Incremental dynamics of prestressed viscoelastic solids and its applications in shear wave elastography

TL;DR

This paper develops a generalized incremental dynamics theory for viscoelastic solids under prestress, enabling accurate shear wave elastography analysis and prestress quantification in tissues.

Contribution

It introduces a unified formalism compatible with various constitutive models, validated by experiments and simulations, for improved tissue characterization in shear wave elastography.

Findings

The theory accurately predicts dispersion curves across frequencies.

It captures the influence of prestress on shear wave properties.

Enables prestress quantification without prior material parameters.

Abstract

Shear wave elastography (SWE) is a promising imaging modality for mechanical characterization of tissues, offering biomarkers with potential for early and precise diagnosis. While various methods have been developed to extract mechanical parameters from shear wave characteristics, their relationships in viscoelastic materials under prestress remain poorly understood. Here, we present a generalized incremental dynamics theory for finite-strain viscoelastic solids. The theory derives small-amplitude viscoelastic wave motions in a material under static pre-stress. The formalism is compatible with a range of existing constitutive models, including both hyperelasticity and viscoelasticity--such as the combination of Gasser-Ogden-Holzapfel (GOH) and Kelvin-Voigt fractional derivative (KVFD) models used in this study. We validate the theory through experiments and numerical simulations on prestressed soft materials and biological tissues, using both optical coherence elastography and ultrasound elastography. The theoretical predictions closely match experimental dispersion curves over a broad frequency range and accurately capture the effect of prestress. Furthermore, the framework reveals the relationships among shear wave phase velocity, attenuation, and principal stresses, enabling prestress quantification in viscoelastic solids without prior knowledge of constitutive parameters. This generalized acousto-viscoelastic formalism is particularly well-suited for high-frequency, high-resolution SWE in tissues under prestress.