Abstract:Dynamic elastography holds great promise for biological tissues characterization. Resulting from the radiation force induced by focused ultrasound beam, plane shear waves are generated within the medium and imaged with an ultrafast ultrasound scanner. Known as Supersonic Shear Imaging (SSI) technique, this method allows, from the measurements of shear wave velocities, to compute shear modulus (µ) maps. Beside, in order to improve tissue diagnostic, the evaluation of the nonlinear elastic moduli could be of som… Show more
“…The thin straight lines correspond to the linear part of the ρv 2 -e curves. Here the initial shear modulus is µ = 6.6 kPa, the thirdorder Landau constant is A = −37.7 kPa, and the coefficient of non-linearity is ν = 3.5, in line with the experimental results of Renier et al [6].…”
Section: Body Wavessupporting
confidence: 88%
“…Finally, the results can easily be expanded in terms of the elongation e = λ − 1. Here we find that (6) and we do not need to specify the higher-order terms for our purpose, which is to establish relationships in the form of Eq. ( 2).…”
“…We conclude this section with an example taken from experimental investigations. Renier et al [6] use a small elongation (compression) to deduce a linear ρv 2 -σ relationship from experimental data on Agar-Gelatin based phantoms: they conclude that for their 5% Gelatin sample, µ ≃ 6.6 kPa and A ≃ −37.7 kPa. Then they use finite-amplitude shear waves to estimate the coefficient of non-linearity: they find ν ≃ 3.5 (see also the combination of Ref.…”
Section: Body Wavesmentioning
confidence: 99%
“…where E is the Green strain tensor and µ, A, and D are second, third-, and fourth-order elasticity constants, respectively, at least 16 articles [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] have studied the dynamics of those solids.…”
Acousto-elasticity is concerned with the propagation of small-amplitude waves in deformed solids. Results previously established for the incremental elastodynamics of exact non-linear elasticity are useful for the determination of third-and fourth-order elastic constants, especially in the case of incompressible isotropic soft solids, where the expressions are particularly simple. Specifically, it is simply a matter of expanding the expression for ρv 2 , where ρ is the mass density and v the wave speed, in terms of the elongation e of a block subject to a uniaxial tension. The analysis shows that in the resulting expression: ρv 2 = a + be + ce 2 , say, a depends linearly on µ; b on µ and A; and c on µ, A, and D, the respective second-, third, and fourth-order constants of incompressible elasticity, for bulk shear waves and for surface waves.
“…The thin straight lines correspond to the linear part of the ρv 2 -e curves. Here the initial shear modulus is µ = 6.6 kPa, the thirdorder Landau constant is A = −37.7 kPa, and the coefficient of non-linearity is ν = 3.5, in line with the experimental results of Renier et al [6].…”
Section: Body Wavessupporting
confidence: 88%
“…Finally, the results can easily be expanded in terms of the elongation e = λ − 1. Here we find that (6) and we do not need to specify the higher-order terms for our purpose, which is to establish relationships in the form of Eq. ( 2).…”
“…We conclude this section with an example taken from experimental investigations. Renier et al [6] use a small elongation (compression) to deduce a linear ρv 2 -σ relationship from experimental data on Agar-Gelatin based phantoms: they conclude that for their 5% Gelatin sample, µ ≃ 6.6 kPa and A ≃ −37.7 kPa. Then they use finite-amplitude shear waves to estimate the coefficient of non-linearity: they find ν ≃ 3.5 (see also the combination of Ref.…”
Section: Body Wavesmentioning
confidence: 99%
“…where E is the Green strain tensor and µ, A, and D are second, third-, and fourth-order elasticity constants, respectively, at least 16 articles [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] have studied the dynamics of those solids.…”
Acousto-elasticity is concerned with the propagation of small-amplitude waves in deformed solids. Results previously established for the incremental elastodynamics of exact non-linear elasticity are useful for the determination of third-and fourth-order elastic constants, especially in the case of incompressible isotropic soft solids, where the expressions are particularly simple. Specifically, it is simply a matter of expanding the expression for ρv 2 , where ρ is the mass density and v the wave speed, in terms of the elongation e of a block subject to a uniaxial tension. The analysis shows that in the resulting expression: ρv 2 = a + be + ce 2 , say, a depends linearly on µ; b on µ and A; and c on µ, A, and D, the respective second-, third, and fourth-order constants of incompressible elasticity, for bulk shear waves and for surface waves.
“…At last, at high deformation, strain and stress are no more negligible, and the shear wave propagation is modified due to the inner stress of the tendon ("acoustoelasticity theory"). Shear nonlinear parameters intervene and, although they are not easily measurable, they should be taken into account (Renier et al, 2007). Helfenstein-Didier et al (2016), in their recent comparison of conventional SWE and new dispersion technique, found a high significant correlation (r=0.84).…”
Classical acoustoelasticity couples small-amplitude elastic wave propagation to an infinitesimal pre-deformation, in order to reveal and evaluate non-destructively third-order elasticity constants. Here, we see that acoustoelasticity can be also be used to determine fourth-order constants, simply by coupling a small-amplitude wave with a small-but-finite pre-deformation. We present results for compressible weakly nonlinear elasticity, we make a link with the historical results of Bridgman on the physics of high pressures, and we show how to determine "D", the so-called fourth-order elasticity constant of soft (incompressible, isotropic) solids by using infinitesimal waves.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.