Characterization of transverse isotropy in compressed tissue-mimicking phantoms

Abstract

Tissues such as skeletal muscle and kidneys have well-defined structure that affects the measurements of mechanical properties. As an approach to characterize the material properties of these tissues, different groups have assumed that they are transversely isotropic (TI) and measure the shear wave velocity as it varies with angle with respect to the structural architecture of the organ. To refine measurements in these organs, it is desirable to have tissue mimicking phantoms that exhibit similar anisotropic characteristics. Some approaches involve embedding fibers into a material matrix. However, if a homogeneous solid is under compression due to a static stress, an acoustoelastic effect can manifest which makes the measured wave velocities change with the compression stress. We propose to exploit this characteristic to demonstrate that stressed tissue mimicking phantoms can be characterized as a TI material. We tested six phantoms made with different concentrations of gelatin and agar. Stress was applied by the weight of a water container centered on top of a plate on top of the phantom. A linear array transducer and a V-1 Verasonics system were used to induce and measure shear waves in the phantoms. The shear wave motion was measured using a compound plane wave imaging technique. Autocorrelation was applied to the received in-phase/quadrature data. The shear wave velocity, c, was estimated using a Radon transform method. The transducer was mounted on a rotating stage so measurements were made every 10° over a range of 0-360°, where the stress is applied along 0-180° direction. The shear moduli were estimated. A TI model was fit to the data and the fractional anisotropy was evaluated. This approach can be used to explore many configurations of transverse isotropy with the same phantom, simply by applying stress to the tissue mimicking phantom.

Comparison of ultrasound elastography, magnetic resonance elastography and finite element model to quantify nonlinear shear modulus

“…This is illustrated by a higher standard deviation (8%) in this configuration for the estimation of the shear modulus at zeros stress compared to As expected by the acoustoelastic theory, for each method a linear relation is observed between the shear modulus and the applied stress. Results obtained with US were consistent with previous works performed in SWE (Gennisson et al 2007, Urban et al 2015, Bernal et al 2016, Aristizabal et al 2018. Regarding the shear wave propagation and the polarization selected, it is observed an increase or a decrease of the shear modulus relatively to the applied stress.…”

A comparison of hyperelastic constitutive models applicable to shear wave elastography (SWE) data in tissue-mimicking materials

“…In the AE-SWE experiments reported in the literature (Jiang et al 2015a, 2015b, Gennisson et al 2007, Urban et al 2015, tissue-mimicking phantoms or ex vivo tissues were compressed along one direction. Particularly, in the work by Jiang et al (2015a), the compression was applied by the face of the transducer and the off axis principle stretches were parameterized as λ 1 = λ, λ 2 = λ −ξ , and ξ) , where λ is the stretch along the compression direction and ξ is a parameter having a value from 0 to 1.…”

“…Other experiments have considered SWE measurements from three orthogonal imaging planes (Gennisson et al 2007, Urban et al 2015 as illustrated in figure 2, though this has yet to be considered in the context Ogden's formulation and the large strain data required to do so (maximum compressive strain in the range of 25%-55%) is lacking. The acoustoelastic equations for these three planes are produced by setting the indices in equation ( 17) Neo-Hookean Ogden (2013…”

Tractable calculation of the Green’s tensor for shear wave propagation in an incompressible, transversely isotropic material

“…Skeletal muscle is an example of a TI material with the symmetry axis defined by the direction of the muscle fibers (Gennisson et al 2010. Stretched or compressed polyvinyl alcohol phantoms also have TI symmetry with the symmetry axis determined by the axis of deformation (Gennisson et al 2007, Chatelin et al 2014, Urban et al 2015. Measurements of shear wave propagation in these materials are typically performed using the exper imental Tractable calculation of the Green's tensor for shear wave propagation in an incompressible, transversely isotropic material geometry shown in figure 1(a) (see, also, figure 2 of Chatelin et al (2014)) and observe propagation in the horizontal (Z = 0) plane in the n direction at an angle θ relative to the symmetry axis.…”