A STUDY OF ULTRASONIC WAVE PROPAGATION IN BONES

In the present work the propagation of ultrasonic waves in human bones is modeled by Biot equations introducing in them viscoelasticity so as to take into account attenuation mechanisms; different models for the latter are introduced and compared. Also, Biot equations are numerically solved using two dimensional finite elements. How different po- rosities affect elastic moduli, phase velocities, visco- dynamic and intrinsic attenuation is also studied.

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

[2]  R. Bruce Lindsay,et al.  Seismic Waves: Radiation, Transmission, and Attenuation , 1965 .

[3]  Joel Koplik,et al.  Theory of dynamic permeability and tortuosity in fluid-saturated porous media , 1987, Journal of Fluid Mechanics.

[4]  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.

[5]  J. Bear.  Dynamics of Fluids in Porous Media , 1975 .

[6]  D. L. Johnson,et al.  Elastodynamics of gels , 1982 .

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

[8]  Dongwoo Sheen,et al.  FREQUENCY DOMAIN TREATMENT OF ONE-DIMENSIONAL SCALAR WAVES , 1993 .

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

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

[11]  R. Lakes,et al.  Investigation of bovine bone by resonant ultrasound spectroscopy and transmission ultrasound , 2002, Biomechanics and modeling in mechanobiology.

[12]  Juan E. Santos,et al.  FREQUENCY DOMAIN WAVE PROPAGATION MODELING IN EXPLORATION SEISMOLOGY , 2001 .

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

[14]  T. Mukerji,et al.  The Rock Physics Handbook , 1998 .

[15]  Jens M. Hovem,et al.  Viscous attenuation of sound in saturated sand , 1979 .

[16]  Don L. Anderson,et al.  Velocity dispersion due to anelasticity; implications for seismology and mantle composition , 1976 .

[17]  T. Plona,et al.  Acoustic slow waves and the consolidation transition , 1982 .

[18]  Jim Douglas,et al.  APPROXIMATION OF SCALAR WAVES IN THE SPACE-FREQUENCY DOMAIN , 1994 .

[19]  M. Biot.  MECHANICS OF DEFORMATION AND ACOUSTIC PROPAGATION IN POROUS MEDIA , 1962 .

[20]  R. Lakes,et al.  Ultrasonic wave propagation and attenuation in wet bone. , 1986, Journal of biomedical engineering.

[21]  C. Ravazzoli,et al.  Reflection and transmission coefficients in fluid‐saturated porous media , 1992 .

[22]  J. Compston,et al.  Age-related changes in trabecular width and spacing in human iliac crest biopsies. , 1989, Bone and mineral.

[23]  Olivier Coussy,et al.  Acoustics of Porous Media , 1988 .

[24]  F. Gaßmann.  Uber die Elastizitat poroser Medien. , 1961 .

[25]  R. Siffert,et al.  Ultrasonic bone assessment: "the time has come". , 2007, Bone.

[26]  R. Sato.  Attenuation of Seismic Waves , 1967 .

[27]  S. Shtrikman,et al.  A variational approach to the theory of the elastic behaviour of multiphase materials , 1963 .

[28]  Maryline Talmant,et al.  Three-dimensional simulations of ultrasonic axial transmission velocity measurement on cortical bone models. , 2004, The Journal of the Acoustical Society of America.

[29]  Amos Nur,et al.  Wave attenuation in partially saturated rocks , 1979 .

[30]  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.

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

[32]  Theo H Smit,et al.  Estimation of the poroelastic parameters of cortical bone. , 2002, Journal of biomechanics.

[33]  THEORETICAL AND EXPERIMENTAL ULTRASONIC CHARACTERIZATION OF ANISOTROPIC PROPERTIES IN CANCELLOUS BONE , 2003 .

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

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

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

[37]  R. Gilbert,et al.  DETERMINATION OF THE PARAMETERS OF CANCELLOUS BONE USING LOW FREQUENCY ACOUSTIC MEASUREMENTS , 2004 .

[38]  S. Cowin.  Bone poroelasticity. , 1999, Journal of biomechanics.

[39]  S. Church.  Ultrasonic , 2010 .

[40]  Andrew N. Norris,et al.  Stoneley-wave attenuation and dispersion in permeable formations , 1989 .

[41]  A. M.,et al.  Theory of Deformation of a Porous Viscoelastic Anisotropic Solid , 2022 .

[42]  W. R. Gardner.  Physics of Flow through Porous Media , 1961 .