Understanding the propagation of acoustic waves
through a liquid-perfused porous solid framework such as cancellous bone is an
important pre-requisite to improve the diagnosis of osteoporosis by ultrasound.
In order to elucidate the propagation dependence upon the material and
structural properties of cancellous bone, several theoretical models have been
considered to date, with Biot-based models demonstrating the greatest
potential. This paper describes the fundamental basis of these models and
reviews their performance.
Cite this paper
Aygün, H. , Attenborough, K. and Postema, M. (2014). A Review of the State of Art in Applying Biot Theory to Acoustic Propagation through the Bone. Open Access Library Journal, 1, e994. doi: http://dx.doi.org/10.4236/oalib.1100994.
Thomsen, J.S., Ebbesen, E.N. and Mosekilde, L. (2002) Age-Related
Differences between Thinning of Horizontal and Vertical Trabeculae in Human
Lumbar Bone as Assessed by a New Computerized Method. Bone, 31, 136-142.
Johnell, O. and Kanis, J.A. (2006) An Estimate of
the Worldwide Prevalence and Disability Associated with Osteoporotic Fractures. Osteoporosis International, 17, 1726-1733. http://dx.doi.org/10.1007/s00198-006-0172-4
Burge, R.T., Worley, D. and Johansen, A. (2001) The Cost of Osteoporotic
Fractures in the UK: Projections for 2000- 2020. Journal of Medical Economics, 4, 51-52. http://dx.doi.org/10.3111/200104051062
Njeh, C.F. and Shepherd, J.A. (2004) Absorptiometric Measurement. In: Langton, C.M. and Njeh, C.F., Eds., The Physical
Measurement of Bone, IOPP, 267-307.
Pothuaud, L. and Majumdar, S. (2004) Magnetic Resonance Imaging. In: Langton, C.M. and Njeh, C.F., Eds., The Physical
Measurement of Bone, IOPP, 379-411.
Njeh, C.F., Boivin, C.M. and Langton, C.M. (1997) The Role of Ultrasound in the Management of
Osteoporosis: A Review. Osteoporosis
International, 7, 7-22. http://dx.doi.org/10.1007/BF01623454
Njeh, C.F., Hodgskinson, R., Currey, J.D. and Langton, C.M. (1996) Orthogonal Relationships
between Ultrasonic Velocity and Material Properties of Bovine Cancellous Bone. Medical Engineering & Physics, 18, 373-381. http://dx.doi.org/10.1016/1350-4533(95)00064-X
Hodgskinson, R., Njeh, C.F., Whitehead, M.A. and
Langton, C.M. (1996) The Non-Linear Relationship between BUA and Porosity in Cancellous Bone. Physics in Medicine & Biology, 41, 2411-2420. http://dx.doi.org/10.1088/0031-9155/41/11/012
Langton, C.M., Whitehead, M.A., Haire, T.J. and
Hodgskinson, R. (1998) Fractal Dimension Predicts Broadband Ultrasound
Attenuation in Stereolithography Models of Cancellous Bone. Physics in Medicine and Biology, 43, 467-471. http://dx.doi.org/10.1088/0031-9155/43/2/019
Langton, C.M., Palmer, S.B. and
Porter, R.W. (1984) The Measurement of Broadband Ultrasonic
Attenuation in Cancellous Bone. Engineering
in Medicine, 13, 89-91. http://dx.doi.org/10.1243/EMED_JOUR_1984_013_022_02
Boutin, C. (2007) Rayleigh Scattering of Acoustic Waves in
Rigid Porous Media. Journal of the
Acoustical Society of America, 122, 1888-1905. http://dx.doi.org/10.1121/1.2756755
Schoenberg, M.and Sen, P.N. (1986) Wave Propagation in Alternating Solid and
Viscous Fluid Layers: Size Effects in Attenuation and Dispersion of Fast and
Slow Waves. Applied Physics Letters, 48, 1249-1251. http://dx.doi.org/10.1063/1.96994
Hughes, E.R.,
Leighton, T.G., Petley, G.W. and White, P.R. (1999) Ultrasonic Propagation in Cancellous
Bone: A New Stratified Model. Ultrasound
in Medicine and Biology, 25, 811-821. http://dx.doi.org/10.1016/S0301-5629(99)00034-4
Hughes, E.R.,
Leighton, T.G., White, P.R. and Petley, G.W. (2007) Investigation
of an Anisotropic Tortuosity in a Biot Model of Ultrasonic Propagation in
Cancellous Bone. Journal of the
Acoustical Society of America, 121, 568-574. http://dx.doi.org/10.1121/1.2387132
Biot, M.A. (1956) Theory of Propagation of Elastic Waves in a Fluid Saturated Porous
Solid. I. Low
Frequency Range. Journal of the
Acoustical Society of America, 28, 168-178. http://dx.doi.org/10.1121/1.1908239
Biot, M.A. (1956) Theory of Propagation of Elastic Waves in a Fluid Saturated Porous
Solid. II.
High Frequency Range. Journal of the
Acoustical Society of America, 28, 179-191. http://dx.doi.org/10.1121/1.1908241
McKelvie, M.L. and
Palmer, S.B. (1991) The Interaction of Ultrasound with Cancellous
Bone. Physics in Medicine and Biology, 36, 1331-1340. http://dx.doi.org/10.1088/0031-9155/36/10/003
Hosokawa, A. and Otani, T. (1997) Ultrasonic Wave Propagation in Bovine
Cancellous Bone. Journal of the Acoustical
Society of America, 101, 558-562. http://dx.doi.org/10.1121/1.418118
Haire, T.J. and
Langton, C.M. (1999) Biot Theory: A Review of Its Application
on Ultrasound Propagation through Cancellous Bone. Bone, 24, 291-295. http://dx.doi.org/10.1016/S8756-3282(99)00011-3
Fellah, Z.E.A., Chapelon, J.Y., Berger, S., Lauriks, W. and Depollier, C. (2004) Ultrasonic Wave Propagation in Human
Cancellous Bone: Application of Biot Theory. Journal of the Acoustical Society of America, 116, 61-73. http://dx.doi.org/10.1121/1.1755239
Sebaa, N., Fellah, Z., Fellah, M., Ogam, E., Wirgin, A., Mitri, F., Depollier, C. and Lauriks, W. (2006) Ultrasonic
Characterisation of Human Cancellous Bone Using the Biot Theory: Inverse
Problem. Journal of the Acoustical Society
of America, 120, 1816-1824. http://dx.doi.org/10.1121/1.2335420
Pakula, M., Padilla, F., Laugier, P. and Kaczmarek, M. (2008) Application of Biot’s Theory to
Ultrasonic Characterization of Human Cancellous Bones. Journal of the Acoustical Society of America, 123, 2415-2423.
Attenborough, K., Qin, Q., Fagan, M.J., Shin, H.C. and
Langton, C.M. (2005) Measurements of Tortuosity in Stereolithographical
Bone Replicas Using Audio-Frequency Pulses. Journal
of the Acoustical Society of America, 118, 2779- 2782.
Carcione, J. (1996) Wave Propagation in Anisotropic,
Saturated Porous Media: Plane-Wave Theory and Numerical Simulation. Journal of the Acoustical Society of America, 99, 2655-2666. http://dx.doi.org/10.1121/1.414809
Roh, H.S., Lee, K.I. and
Yoon, S.W. (2003) Acoustic Characteristics of a Non-Rigid
Porous Medium with Circular Cylindrical Pores. Journal of the Korean Physical Society, 45, 55-62.
Attenborough, K. (1983) Acoustic Characteristics of Rigid Fibrous
Absorbents and Granular Materials.Journal
of the Acoustical Society of America, 73,
785-799. http://dx.doi.org/10.1121/1.389045
Lee, K.I., Roh, H.S. and
Yoon, S.W. (2003) Acoustic Wave Propagation in Bovine
Cancellous Bone: Application of the Modified Biot-Attenborough Model. Journal of the Acoustical Society of America, 114, 2284-2293. http://dx.doi.org/10.1121/1.1610450
Lee, K.I. and
Yoon, S.W. (2006) Comparison of Acoustic Characteristics
Predicted by Biot’s Theory and the Modified Biot-Attenborough Model in
Cancellous Bone. Journal of Biomechanics, 39, 364-368. http://dx.doi.org/10.1016/j.jbiomech.2004.12.004
Lee, K.I., Hughes, E.R.,
Humphery, V.F., Leighton, T.G. and Choi, M.J. (2007) Empirical Angle-Dependent Biot and MBA
Models for Acoustic Anisotropy in Cancellous Bone. Physics in Medicine and Biology, 52, 59-73. http://dx.doi.org/10.1088/0031-9155/52/1/005
Aygün, H., Attenborough, K., Postema, M., Lauriks, W. and Langton, C.M. (2009) Predictions of Angle-Dependent
Tortuosity and Elasticity Effects on Sound Propagation in Cancellous Bone. Journal
of the Acoustical Society of America, 126, 3286-3290. http://dx.doi.org/10.1121/1.3242358
Aygün, H., Attenborough, K., Lauriks, W. and Langton, C.M. (2010) Ultrasonic Wave Propagation in Stereo-Lithographical Bone Replicas. Journal
of the Acoustical Society of America, 127, 3781-3789. http://dx.doi.org/10.1121/1.3397581
Aygün, H., Attenborough, K., Lauriks, W., Rubini, P.A. and Langton, C.M. (2011) Wave Propagation in Stereo- Lithographical (STL)
Bone Replicas at Oblique Incidence. Applied Acoustics, 72, 458-463. http://dx.doi.org/10.1016/j.apacoust.2011.01.010
Johnson, D.L., Koplik, J. and Dashen, R. (1987) Theory of Dynamic Permeability and
Tortuosity in Fluid-Saturated Porous Media. Journal
of Fluid Mechanics, 176, 379-402. http://dx.doi.org/10.1017/S0022112087000727
Williams, J.L. (1992) Ultrasonic Wave Propagation in
Cancellous and Cortical Bone: Predictions of Some Experimental Results by
Biot’s Theory. Journal of the Acoustical
Society of America, 91, 1106-1112. http://dx.doi.org/10.1121/1.402637
Leclaire, P., Swift, M.J. and Horoshenkov, K.V. (1998) Determining the Specific Area of Porous
Acoustic Materials from Water Extraction Data. Journal of Applied Physics, 84,
6886-6890. http://dx.doi.org/10.1063/1.368985
Haiat, G., Lhémery, A., Padilla, F., Laugier, P. and Naili, S. (2008) Modelling of “Anomalous” Velocity Dispersion
in Trabecular Bone: Effect of Maultiple Scattering and of Viscous Absorption. Euro-Noise,
Paris.
Atalla, N., Panneton, R. and Deberque, P. (1997) A Mixed Displacement-Pressure Formulation
for Poroelastic Materials. Journal of Acoustical Society of America, 104, 1444-1452. http://dx.doi.org/10.1121/1.424355
Gorog, S., Panneton, R. and Atalla, N. (1997) Mixed
Displacement-Pressure Formulation for Acoustic Anisotropic Open Porous Media. Journal of Applied Physics, 82, 4192-4196.
Horlin, N.E., Nordstrom, M. and Goransson, P. (2001) A 3-D Hierarchical
FE Formulation of Biots Equations for Elastoacoustic Modeling of Porous Media. Journal of Sound and Vibration, 245, 633-652. http://dx.doi.org/10.1006/jsvi.2000.3556
Panneton, R. and Atalla, N. (1998) An Efficient Scheme for Solving the Three-Dimensional Poroelasticity
Problem in Acoustics.Journal of the
Acoustical Society of America, 101, 3287-3298. http://dx.doi.org/10.1121/1.418345