Viscoelastic Response Ultrasound Derived Relative Elasticity and Relative Viscosity Reflect True Elasticity and Viscosity: <i>In Silico</i> and Experimental Demonstration

Abstract

Viscoelastic response (VisR) ultrasound characterizes the viscoelastic properties of tissue by fitting acoustic radiation force (ARF)-induced displacements in the region of ARF excitation to a 1-D mass-spring-damper(MSD) model. Elasticity and viscosity are calculated separately but relative to the applied ARF amplitude. We refer to these parameters as “relative elasticity (RE)” and “relative viscosity (RV).” We herein test the hypothesis that RE and RV linearly correlate to true elasticity and viscosity in tissue. VisR imaging was simulated in 144 homogeneous viscoelastic materials with varying elasticities and viscosities. Derived RE linearly correlated with material elasticity and varied by an average of 2.52% when the material viscosity changed from 0.1 to 1.3 Pa · s. Derived RV linearly correlated with material viscosity but varied by an average of 102.5% when material elasticity changed from 3.33 to 20 kPa. The effect of elasticity on RV measurement was compensated using the slope of the linear relationship between RV and natural frequency (ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> ). After compensation, RV <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">EC</sup> (elasticity compensated RV) linearly correlated with material viscosity and varied by less than 1.00% on average when the modeled shear elastic modulus changed from 3.3 to 20 kPa. In addition to elasticity compensation, variation in ARF amplitude over depth was compensated, yielding RE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DC</sub> and RV <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DC</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">EC</sup> . RE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DC</sub> and RV <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DC</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">EC</sup> successfully contrasted elastic and viscous inclusions, respectively, in three simulated phantoms. Experimentally, in the homogeneous oil-in-gelatin phantoms and excised livers, RE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DC</sub> linearly correlated with shear wave dispersion ultrasound vibrometry (SDUV) derived shear elastic modulus, and RV <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DC</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">EC</sup> linearly correlated with SDUV-derived shear viscosity. In excised livers containing viscoelastic oil-in-gelatin inclusions, the inclusions were successfully contrasted from the liver background by both REDC and RVECDC. These results suggest that RE and RV are relevant for qualitatively assessing the elastic and viscous properties of tissue.