Mechanisms of Interaction of Ultrasound With Cancellous Bone: A Review

Ultrasound is now a clinically accepted modality in the management of osteoporosis. The most common commercial clinical devices assess fracture risk from measurements of attenuation and sound speed in cancellous bone. This review discusses fundamental mechanisms underlying the interaction between ultrasound and cancellous bone. Because of its two-phase structure (mineralized trabecular network embedded in soft tissue—marrow), its anisotropy, and its inhomogeneity, cancellous bone is more difficult to characterize than most soft tissues. Experimental data for the dependencies of attenuation, sound speed, dispersion, and scattering on ultrasound frequency, bone mineral density, composition, microstructure, and mechanical properties are presented. The relative roles of absorption, scattering, and phase cancellation in determining attenuation measurements in vitro and in vivo are delineated. Common speed of sound metrics, which entail measurements of transit times of pulse leading edges (to avoid multipath interference), are greatly influenced by attenuation, dispersion, and system properties, including center frequency and bandwidth. However, a theoretical model has been shown to be effective for correction for these confounding factors in vitro and in vivo. Theoretical and phantom models are presented to elucidate why cancellous bone exhibits negative dispersion, unlike soft tissue, which exhibits positive dispersion. Signal processing methods are presented for separating “fast” and “slow” waves (predicted by poroelasticity theory and supported in cancellous bone) even when the two waves overlap in time and frequency domains. Models to explain dependencies of scattering on frequency and mean trabecular thickness are presented and compared with measurements. Anisotropy, the effect of the fluid filler medium (marrow in vivo or water in vitro), phantoms, computational modeling of ultrasound propagation, acoustic microscopy, and nonlinear properties in cancellous bone are also discussed.

[1]  K. Wear Estimation of fast and slow wave properties in cancellous bone using Prony's method and curve fitting. , 2013, The Journal of the Acoustical Society of America.

[2]  K. Wear A stratified model to predict dispersion in trabecular bone , 2001, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[3]  Wave propagation in stereo-lithographical (STL) bone replicas at oblique incidence , 2011 .

[4]  S. Cummings,et al.  Bone density at various sites for prediction of hip fractures , 1993, The Lancet.

[5]  J. Faran Sound Scattering by Solid Cylinders and Spheres , 1951 .

[6]  Ultrasonic wave propagation in water-saturated aluminum foams , 1998 .

[7]  F. Padilla,et al.  Optimal Prediction of Bone Mineral Density with Ultrasonic Measurements in Excised Human Femur , 2005, Calcified Tissue International.

[8]  P. Laugier,et al.  Comparative investigation of elastic properties in a trabecula using micro-Brillouin scattering and scanning acoustic microscopy. , 2012, The Journal of the Acoustical Society of America.

[9]  H. K. Genant,et al.  Comparison of Six Calcaneal Quantitative Ultrasound Devices: Precision and Hip Fracture Discrimination , 2000, Osteoporosis International.

[10]  G. Breart,et al.  Ultrasonographic heel measurements to predict hip fracture in elderly women: the EPIDOS prospective study , 1996, The Lancet.

[11]  Juha Töyräs,et al.  Ability of ultrasound backscattering to predict mechanical properties of bovine trabecular bone. , 2004, Ultrasound in medicine & biology.

[12]  Brian S Garra,et al.  Measurements of ultrasonic backscattered spectral centroid shift from spine in vivo: methodology and preliminary results. , 2009, Ultrasound in medicine & biology.

[13]  Kang I L Lee,et al.  Correlations between acoustic properties and bone density in bovine cancellous bone from 0.5 to 2 MHz. , 2003, The Journal of the Acoustical Society of America.

[14]  B. Garra,et al.  Assessment of bone density using ultrasonic backscatter. , 1998, Ultrasound in medicine & biology.

[15]  F. Padilla,et al.  Sensitivity of QUS parameters to controlled variations of bone strength assessed with a cellular model , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[16]  A Hosokawa Ultrasonic pulse waves in cancellous bone analyzed by finite-difference time-domain methods. , 2006, Ultrasonics.

[17]  Ultrasonic properties in marrow-filled and water-filled bovine femoral trabecular bones in vitro. , 2012, The Journal of the Acoustical Society of America.

[18]  Comparison of the Faran Cylinder Model and the Weak Scattering Model for predicting the frequency dependence of backscatter from human cancellous femur in vitro. , 2008, The Journal of the Acoustical Society of America.

[19]  K. Wear,et al.  Anisotropy of ultrasonic backscatter and attenuation from human calcaneus: implications for relative roles of absorption and scattering in determining attenuation. , 2000, The Journal of the Acoustical Society of America.

[20]  P. Nicholson,et al.  Quantitative Ultrasound Does Not Reflect Mechanically Induced Damage in Human Cancellous Bone , 2000, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[21]  M. Kaczmarek,et al.  Short ultrasonic waves in cancellous bone. , 2002, Ultrasonics.

[22]  F. Peyrin,et al.  Adaptive remodeling of trabecular bone core cultured in 3-D bioreactor providing cyclic loading: an acoustic microscopy study. , 2010, Ultrasound in medicine & biology.

[23]  Christian M Langton,et al.  Pulse-echo ultrasound transit time spectroscopy: A comparison of experimental measurement and simulation prediction , 2016, Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine.

[24]  G Berger,et al.  In vitro assessment of the relationship between acoustic properties and bone mass density of the calcaneus by comparison of ultrasound parametric imaging and quantitative computed tomography. , 1997, Bone.

[25]  J. Jurvelin,et al.  Differences in acoustic impedance of fresh and embedded human trabecular bone samples-Scanning acoustic microscopy and numerical evaluation. , 2016, The Journal of the Acoustical Society of America.

[26]  C-C Glüer,et al.  In vitro speed of sound measurement at intact human femur specimens. , 2005, Ultrasound in medicine & biology.

[27]  M. Fellah,et al.  Application of the Biot model to ultrasound in bone: Inverse problem , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[28]  Pascal Laugier,et al.  Dynamic coherent backscattering in a heterogeneous absorbing medium: Application to human trabecular bone characterization , 2005 .

[29]  K. Wear,et al.  Measurements of phase velocity and group velocity in human calcaneus. , 2000, Ultrasound in medicine & biology.

[30]  Hiroshi Kanai,et al.  Attempt at standardization of bone quantitative ultrasound in Japan , 2017, Journal of Medical Ultrasonics.

[31]  S. Majumdar,et al.  Ultrasound Velocity of Trabecular Cubes Reflects Mainly Bone Density and Elasticity , 2014, Calcified Tissue International.

[32]  Hiroshi Hosoi,et al.  Numerical and experimental study on the wave attenuation in bone--FDTD simulation of ultrasound propagation in cancellous bone. , 2008, Ultrasonics.

[33]  K. Wear The dependence of time-domain speed-of-sound measurements on center frequency, bandwidth, and transit-time marker in human calcaneus in vitro. , 2007, The Journal of the Acoustical Society of America.

[34]  L. Le,et al.  Micro-scale finite element modeling of ultrasound propagation in aluminum trabecular bone-mimicking phantoms: A comparison between numerical simulation and experimental results. , 2016, Ultrasonics.

[35]  J Y Rho,et al.  The nonlinear transition period of broadband ultrasound attenuation as bone density varies. , 1996, Journal of biomechanics.

[36]  A. Derode,et al.  Measurements of ultrasound velocity and attenuation in numerical anisotropic porous media compared to Biot's and multiple scattering models. , 2014, Ultrasonics.

[37]  S. Kaste,et al.  Ultrasonic characterization of cancellous bone using apparent integrated backscatter , 2006, Physics in medicine and biology.

[38]  F. Peyrin,et al.  Prediction of backscatter coefficient in trabecular bones using a numerical model of three-dimensional microstructure. , 2003, The Journal of the Acoustical Society of America.

[39]  R. F. Wagner,et al.  Statistics of Speckle in Ultrasound B-Scans , 1983, IEEE Transactions on Sonics and Ultrasonics.

[40]  Juha Töyräs,et al.  Ultrasound backscatter imaging provides frequency-dependent information on structure, composition and mechanical properties of human trabecular bone. , 2009, Ultrasound in medicine & biology.

[41]  M. Bouxsein,et al.  Effect of Temperature on Ultrasonic Properties of the Calcaneus In Situ , 2002, Osteoporosis International.

[42]  M. Matsukawa,et al.  Local ultrasonic wave velocities in trabeculae measured by micro-Brillouin scattering. , 2014, Journal of the Acoustical Society of America.

[43]  G. L. Bretthorst,et al.  Bayesian estimation of the underlying bone properties from mixed fast and slow mode ultrasonic signals. , 2007, The Journal of the Acoustical Society of America.

[44]  Y.-X. Qin,et al.  Bone surface topology mapping and its role in trabecular bone quality assessment using scanning confocal ultrasound , 2007, Osteoporosis International.

[45]  A. J. Clarke,et al.  The measurement of the velocity of ultrasound in fixed trabecular bone using broadband pulses and single-frequency tone bursts. , 1996, Physics in medicine and biology.

[46]  G. Van der Perre,et al.  The correlation between the SOS in trabecular bone and stiffness and density studied by finite-element analysis , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[47]  J. Rho,et al.  Effect of marrow on the high frequency ultrasonic properties of cancellous bone. , 2002, Physics in medicine and biology.

[48]  Numerical analysis of uncertainties in dual frequency bone ultrasound technique. , 2010, Ultrasound in medicine & biology.

[49]  D. Keedy,et al.  Ultrasonic characterization of human cancellous bone in vitro using three different apparent backscatter parameters in the frequency range 0.6-15.0 mhz , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[50]  M. Matsukawa,et al.  Properties of ultrasonic waves in bovine bone marrow. , 2011, Ultrasound in medicine & biology.

[51]  Timothy G Leighton,et al.  Investigation of an anisotropic tortuosity in a biot model of ultrasonic propagation in cancellous bone. , 2007, The Journal of the Acoustical Society of America.

[52]  M. Matsukawa,et al.  Ultrasonic wave properties of human bone marrow in the femur and tibia. , 2015, The Journal of the Acoustical Society of America.

[53]  C. Rubin,et al.  Ultrasonic Wave Propagation in Trabecular Bone Predicted by the Stratified Model , 2001, Annals of Biomedical Engineering.

[54]  R C Waag,et al.  Normalization of ultrasonic scattering measurements to obtain average differential scattering cross sections for tissues. , 1983, The Journal of the Acoustical Society of America.

[55]  H. Trębacz,et al.  Ultrasound Velocity and Attenuation in Cancellous Bone Samples from Lumbar Vertebra and Calcaneus , 1999, Osteoporosis International.

[56]  Pascal Laugier,et al.  Estimation of Trabecular Thickness Using Ultrasonic Backcatter , 2006, Ultrasonic imaging.

[57]  R. Gilbert,et al.  Wavelet decomposition of transmitted ultrasound wave through a 1-D muscle-bone system. , 2011, Journal of biomechanics.

[58]  R. Strelitzki,et al.  The influence of porosity and pore size on the ultrasonic properties of bone investigated using a phantom material , 2005, Osteoporosis International.

[59]  Gangming Luo,et al.  Ultrasound simulation in bone , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[60]  A. Wilson,et al.  A backscatter difference technique for ultrasonic bone assessment. , 2012, The Journal of the Acoustical Society of America.

[61]  B. Elmann-Larsen,et al.  Quantitative Ultrasound Imaging of the Calcaneus: Precision and Variations During a 120-Day Bed Rest , 2000, Calcified Tissue International.

[62]  C-C Glüer,et al.  [Quantitative ultrasound]. , 2006, Der Radiologe.

[63]  Dependences of ultrasonic properties on the propagation angle with respect to the trabecular alignment in trabecular bone , 2014 .

[64]  K. Lee Correlations of group velocity, phase velocity, and dispersion with bone density in bovine trabecular bone. , 2011, The Journal of the Acoustical Society of America.

[65]  K. Wear Mechanisms for attenuation in cancellous-bone-mimicking phantoms , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[66]  K. Wear,et al.  Scattering by Trabecular Bone , 2011 .

[67]  G T Clement,et al.  A non-invasive method for focusing ultrasound through the human skull. , 2002, Physics in medicine and biology.

[68]  Min Joo Choi,et al.  Phase velocity and normalized broadband ultrasonic attenuation in Polyacetal cuboid bone-mimicking phantoms. , 2007, The Journal of the Acoustical Society of America.

[69]  Jordan P. Ankersen,et al.  Ultrasonic backscatter difference measurements of cancellous bone from the human femur: Relation to bone mineral density and microstructure. , 2018, The Journal of the Acoustical Society of America.

[70]  K. Wear,et al.  A numerical method to predict the effects of frequency-dependent attenuation and dispersion on speed of sound estimates in cancellous bone. , 2001, The Journal of the Acoustical Society of America.

[71]  Yi-Xian Qin,et al.  Frequency specific ultrasound attenuation is sensitive to trabecular bone structure. , 2012, Ultrasound in medicine & biology.

[72]  Timothy G Leighton,et al.  Estimation of critical and viscous frequencies for Biot theory in cancellous bone. , 2003, Ultrasonics.

[73]  Modelling Nonlinear Ultrasound Propagation in Bone , 2006 .

[74]  Mark R Holland,et al.  Anomalous negative dispersion in bone can result from the interference of fast and slow waves. , 2006, The Journal of the Acoustical Society of America.

[75]  G. Haïat,et al.  Ultrasound Speed of Sound Measurements in Trabecular Bone Using the Echographic Response of a Metallic Pin. , 2015, Ultrasound in medicine & biology.

[76]  R. B. Ashman,et al.  Elastic properties of cancellous bone: measurement by an ultrasonic technique. , 1987, Journal of biomechanics.

[77]  M. Muller,et al.  Microstructural characterization of trabecular bone using ultrasonic backscattering and diffusion parameters. , 2017, The Journal of the Acoustical Society of America.

[78]  C. Langton,et al.  Solid volume fraction estimation of bone:marrow replica models using ultrasound transit time spectroscopy. , 2016, Ultrasonics.

[79]  J. Litniewski,et al.  Statistics of the envelope of ultrasonic backscatter from human trabecular bone. , 2011, The Journal of the Acoustical Society of America.

[80]  E. Madsen,et al.  Interlaboratory Comparison of Ultrasonic Backscatter Coefficient Measurements From 2 to 9 MHz , 2005, Journal of ultrasound in medicine : official journal of the American Institute of Ultrasound in Medicine.

[81]  J. Jurvelin,et al.  Effect of bone marrow on acoustic properties of trabecular bone--3D finite difference modeling study. , 2009, Ultrasound in medicine & biology.

[82]  C.M. Langton,et al.  The Measurement of Broadband Ultrasonic Attenuation in Cancellous Bone-A Review of the Science and Technology , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[83]  Robert P. Gilbert,et al.  A quantitative ultrasound model of the bone with blood as the interstitial fluid , 2012, Math. Comput. Model..

[84]  M. Bouxsein,et al.  Bone marrow influences quantitative ultrasound measurements in human cancellous bone. , 2002, Ultrasound in medicine & biology.

[85]  Juha Töyräs,et al.  Influence of overlying soft tissues on trabecular bone acoustic measurement at various ultrasound frequencies. , 2006, Ultrasound in medicine & biology.

[86]  Hiroshi Hosoi,et al.  Propagation of fast and slow waves in cancellous bone: Comparative study of simulation and experiment , 2009 .

[87]  K. Wear,et al.  Frequency dependence of backscatter from thin, oblique, finite-length cylinders measured with a focused transducer - with applications in cancellous bone , 2008, 2008 IEEE Ultrasonics Symposium.

[88]  J Töyräs,et al.  Bone mineral density, ultrasound velocity, and broadband attenuation predict mechanical properties of trabecular bone differently. , 2002, Bone.

[89]  D. Deligianni,et al.  Characterization of dense bovine cancellous bone tissue microstructure by ultrasonic backscattering using weak scattering models. , 2007, The Journal of the Acoustical Society of America.

[90]  K. Wear,et al.  The Effect of Phase Cancellation on Estimates of Calcaneal Broadband Ultrasound Attenuation in Vivo , 2007, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[91]  Katsunori Mizuno,et al.  Determining attenuation properties of interfering fast and slow ultrasonic waves in cancellous bone. , 2011, The Journal of the Acoustical Society of America.

[92]  Keith A Wear,et al.  The dependencies of phase velocity and dispersion on trabecular thickness and spacing in trabecular bone-mimicking phantoms. , 2005, The Journal of the Acoustical Society of America.

[93]  Martin Heller,et al.  In vivo measurements of ultrasound transmission through the human proximal femur. , 2008, Ultrasound in medicine & biology.

[94]  Jinsong Huang,et al.  Characterization of a polymer, open-cell rigid foam that simulates the ultrasonic properties of cancellous bone. , 2018, The Journal of the Acoustical Society of America.

[95]  Stephen C Cowin,et al.  Fabric dependence of bone ultrasound. , 2010, Acta of bioengineering and biomechanics.

[96]  P. Laugier,et al.  In vitro measurement of the frequency-dependent attenuation in cancellous bone between 0.2 and 2 MHz. , 2000, The Journal of the Acoustical Society of America.

[97]  A. S. Ahuja,et al.  Effect of Particle Viscosity on Propagation of Sound in Suspensions and Emulsions , 1972 .

[98]  K. Wear,et al.  Relationships of ultrasonic backscatter with ultrasonic attenuation, sound speed and bone mineral density in human calcaneus. , 2000, Ultrasound in medicine & biology.

[99]  Stephen C Cowin,et al.  Fabric dependence of wave propagation in anisotropic porous media , 2011, Biomechanics and modeling in mechanobiology.

[100]  W. Hendee,et al.  Effects of particle shape and orientation on propagation of sound in suspensions , 1978 .

[101]  E Ogam,et al.  Ultrasonic characterization of human cancellous bone using the Biot theory: inverse problem. , 2006, The Journal of the Acoustical Society of America.

[102]  C F Njeh,et al.  The effect of cortical endplates on ultrasound velocity through the calcaneus: an in vitro study. , 1997, The British journal of radiology.

[103]  R. Strelitzki On the measurement of the velocity of ultrasound in the os calcis using short pulses , 1996 .

[104]  J. A. Evans,et al.  An investigation of the measurement of broadband ultrasonic attenuation in trabecular bone. , 1996, Ultrasonics.

[105]  F. Peyrin,et al.  Frequency dependence of ultrasonic backscattering in cancellous bone: autocorrelation model and experimental results. , 2000, The Journal of the Acoustical Society of America.

[106]  K Engelke,et al.  Site‐matched calcaneal measurements of broad‐band ultrasound attenuation and single X‐ray absorptiometry: Do they measure different skeletal properties? , 1992, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[108]  M. O’Donnell,et al.  Quantitative broadband ultrasonic backscatter: An approach to nondestructive evaluation in acoustically inhomogeneous materials , 1981 .

[109]  G. Berger,et al.  Broadband ultrasonic attenuation imaging: A new imaging technique of the os calcis , 1994, Calcified Tissue International.

[110]  A. Hosokawa,et al.  Ultrasonic wave propagation in bovine cancellous bone. , 1997, The Journal of the Acoustical Society of America.

[111]  B Bianco,et al.  Computational methods for ultrasonic bone assessment. , 1999, Ultrasound in medicine & biology.

[112]  J. G. Mottley,et al.  The measurement of backscatter coefficient from a broadband pulse-echo system: a new formulation , 1997, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[113]  M. Matsukawa,et al.  Two-wave propagation imaging to evaluate the structure of cancellous bone , 2012, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[114]  K. Wear Fundamental precision limitations for measurements of frequency dependence of backscatter: applications in tissue-mimicking phantoms and trabecular bone. , 2001, The Journal of the Acoustical Society of America.

[115]  P A Lewin,et al.  Estimation of ultrasonic attenuation in a bone using coded excitation. , 2003, Ultrasonics.

[116]  Goutam Ghoshal,et al.  On the estimation of backscatter coefficients using single-element focused transducers. , 2011, The Journal of the Acoustical Society of America.

[117]  M. Matsukawa,et al.  Fast characterization of two ultrasound longitudinal waves in cancellous bone using an adaptive beamforming technique. , 2015, The Journal of the Acoustical Society of America.

[118]  B. Hoffmeister Frequency dependence of apparent ultrasonic backscatter from human cancellous bone , 2011, Physics in medicine and biology.

[119]  Yi-Xian Qin,et al.  Prediction of trabecular bone principal structural orientation using quantitative ultrasound scanning. , 2012, Journal of biomechanics.

[120]  W. Lauriks,et al.  Application of the Biot model to ultrasound in bone: Direct problem , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[121]  J. Jurvelin,et al.  Effects of non-optimal focusing on dual-frequency ultrasound measurements of bone , 2011, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[122]  H. Franklin,et al.  Multiple scattering in a trabecular bone: influence of the marrow viscosity on the effective properties. , 2003, The Journal of the Acoustical Society of America.

[123]  Yi-Xian Qin,et al.  Characterization of the trabecular bone structure using frequency modulated ultrasound pulse. , 2009, The Journal of the Acoustical Society of America.

[124]  K. Wear,et al.  The relationship between ultrasonic backscatter and bone mineral density in human calcaneus , 2000, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[125]  J.J. Kaufman,et al.  Diffraction effects in insertion mode estimation of ultrasonic group velocity , 1995, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[126]  J. Medige,et al.  Ultrasound velocity and broadband attenuation over a wide range of bone mineral density , 2005, Osteoporosis International.

[127]  M. Matsukawa,et al.  Influence of cancellous bone microstructure on two ultrasonic wave propagations in bovine femur: an in vitro study. , 2010, The Journal of the Acoustical Society of America.

[128]  J. Currey,et al.  Prediction of mechanical properties of the human calcaneus by broadband ultrasonic attenuation. , 1996, Bone.

[129]  A. Derode,et al.  Simulations of ultrasound propagation in random arrangements of elliptic scatterers: occurrence of two longitudinal waves. , 2013, The Journal of the Acoustical Society of America.

[130]  J F Greenleaf,et al.  Scattering of ultrasound by tissues. , 1984, Ultrasonic imaging.

[131]  M. Matsukawa,et al.  An experimental study on the ultrasonic wave propagation in cancellous bone: waveform changes during propagation. , 2013, The Journal of the Acoustical Society of America.

[132]  C F Njeh,et al.  The ability of ultrasound velocity to predict the stiffness of cancellous bone in vitro. , 1997, Bone.

[133]  Amir Manbachi,et al.  Slow and fast ultrasonic wave detection improvement in human trabecular bones using Golay code modulation. , 2012, The Journal of the Acoustical Society of America.

[134]  P. Rüegsegger,et al.  The ability of three-dimensional structural indices to reflect mechanical aspects of trabecular bone. , 1999, Bone.

[135]  A. Hosokawa Numerical investigation of ultrasound refraction caused by oblique orientation of trabecular network in cancellous bone , 2011, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[136]  K. Lee Correlations of linear and nonlinear ultrasound parameters with density and microarchitectural parameters in trabecular bone. , 2013, The Journal of the Acoustical Society of America.

[137]  R. Gilbert,et al.  Recovery of parameters of cancellous bone by acoustic interrogation , 2016 .

[138]  X. Guo,et al.  Trabecular plates and rods determine elastic modulus and yield strength of human trabecular bone. , 2015, Bone.

[139]  R. Maev,et al.  A novel composite material specifically developed for ultrasound bone phantoms: cortical, trabecular and skull , 2013, Physics in medicine and biology.

[140]  J Töyräs,et al.  Bone properties as estimated by mineral density, ultrasound attenuation, and velocity. , 1999, Bone.

[141]  K. Wear,et al.  A method for improved standardization of in vivo calcaneal time-domain speed-of-sound measurements , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[142]  Arnaud Derode,et al.  Local measurements of the diffusion constant in multiple scattering media: Application to human trabecular bone imaging , 2008 .

[143]  K. Wear Nonlinear attenuation and dispersion in human calcaneus in vitro: statistical validation and relationships to microarchitecture. , 2015, The Journal of the Acoustical Society of America.

[144]  S. Cowin,et al.  Fabric dependence of quasi-waves in anisotropic porous media. , 2011, The Journal of the Acoustical Society of America.

[145]  Katsunori Mizuno,et al.  Propagation of two longitudinal waves in a cancellous bone with the closed pore boundary. , 2011, The Journal of the Acoustical Society of America.

[146]  D. Ta,et al.  Signal of Interest Selection Standard for Ultrasonic Backscatter in Cancellous Bone Evaluation. , 2015, Ultrasound in medicine & biology.

[147]  Françoise Peyrin,et al.  Variations of microstructure, mineral density and tissue elasticity in B6/C3H mice. , 2007, Bone.

[148]  E. Feleppa,et al.  Theoretical framework for spectrum analysis in ultrasonic tissue characterization. , 1983, The Journal of the Acoustical Society of America.

[149]  M. Matsukawa,et al.  Application of a micro-Brillouin scattering technique to characterize bone in the GHz range. , 2014, Ultrasonics.

[150]  C. Turner,et al.  Ultrasonic velocity as a predictor of strength in bovine cancellous bone , 1991, Calcified Tissue International.

[151]  Pascal Laugier,et al.  Ultrasound to Assess Bone Quality , 2014, Current Osteoporosis Reports.

[152]  A. Hosokawa Numerical analysis of variability in ultrasound propagation properties induced by trabecular microstructure in cancellous bone , 2009, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[153]  K Zacharias,et al.  Microdamage evaluation in human trabecular bone based on nonlinear ultrasound vibro-modulation (NUVM). , 2009, Journal of biomechanics.

[154]  B. Hoffmeister,et al.  Effect of gate choice on backscatter difference measurements of cancellous bone. , 2017, The Journal of the Acoustical Society of America.

[155]  E. Seeman Age- and menopause-related bone loss compromise cortical and trabecular microstructure. , 2013, The journals of gerontology. Series A, Biological sciences and medical sciences.

[156]  L. Cardoso,et al.  Changes of elastic constants and anisotropy patterns in trabecular bone during disuse-induced bone loss assessed by poroelastic ultrasound. , 2015, Journal of biomechanical engineering.

[157]  Ralph Müller,et al.  Volumetric spatial decomposition of trabecular bone into rods and plates--a new method for local bone morphometry. , 2006, Bone.

[158]  Adam Q Bauer,et al.  Bone sonometry: reducing phase aberration to improve estimates of broadband ultrasonic attenuation. , 2009, The Journal of the Acoustical Society of America.

[159]  Tainsong Chen,et al.  The measurements of ultrasound parameters on calcaneus by two-sided interrogation techniques , 2005 .

[160]  E. Jaynes,et al.  Kramers–Kronig relationship between ultrasonic attenuation and phase velocity , 1981 .

[161]  A. Hosokawa Numerical analysis of ultrasound backscattered waves in cancellous bone using a finite-difference time-domain method: isolation of the backscattered waves from various ranges of bone depths , 2015, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control.

[162]  Pascal Laugier,et al.  Inverse problems in cancellous bone: estimation of the ultrasonic properties of fast and slow waves using Bayesian probability theory. , 2010, The Journal of the Acoustical Society of America.

[163]  F Peyrin,et al.  Ultrasonic characterization of human cancellous bone using transmission and backscatter measurements: relationships to density and microstructure. , 2002, Bone.

[164]  R. Gilbert,et al.  Recovery of the parameters of cancellous bone by inversion of effective velocities, and transmission and reflection coefficients , 2011 .

[165]  Ying Li,et al.  Relationships of Ultrasonic Backscatter With Bone Densities and Microstructure in Bovine Cancellous Bone , 2018, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control.

[166]  Kang I L Lee,et al.  Dependences of quantitative ultrasound parameters on frequency and porosity in water-saturated nickel foams. , 2014, The Journal of the Acoustical Society of America.

[167]  Anne-Marie Schott,et al.  Quantitative ultrasound in the management of osteoporosis: the 2007 ISCD Official Positions. , 2008, Journal of clinical densitometry : the official journal of the International Society for Clinical Densitometry.

[168]  A generalized harmonic analysis of ultrasound waves propagating in cancellous bone , 2014 .

[169]  M Defontaine,et al.  2D arrays device for calcaneus bone transmission: an alternative technological solution using crossed beam forming. , 2004, Ultrasonics.

[170]  A. Napoli,et al.  International consensus on use of focused ultrasound for painful bone metastases: Current status and future directions , 2015, International journal of hyperthermia : the official journal of European Society for Hyperthermic Oncology, North American Hyperthermia Group.

[171]  P. Laugier,et al.  A method for the estimation of femoral bone mineral density from variables of ultrasound transmission through the human femur. , 2007, Bone.

[172]  M. Mohamed,et al.  Propagation of ultrasonic waves through demineralized cancellous bone , 2003, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[173]  J. Williams Ultrasonic wave propagation in cancellous and cortical bone: prediction of some experimental results by Biot's theory. , 1992, The Journal of the Acoustical Society of America.

[174]  Pascal Laugier,et al.  Measurement of integrated backscatter coefficient of trabecular bone , 1996, 1996 IEEE Ultrasonics Symposium. Proceedings.

[175]  J. Zagzebski,et al.  Comparison of speed of sound and ultrasound attenuation in the os calcis to bone density of the radius, femur and lumbar spine. , 1989, Clinical physics and physiological measurement : an official journal of the Hospital Physicists' Association, Deutsche Gesellschaft fur Medizinische Physik and the European Federation of Organisations for Medical Physics.

[176]  P. Lewin,et al.  Semi-empirical bone model for determination of trabecular structure properties from backscattered ultrasound. , 2009, Ultrasonics.

[177]  P. Laugier,et al.  Application of Biot's theory to ultrasonic characterization of human cancellous bones: determination of structural, material, and mechanical properties. , 2008, The Journal of the Acoustical Society of America.

[178]  P Rüegsegger,et al.  Do quantitative ultrasound measurements reflect structure independently of density in human vertebral cancellous bone? , 1998, Bone.

[179]  Steven K. Boyd,et al.  High-Resolution Peripheral Quantitative Computed Tomography for the Assessment of Bone Strength and Structure: A Review by the Canadian Bone Strength Working Group , 2013, Current Osteoporosis Reports.

[180]  Pascal Laugier,et al.  Computer simulations of ultrasonic propagation in trabecular bone , 2007, Comput. Biol. Medicine.

[181]  G. Renaud,et al.  Exploration of trabecular bone nonlinear elasticity using time-of-flight modulation , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[182]  Dan Li,et al.  Effect of Spectral Estimation on Ultrasonic Backscatter Parameters in Measurements of Cancellous Bones , 2019, IEEE Access.

[183]  C. Depollier,et al.  Transient ultrasound propagation in porous media using Biot theory and fractional calculus: application to human cancellous bone. , 2013, The Journal of the Acoustical Society of America.

[184]  P. Laugier,et al.  Influence of the precision of spectral backscatter measurements on the estimation of scatterers size in cancellous bone. , 2004, Ultrasonics.

[185]  A. Bauer,et al.  Is the Kramers-Kronig relationship between ultrasonic attenuation and dispersion maintained in the presence of apparent losses due to phase cancellation? , 2007, The Journal of the Acoustical Society of America.

[186]  M. Bouxsein,et al.  Scattering of ultrasound in cancellous bone: predictions from a theoretical model. , 2000, Journal of biomechanics.

[187]  Hirotaka Imaizumi,et al.  Applicability of Finite-Difference Time-Domain Method to Simulation of Wave Propagation in Cancellous Bone , 2006 .

[188]  Pascal Laugier,et al.  Propagation of two longitudinal waves in human cancellous bone: an in vitro study. , 2009, The Journal of the Acoustical Society of America.

[189]  Ying Li,et al.  An Ultrasonic Backscatter Instrument for Cancellous Bone Evaluation in Neonates , 2015 .

[190]  P. Laugier,et al.  Quantitative Ultrasound Assessment of Cortical Bone Properties Beyond Bone Mineral Density , 2019, IRBM.

[191]  A. Hosokawa Effect of porosity distribution in the propagation direction on ultrasound waves through cancellous bone , 2010, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[192]  Françoise Peyrin,et al.  Variation of Ultrasonic Parameters With Microstructure and Material Properties of Trabecular Bone: A 3D Model Simulation , 2007, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[193]  H. K. Genant,et al.  Broadband ultrasound attenuation signals depend on trabecular orientation: An in vitro study , 1993, Osteoporosis International.

[194]  Ryosuke O. Tachibana,et al.  Multichannel instantaneous frequency analysis of ultrasound propagating in cancellous bone. , 2014, The Journal of the Acoustical Society of America.

[195]  P. Laugier,et al.  Instrumentation for in vivo ultrasonic characterization of bone strength , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[196]  P. Laugier,et al.  Ultrasound images of the os calcis: a new method of assessment of bone status , 1993 .

[197]  Dean Ta,et al.  Measurement of tortuosity in aluminum foams using airborne ultrasound. , 2010, Ultrasonics.

[198]  F. Padilla,et al.  A device for in vivo measurements of quantitative ultrasound variables at the human proximal femur , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[199]  C M Langton,et al.  Development of a cancellous bone structural model by stereolithography for ultrasound characterisation of the calcaneus. , 1997, Medical engineering & physics.

[200]  A. Moayyeri,et al.  Quantitative ultrasound of the heel and fracture risk assessment: an updated meta-analysis , 2011, Osteoporosis International.

[201]  A. Hosokawa,et al.  Acoustic anisotropy in bovine cancellous bone. , 1998, The Journal of the Acoustical Society of America.

[202]  J. Rho,et al.  Effect of Collagen and Mineral Content on the High-Frequency Ultrasonic Properties of Human Cancellous Bone , 2002, Osteoporosis International.

[203]  M J Lammi,et al.  Acoustic properties of trabecular bone--relationships to tissue composition. , 2007, Ultrasound in medicine & biology.

[204]  L. Le An investigation of pulse-timing techniques for broadband ultrasonic velocity determination in cancellous bone: a simulation study. , 1998, Physics in medicine and biology.

[205]  J. Barger,et al.  Acoustical properties of the human skull. , 1978, The Journal of the Acoustical Society of America.

[206]  K. Wear,et al.  Characterization of trabecular bone using the backscattered spectral centroid shift , 2003, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[207]  A. P. Holt,et al.  Effect of the cortex on ultrasonic backscatter measurements of cancellous bone , 2011, Physics in medicine and biology.

[208]  R. Siffert,et al.  3D Simulation of Ultrasound in the Ultra-Distal Human Radius , 2012 .

[209]  K. Wear,et al.  Ultrasonic scattering from cancellous bone: A review , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[210]  Juha Töyräs,et al.  Ultrasonic characterization of human trabecular bone microstructure , 2006, Physics in medicine and biology.

[211]  Srinidhi Nagaraja,et al.  Relationships among ultrasonic and mechanical properties of cancellous bone in human calcaneus in vitro. , 2017, Bone.

[212]  C. Langton,et al.  Experimental and computer simulation validation of ultrasound phase interference created by lateral inhomogeneity of transit time in replica bone: marrow composite models , 2013, Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine.

[213]  D. Ta,et al.  Analysis of apparent integrated backscatter coefficient and backscattered spectral centroid shift in Calcaneus in vivo for the ultrasonic evaluation of osteoporosis. , 2014, Ultrasound in medicine & biology.

[214]  E. Mittra,et al.  Determination of ultrasound phase velocity in trabecular bone using time dependent phase tracking technique. , 2006, Journal of biomechanical engineering.

[215]  Weiqi Wang,et al.  Analysis of frequency dependence of ultrasonic backscatter coefficient in cancellous bone. , 2008, The Journal of the Acoustical Society of America.

[216]  K. Il Lee,et al.  Frequency-dependent attenuation and backscatter coefficients in bovine trabecular bone from 0.2 to 1.2 MHz. , 2012, The Journal of the Acoustical Society of America.

[217]  P. Lewin,et al.  Improving broadband ultrasound attenuation assessment in cancellous bone by mitigating the influence of cortical bone: Phantom and in‐vitro study , 2019, Ultrasonics.

[218]  J. A. Evans,et al.  On the ultrasonic attenuation and its frequency dependence in the os calcis assessed with a multielement receiver. , 1999, Ultrasound in medicine & biology.

[219]  J Töyräs,et al.  Spatial variation of acoustic properties is related with mechanical properties of trabecular bone , 2007, Physics in medicine and biology.

[220]  G Van der Perre,et al.  A comparison of time-domain and frequency-domain approaches to ultrasonic velocity measurement in trabecular bone. , 1996, Physics in medicine and biology.

[221]  The dependence of broadband ultrasound attenuation on phase interference in thin plates of variable thickness and curvature: a comparison of experimental measurement and computer simulation , 2018, Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine.

[222]  Katsunori Mizuno,et al.  Two-wave behavior under various conditions of transition area from cancellous bone to cortical bone. , 2014, Ultrasonics.

[223]  Suk Wang Yoon,et al.  Acoustic wave propagation in bovine cancellous bone: application of the Modified Biot-Attenborough model. , 2003, The Journal of the Acoustical Society of America.

[224]  C. Langton,et al.  Bone volume fraction and structural parameters for estimation of mechanical stiffness and failure load of human cancellous bone samples; in-vitro comparison of ultrasound transit time spectroscopy and X-ray μCT. , 2018, Bone.

[225]  W. Lauriks,et al.  Ultrasonic wave propagation in human cancellous bone: application of Biot theory. , 2004, The Journal of the Acoustical Society of America.

[226]  B. Hoffmeister,et al.  Effect of intervening tissues on ultrasonic backscatter measurements of bone: An in vitro study. , 2015, The Journal of the Acoustical Society of America.

[227]  F. Padilla,et al.  Femur ultrasound (FemUS)—first clinical results on hip fracture discrimination and estimation of femoral BMD , 2010, Osteoporosis International.

[228]  A Lhémery,et al.  Velocity dispersion in trabecular bone: influence of multiple scattering and of absorption. , 2008, The Journal of the Acoustical Society of America.

[229]  M. Biot Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. II. Higher Frequency Range , 1956 .

[230]  J.J. Kaufman,et al.  Diffraction correction methods for insertion ultrasound attenuation estimation , 1993, IEEE Transactions on Biomedical Engineering.

[231]  Tainsong Chen,et al.  Measurements of acoustic dispersion on calcaneus using spilt spectrum processing technique. , 2006, Medical engineering & physics.

[232]  Wei Lin,et al.  The influence of cortical end-plate on broadband ultrasound attenuation measurements at the human calcaneus using scanning confocal ultrasound. , 2005, The Journal of the Acoustical Society of America.

[233]  M. Ragozzino Analysis of the error in measurement of ultrasound speed in tissue due to waveform deformation by frequency-dependent attenuation. , 1981, Ultrasonics.

[234]  Pascal Laugier,et al.  Prediction of frequency-dependent ultrasonic backscatter in cancellous bone using statistical weak scattering model. , 2003, Ultrasound in medicine & biology.

[235]  J.J. Kaufman,et al.  Ultrasonic assessment of human and bovine trabecular bone: a comparison study , 1996, IEEE Transactions on Biomedical Engineering.

[236]  Yi-Xian Qin,et al.  Enhanced correlation between quantitative ultrasound and structural and mechanical properties of bone using combined transmission-reflection measurement. , 2015, The Journal of the Acoustical Society of America.

[237]  T. Otani,et al.  Novel ultrasonic bone densitometry based on two longitudinal waves: significant correlation with pQCT measurement values and age-related changes in trabecular bone density, cortical thickness, and elastic modulus of trabecular bone in a normal Japanese population , 2010, Osteoporosis International.

[238]  T. Keaveny,et al.  Trabecular bone strength predictions using finite element analysis of micro-scale images at limited spatial resolution. , 2009, Bone.

[239]  M. Dreher,et al.  Relationships of quantitative ultrasound parameters with cancellous bone microstructure in human calcaneus in vitro. , 2012, The Journal of the Acoustical Society of America.

[240]  W. Hayes,et al.  A 20-year perspective on the mechanical properties of trabecular bone. , 1993, Journal of biomechanical engineering.

[241]  Raafat George Saadé,et al.  Understanding velocity of sound in trabecular bone via computer simulations , 2006, Comput. Biol. Medicine.

[242]  C. Burckhardt Speckle in ultrasound B-mode scans , 1978, IEEE Transactions on Sonics and Ultrasonics.

[243]  P H Nicholson,et al.  A model for ultrasonic scattering in cancellous bone based on velocity fluctuations in a binary mixture. , 1998, Physiological measurement.

[244]  Françoise Peyrin,et al.  Attenuation in trabecular bone: A comparison between numerical simulation and experimental results in human femur. , 2007, The Journal of the Acoustical Society of America.

[245]  T. Otani,et al.  Measurement of human trabecular bone by novel ultrasonic bone densitometry based on fast and slow waves , 2009, Osteoporosis International.

[246]  S. Ueha,et al.  Estimation of Trabecular Bone Axis for Characterization of Cancellous Bone Using Scattered Ultrasonic Wave. , 1998 .

[247]  M. Bouxsein,et al.  Quantitative Ultrasound of the Calcaneus Reflects the Mechanical Properties of Calcaneal Trabecular Bone , 1997, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[248]  J. Jurvelin,et al.  Dual-frequency ultrasound--new pulse-echo technique for bone densitometry. , 2008, Ultrasound in medicine & biology.

[249]  J. A. Evans,et al.  Dependence of the velocity and attenuation of ultrasound in bone on the mineral content. , 1991, Physics in medicine and biology.

[250]  A. Hosokawa Development of a numerical cancellous bone model for finite-difference time-domain simulations of ultrasound propagation , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[251]  K. Wear Group velocity, phase velocity, and dispersion in human calcaneus in vivo. , 2007, The Journal of the Acoustical Society of America.

[252]  A. Meunier,et al.  IN VITRO ACOUSTIC WAVE PROPAGATION IN HUMAN AND BOVINE CANCELLOUS BONE AS PREDICTED BY BIOT'S THEORY , 2008 .

[253]  A. Laib,et al.  The dependence of ultrasonic backscatter on trabecular thickness in human calcaneus: theoretical and experimental results , 2003, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[254]  M. Matsukawa,et al.  Influence of the circumferential wave on the fast and slow wave propagation in small distal radius bone , 2014 .

[255]  R Barkmann,et al.  Numerical simulation of the dependence of quantitative ultrasonic parameters on trabecular bone microarchitecture and elastic constants. , 2006, Ultrasonics.

[256]  Decomposition of two-component ultrasound pulses in cancellous bone using modified least squares prony method--phantom experiment and simulation. , 2010, Ultrasound in medicine & biology.

[257]  J. G. Miller,et al.  Anisotropy of the ultrasonic attenuation in soft tissues: measurements in vitro. , 1990, The Journal of the Acoustical Society of America.

[258]  E. Madsen,et al.  Method of data reduction for accurate determination of acoustic backscatter coefficients. , 1984, The Journal of the Acoustical Society of America.

[259]  T Chen,et al.  A novel method to measure acoustic speed of bone tissue. , 1997, Ultrasound in medicine & biology.

[260]  C. Langton,et al.  Comparison of bone mineral density and quantitative ultrasound of the calcaneus: site-matched correlation and discrimination of axial BMD status. , 2000, The British journal of radiology.

[261]  W. Lauriks,et al.  Predictions of angle dependent tortuosity and elasticity effects on sound propagation in cancellous bone. , 2009, The Journal of the Acoustical Society of America.

[262]  C. Langton,et al.  Estimation of mechanical stiffness by finite element analysis of ultrasound computed tomography (UCT-FEA); a comparison with X-ray µCT based FEA in cancellous bone replica models , 2018 .

[263]  S. Adeeb,et al.  The finite element method for micro-scale modeling of ultrasound propagation in cancellous bone. , 2014, Ultrasonics.

[264]  J. Rho,et al.  Low-megahertz ultrasonic properties of bovine cancellous bone. , 2000, Bone.

[265]  Ultrasound propagation in trabecular bone: a numerical study of the influence of microcracks. , 2014, Ultrasonics.

[266]  F Peyrin,et al.  Relationships of trabecular bone structure with quantitative ultrasound parameters: in vitro study on human proximal femur using transmission and backscatter measurements. , 2008, Bone.

[267]  Keith A Wear,et al.  Interference between wave modes may contribute to the apparent negative dispersion observed in cancellous bone. , 2008, The Journal of the Acoustical Society of America.

[268]  Sadayuki Ueha,et al.  Ultrasonic Scattering Study of Cancellous Bone for Osteoporosis Diagnosis , 1996 .

[269]  K. Lee Dependences of ultrasonic properties on frequency and trabecular spacing in trabecular-bone-mimicking phantoms. , 2015, The Journal of the Acoustical Society of America.

[270]  R. Gilbert,et al.  SIMULATION OF A MIXTURE MODEL FOR ULTRASOUND PROPAGATION THROUGH CANCELLOUS BONE USING STAGGERED-GRID FINITE DIFFERENCES , 2013 .

[271]  E. Bossy,et al.  Three-dimensional simulation of ultrasound propagation through trabecular bone structures measured by synchrotron microtomography , 2005, Physics in medicine and biology.

[272]  S B Palmer,et al.  In vitro comparison of quantitative computed tomography and broadband ultrasonic attenuation of trabecular bone. , 1989, Bone.

[273]  V Bousson,et al.  In vitro ultrasonic characterization of human cancellous femoral bone using transmission and backscatter measurements: relationships to bone mineral density. , 2006, The Journal of the Acoustical Society of America.

[274]  C. Langton,et al.  Biot theory: a review of its application to ultrasound propagation through cancellous bone. , 1999, Bone.

[275]  G. Berger,et al.  Ultrasound parametric imaging of the calcaneus:In vivo results with a new device , 1996, Calcified Tissue International.

[276]  P. Laugier,et al.  Velocity dispersion of acoustic waves in cancellous bone , 1998, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[277]  U. P. S. T. Force,et al.  Screening for Osteoporosis: U.S. Preventive Services Task Force Recommendation Statement , 2011, Annals of Internal Medicine.

[278]  K. Wear,et al.  Fast and slow wave detection in bovine cancellous bone in vitro using bandlimited deconvolution and Prony's method. , 2014, The Journal of the Acoustical Society of America.

[279]  Christian M Langton,et al.  Measurements of tortuosity in stereolithographical bone replicas using audiofrequency pulses. , 2005, The Journal of the Acoustical Society of America.

[280]  R. Bishop,et al.  Stress Waves in Solids , 1954, Nature.

[281]  Bert Van Rietbergen,et al.  Finite Element Analysis Based on In Vivo HR‐pQCT Images of the Distal Radius Is Associated With Wrist Fracture in Postmenopausal Women , 2007, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[282]  C. M. Langton,et al.  Prediction of Human Femoral Bone Strength Using Ultrasound Velocity and BMD: An In Vitro Study , 1997, Osteoporosis International.

[283]  Keith A Wear,et al.  The dependencies of phase velocity and dispersion on volume fraction in cancellous-bone-mimicking phantoms. , 2009, The Journal of the Acoustical Society of America.

[285]  P.H.F. Nicholson,et al.  Ultrasound and the biomechanical competence of bone , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[286]  G. Schmitz,et al.  Model-based estimation of quantitative ultrasound variables at the proximal femur , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[287]  Numerical investigation of reflection properties of fast and slow longitudinal waves in cancellous bone: Variations with boundary medium , 2014 .

[288]  D. Ta,et al.  Measurement of the Human Calcaneus In Vivo Using Ultrasonic Backscatter Spectral Centroid Shift , 2016, Journal of ultrasound in medicine : official journal of the American Institute of Ultrasound in Medicine.

[289]  Vu-Hieu Nguyen,et al.  Simulation of ultrasonic wave propagation in anisotropic cancellous bone immersed in fluid , 2010 .

[290]  H Gemmeke,et al.  Comparison of active-set method deconvolution and matched-filtering for derivation of an ultrasound transit time spectrum , 2015, Physics in medicine and biology.

[291]  C. Hellmich,et al.  A Multiscale Poromicromechanical Approach to Wave Propagation and Attenuation in Bone , 2013 .

[292]  H. Kanai,et al.  Fast decomposition of two ultrasound longitudinal waves in cancellous bone using a phase rotation parameter for bone quality assessment: Simulation study. , 2017, Journal of the Acoustical Society of America.

[293]  Georg Schmitz,et al.  Estimation of multipath transmission parameters for quantitative ultrasound measurements of bone , 2013, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control.

[294]  M. Kaczmarek,et al.  Identification of Drag Parameters of Flow in High Permeability Materials by U-Tube Method , 2013, Transport in Porous Media.

[295]  P R White,et al.  Ultrasonic propagation in cancellous bone: a new stratified model. , 1999, Ultrasound in medicine & biology.

[296]  M. Fini,et al.  Influence of density, elasticity, and structure on ultrasound transmission through trabecular bone cylinders , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[297]  Chan Zhang,et al.  Measurements of ultrasonic phase velocities and attenuation of slow waves in cellular aluminum foams as cancellous bone-mimicking phantoms. , 2011, The Journal of the Acoustical Society of America.

[298]  K. Wear,et al.  The effects of frequency-dependent attenuation and dispersion on sound speed measurements: applications in human trabecular bone , 2000, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[299]  W. Lauriks,et al.  Ultrasonic wave propagation in stereo-lithographical bone replicas. , 2010, The Journal of the Acoustical Society of America.

[300]  Weiqi Wang,et al.  Simplified inverse filter tracking algorithm for estimating the mean trabecular bone spacing , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[301]  R. S. Siffert,et al.  Influence of marrow on ultrasonic velocity and attenuation in bovine trabecular bone , 1996, Calcified Tissue International.

[302]  R. Lew,et al.  The relationship between ultrasound and densitometric measurements of bone mass at the calcaneus in women , 1992, Calcified Tissue International.

[303]  A. Hosokawa Numerical investigation of ultrasound reflection and backscatter measurements in cancellous bone on various receiving areas. , 2014, Ultrasonics.

[304]  J. Katz,et al.  Scanning Acoustic Microscopy Study of Human Cortical and Trabecular Bone , 2001, Annals of Biomedical Engineering.

[305]  C F Njeh,et al.  Orthogonal relationships between ultrasonic velocity and material properties of bovine cancellous bone. , 1996, Medical engineering & physics.

[306]  Laurent Sedel,et al.  In Vitro Acoustic Waves Propagation in Human and Bovine Cancellous Bone , 2003, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[307]  M. Matsukawa,et al.  Effects of structural anisotropy of cancellous bone on speed of ultrasonic fast waves in the bovine femur , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[308]  B. Hoffmeister,et al.  Ultrasonic backscatter from cancellous bone: the apparent backscatter transfer function , 2015, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control.

[309]  Mark B. Flegg,et al.  A deconvolution method for deriving the transit time spectrum for ultrasound propagation through cancellous bone replica models , 2014, Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine.

[310]  Gangming Luo,et al.  On the relative contributions of absorption and scattering to ultrasound attenuation in trabecular bone: a simulation study , 2003, IEEE Symposium on Ultrasonics, 2003.

[311]  Keith A Wear,et al.  Measurement of dependence of backscatter coefficient from cylinders on frequency and diameter using focused transducers--with applications in trabecular bone. , 2004, The Journal of the Acoustical Society of America.

[312]  Gangming Luo,et al.  A portable real-time ultrasonic bone densitometer. , 2007, Ultrasound in medicine & biology.

[313]  Kay Raum,et al.  Stimulation of bone repair with ultrasound: a review of the possible mechanic effects. , 2014, Ultrasonics.

[314]  Timothy G Leighton,et al.  Predictions of the modified Biot-Attenborough model for the dependence of phase velocity on porosity in cancellous bone. , 2007, Ultrasonics.

[315]  K. Lee Relationships of linear and nonlinear ultrasound parameters with porosity and trabecular spacing in trabecular-bone-mimicking phantoms. , 2016, The Journal of the Acoustical Society of America.

[316]  P. Laugier,et al.  Quantitative Ultrasound and the Management of Osteoporosis , 2013 .

[317]  M. Biot Theory of Propagation of Elastic Waves in a Fluid‐Saturated Porous Solid. I. Low‐Frequency Range , 1956 .

[318]  K. Wear Frequency dependence of ultrasonic backscatter from human trabecular bone: theory and experiment. , 1999, The Journal of the Acoustical Society of America.

[319]  L. J. Busse,et al.  Detection of spatially nonuniform ultrasonic radiation with phase sensitive (piezoelectric) and phase insensitive (acoustoelectric) receivers , 1981 .

[320]  F. Padilla,et al.  Effects of frequency-dependent attenuation and velocity dispersion on in vitro ultrasound velocity measurements in intact human femur specimens , 2006, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[321]  A. Vaziri,et al.  Biomechanics and mechanobiology of trabecular bone: a review. , 2015, Journal of biomechanical engineering.

[322]  C. Langton,et al.  The measurement of broadband ultrasonic attenuation in cancellous bone. , 1984, Engineering in medicine.

[323]  K. Wear Time-domain separation of interfering waves in cancellous bone using bandlimited deconvolution: simulation and phantom study. , 2014, The Journal of the Acoustical Society of America.

[324]  Adam Q Bauer,et al.  Negative dispersion in bone: the role of interference in measurements of the apparent phase velocity of two temporally overlapping signals. , 2008, The Journal of the Acoustical Society of America.

[325]  Tony Evans Bone Ultrasound , 1993 .

[326]  T. Keaveny,et al.  The influence of boundary conditions and loading mode on high-resolution finite element-computed trabecular tissue properties. , 2009, Bone.

[327]  G. Pharr,et al.  The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques. , 1999, Journal of biomechanics.

[328]  I. Kiviranta,et al.  Prediction of density and mechanical properties of human trabecular bone in vitro by using ultrasound transmission and backscattering measurements at 0.2–6.7 MHz frequency range , 2005, Physics in medicine and biology.

[329]  T. Keaveny,et al.  Trabecular bone modulus-density relationships depend on anatomic site. , 2003, Journal of biomechanics.

[330]  S. Palmer,et al.  The interaction of ultrasound with cancellous bone. , 1991, Physics in medicine and biology.

[331]  C M Sehgal Quantitative relationship between tissue composition and scattering of ultrasound. , 1993, The Journal of the Acoustical Society of America.

[332]  C F Njeh,et al.  The non-linear relationship between BUA and porosity in cancellous bone. , 1996, Physics in medicine and biology.

[333]  K. Wear,et al.  Relationships among calcaneal backscatter, attenuation, sound speed, hip bone mineral density, and age in normal adult women. , 2001, The Journal of the Acoustical Society of America.

[334]  Yi-Xian Qin,et al.  Effects of phase cancellation and receiver aperture size on broadband ultrasonic attenuation for trabecular bone in vitro. , 2011, Ultrasound in medicine & biology.

[335]  P. Laugier,et al.  Assessment of the relationship between broadband ultrasound attenuation and bone mineral density at the calcaneus using BUA imaging and DXA , 2005, Osteoporosis International.

[336]  Mickael Tanter,et al.  Attenuation, scattering, and absorption of ultrasound in the skull bone. , 2011, Medical physics.

[337]  K. Waters,et al.  Kramers-Kronig analysis of attenuation and dispersion in trabecular bone. , 2005, The Journal of the Acoustical Society of America.

[338]  J G Truscott,et al.  A phantom for quantitative ultrasound of trabecular bone. , 1994, Physics in medicine and biology.

[339]  Pascal Laugier,et al.  Influence of the filling fluid on frequency-dependent velocity and attenuation in cancellous bones between 0.35 and 2.5 MHz. , 2009, The Journal of the Acoustical Society of America.

[340]  Jean-Pierre Remenieras,et al.  Application of nonlinear phenomena induced by focused ultrasound to bone imaging. , 2003, Ultrasound in medicine & biology.

[341]  J. Litniewski Determination of the elasticity coefficient for a single trabecula of a cancellous bone: scanning acoustic microscopy approach. , 2005, Ultrasound in medicine & biology.

[342]  Ultrasonic wave propagation through porous ceramics at different angles of propagation , 2015 .

[343]  G W Petley,et al.  Broadband ultrasonic attenuation: are current measurement techniques inherently inaccurate? , 1995, The British journal of radiology.

[344]  Andres Laib,et al.  Comparison of measurements of phase velocity in human calcaneus to Biot theory. , 2005, The Journal of the Acoustical Society of America.

[345]  James A. Zagzebski,et al.  Ultrasound transmission measurements through the os calcis , 1991, Calcified Tissue International.

[346]  M. Matsukawa,et al.  Effect of medullary cavity in cancellous bone on two-wave phenomenon , 2016 .

[347]  K. Wear,et al.  Conventional, Bayesian, and Modified Prony's methods for characterizing fast and slow waves in equine cancellous bone. , 2015, The Journal of the Acoustical Society of America.

[348]  K. Wear Ultrasonic attenuation in human calcaneus from 0.2 to 1.7 MHz , 2001, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[349]  James G. Miller,et al.  Cancellous bone fast and slow waves obtained with Bayesian probability theory correlate with porosity from computed tomography. , 2012, The Journal of the Acoustical Society of America.

[350]  M Matsukawa,et al.  Trabecular and cortical bone separately assessed at radius with a new ultrasound device, in a young adult population with various physical activities. , 2010, Bone.

[351]  A Hosokawa Simulation of ultrasound propagation through bovine cancellous bone using elastic and Biot's finite-difference time-domain methods. , 2005, The Journal of the Acoustical Society of America.

[352]  C. Rubin,et al.  Prediction of trabecular bone qualitative properties using scanning quantitative ultrasound. , 2013, Acta astronautica.

[353]  Renaud Boistel,et al.  Experimental observation of ultrasound fast and slow waves through three-dimensional printed trabecular bone phantoms. , 2016, The Journal of the Acoustical Society of America.

[354]  K. Wear,et al.  The effect of phase cancellation on estimates of broadband ultrasound attenuation and backscatter coefficient in human calcaneus in vitro , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[355]  S. Boonen,et al.  Quantitative Ultrasound and Trabecular Architecture in the Human Calcaneus * , 2001, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[356]  R. Gilbert,et al.  Transfer functions for a one-dimensional fluid–poroelastic system subject to an ultrasonic pulse , 2012 .

[357]  C C Glüer,et al.  Osteoporosis: association of recent fractures with quantitative US findings. , 1996, Radiology.

[358]  Keith A Wear,et al.  Cancellous bone analysis with modified least squares Prony's method and chirp filter: phantom experiments and simulation. , 2010, The Journal of the Acoustical Society of America.

[359]  J Töyräs,et al.  Ultrasound backscatter measurements of intact human proximal femurs--relationships of ultrasound parameters with tissue structure and mineral density. , 2014, Bone.

[360]  L. Le,et al.  The analysis and compensation of cortical thickness effect on ultrasonic backscatter signals in cancellous bone , 2014 .