Rayleigh-Lamb wave propagation on a fractional order viscoelastic plate

Journal of the Acoustical Society of America

Volumn 129, Issue 2, 2011, Pages 1036-1045

  Meral, F Can ^a   Royston, Thomas J ^b   Magin, Richard L ^c  

^a University of Illinois at Chicago   (United States)

^b UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

^c University of Illinois at Chicago   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANTI-SYMMETRIC; BIOLOGICAL TISSUES; DAMPING COMPONENTS; EXPERIMENTAL MEASUREMENTS; FIRST DERIVATIVE; FRACTIONAL DERIVATIVES; FRACTIONAL ORDER; FREQUENCY RANGES; INTEGER ORDER; OUT-OF-PLANE; RAYLEIGH-LAMB WAVES; SUB-SURFACES; SURFACE WAVE MOTION; THEORETICAL SOLUTIONS; TISSUE MIMICKING PHANTOM; VISCO-ELASTIC MATERIAL; VISCOELASTIC HALF-SPACE; VISCOELASTIC PLATES; VISCOELASTIC PROPERTIES; VOIGT MODEL;

BIOLOGICAL MATERIALS; ELASTIC WAVES; EXCITED STATES; EXPERIMENTS; SURFACE WAVES; SURFACES; ULTRASONIC WAVES; VISCOELASTICITY; WAVE PROPAGATION;

SHEAR FLOW;

SILICONE DERIVATIVE;

ARTICLE; COMPARATIVE STUDY; COMPUTER SIMULATION; DOPPLER FLOWMETRY; ELASTICITY; EQUIPMENT DESIGN; FINITE ELEMENT ANALYSIS; IMAGE QUALITY; INSTRUMENTATION; MATHEMATICAL COMPUTING; MOTION; THEORETICAL MODEL; TIME; ULTRASOUND; VIBRATION; VISCOSITY;

COMPUTER SIMULATION; DOPPLER EFFECT; ELASTICITY; EQUIPMENT DESIGN; FINITE ELEMENT ANALYSIS; MODELS, THEORETICAL; MOTION; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; PHANTOMS, IMAGING; SILICONES; TIME FACTORS; ULTRASONICS; VIBRATION; VISCOSITY;

EID: 79952143757     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.3531936     Document Type: Article

References (40)

1. F. C. Meral, T. J. Royston, and R. L. Magin, Surface response of a fractional order viscoelastic halfspace to surface and subsurface sources., J. Acoust. Soc. Am. 126, 3278-3285 (2009). 10.1121/1.3242351
2. S. F. Othman, H. Xu, T. J. Royston, and R. L. Magin, Microscopic magnetic resonance elastography (MRE)., Magn. Reson. Med. 54, 605-614 (2005). 10.1002/mrm.v54:3
3. L. Gao, K. J. Parker, S. K. Alam, and R. M. Lerner, Sonoelasticity imaging: Theory and experimental verification., J. Acoust. Soc. Am. 97, 3875-3886 (1995). 10.1121/1.412399
4. S. Catheline, F. Wu, and M. Fink, A solution to diffraction biases in sonoelasticity: The acoustic impulse technique., J. Acoust. Soc. Am. 105, 2941-2950 (1999). 10.1121/1.426907 (Pubitemid 29218410)
5. Y. Yamakoshi, J. Sato, and T. Sato, Ultrasonic imaging of internal vibration of soft tissue under forced vibration., IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37, 45-53 (1990). 10.1109/58.46969 (Pubitemid 20666601)
6. R. Muthupillai, D. J. Lomas, P. J. Rossman, J. F. Greenleaf, A. Manduca, and R. L. Ehman, Magnetic resonance elastography by direct visualization of propagating acoustic strain waves., Science 269, 1854-1857 (1995). 10.1126/science.7569924
7. F. A. Duck, Physical Properties of Tissue: A Comprehensive Reference Book (Academic Press, New York, 1990), pp. 225-229 317, Table 7.5 and pp. 279-229 317, Table 8.1 for T1 and Table 8.5 for T2.
8. V. Kuperman, Magnetic Resonance Imaging: Physical Principles and Applications (Academic Press, New York, 2000), pp. 57-76, Table 4.1.
9. K. Hoyt, T. Kneezel, B. Castaneda, and K. J. Parker, Quantitative sonoelastography for the in vivo assessment of skeletal muscle viscoelasticty., Phys. Med. Biol. 53, 4063-4080 (2008). 10.1088/0031-9155/53/15/004
10. Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissues, 2nd ed. (Springer-Verlag, New York, 1993), pp. 336-343.
11. A. P. Sarvazyan, O. V. Rudenko, S. D. Swanson, J. B. Fowlkes, and S. Y. Emelianov, Shear wave elasticity imaging: A new ultrasonic technology of medical diagnostics., Ultrasound Med. Biol. 24, 1419-1435 (1998). 10.1016/S0301- 5629(98)00110-0 (Pubitemid 29003664)
12. M. Yin, J. Talwalkar, K. Glaser, A. Manduca, R. Grimm, P. Rossman, J. Fidler, and R. L. Ehman, Assessment of hepatic fibrosis with magnetic resonance elastography., Clin. Gastroenterol. Hepatol. 5, 1207-1213 (2007). 10.1016/j.cgh.2007.06.012 (Pubitemid 47488968)
13. R. Muthupillai, P. J. Rossman, D. J. Lomas, J. F. Greenleaf, S. J. Riederer, and R. L. Ehman, Magnetic resonance imaging of transverse acoustic strain waves., Magn. Reson. Med. 36, 266-274 (1996). 10.1002/mrm.v36:2 (Pubitemid 26271747)
14. T. E. Oliphant, A. Manduca, R. L. Ehman, and J. F. Greenleaf, Complex-valued stiffness reconstruction for magnetic resonance elastography by algebraic inversion of the differential equation., Magn. Reson. Med. 45, 299-310 (2001). 10.1002/1522-2594(200102)45:2<>1.0.CO;2-7 (Pubitemid 32119014)
15. J. Romano, J. J. Shirron, and J. A. Bucaro, On the noninvasive determination of material parameters from a knowledge of elastic displacements: Theory and numerical simulation., IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 751-759 (1998). 10.1109/58.677725 (Pubitemid 128748734)
16. A. J. Romano, J. A. Bucaro, R. L. Ehman, and J. J. Shirron, Evaluation of a material parameter extraction algorithm using MRI-based displacement measurements., IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1575-1581 (2000). 10.1109/58.883546 (Pubitemid 32076225)
17. E. E. van Houten, M. M. Doyley, F. E. Kennedy, J. B. Weaver, and K. D. Paulsen, Initial in vivo experience with steady-state subzone-based MR elastography of the human breast., J. Magn. Reson. Imaging 17, 72-85 (2003). 10.1002/jmri.v17:1 (Pubitemid 36034137)
18. E. E. van Houten, M. M. Doyley, F. E. Kennedy, K. D. Paulsen, and J. B. Weaver, A three-parameter mechanical property reconstruction method for MR-based elastic property imaging., IEEE Trans. Med. Imaging 24, 311-324 (2005). 10.1109/TMI.2004.842451
19. S. Papazoglou, U. Hamhaber, J. Braun, and I. Sack, Algebraic Helmholtz inversion in planar magnetic resonance elastography., Phys. Med. Biol. 53, 3147-3158 (2008). 10.1088/0031-9155/53/12/005 (Pubitemid 351892392)
20. R. W. Chan and I. R. Titze, Effect of postmortem changes and freezing on the viscoelastic properties of vocal fold tissues., Ann. Biomed. Eng. 31, 482-491 (2003). 10.1114/1.1561287
21. D. Craiem and R. Armentano, A fractional derivative model to describe arterial viscoelasticity., Biorheology 44, 251-263 (2007). (Pubitemid 350261816)
22. M. Z. Kiss, T. Varghese, and T. J. Hall, Viscoelastic characterization of in vitro canine tissue., Phys. Med. Biol. 49, 4207-4218 (2004). 10.1088/0031-9155/49/18/002 (Pubitemid 39302683)
23. D. Klatt, U. Hamhaber, P. Asbach, J. Braun, and I. Sack, Noninvasive assessment of the rheological behavior of human organs using multifrequency MR elastography: A study of brain and liver viscoelasticity., Phys. Med. Biol. 52, 7281-7294 (2007). 10.1088/0031-9155/52/24/006 (Pubitemid 350242840)
24. R. Sinkus, K. Siegmann, T. Xydeas, M. Tanter, C. Claussen, and M. Fink, MR elastography of breast lesions: Understanding the solid/liquid duality can improve the specificity of contrast-enhanced MR mammography., Magn. Reson. Med. 58, 1135-1144 (2007). 10.1002/mrm.v58:6 (Pubitemid 350234200)
25. C. Coussot, S. Kalyanam, R. Yapp, and M. Insana, Fractional derivative models for ultrasonic characterization of polymer and breast tissue viscoelasticity., IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56, 715-726 (2009). 10.1109/TUFFC.2009.1094
26. R. C. Koeller, Applications of fractional calculus to the theory of viscoelasticity., J. Appl. Mech. 51, 299-307 (1984). 10.1115/1.3167616 (Pubitemid 14583151)
27. R. L. Bagley and P. J. Torvik, On the fractional calculus model of viscoelastic behavior., J. Rheol. 30, 133-155 (1986). 10.1122/1.549887 (Pubitemid 16535851)
28. G. L. Sloninsky, Laws of mechanical relaxation processes in polymers., J. Polym. Sci., Part C 16, 1667-1672 (1967).
29. H. Schiessel and A. Blumen, Hierarchical analogues to fractional relaxation equations., J. Phys. A 26, 5057-5069 (1993). 10.1088/0305-4470/26/19/ 034
30. D. Klatt, P. Asbach, R. Somasundaram, B. Hamm, J. Braun, and I. Sack, Assessment of the solid-liquid behavior of the liver for the diagnosis of diffuse disease using magnetic resonance elastography., Rfo 180, 1106-1109 (2008) (in German).
31. I. Sack, B. Beierbach, J. Wuerfel, D. Klatt, U. Hamhaber, S. Papazoglou, P. Martus, and J. Braun, The impact of aging and gender on brain viscoelasticity., Neuroimage 46, 652-657 (2009). 10.1016/j.neuroimage.2009.02. 040
32. T. J. Royston, H. A. Mansy, and R. H. Sandier, Excitation and propagation of surface waves on a viscoelastic half-space with application to medical diagnosis., J. Acoust. Soc. Am. 106, 3678-3686 (1999). 10.1121/1.428219 (Pubitemid 129520731)
33. T. J. Royston, Y. Yazicioglu, and F. Loth, Surface response of a viscoelastic medium to subsurface acoustic sources with application to medical diagnosis., J. Acoust. Soc. Am. 113, 1109-1121 (2003). 10.1121/1.1536153 (Pubitemid 36240737)
34. K. F. Graff, Wave Motion in Elastic Solids (Ohio State University Press, Dover Publications Inc., New York, 1975), pp. 435-460.
35. L. E. Goodman, Circular-crested vibrations of an elastic solid bounded by two parallel planes., in Proceedings of the 1st National Congress of Applied Mechanics, ASME, New York (1952), pp. 65-73.
36. W. P. Rogers, Elastic property measurement using Rayleigh-Lamb waves., Res. Nondestruct. Eval. 6, 185-208 (1995).
37. B. Karp, Generation of symmetric Lamb waves by non-uniform excitations., J. Sound Vib. 312, 195-209 (2008). 10.1016/j.jsv.2007.10.041 (Pubitemid 351240929)
38. T. J. Royston, X. Zhang, H. A. Mansy, and R. H. Sandier, Modeling sound transmission through the pulmonary system and chest with application to diagnosis of a collapsed lung., J. Acoust. Soc. Am. 111, 1931-1946 (2002). 10.1121/1.1452742 (Pubitemid 34297248)
39. R. L. Magin, Fractional Calculus in Bioengineering (Begell House, Redding, CT, 2006), pp. 269-355.
40. I. A. Viktorov, Rayleigh and Lamb Waves Physical Theory and Applications (Plenum Press, New York, 1967), pp. 71-72.