Uniqueness of dynamic elastography for isotropic standard linear solid viscoelastic media

TL;DR

This paper proves the uniqueness of identifying viscoelastic properties of isotropic tissues in dynamic elastography using wave speed measurements, extending previous elastic models to viscoelastic ones.

Contribution

It generalizes the uniqueness results from elastic to viscoelastic models, specifically for the extended Maxwell and standard linear solid models.

Findings

Shear wave speed can be uniquely determined from a single measurement.

The results apply to isotropic extended Maxwell and standard linear solid models.

The proof adapts the 'shrink and spread' argument to viscoelastic media.

Abstract

Dynamic elastography is a widely used, safe, convenient, and cost-effective method to aid in medical diagnosis. It visualizes the wave field propagating through living tissues and quantitatively determines the wave propagation speed from the acquired data, thereby enabling the extraction of the viscoelastic properties of in vivo tissues. Notably, this identification process relies on the mathematical modeling of the viscoelastic characteristics of living tissues. When living tissues are simply modeled as isotropic elastic media, J. McLaughlin and J. Yoon established the uniqueness of the identification in \cite{MY} by reasoning that they called the ``shrink and spread argument". Given the realistic viscoelastic nature of biological tissues, generalizing their results by adopting viscoelastic models is of great significance. In this paper, using their reasoning, we prove the uniqueness of identification for two typical viscoelastic media: the isotropic extended Maxwell model and the isotropic extended standard linear solid model. More precisely, we demonstrate that the shear wave speed within a region of interest $\Omega$ can be uniquely determined from a single measurement of the wave field in $\Omega$.