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

Viscoelastic response (VisR) ultrasound is an acoustic radiation force (ARF)-based imaging method that fits induced displacements to a one-dimensional (1-D) 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 with true simulated τ values to assess VisR's relevance to quantifying viscoelasticity. With regard 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.