P. Ammann and R. Rizzoli, Bone strength and its determinants, Osteoporosis International, vol.18, issue.S3, pp.13-18, 2003.
DOI : 10.1016/S8756-3282(00)00268-4

R. Barkmann, E. Kantorovich, C. Singal, D. Hans, H. K. Genant et al., A New Method for Quantitative Ultrasound Measurements at Multiple Skeletal Sites, Journal of Clinical Densitometry, vol.3, issue.1, pp.1-7, 2000.
DOI : 10.1385/JCD:3:1:001

C. Baron, M. Talmant, and P. Laugier, 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

E. Bossy, M. Talmant, and P. Laugier, Effect of bone cortical thickness on velocity measurements using ultrasonic axial transmission: A 2D simulation study, The Journal of the Acoustical Society of America, vol.112, issue.1, 2002.
DOI : 10.1121/1.1480836

E. Bossy, M. Talmant, and P. Laugier, Bidirectional axial transmission can improve accuracy and precision of ultrasonic velocity measurement in cortical bone: a validation on test materials, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.51, issue.1, pp.71-79, 2004.
DOI : 10.1109/TUFFC.2004.1268469

E. Bossy, M. Talmant, and P. Laugier, 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, 2004.
DOI : 10.1121/1.1689960

URL : https://hal.archives-ouvertes.fr/hal-00109676

E. Bossy, M. Talmant, F. Peyrin, L. Akrout, P. Cloetens et al., An In Vitro Study of the Ultrasonic Axial Transmission Technique at the Radius: 1-MHz Velocity Measurements Are Sensitive to Both Mineralization and Intracortical Porosity, Journal of Bone and Mineral Research, vol.115, issue.Suppl 1, pp.1548-1556, 2004.
DOI : 10.1359/JBMR.040513

URL : https://hal.archives-ouvertes.fr/hal-00109675

A. M. Jeantet and J. D. Laredo, Distribution of intracortical porosity in human midfemoral cortex by age and gender, J. Bone Miner. Res, vol.16, issue.7, pp.1308-1317, 2001.

R. Cobbold, N. Sushilov, and A. Weathermon, Transient propagation in media with classical or power-law loss, The Journal of the Acoustical Society of America, vol.116, issue.6, pp.3294-303, 2004.
DOI : 10.1121/1.1823271

C. Desceliers, C. Soize, Q. Grimal, G. Haïat, and S. Naili, A time-domain method to solve transient elastic wave propagation in a multilayer medium with a hybrid spectral-finite element space approximation, Wave Motion, vol.45, issue.4, pp.383-399, 2008.
DOI : 10.1016/j.wavemoti.2007.09.001

URL : https://hal.archives-ouvertes.fr/hal-00686136

X. N. Dong and X. E. Guo, 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

K. Dussik and D. Fritch, Deterimination of sound attenuation and sound velocity in the structure constituting the joints, and of the ultrasonic field distribution with the joints of living tissues and anatomical preparations, both in normal and pathological conditions, 1956.

E. Sariti, A. Evans, J. Truscott, and J. , The temperature dependence of the speed of sound in bovine bone marrow at 750 kHz, Ultrasound in Medicine & Biology, vol.32, issue.6, pp.985-994, 2006.
DOI : 10.1016/j.ultrasmedbio.2006.02.1412

A. Fritsch and C. Hellmich, ???Universal??? microstructural patterns in cortical and trabecular, extracellular and extravascular bone materials: Micromechanics-based prediction of anisotropic elasticity, Journal of Theoretical Biology, vol.244, issue.4, pp.597-620, 2007.
DOI : 10.1016/j.jtbi.2006.09.013

B. Garcia, R. Cobbold, F. Foster, and K. Mcneill, Ultrasonic Attenuation in Bone, 1978 Ultrasonics Symposium, pp.327-330, 1978.
DOI : 10.1109/ULTSYM.1978.197055

S. Goss, R. Johnston, and F. Dunn, Comprehensive compilation of empirical ultrasonic properties of mammalian tissues, The Journal of the Acoustical Society of America, vol.64, issue.2, pp.423-457, 1978.
DOI : 10.1121/1.382016

Q. Grimal and S. Naili, A theoretical analysis in the time-domain of wave reflection on a bone plate, Journal of Sound and Vibration, vol.298, issue.1-2, pp.12-29, 2006.
DOI : 10.1016/j.jsv.2006.04.037

G. Haiat, A. Lhemery, F. Renaud, F. Padilla, P. Laugier et al., Velocity dispersion in trabecular bone: Influence of multiple scattering and of absorption, The Journal of the Acoustical Society of America, vol.124, issue.6, 2008.
DOI : 10.1121/1.3003077

URL : https://hal.archives-ouvertes.fr/hal-00711777

G. Haiat, S. Naili, Q. Grimal, M. Talmant, C. Desceliers et al., 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

G. Haiat, F. Padilla, R. Barkmann, S. Dencks, U. Moser et al., Optimal Prediction of Bone Mineral Density with Ultrasonic Measurements in Excised Human Femur, Calcified Tissue International, vol.12, issue.3, pp.186-92, 2005.
DOI : 10.1007/s00223-005-0057-0

G. Haiat, F. Padilla, R. Cleveland, and P. Laugier, Effects of frequency-dependent attenuation and velocity dispersion on in vitro ultrasound velocity measurements in intact human femur specimens, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.53, issue.1, pp.39-51, 2006.
DOI : 10.1109/TUFFC.2006.1588390

G. Haiat, M. Sasso, S. Naili, and M. Matsukawa, Ultrasonic velocity dispersion in bovine cortical bone: An experimental study, The Journal of the Acoustical Society of America, vol.124, issue.3, pp.1811-1821, 2008.
DOI : 10.1121/1.2950091

URL : https://hal.archives-ouvertes.fr/hal-00845611

S. Han, J. Rho, J. Medige, and I. Ziv, Ultrasound velocity and broadband attenuation over a wide range of bone mineral density, Osteoporosis International, vol.10, issue.4, pp.291-296, 1996.
DOI : 10.1007/BF01623387

D. Hans, S. K. Srivastav, C. Singal, R. Barkmann, C. F. Njeh et al., Does Combining the Results from Multiple Bone Sites Measured by a New Quantitative Ultrasound Device Improve Discrimination of Hip Fracture?, Journal of Bone and Mineral Research, vol.27, issue.4, pp.644-651, 1999.
DOI : 10.1359/jbmr.1999.14.4.644

R. S. Lakes, H. S. Yoon, and J. L. Katz, Ultrasonic wave propagation and attenuation in wet bone, Journal of Biomedical Engineering, vol.8, issue.2, pp.143-148, 1986.
DOI : 10.1016/0141-5425(86)90049-X

C. M. Langton, A. V. Ali, C. M. Riggs, J. A. Evans, and W. Bonfield, A contact method for the assessment of ultrasonic velocity and broadband attenuation in cortical and cancellous bone, Clinical Physics and Physiological Measurement, vol.11, issue.3, pp.243-249, 1990.
DOI : 10.1088/0143-0815/11/3/007

S. Lees and D. Z. Klopholz, Sonic velocity and attenuation in wet compact cow femur for the frequency range 5 to 100 MHz, Ultrasound in Medicine & Biology, vol.18, issue.3, pp.303-308, 1992.
DOI : 10.1016/0301-5629(92)90099-V

J. Lehman and E. Johnson, Some factors influencing the temperature distribution in thighs exposed to ultrasound, Arch. Phys. Med. Rehab, vol.39, pp.347-356, 1958.

K. Macocco, Q. Grimal, S. Naili, and C. Soize, Mod??lisation probabiliste d'une exp??rience ultrasonore : calcul de la dispersion sur les mesures de c??l??rit??, Comptes Rendus M??canique, vol.333, issue.7, pp.565-573, 2005.
DOI : 10.1016/j.crme.2005.06.005

K. Macocco, Q. Grimal, S. Naili, and C. Soize, Elastoacoustic model with uncertain mechanical properties for ultrasonic wave velocity prediction: Application to cortical bone evaluation, The Journal of the Acoustical Society of America, vol.119, issue.2, pp.729-740, 2006.
DOI : 10.1121/1.2146110

URL : https://hal.archives-ouvertes.fr/hal-00686156

P. M. Mayhew, C. D. Thomas, J. G. Clement, N. Loveridge, T. J. Beck et al., Relation between age, femoral neck cortical stability, and hip fracture risk, The Lancet, vol.366, issue.9480, pp.129-135, 2005.
DOI : 10.1016/S0140-6736(05)66870-5

P. Moilanen, M. Talmant, V. Kilappa, P. Nicholson, S. Cheng et al., 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.2364-73, 2008.
DOI : 10.1121/1.2973228

F. Moser, L. Jacobs, and J. Qu, Modeling elastic wave propagation in waveguides with the finite element method, NDT & E International, vol.32, issue.4, 1999.
DOI : 10.1016/S0963-8695(98)00045-0

V. C. Protopappas, I. C. Kourtis, L. C. Kourtis, K. N. Malizos, C. V. Massalas et al., 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, p.3907, 2007.
DOI : 10.1121/1.2354067

K. Raum, R. O. Cleveland, F. Peyrin, and P. Laugier, Derivation of elastic stiffness from site-matched mineral density and acoustic impedance maps, Physics in Medicine and Biology, vol.51, issue.3, 2006.
DOI : 10.1088/0031-9155/51/3/018

URL : https://hal.archives-ouvertes.fr/hal-00443423

K. Raum, I. Leguerney, F. Chandelier, E. Bossy, M. Talmant et al., Bone microstructure and elastic tissue properties are reflected in QUS axial transmission measurements, Ultrasound in Medicine & Biology, vol.31, issue.9, pp.31-1225, 2005.
DOI : 10.1016/j.ultrasmedbio.2005.05.002

URL : https://hal.archives-ouvertes.fr/hal-00443425

D. T. Reilly and A. H. Burnstein, 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

J. Y. Rho, 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

H. Rico, The Therapy of Osteoporosis and the Importance of Cortical Bone, Calcified Tissue International, vol.47, issue.51, pp.431-432, 1997.
DOI : 10.1007/s002239900361

M. Sasso, G. Haïat, Y. Yamato, S. Naili, and M. Matsukawa, Frequency Dependence of Ultrasonic Attenuation in Bovine Cortical Bone: An In Vitro Study, Ultrasound in Medicine & Biology, vol.33, issue.12, pp.33-1933, 2007.
DOI : 10.1016/j.ultrasmedbio.2007.05.022

URL : https://hal.archives-ouvertes.fr/hal-00718873

M. Sasso, G. Haïat, Y. Yamato, S. Naili, and M. Matsukawa, Dependence of ultrasonic attenuation on bone mass and microstructure in bovine cortical bone, Journal of Biomechanics, vol.41, issue.2, pp.347-355, 2008.
DOI : 10.1016/j.jbiomech.2007.09.001

D. G. Seeley, W. S. Browner, M. C. Nevitt, H. K. Genant, J. C. Scott et al., Which fractures are associated with low appendicular bone mass in elderly women? The Study of Osteoporotic Fractures Research Group, Ann. Intern. Med, issue.11, pp.115-837, 1991.

L. Serpe and J. Rho, The nonlinear transition period of broadband ultrasound attenuation as bone density varies, Journal of Biomechanics, vol.29, issue.7, pp.963-966, 1996.
DOI : 10.1016/0021-9290(95)00146-8

M. R. Stegman, R. P. Heaney, D. Travers-gustafson, and J. Leist, Cortical ultrasound velocity as an indicator of bone status, Osteoporosis International, vol.8, issue.5, pp.349-533, 1995.
DOI : 10.1007/BF01622257

C. D. Thomas, S. A. Feik, C. , and J. G. , Regional variation of intracortical porosity in the midshaft of the human femur: age and sex differences, Journal of Anatomy, vol.27, issue.2, pp.115-125, 2005.
DOI : 10.1016/S8756-3282(97)00227-5

C. H. Turner, Biomechanics of Bone: Determinants of Skeletal Fragility and Bone Quality, Osteoporosis International, vol.13, issue.2, pp.97-104, 2002.
DOI : 10.1007/s001980200000

K. A. Wear, The effects of frequency-dependent attenuation and dispersion on sound speed measurements: applications in human trabecular bone, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.47, issue.1, pp.265-273, 2000.
DOI : 10.1109/58.818770

K. A. Wear, A numerical method to predict the effects of frequency-dependent attenuation and dispersion on speed of sound estimates in cancellous bone, The Journal of the Acoustical Society of America, vol.109, issue.3, 2001.
DOI : 10.1121/1.1344161

. Who-study and . Group, Assessment of fracture risk and its application to screening for postmenopausal osteoporosis, World Health Organization, 1994.

M. Wismer, Finite element analysis of broadband acoustic pulses through inhomogenous media with power law attenuation, The Journal of the Acoustical Society of America, vol.120, issue.6, pp.3493-502, 2006.
DOI : 10.1121/1.2354032

P. Zysset, X. Guo, C. Hoffler, K. Moore, and S. Goldstein, Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur, Journal of Biomechanics, vol.32, issue.10, pp.32-1005, 1999.
DOI : 10.1016/S0021-9290(99)00111-6