Comparison of simulation methods for ultrasound shear wave elastography: FEM vs. Green´s functions

Ultrasound shear wave elastography (SWE) uses acoustic radiation force (ARF) to create shear waves in soft tissue. It is a non-invasive way for extracting quantitative tissue viscoelasticity information, as the tissue shear modulus and viscosity can be estimated by tracking the shear wave propagation speed. Soft tissues are in general viscoelastic, so it is important to develop simulation tools that can predict and analyze the viscoelastic tissue response to the applied ARF. We have created a 3D finite element model using PZFlex software for simulating from the acoustic field of the transducer to the shear wave propagation in homogenous or heterogeneous media. In parallel, we have also derived two exact Green´s functions of the Voigt-model-based Navier´s equation that can handle high viscosity, one in the position and temporal frequency x-ω domain and the other in the spatial frequency and time k-t domain. The media of interest are infinite, homogenous, isotropic, and viscoelastic solids described by the Voigt model. Green´s functions of position and time can be obtained from these exact solutions via inverse Fourier transform. We compared the two simulation methods on one common SWE setting built upon a curve-linear probe and homogenous soft tissue media with various shear modulus and viscosity. Our results showed very good agreement between the two simulation methods on shear wave displacement temporal profiles (R²≥0.972). Both simulation tools are useful for developing and validating shear wave induction schemes and viscoelasticity estimation algorithms in SWE.