Transient elastography is a powerful tool to measure the speed of low-frequency shear waves in soft tissues and thus to determine the second-order elastic modulus μ (or the Young’s modulus E). In this paper, it is shown how transient elastography can also achieve the measurement of the nonlinear third-order elastic moduli of an Agar-gelatin-based phantom. This method requires speed measurements of polarized elastic waves measured in a statically stressed isotropic medium. A static uniaxial stress induces a hexagonal anisotropy (transverse isotropy) in solids. In the special case of uniaxially stressed isotropic media, the anisotropy is not caused by linear elastic coefficients but by the third-order nonlinear elastic constants, and the medium recovers its isotropic properties as soon as the uniaxial stress disappears. It has already been shown how transient elastography can measure the elastic (second-order) moduli in a media with transverse isotropy such as muscles. Consequently this method, based on the measurement of the speed variations of a low-frequency (50-Hz) polarized shear strain waves as a function of the applied stress, allows one to measure the Landau moduli A, B, C that completely describe the third-order nonlinearity. The several orders of magnitude found among these three constants can be justified from the theoretical expression of the internal energy.
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December 2003
December 02 2003
Measurement of elastic nonlinearity of soft solid with transient elastography
S. Catheline;
S. Catheline
Laboratoire Ondes et Acoustique, ESPCI, Université Paris VII, U.M.R. C.N.R.S. 7587, 10 rue Vauquelin, 75231 Paris cedex 05, France
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J.-L. Gennisson;
J.-L. Gennisson
Laboratoire Ondes et Acoustique, ESPCI, Université Paris VII, U.M.R. C.N.R.S. 7587, 10 rue Vauquelin, 75231 Paris cedex 05, France
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M. Fink
M. Fink
Laboratoire Ondes et Acoustique, ESPCI, Université Paris VII, U.M.R. C.N.R.S. 7587, 10 rue Vauquelin, 75231 Paris cedex 05, France
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J. Acoust. Soc. Am. 114, 3087–3091 (2003)
Article history
Received:
September 23 2002
Accepted:
July 21 2003
Citation
S. Catheline, J.-L. Gennisson, M. Fink; Measurement of elastic nonlinearity of soft solid with transient elastography. J. Acoust. Soc. Am. 1 December 2003; 114 (6): 3087–3091. https://doi.org/10.1121/1.1610457
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