Application of the biot model to ultrasound in bone: Direct problem

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

Volumn 55, Issue 7, 2008, Pages 1508-1515

  Fellah, Zine E A ^b   Sebaa, Naima ^c   Fellah, Mohamed ^d   Mitri, Farid G ^a,e   Ogam, Erick ^b   Lauriks, Walter ^c   Depollier, Claude ^f  

^a IEEE

^b LABORATOIRE DE MÉCANIQUE ET D ACOUSTIQUE   (France)

^c UNIVERSITY OF LEUVEN   (Belgium)

^d UNIVERSITY OF SCIENCES AND TECHNOLOGY HOUARI BOUMEDIENE   (Algeria)

^e MAYO CLINIC   (United States)

^f UNIVERSITÉ DU MAINE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

POROUS MATERIALS; ULTRASONICS; WAVE PROPAGATION;

BIOT MODELS; BIOT'S THEORY; CANCELLOUS BONE; DIRECT PROBLEMS; FAST AND SLOW WAVE; TRANSMISSION COEFFICIENTS;

BONE;

ARTICLE; BIOLOGICAL MODEL; BONE; BONE DENSITY; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; ECHOGRAPHY; ELASTOGRAPHY; IMAGE QUALITY; MECHANICAL STRESS; METHODOLOGY; PHYSIOLOGY; RADIATION SCATTERING; VISCOSITY; YOUNG MODULUS;

BONE AND BONES; BONE DENSITY; COMPUTER SIMULATION; ELASTIC MODULUS; ELASTICITY IMAGING TECHNIQUES; IMAGE INTERPRETATION, COMPUTER-ASSISTED; MODELS, BIOLOGICAL; PHANTOMS, IMAGING; SCATTERING, RADIATION; STRESS, MECHANICAL; ULTRASONOGRAPHY; VISCOSITY;

EID: 47849110958     PISSN: 08853010     EISSN: None     Source Type: Journal    
DOI: 10.1109/TUFFC.2008.826     Document Type: Article

References (48)

1. M. A. Biot, "The theory of propagation of elastic waves in fluid-saturated porous solid. I. Low frequency range," J. Acoust. Soc. Amer., vol. 28, pp. 168-178, 1956.
2. M. A. Biot, "The theory of propagation of elastic waves in fluid-saturated porous solid. I. Higher frequency range," J. Acoust. Soc. Amer., vol. 28, pp. 179-191, 1956.
3. R. Lakes, H. S. Yoon, and J. L. Katz, "Slow compressional wave propagation in wet human and bovine cortical bone," Science, vol. 220, pp. 513-515, 1983.
4. J. L. Wilson, "Ultrasonic wave propagation in cancellous bone and cortical bone: Prediction of some experimental results by Biot's theory," J. Acoust. Soc. Amer., vol. 91, pp. 1106-1112, 1992.
5. W. Lauriks, J. Thoen, I. Van Asbroeck, G. Lowet, and G. Vanderperre, "Propagation of ultrasonic pulses through trabecular bone," J. Physique IV, vol. 4, pp. 1255-1258, 1994.
6. M. L. McKelvie and S. B. Palmer, "The intercation of ultrasound with cancellous bone," Phys. Med. Biol., vol. 36, no. 10, pp. 1331-1340, 1991.
7. T. J. Haire and C. M. Langton, "Biot theory: A review of its application on ultrasound propagation through cancellous bone," Bone, vol. 24, no. 4, pp. 291-295, 1999.
8. A. Hosokawa, and T. Otani, "Ultrasonic wave propagation in bovine cancellous bone," J. Acoust. Soc. Amer., vol. 101, pp. 558-562, 1997.
9. A. Hosokawa, and T. Otani, "Acoustic anisotropy in bovine cancellous bone," J. Acoust. Soc. Amer., vol. 103, pp. 2718-2722, 1998.
10. G. Krichhoff, "Uber der Einfluss Wärmeleitung in einem Gase auf die Schallbewegung," Ann. Phys. Chem., vol. 134, pp. 177-193, 1868.
11. C. Zwikker and C. W. Kosten, Sound Absorbing Materials. New York: Elsevier, 1949.
12. H. Tijdeman, "On the propagation of sound waves in cylindrical tubes," J. Sound Vibr., vol. 39, pp. 1-33, 1975.
13. M. R. Stinson, "The propagation of plane sound waves in narrow and wide circular tubes, and generalization to uniform tubes of arbitrary cross-sectional shape," J. Acoust. Soc. Amer., vol. 89, pp. 550-558, 1991.
14. A. Craggs and J. G. Hildebrandt, "Effective densities and resistivities for acoustic propagation in narrow tubes," J. Sound Vibr., vol. 92, pp. 321-331, 1984.
15. A. Craggs and J. G. Hildebrandt, "The normal incidence absorption coefficient of a matrix of narrow tubes with constant cross-section," J. Sound Vibr., vol. 105, pp. 101-107, 1986.
16. K. H. Hubner, The Finite Element Method for Engineers. New York: Wiley-Interscience, 1974.
17. O. C. Zienkiewicz, The Finite Element Method in Engineering Science. London: McGraw-Hill, 1971.
18. K. Attenborough, "Acoustical characteristics of porous materials," Phys. Rev., vol. 82, pp. 179-227, 1982.
19. D. L. Johnson, J. Koplik, and R. Dashen, "Theory of dynamic permeability and tortuosity in fluid-saturated porous media," J. Fluid Mech., vol. 176, pp. 379-402, 1987.
20. J. F. Allard, Propagation of Sound in Porous Media: Modeling Sound Absorbing Materials. London: Chapman and Hall, 1993.
21. J. F. Allard, M. Henry, and J. Tizianel, "Sound propagation in air-saturated random packings of beads," J. Acoust. Soc. Amer., vol. 104, no. 4, pp. 2004-2007, 1998.
22. Y. Champoux and J. F. Allard, "Dynamic tortuosity and bulk modulus in air-saturated porous media," J. Appl. Phys., vol. 70, no. 4, pp. 1975-1979, 1991.
23. D. M. J. Smeulders, R. L. G. M. Eggels, and M. E. H. Van Dongen, "Dynamic permeability: Reformulation of theory and new experimental and numerical data," J. Fluid Mech., vol. 245, pp. 211-227, 1992.
24. Z. E. A. Fellah and C. Depollier, "Transient acoustic wave propagation in rigid porous media: A time-domain approach," J. Acoust. Soc. Amer., vol. 107, pp. 683-688, 2000.
25. Z. E. A. Fellah, C. Depollier, and M. Fellah, "An approach to direct and inverse time-domain scattering of acoustic waves from rigid porous materials by a fractional calculus based method," J. Sound Vibr., vol. 244, pp. 359-366, 2001.
26. Z. E. A. Fellah, C. Depollier, and M. Fellah, "Application of fractional calculus to the sound waves propagation in rigid porous materials: Validation via ultrasonic measurements," Acia Acustica, vol. 88, pp. 34-39, 2002.
27. Z. E. A. Fellah, M. Fellah, W. Lauriks, and C. Depollier, "Direct and inverse scattering of transient acoustic waves by a, slab of rigid porous material," J. Acoust. Soc. Amer., vol. 113, pp. 61-73, 2003.
28. Z. E. A. Fellah, S. Berger, W. Lauriks, C. Depollier, and M. Fellah, "Measuring the porosity of porous materials having a rigid frame via reflected waves: A time domain analysis with fractional derivatives," J. Appl. Phys., vol. 93, no. 1, pp. 296-303, 2003.
29. P. Leclaire, L. Kelders, W. Lauriks, C. Glorieux, and J. Thoen, "Determination of the viscous characteristic length in air-filled porous materials by ultrasonic attenuation measurements," J. Acoust. Soc. Amer., vol. 99, pp. 1944-1948, 1996.
30. P. Leclaire, L. Kelders, W. Lauriks, M. Melon, N. Brown, and B. Castagnede, "Determination of the viscous and thermal characteristic lengths of plastic foams by ultrasonic measurements in helium and air," J. Appl. Phys., vol. 80, pp. 2009-2012, 1996.
31. P. Leclaire, L. Kelders, W. Lauriks, J. F. Allard, and C. Glorieux, "Ultrasonic wave propagation in reticulated foams saturated by different gases: High frequency limit of the classical models," Appl. Phys. Lett., vol. 69, pp. 2641-2643, 1996.
32. J. M. Carcione, "Wave fields in real media: Wave propagation in anisotropic, anelastic and porous media," in Handbook of Geophysical Exploration. K. Helbig and S. Treitel, Eds. Oxford, UK: Pergamon, Elseiver Science, Ltd., 2001.
33. D. Lafarge, P. Lemarnier, J. F. Allard, and V. Tarnow, "Dynamic compressibility of air in porous structures at audible frequencies," J. Acoust. Soc. Amer., vol. 102, pp. 1995-2006, 1997.
34. D. Lafarge, "Sound propagation in porous materials having a rigid frame saturated by gas," Ph.D. dissertation, Université du Maine, Le Mans, France, 1993. (in French)
35. K. A. Wear, "Frequency dependence of ultrasonic backscatter from human trabecular bone: Theory and experiment," J. Acoust. Soc. Amer., vol. 106, pp. 3659-3664, 1999.
36. S. Chaffai, V. Roberjot, F. Peyrin, G. Berger, and P. Laugier, "Frequency dependence of ultrasonic backscattering in cancellous bone: Autocorrelation model and experimental results," J. Acoust. Soc. Amer., vol. 108, pp. 2403-2411, 2000.
37. F. Luppe, J. M. Conoir, and H. Franklin, "Scattering by a fluid cylinder in a porous medium: Application to trabecular bone," J. Acoust. Soc. Amer., vol. 111, pp. 2573-2582, 2002.
38. T. J. Plona, "Observation of the second bulk compressional wave in a porous medium at ultrasonic frequencies," Appl. Phys. Lett., vol. 36, pp. 256-261, 1980.
39. D. L. Johnson, "Equivalence between fourth sound in liquid He II at low temperatures and the Biot slow wave in consolidate porous media," Appl. Phys. Lett., vol. 37, pp. 1065-1067, 1980.
40. D. L. Johnson and T. J. Plona, "Acoustic slow waves and the consolidation transition," J. Acoust. Soc. Amer., vol. 72, pp. 556-565, 1982.
41. D. L. Johnson, T. J. Plona, C. Scala, F. Psierb, and H. Kojima, "Tortuosity and acoustic slow waves," Phys. Rev. Lett., vol. 49, pp. 1840-1844, 1982.
42. M. E. H. Van Dongen, D. M. Smeulders, T. Kitamura, and K. Takayama, "Acustica,"
43. A. N. Norris, "On the viscodynamic operator in Biot's equations of poroelasticity," J. Wave Mater. Interact., vol. 1, pp. 365-379, 1986.
44. P. N. J. Rasolofosaon, "Importance of interface hydraulic condition on the generation of second bulk compressional wave in porous media," Appl. Phys. Lett., vol. 52, pp. 780-782, 1988.
45. R. Burridge and J. B. Keller, "Poroelasticity equations derived from microstructure," J. Acoust. Soc. Amer., vol. 105, pp. 626-632, 1985.
46. S. R. Pride, A. F. Gangi, and F. D. Moran, "Deriving the equations of motion for porous isotropic media," J. Acoust. Soc. Amer., vol. 92, pp. 3278-3290, 1992.
47. S. R. Pride and J. G. Berryman, "Connecting theory to experiments in poroelasticity," J. Mech. Phys. Solids, vol. 40, pp. 719-747, 1998.
48. C. Depollier, J. F. Allard, and W. Lauriks, "Biot theory and stress-strain equations in porous sound-absorbing materials," J. Acoust. Soc. Amer., vol. 84, no. 6, pp. 2277-2279, 1988.