Loss tangent and complex modulus estimated by acoustic radiation force creep and shear wave dispersion

Abstract

Elasticity imaging methods have been used to study tissue mechanical properties and have demonstrated that tissue elasticity changes with disease state. In current shear wave elasticity imaging methods typically only shear wave speed is measured and rheological models, e.g., Kelvin-Voigt, Maxwell and Standard Linear Solid, are used to solve for tissue mechanical properties such as the shear viscoelastic complex modulus. This paper presents a method to quantify viscoelastic material properties in a model-independent way by estimating the complex shear elastic modulus over a wide frequency range using time-dependent creep response induced by acoustic radiation force. This radiation force induced creep (RFIC) method uses a conversion formula that is the analytic solution of a constitutive equation. The proposed method in combination with Shearwave Dispersion Ultrasound Vibrometry (SDUV) is used to measure the complex modulus so that knowledge of the applied radiation force magnitude is not necessary. The conversion formula is shown to be sensitive to sampling frequency and the first reliable measure in time according to numerical simulations using the Kelvin-Voigt model creep strain and compliance. Representative model-free shear complex moduli from homogeneous tissue mimicking phantoms and one excised swine kidney were obtained. This work proposes a novel model-free ultrasound-based elasticity method that does not require a rheological model with associated fitting requirements.

Dynamic Simulation of Viscoelastic Soft Tissue in Acoustic Radiation Force Creep Imaging

“…Alterna tively, the ARF induced creep imaging methods use the responses in the region of excitation where the measured displacements have a high SNR. In these methods, SDF models that represent point-by-point characteristics have been used to model the relation ' between the creep displacement and the step ARF [7][8][9][10][11], Conse quently, the soft tissue viscoelasticity can be estimated by fitting these simplified models with the measured time-dependent creep displacement. The physical basis for the SDF assumption is that the ARF induced motion is highly localized, and the response of the tissue is assumed to be only related to the local distribution of the mechanical properties.…”

Complex shear modulus quantification from acoustic radiation force creep-recovery and shear wave propagation

“…This paper presents a method to quantify viscoelastic parameter in a model-independent way by estimating the complex shear modulus from recovery response after acoustic radiation force induced creep. Some of the content of this paper is similar to Amador et al [4]. The method theory is illustrated by Matlab simulation using Kelvin-Voigt model.…”

“…As described in Amador et al [4], assuming that compliance is proportional to radiation force induced displacement u(t) by a factor β, Evan's conversion formula (2) gives a relative complex modulus C*(ω) from the displacement u(t).…”

“…The majority of current methods, including shear wave and quasi-static excitation, rely on rheological models to estimate mechanical properties such as elasticity and viscosity. Recently, it has been shown that the quasi-static response from acoustic radiation force excitation (creep) can be used to quantify viscoelastic parameter in a model-independent way by estimating the complex shear modulus from creep displacement response [4]. In these acoustic radiation forced induced creep methods, two types of ultrasound beams are used [3].…”

“…Currently, both creep and recovery are induced and monitored but only creep displacement is used to estimate the model-independent complex shear modulus [4]. A limitation of this model-independent method, is that to study viscoelastic parameters over a wider range of frequencies, the creep period needs to be maintained for long times, for instance up to 30 ms, which means that the total exposure time to acoustic radiation force in some cases may be too large.…”