Measurement of viscoelastic properties of homogeneous soft solid using transient elastography: An inverse problem approach

Abstract

Two main questions are at the center of this paper. The first one concerns the choice of a rheological model in the frequency range of transient elastography, sonoelasticity or NMR elastography for soft solids (20-1000 Hz). Transient elastography experiments based on plane shear waves that propagate in an Agar-gelatin phantom or in bovine muscles enable one to quantify their viscoelastic properties. The comparison of these experimental results to the prediction of the two simplest rheological models indicate clearly that Voigt's model is the better. The second question studied in the paper deals with the feasibility of quantitative viscosity mapping using inverse problem algorithm. In the ideal situation where plane shear waves propagate in a sample, a simple inverse problem based on the Helmholtz equation correctly retrieves both elasticity and viscosity. In a more realistic situation with nonplane shear waves, this simple approach fails. Nevertheless, it is shown that quantitative viscosity mapping is still possible if one uses an appropriate inverse problem that fully takes into account diffraction in solids.

New insights on contraction efficiency in patients with Duchenne muscular dystrophy

“…The ultrasound B-mode images were used to determine the region of interest for each contraction (i.e., between the two aponeurosis of the BB muscle) (19). The displacements along the ultrasound beam axis were calculated using a one-dimensional cross correlation of the windows of consecutive radio-frequency signals (3,9). Thus the tissue motion between the two consecutive images (i.e., particle velocity) was measured with micrometric precision.…”

Analyzing and modeling rheological behavior of liver fibrosis in rats using shear viscoelastic moduli

“…Generally, the Voigt model is a classic rheological model used in ultrasound methods (Zheng et al, 2007;Chen S. et al, 2009;Chen X. et al, 2013), but its application was not extensively compared with other models for liver study (Chen et al, 2004;2009;Catheline et al, 2004;Gennisson et al, 2010;Orescanin and Insana, 2010;Mitri et al, 2011). Our next work will assess the feasibility of the Zener model in the estimation of viscoelastic parameters for liver fibrosis staging in ultrasonic elastography methods.…”

“…The speed of shear waves propogating in porcine livers was measured at multiple frequencies by shearwave dispersion ultrasound vibrometry (SDUV) and shear viscoelasticity parameters were estimated by fitting the shear wave speed dispersion curves according to the Voigt model (Chen et al, 2009). The Voigt model was also applied to viscoelastic properties of bovine muscles using transient elastography (Catheline et al, 2004) and in vivo human brachialis muscle using a noninvasive ultrasound-based technique by supersonic shear wave image (SSI) (Gennisson et al, 2010). Among these models, the Voigt model is widely used to explain rheological behavior of normal tissue due to a simple formation of one spring and one dashpot.…”

On a nonlinear inverse problem in viscoelasticity

“…In medecine, tomography techniques using mechanical loads such as antiplane shear loading on life tissue, considered as a viscoelastic medium, have been worked out for Kelvin-Voigt's viscoelasticity (Catheline et al [12], Muller et al [18]) and for pure elasticity. In the elastic case, solutions to crack inverse problems in 2D and 3D are already known, see Andrieux and Ben Abda [4], Andrieux et al [5], Bui et al [8].…”