vol.4, issue.1, pp.107-117, 1979. ,
DOI : 10.1177/00220345780570032201
The relationship between elastic properties and microstructure of bovine cortical bone, Journal of Biomechanics, vol.17, issue.4, pp.231-240, 1984. ,
DOI : 10.1016/0021-9290(84)90134-9
Mechanical properties of metaphyseal bone in the proximal femur, Journal of Biomechanics, vol.24, issue.5, pp.317-3290021, 1991. ,
DOI : 10.1016/0021-9290(91)90350-V
Fetal head molding: An investigation utilizing a finite element model of the fetal parietal bone, Journal of Biomechanics, vol.13, issue.1, pp.17-26, 1980. ,
DOI : 10.1016/0021-9290(80)90004-4
Biomechanical evaluation of fetal calf skull as a model for testing halo-pin designs for use in children, J. Biomech, vol.40, pp.1137-1144, 2007. ,
Bone Elasticity and Ultrasound Velocity Are Affected by Subtle Changes in the Organic Matrix, Journal of Bone and Mineral Research, vol.20, issue.7, pp.114-121, 1998. ,
DOI : 10.2106/00004623-197557070-00013
The dependence of transversely isotropic elasticity of human femoral cortical bone on porosity, Journal of Biomechanics, vol.37, issue.8, pp.1281-1287, 2004. ,
DOI : 10.1016/j.jbiomech.2003.12.011
Compressive behaviour of child and adult cortical bone, Bone, vol.49, issue.4, pp.769-776, 2011. ,
DOI : 10.1016/j.bone.2011.06.035
The elastic and ultimate properties of compact bone tissue, Journal of Biomechanics, vol.8, issue.6, pp.393-4050021, 1975. ,
DOI : 10.1016/0021-9290(75)90075-5
The elastic modulus for bone, Journal of Biomechanics, vol.7, issue.3, pp.271-2750021, 1974. ,
DOI : 10.1016/0021-9290(74)90018-9
An ultrasonic method for measuring the elastic properties of human tibial cortical and cancellous bone, Ultrasonics, vol.34, issue.8, pp.777-783, 1996. ,
DOI : 10.1016/S0041-624X(96)00078-9
Anatomic variation in the elastic inhomogeneity and anisotropy of human femoral cortical bone tissue is consistent across multiple donors, Journal of Biomechanics, vol.44, issue.9, pp.1817-1820, 2011. ,
DOI : 10.1016/j.jbiomech.2011.04.009
Relations Between Age, Mineral Density and Mechanical Properties of Human Femoral Compacta, Acta Orthopaedica Scandinavica, vol.43, issue.5, pp.496-502, 1976. ,
DOI : 10.1259/0007-1285-43-516-886
Pamidronate does not adversely affect bone intrinsic material properties in children with osteogenesis imperfecta, Bone, vol.39, issue.3, pp.616-622, 2006. ,
DOI : 10.1016/j.bone.2006.02.071
Ultrasonic wave propagation in human cortical bone???II. Measurements of elastic properties and microhardness, Journal of Biomechanics, vol.9, issue.7, pp.459-4640021, 1976. ,
DOI : 10.1016/0021-9290(76)90089-0
Changes in the Stiffness, Strength, and Toughness of Human Cortical Bone With Age, Bone, vol.22, issue.1, pp.57-66, 1998. ,
DOI : 10.1016/S8756-3282(97)00228-7
Surgeries were performed at the Timone Hospital All children were ambulatory prior to surgery and none received medications known to affect bone remodeling In accordance with the French code of public health and after approbation of the study by the committee for the protection of persons, informed consents were obtained from children's legal guardians. In addition, bone samples were harvested in the distal 1/3 of the fibula from 16 human donors (7 males and 9 females, mean age7SD: 75.0712.9 years, range: 50?91 years) Autopsies were performed between 2010 and 2012 under the guidance of the INSERM UMR-S 1033, bone remodeling parameters) and the IFSTTAR UMR-T 9406, 2007. ,
Aging of Microstructural Compartments in Human Compact Bone, Journal of Bone and Mineral Research, vol.48, issue.Suppl 1, pp.1012-1019, 2003. ,
DOI : 10.2106/00004623-196648010-00014
A continuous wave technique for the measurement of the elastic properties of cortical bone, Journal of Biomechanics, vol.17, issue.5, pp.349-361, 1984. ,
DOI : 10.1016/0021-9290(84)90029-0
Osteocyte regulation of bone mineral: a little give and take, Osteoporosis International, vol.14, issue.Pt 2, pp.2067-2079, 2012. ,
DOI : 10.1359/jbmr.1999.14.12.2015
Trabecular and Cortical Microstructure and Fragility of the Distal Radius in Women, Journal of Bone and Mineral Research, vol.49, issue.4, pp.621-629, 2015. ,
DOI : 10.1016/j.bone.2011.08.009
Risedronate Slows or Partly Reverses Cortical and Trabecular Microarchitectural Deterioration in Postmenopausal Women, Journal of Bone and Mineral Research, vol.74, issue.2, pp.380-388, 2014. ,
DOI : 10.1007/s00223-003-0042-4
Bone???s Material Constituents and their Contribution to Bone Strength in Health, Disease, and Treatment, Calcified Tissue International, vol.23, issue.2, 2015. ,
DOI : 10.1359/jbmr.071014
Cortical Porosity Identifies Women With Osteopenia at Increased Risk for Forearm Fractures, Journal of Bone and Mineral Research, vol.39, issue.4, pp.1356-1362, 2014. ,
DOI : 10.1118/1.3689813
Effect of porosity on effective diagonal stiffness coefficients (cii) and elastic anisotropy of cortical bone at 1 MHz: a finite-difference time domain study, J. Acoust. Soc. Am, vol.122, 1810. ,
Regional differences in cortical porosity in the fractured femoral neck, Bone, vol.24, issue.1, pp.57-64, 1999. ,
DOI : 10.1016/S8756-3282(98)00143-4
Super-osteons (remodeling clusters) in the cortex of the femoral shaft: Influence of age and gender, The Anatomical Record, vol.21, issue.4, pp.378-386, 2001. ,
DOI : 10.1016/S8756-3282(97)00173-7
Accurate measurement of cortical bone elasticity tensor with resonant ultrasound spectroscopy, Journal of the Mechanical Behavior of Biomedical Materials, vol.18, pp.12-19, 2013. ,
DOI : 10.1016/j.jmbbm.2012.09.017
Fracture risk and height: An association partly accounted for by cortical porosity of relatively thinner cortices, Journal of Bone and Mineral Research, vol.162, issue.7, pp.2017-2026, 2013. ,
DOI : 10.1093/aje/kwi258
Remodeling markers are associated with larger intracortical surface area but smaller trabecular surface area: A twin study, Bone, vol.49, issue.6, pp.1125-1130, 2011. ,
DOI : 10.1016/j.bone.2011.08.009
The amazing osteocyte, Journal of Bone and Mineral Research, vol.58, issue.(suppl1), pp.229-238, 2011. ,
DOI : 10.1093/jmicro/dfp032
Volumetric quantitative computed tomography of the proximal femur: relationships linking geometric and densitometric variables to bone strength. Role for compact bone, Osteoporosis International, vol.217, issue.4, pp.855-864, 2006. ,
DOI : 10.1148/radiology.217.1.r00se11179
Architecture of cortical bone determines in part its remodelling and structural decay, Bone, vol.55, issue.2, pp.353-358, 2013. ,
DOI : 10.1016/j.bone.2013.04.020
Cortical bone: a target for fracture prevention?, The Lancet, vol.375, issue.9727, pp.1672-1673, 2010. ,
DOI : 10.1016/S0140-6736(10)60444-8
MECHANISMS RESPONSIBLE FOR LONGITUDINAL GROWTH OF THE CORTEX, The Journal of Bone and Joint Surgery-American Volume, vol.85, issue.9, pp.85-1739, 2003. ,
DOI : 10.2106/00004623-200309000-00013
3D characterization of pores in the cortical bone of human femur in the elderly at different locations as determined by synchrotron micro-computed tomography images, Osteoporosis International, vol.41, issue.Suppl 1, pp.1023-1033, 2013. ,
DOI : 10.1016/j.patcog.2007.12.011
URL : https://hal.archives-ouvertes.fr/hal-00796435
Age- and gender-dependent changes in three-dimensional microstructure of cortical and trabecular bone at the human femoral neck, Osteoporosis International, vol.19, issue.4, pp.627-636, 2010. ,
DOI : 10.2106/00004623-199703000-00016
Age-Related Changes in Bone Remodelling and Structure in Men: Histomorphometric Studies, Journal of Osteoporosis, vol.90, issue.5, 2011. ,
DOI : 10.1007/BF02058664
Age-dependent change in the 3D structure of cortical porosity at the human femoral midshaft, Bone, vol.40, issue.4, pp.957-965, 2007. ,
DOI : 10.1016/j.bone.2006.11.011
The mechanical properties of bone tissue in children, The Journal of Bone & Joint Surgery, vol.57, issue.6, pp.810-814, 1975. ,
DOI : 10.2106/00004623-197557060-00015
The dependence of transversely isotropic elasticity of human femoral cortical bone on porosity, Journal of Biomechanics, vol.37, issue.8, pp.1281-1287, 2004. ,
DOI : 10.1016/j.jbiomech.2003.12.011
Functions of the haversian system, American Journal of Anatomy, vol.43, issue.3, pp.269-305, 1962. ,
DOI : 10.1001/archsurg.1934.01180040042005
Anatomic variation in the elastic anisotropy of cortical bone tissue in the human femur, Journal of the Mechanical Behavior of Biomedical Materials, vol.2, issue.3, pp.255-263, 2009. ,
DOI : 10.1016/j.jmbbm.2008.08.005
Change in porosity is the major determinant of the variation of cortical bone elasticity at the millimeter scale in aged women, Bone, vol.49, issue.5, pp.1020-1026, 2011. ,
DOI : 10.1016/j.bone.2011.08.002
URL : https://hal.archives-ouvertes.fr/hal-01301976
Can the diverse elastic properties of trabecular and cortical bone be attributed to only a few tissue-independent phase properties and their interactions?, Biomechanics and Modeling in Mechanobiology, vol.2, issue.4, pp.219-238, 2004. ,
DOI : 10.1007/s10237-004-0040-0
A new method for the model-independent assessment of thickness in three-dimensional images, Journal of Microscopy, vol.185, issue.1, pp.67-75, 1997. ,
DOI : 10.1046/j.1365-2818.1997.1340694.x
Skeletal adaptations during growth, Triangle; Sandoz J. Med. Sci, vol.31, pp.77-88, 1992. ,
The microscopic determination of age in human bone, American Journal of Physical Anthropology, vol.1, issue.2, pp.149-164, 1965. ,
DOI : 10.1002/ajpa.1330230215
Expansion of the medullary cavity at the expense of cortex in postmenopausal osteoporosis, Metabolic Bone Disease and Related Research, vol.5, issue.5, pp.223-228, 1984. ,
DOI : 10.1016/0221-8747(84)90063-8
Effects of Sex and Age on Bone Microstructure at the Ultradistal Radius: A Population-Based Noninvasive In Vivo Assessment, Journal of Bone and Mineral Research, vol.12, issue.1, pp.124-131, 2006. ,
DOI : 10.1259/bjr.73.865.10721315
Elastic and physicochemical relationships within cortical bone, Journal of Biomedical Materials Research, vol.17, issue.4, pp.479-488, 2000. ,
DOI : 10.1016/1350-4533(95)97314-F
Analyzing the anisotropic Hooke's law for the children's cortical bone, J. Mech. Behav. Biomed. Mater, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01167006
Mean wall thickness of trabecular bone packets in the human iliac crest: Changes with age, Calcified Tissue Research, vol.74, issue.1, pp.13-17, 1978. ,
DOI : 10.1159/000143361
Early identification of children predisposed to low peak bone mass and osteoporosis later in life, J. Clin. Endocrinol . Metab, vol.85, pp.3908-3918, 2000. ,
Three-dimensional reconstruction of Haversian systems in human cortical bone using synchrotron radiation-based micro-CT: morphology and quantification of branching and transverse connections across age, Journal of Anatomy, vol.iv, issue.1, 2016. ,
DOI : 10.1159/000141798
Longitudinal elastic properties and porosity of cortical bone tissue vary with age in human proximal femur, Bone, vol.53, issue.2, pp.451-458, 2013. ,
DOI : 10.1016/j.bone.2013.01.015
Age-related changes in the tensile properties of cortical bone. The relative importance of changes in porosity, mineralization, and microstructure., The Journal of Bone & Joint Surgery, vol.75, issue.8, pp.1193-1205, 1993. ,
DOI : 10.2106/00004623-199308000-00009
Validation of a novel microradiography device for characterization of bone mineralization, J. X-ray Sci. Technol, vol.23, pp.201-211, 2015. ,
Three-dimensional methods for quantification of cancellous bone architecture, Bone, vol.20, issue.4, pp.315-328, 1997. ,
DOI : 10.1016/S8756-3282(97)00007-0
3D Assessment of Cortical Bone Porosity and Tissue Mineral Density Using High-Resolution ??CT: Effects of Resolution and Threshold Method, Journal of Bone and Mineral Research, vol.104, issue.1, pp.142-150, 2014. ,
DOI : 10.1172/JCI6730
Osteonal and hemi-osteonal remodeling: The spatial and temporal framework for signal traffic in adult human bone, Journal of Cellular Biochemistry, vol.13, issue.3, pp.273-286, 1994. ,
DOI : 10.1007/978-3-642-77991-6
The two faces of growth: Benefits and risks to bone integrity, Osteoporosis International, vol.37, issue.Suppl 1, pp.382-398, 1994. ,
DOI : 10.1111/j.1532-5415.1989.tb01562.x
Structural and cellular changes during bone growth in healthy children, Bone, vol.27, issue.4, pp.487-494, 2000. ,
DOI : 10.1016/S8756-3282(00)00353-7
Regional Heterogeneity in the Configuration of the Intracortical Canals of the Femoral Shaft, Calcified Tissue International, vol.89, issue.Suppl 2, 2015. ,
DOI : 10.1002/path.1700890118
Demonstration of osteocytic perilacunar/canalicular remodeling in mice during lactation, Journal of Bone and Mineral Research, vol.65, issue.6, pp.1018-1029, 2012. ,
DOI : 10.1002/jbmr.5650091105
Dependence of bone yield (volume of bone formed per unit of cement surface area) on resorption cavity size during osteonal remodeling in human rib: implications for osteoblast function and the pathogenesis of age-related bone loss, Journal of Bone and Mineral Research, vol.1116, issue.2, pp.423-430, 2010. ,
DOI : 10.1016/j.bone.2006.06.031
The dynamics of bone structure development during pubertal growth, J. Musculoskelet. Neuronal Interact, vol.12, pp.1-6, 2012. ,
Intracortical remodeling during human bone development???A histomorphometric study, Bone, vol.40, issue.2, pp.274-280, 2007. ,
DOI : 10.1016/j.bone.2006.09.012
Bone Remodeling Increases Substantially in the Years After Menopause and Remains Increased in Older Osteoporosis Patients, Journal of Bone and Mineral Research, vol.87, issue.Suppl, pp.1628-1633, 2004. ,
DOI : 10.7326/0003-4819-114-11-919
Resonant ultrasound spectroscopy for materials with high damping and samples of arbitrary geometry, Journal of Geophysical Research: Solid Earth, vol.90, issue.B10, pp.4898-4916, 2015. ,
DOI : 10.1121/1.401643
Morphology of the Drifting Osteon, Cells Tissues Organs, vol.164, issue.4, pp.192-204, 1999. ,
DOI : 10.1159/000016659
Collagen cross-links as a determinant of bone quality: a possible explanation for bone fragility in aging, osteoporosis, and diabetes mellitus, Osteoporosis International, vol.43, issue.Suppl, pp.195-214, 2010. ,
DOI : 10.1016/0925-4439(95)00119-0
Stiffness of compact bone: Effects of porosity and density, Journal of Biomechanics, vol.21, issue.1, pp.13-16, 1988. ,
DOI : 10.1016/0021-9290(88)90186-8
Childhood Cortical Porosity Is Related to Microstructural Properties of the Bone-Muscle Junction, Journal of Bone and Mineral Research, vol.39, issue.12, pp.144-155, 2015. ,
DOI : 10.1002/jbmr.1969
Cortical porosity in children is determined by age-dependent osteonal morphology, Bone, vol.55, issue.2, pp.476-486, 2013. ,
DOI : 10.1016/j.bone.2013.03.021
Cortical bone development in black and white South African children: Iliac crest histomorphometry, Bone, vol.44, issue.4, pp.603-611, 2009. ,
DOI : 10.1016/j.bone.2008.12.009
Structural basis of growth-related gain and agerelated loss of bone strength, Rheumatol. Oxf. J, vol.47, pp.2-8, 2008. ,
Bone quality?the material and structural basis of bone strength and fragility. New Engl, J Med, vol.354, pp.2250-2261, 2006. ,
Do osteocytes contribute to bone mineral homeostasis? Osteocytic osteolysis revisited, Bone, vol.44, issue.1, pp.11-16, 2009. ,
DOI : 10.1016/j.bone.2008.09.017
Increase in pore area, and not pore density, is the main determinant in the development of porosity in human cortical bone, Journal of Anatomy, vol.1, issue.2, pp.219-230, 2006. ,
DOI : 10.1016/S8756-3282(97)00227-5
The ability of three-dimensional structural indices to reflect mechanical aspects of trabecular bone, Bone, vol.25, issue.1, pp.55-60, 1999. ,
DOI : 10.1016/S8756-3282(99)00098-8
Hierarchical perspective of bone toughness ??? from molecules to fracture, International Materials Reviews, vol.23, issue.2, pp.245-263, 2014. ,
DOI : 10.1016/j.ijfatigue.2006.09.010
Histomorphometric analysis of dynamic parameters of trabecular bone formation in the iliac crest of Normal British subjects, Metabolic Bone Disease and Related Research, vol.5, issue.2, 1983. ,
DOI : 10.1016/0221-8747(83)90004-8
Rapid growth produces transient cortical weakness: A risk factor for metaphyseal fractures during puberty, Journal of Bone and Mineral Research, vol.27, issue.4, pp.1521-1526, 2010. ,
DOI : 10.2106/00004623-197557060-00015
The influence of bone morphology on fracture toughness of the human femur and tibia, Bone, vol.21, issue.5, pp.453-459, 1997. ,
DOI : 10.1016/S8756-3282(97)00173-7
Fracture toughness of human femoral neck: effect of microstructure, composition, and age, Bone, vol.26, issue.5, pp.499-504, 2000. ,
DOI : 10.1016/S8756-3282(00)00258-1
A new method of segmentation of compact-appearing, transitional and trabecular compartments and quantification of cortical porosity from high resolution peripheral quantitative computed tomographic images, Bone, vol.54, issue.1, pp.8-20, 2013. ,
DOI : 10.1016/j.bone.2013.01.007
Intracortical remodelling and porosity in the distal radius and post-mortem femurs of women: a cross-sectional study, The Lancet, vol.375, issue.9727, pp.1729-1736, 2010. ,
DOI : 10.1016/S0140-6736(10)60320-0