A comparison of hyperelastic constitutive models applicable to Shear Wave Elastography (SWE) data in tissue-mimicking materials

Abstract

Shear wave elastography (SWE) techniques have received substantial attention in recent years. Strong experimental data in SWE suggest that shear wave speed changes significantly due to the known acoustoelastic effect (AE). This presents both challenges and opportunities toward in vivo characterization of biological soft tissues. In this work, under the framework of continuum mechanics, we model a tissue-mimicking material as a homogeneous, isotropic, incompressible, hyperelastic material. Our primary objective is to quantitatively and qualitatively compare experimentally measured acoustoelastic data with model-predicted outcomes using multiple strain energy functions. Our analysis indicated that the classic neo-Hookean and Mooney-Rivlin models are inadequate for modeling the AE in tissue-mimicking materials. However, a subclass of strain energy functions containing both high-order /exponential term(s) and second-order invariant dependence showed good agreement with experimental data. Based on data investigated, we also found that discrepancies may exist between parameters inversely estimated from uniaxial compression and SWE data. Overall, our findings may improve our understanding of clinical SWE results.

Shear Induced Non-Linear Elasticity Imaging: Elastography for Compound Deformations

“…Note that nonlinear shear modulus A cannot be obtained directly from COMSOL multiphysics. With the knowledge of the simulated strain, stress outputs and the assumption of the linear shear modulus, ( 21), (22), and (23) were used to obtain A by compound, shear and compressional estimator, respectively. We used compound NLSM estimator to estimate A in subsequent studies unless otherwise mentioned.…”

“…The acoustoelastic formulations proposed by Gennison et al [1] to relate shear wave speed to nonlinear elasticity constants is restricted to a Green strain energy function. Rosen et al [22]- [23] evaluated the use of several hyperelastic strain energy functions to represent acoustoelastic shear wave data and investigated the consistency of the nonlinear elastic parameters.…”

Linear, weakly nonlinear and fully nonlinear models for soft tissues: which ones provide the most reliable estimations of the stiffness?

“…Recently, Jiang et al . [18,19] characterized some nonlinear elastic properties of soft tissues by using acoustoelasticity [20]. In particular, Jiang et al [18,19] considered incremental infinitesimal shearing motions superposed to a large static homogeneous deformation and estimated some elastic moduli from the analysis of the propagation of transverse waves.…”

“…[18,19] characterized some nonlinear elastic properties of soft tissues by using acoustoelasticity [20]. In particular, Jiang et al [18,19] considered incremental infinitesimal shearing motions superposed to a large static homogeneous deformation and estimated some elastic moduli from the analysis of the propagation of transverse waves. Since a large pre-deformation is considered; with this approach one can infer the value of the infinitesimal shear modulus μ instead of the linear shear modulus μL, as well as the values of other elastic moduli involved in the propagation of shear waves [19].…”

An in silico-based review on anisotropic hyperelastic constitutive models for soft biological tissues

“…Mihai et al [60] reviewed models used for the brain and fat tissues, and successfully compared their performance ability under different loading conditions. Furthermore, Rosen and Jiang [70] investigated current isotropic hyperelastic laws able to model tissue-mimicking materials characterized through shear wave elastography. Martins et al [54] carried out a concise review on isotropic models subjected to uniaxial loading.…”