Acoustic wave propagation in bovine cancellous bone: application of the Modified Biot-Attenborough model.

Acoustic wave propagation in bovine cancellous bone is experimentally and theoretically investigated in the frequency range of 0.5-1 MHz. The phase velocity, attenuation coefficient, and broadband ultrasonic attenuation (BUA) of bovine cancellous bone are measured as functions of frequency and porosity. For theoretical estimation, the Modified Biot-Attenborough (MBA) model is employed with three new phenomenological parameters: the boundary condition, phase velocity, and impedance parameters. The MBA model is based on the idealization of cancellous bone as a nonrigid porous medium with circular cylindrical pores oriented normal to the surface. It is experimentally observed that the phase velocity is approximately nondispersive and the attenuation coefficient linearly increases with frequency. The MBA model predicts a slightly negative dispersion of phase velocity linearly with frequency and the nonlinear relationships of attenuation and BUA with porosity. The experimental results are in good agreement with the theoretical results estimated with the MBA model. It is expected that the MBA model can be usefully employed in the field of clinical bone assessment for the diagnosis of osteoporosis.

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

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

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

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

[5]  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.

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

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

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

[9]  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.

[10]  S. Lang,et al.  Ultrasonic method for measuring elastic coefficients of bone and results on fresh and dried bovine bones. , 1970, IEEE transactions on bio-medical engineering.

[11]  A M Schott,et al.  Do ultrasound measurements on the os calcis reflect more the bone microarchitecture than the bone mass?: a two-dimensional histomorphometric study. , 1995, Bone.

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

[13]  Frequency Dependence of Ultrasonic Characteristics of Cancellous Bone , 1982 .

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

[15]  S. Goldstein,et al.  Three quantitative ultrasound parameters reflect bone structure , 1994, Calcified Tissue International.

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

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

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

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

[20]  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.

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

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

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

[24]  J. A. Evans,et al.  Ultrasonic attenuation and velocity in bone. , 1990, Physics in medicine and biology.

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

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

[27]  K. Attenborough.  Acoustical characteristics of rigid fibrous absorbents and granular materials , 1983 .

[28]  Laszlo Adler,et al.  Reflection and transmission of elastic waves from a fluid‐saturated porous solid boundary , 1990 .

[29]  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.

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

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

[32]  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.

[33]  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.

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

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

[36]  Michael Schoenberg,et al.  Wave propagation in alternating solid and fluid layers , 1984 .

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

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