Simulation of nonlinear transient elastography: finite element model for the propagation of shear waves in homogeneous soft tissues

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Abstract
In this study, visco‐hyperelastic Landau's model, which is widely used in acoustical physic field, is introduced into a finite element formulation. It is designed to model the nonlinear behaviour of finite amplitude shear waves in soft solids, typically, in biological tissues. This law is used in finite element models based on elastography, experiments reported in Jacob et al, the simulations results show a good agreement with the experimental study: It is observed in both that a plane shear wave generates only odd harmonics and a nonplane wave generates both odd and even harmonics in the spectral domain. In the second part, a parametric study is performed to analyse the influence of different factors on the generation of odd harmonics of plane wave. A quantitative relation is fitted between the odd harmonic amplitudes and the non‐linear elastic parameter of Landau's model, which provides a practical guideline to identify the non‐linearity of homogeneous tissues using elastography experiment.

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