Study of elastic non-linearity of soft solids with transient elastography

Transient elastography has shown its efficiency to map the elastic properties of soft tissues. Now like other elastic imaging techniques (sonoelastography or magnetic resonance elastography) transient elastography is faced to the following problem:in order to properly discriminate tumors, additional information such as viscosity, anisotropy or nonlinearity is needed. If nonlinearity has long been studied in metals, crystals or rocks, only a few experimental works are found in the literature concerning soft tissues and none on shear waves. Thanks to the ultrafast scanner that can map the displacement field of shear waves, we present in this paper an overview of three experiments that allow to illustrate and quantify the nonlinear behavior of soft tissue phantoms. In the first one, a static stress is applied on an Agar-gelatin based sample. The change on the shear wave speed characterizes the nonlinear elastic Landau moduli (A=50 kPa, B=7 GPa, C=11 GPa). The surprising difference found between these constants are thought to be closely related to the huge difference between the linear Lame coefficients (λ>>μ). It is the acoustoelasticity experiment. In the second one, we present an experimental observation of a shock shear wave. The very weak Young´s modulus of the tissue phantom allows one to generate plane shear wave with a Mach number as high as unity. In this extreme configuration, the agreement with the numerical simulation of the modified Burgers equation is remarkable. It is the finite-amplitude shear wave experiment. At last, the interaction between two plane transverse waves with frequencies ω₁ and ω₂ is carefully studied. Harmonics and secondary waves are created during the propagation at the frequencies (3ω₁, 3ω₂, ω₁+2ω₂, ω₁-2ω₂, ω₂+2ω₁, ω₂-2ω₁). It is the nonlinear interaction experiment. The nonlinear coefficients deduced from the two latter experiments are comparable to the order of magnitude of the Landau coefficients found from the first experiment.