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

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, 1 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.

A 2D finite element model for shear wave propagation in biological soft tissues: Application to magnetic resonance elastography

“…It is thus not adapted to the simulation of transient but of harmonic shear waves only, at the opposite of some of the FEM previously proposed for elastography. 33,34 The displacement fields computed from the 2D-FEM are in good agreement with those obtained experimentally in both the background of the phantom and in the soft inclusion ( Figure 6). The agreement is better in wavelength than in amplitude and attenuation.…”

“…The FSDT 2D‐FEM focuses in the investigation of the steady‐state response. It is thus not adapted to the simulation of transient but of harmonic shear waves only, at the opposite of some of the FEM previously proposed for elastography …”

“…FEMs have been used to simulate impulsive excitations and shear wave propagation in transversely isotropic elastic or viscoelastic soft tissues in 2D or 3D models, mostly solved with commercialized software. A mass‐scaling method coupled with a viscohyperelastic Landau's model has been recently proposed to simulate nonlinear transient elastography using plane‐strain hypothesis . 3D‐FEMs are computationally expensive compared to 2D‐FEMs.…”

“…A mass-scaling method coupled with a viscohyperelastic Landau's model has been recently proposed to simulate nonlinear transient elastography using plane-strain hypothesis. 33,34 3D-FEMs are computationally expensive compared to 2D-FEMs. In most cases, MRE data are 2D images and most MRE methods perform identification on 2D, with corresponding available information.…”

Piecewise parabolic method for propagation of shear shock waves in relaxing soft solids: One‐dimensional case

“…In the previous decade, nonlinear shear waves in soft solids were described using Landau's classical model containing the third‐ and fourth‐order Lagrangian strain tensor invariants . A comparative study of the three models mentioned above highlights the ability of Landau's model to describe strongly nonlinear media …”