On the Quantitative Potential of Viscoelastic Response (VisR) Ultrasound Using the One-Dimensional Mass-Spring-Damper Model

Abstract

Viscoelastic Response (VisR) ultrasound is an acoustic radiation force (ARF)-based imaging method that fits induced displacements to a one-dimensional (1D) mass-spring-damper (MSD) model to estimate the ratio of viscous to elastic moduli, τ, in viscoelastic materials. Error in VisR τ estimation arises from inertia and acoustic displacement underestimation. These error sources are herein evaluated using finite element method (FEM) simulations, error correction methods are developed, and corrected VisR τ estimates are compared to true simulated τ values to assess VisR’s relevance to quantifying viscoelasticity. In regards to inertia, adding a mass term in series with the Voigt model, to achieve the MSD model, accounts for inertia due to tissue mass when ideal point force excitations are used. However, when volumetric ARF excitations are applied, the induced complex system inertia is not described by the single-degree-of-freedom MSD model, causing VisR to overestimate τ. Regarding acoustic displacement underestimation, associated deformation of ARF-induced displacement profiles further distorts VisR τ estimates. However, median error in VisR τ is reduced to approximately −10% using empirically derived error correction functions applied to simulated viscoelastic materials with viscous and elastic properties representative of tissue. The feasibility of corrected VisR imaging is then demonstrated in vivo in the rectus femoris muscle of an adult with no known neuromuscular disorders. These results suggest VisR’s potential relevance to quantifying viscoelastic properties clinically.

Renal Allograft Rejection: Noninvasive Ultrasound- and MRI-Based Diagnostics

“…Viscoelastic response (VisR) ultrasound is an alternative ARF-based tool using two co-localized ARF impulses to delineate tissue properties by measuring viscosity and elasticity (for details, see [40]). Hossain et al performed a prospective study with 44 patients to examine the ability of VisR to evaluate renal transplant status.…”

Viscoelastic parameters as discriminators of breast masses: Initial human study results

“…Voigt model has been shown to outperform the Maxwell model for the agar-gelatin phantom and bovine muscles [ 28 ]. The effect of inertia is neglected as other studies have shown that the percentage error in the estimated time constant after correction was only 10% [ 18 ]. Also due to the complexity of the three dimensional acoustic radiation force push, a correction function had to be derived empirically [ 18 ].…”

“…The effect of inertia is neglected as other studies have shown that the percentage error in the estimated time constant after correction was only 10% [ 18 ]. Also due to the complexity of the three dimensional acoustic radiation force push, a correction function had to be derived empirically [ 18 ]. The Voigt model consists of a spring and dashpot in parallel, where spring represents the elastic part of the medium and the dashpot represents the viscous part.…”

Evaluating Renal Transplant Status Using Viscoelastic Response (VisR) Ultrasound

“…Then, the ratios of a given median VisR measure for all possible ROI combinations (for example, the ratio of τ in the oC to the cC, or the ratio of RE in the iC to the oP) were calculated. These ratio calculations were performed to control for subject-to-subject variations in VisR outcome metrics, which arise from variability in the ARF amplitude (Selzo et al, 2016; Zhao, 2013). Note that ARF amplitude varies with system power level, duration of the ARF excitation, focal depth, tissue attenuation, and phase aberration.…”

“…An alternative ARF-based approach to interrogating the elastic and viscous properties of tissue is Viscoelastic Response (VisR) ultrasound, which is described in detail in: (Selzo et al, 2016; Selzo and Gallippi, 2013). Briefly, VisR is performed using two co-localized ARF impulses that are separated by < 1 ms in time.…”