The assessment of viscoelastic properties of soft tissues is enjoying a growing interest in the field of medical imaging as pathologies are often correlated with a local change of stiffness. To date, advanced techniques in that field have been concentrating on the estimation of the second order elastic modulus (mu). In this paper, the nonlinear behavior of quasi-incompressible soft solids is investigated using the supersonic shear imaging technique based on the remote generation of polarized plane shear waves in tissues induced by the acoustic radiation force. Applying a theoretical approach of the strain energy in soft solid [Hamilton et al., J. Acoust. Soc. Am. 116, 41-44 (2004)], it is shown that the well-known acoustoelasticity experiment allowing the recovery of higher order elastic moduli can be greatly simplified. Experimentally, it requires measurements of the local speed of polarized plane shear waves in a statically and uniaxially stressed isotropic medium. These shear wave speed estimates are obtained by imaging the shear wave propagation in soft media with an ultrafast echographic scanner. In this situation, the uniaxial static stress induces anisotropy due to the nonlinear effects and results in a change of shear wave speed. Then the third order elastic modulus (A) is measured in agar-gelatin-based phantoms and polyvinyl alcohol based phantoms.

This paper describes nonlinear shear wave experiments conducted in soft solids with transient elastography technique. The nonlinear solutions that theoretically account for plane and nonplane shear wave propagation are compared with experimental results. It is observed that the cubic nonlinearity implied in high amplitude transverse waves at f(0)=100 Hz results in the generation of odd harmonics 3f(0), 5f(0). In the case of the nonlinear interaction between two transverse waves at frequencies f(1) and f(2), the resulting harmonics are f(i)+/-2f(j)(i,j=1,2). Experimental data are compared to numerical solutions of the modified Burgers equation, allowing an estimation of the nonlinear parameter relative to shear waves. The definition of this combination of elastic moduli (up to fourth order) can be obtained using an energy development adapted to soft solid. In the more complex situation of nonplane shear waves, the quadratic nonlinearity gives rise to more usual harmonics, at sum and difference frequencies, f(i)+/-f(j). All components of the field have to be taken into account.

Measurements of the static displacement induced by the radiation stress associated with a longitudinal acoustic wave propagating in a solid are presented. Acoustic tone bursts were launched into fused silica and duraluminum samples. The static displacement was measured at the sample free surface with an optical interferometer. The role of the nonlinearity parameter and the variations of the dc pulse amplitude with the acoustic energy confirm results obtained by other authors. However, our conclusions on the dc pulse shape, on the influence of the tone burst duration, and of the propagation distance on the dc pulse amplitude are different.