scholarly journals Fluids Alter Elasticity Measurements: Porous Wave Propagation Accounts for Shear Wave Dispersion in Elastography

2021 ◽  
Vol 9 ◽  
Author(s):  
Johannes Aichele ◽  
Stefan Catheline
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Shear Wave ◽  
Wave Dispersion ◽  
Elastic Wave Propagation ◽  
Elastic Model ◽  
Fluid Viscosity ◽  
Wave Speeds ◽  
Wide Range

In shear wave elastography, rotational wave speeds are converted to elasticity measures using elastodynamic theory. The method has a wide range of applications and is the gold standard for non-invasive liver fibrosis detection. However, the observed shear wave dispersion of in vivo human liver shows a mismatch with purely elastic and visco-elastic wave propagation theory. In a laboratory phantom experiment we demonstrate that porosity and fluid viscosity need to be considered to properly convert shear wave speeds to elasticity in soft porous materials. We extend this conclusion to the clinical application of liver stiffness characterization by revisiting in vivo studies of liver elastography. To that end we compare Biot’s theory of poro-visco-elastic wave propagation to Voigt’s visco-elastic model. Our results suggest that accounting for dispersion due to fluid viscosity could improve shear wave imaging in the liver and other highly vascularized organs.

Reflection and Refraction of Weak Elastic-Plastic Waves

1974 ◽  
Vol 41 (1) ◽  
pp. 117-123 ◽  
Author(s):  
W. E. Jahsman
Keyword(s):  
Plastic Deformation ◽  
Wave Propagation ◽  
Elastic Wave ◽  
Elastic Wave Propagation ◽  
Angle Of Incidence ◽  
Singular Surfaces ◽  
Direction Parallel ◽  
Wave Speeds ◽  
Elastic Plastic ◽  
Weak Discontinuities

The method of singular surfaces is used to obtain expressions for the amplitudes of weak discontinuities reflected from or transmitted across interfaces between solids of dissimilar elastic-plastic properties. Here weak discontinuities are taken to mean discontinuities in derivatives of stress, strain, and velocity components. These discontinuities occur across singular surfaces which propagate at characteristic wave speeds and are referred to as weak waves. Analogous to elastic wave propagation results, two reflected and two refracted fronts satisfy stress and velocity continuity conditions in media prestressed into the plastic range. However, the speeds of these fronts are generally less than the elastic dilatational and shear wave speeds, and the amplitudes of the reflected and refracted discontinuities can differ dramatically from their elastic counterparts. Numerical examples are considered in which weak waves are reflected from rigid and stress-free surfaces. The medium through which the waves pass is prestressed in the direction parallel to the reflecting surface. Results are presented which show the dependence of the reflected velocity and stress discontinuity amplitudes on the angle of incidence of the oncoming wave. As compared to elastic wave propagation, the presence of plastic deformation reduces the amplitude of the reflected front which travels at the speed of the incident front and raises the amplitude of the other reflected front. The most pronounced effect of plastic deformation is found when the incident front travels at the slow wave speed (SV-type wave). In this case, the critical angle of incidence (beyond which reflected weak waves alone cannot satisfy the boundary conditions) decreases to 22.5 deg from the elastic value of 30 deg when Poisson’s ratio is 1/3. It is conjectured that elastic-plastic surface waves may be needed to satisfy the interface conditions at incidence angles beyond this critical value.

Elastic wave propagation in bone in vivo: Methodology

1995 ◽  
Vol 28 (4) ◽  
pp. 471-478 ◽  
Author(s):  
Sulin Cheng ◽  
Jussi Timonen ◽  
Harri Suominen
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Elastic Wave Propagation

scholarly journals Shear Wave Propagation and Estimation of Material Parameters in a Nonlinear, Fibrous Material

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Zuoxian Hou ◽  
Ruth J. Okamoto ◽  
Philip V. Bayly
Keyword(s):  
Wave Propagation ◽  
Shear Wave ◽  
Shear Waves ◽  
Material Model ◽  
Model Parameters ◽  
Single Family ◽  
Wave Speeds ◽  
Material Parameters ◽  
Hgo Model

Abstract This paper describes the propagation of shear waves in a Holzapfel–Gasser–Ogden (HGO) material and investigates the potential of magnetic resonance elastography (MRE) for estimating parameters of the HGO material model from experimental data. In most MRE studies the behavior of the material is assumed to be governed by linear, isotropic elasticity or viscoelasticity. In contrast, biological tissue is often nonlinear and anisotropic with a fibrous structure. In such materials, application of a quasi-static deformation (predeformation) plays an important role in shear wave propagation. Closed form expressions for shear wave speeds in an HGO material with a single family of fibers were found in a reference (undeformed) configuration and after imposed predeformations. These analytical expressions show that shear wave speeds are affected by the parameters (μ0, k1, k2, κ) of the HGO model and by the direction and amplitude of the predeformations. Simulations of corresponding finite element (FE) models confirm the predicted influence of HGO model parameters on speeds of shear waves with specific polarization and propagation directions. Importantly, the dependence of wave speeds on the parameters of the HGO model and imposed deformations could ultimately allow the noninvasive estimation of material parameters in vivo from experimental shear wave image data.

scholarly journals An Effective Way to Control Numerical Instability of a Nonordinary State-Based Peridynamic Elastic Model

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Xin Gu ◽  
Qing Zhang ◽  
Yangtian Yu
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Control Method ◽  
Elastic Wave Propagation ◽  
Benchmark Problems ◽  
Elastic Model ◽  
Numerical Instability ◽  
Force Coefficient ◽  
Calculated Stress ◽  
Instability Control

The constitutive modeling and numerical implementation of a nonordinary state-based peridynamic (NOSB-PD) model corresponding to the classical elastic model are presented. Besides, the numerical instability problem of the NOSB-PD model is analyzed, and a penalty method involving the hourglass force is proposed to control the instabilities. Further, two benchmark problems, the static elastic deformation of a simple supported beam and the elastic wave propagation in a two-dimensional rod, are discussed with the present method. It proves that the penalty instability control method is effective in suppressing the displacement oscillations and improving the accuracy of calculated stress fields with a proper hourglass force coefficient, and the NOSB-PD approach with instability control can analyze the problems of structure deformation and elastic wave propagation well.

Study on the Characteristics of Elastic Wave Propagation in Corrugated Fiberboard

2011 ◽  
Vol 339 ◽  
pp. 637-641
Author(s):  
Yi Ding ◽  
Zhi Hui Yu ◽  
Shan Qi Zeng ◽  
Guo Zhi Li
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Elastic Wave Propagation ◽  
Uniform Load ◽  
Mathematical Basis ◽  
Wide Range ◽  
Cushioning Package ◽  
Corrugated Fiberboard

Corrugated fiberboard is considered as the world’s environmentally acceptable packaging that has a wide range of applications in packaging field. Through studying the characteristics of elastic wave propagation in the Corrugated fiberboard, this paper inferences variations of displacement and stress with time, when the corrugated fiberboard suffering the uniform load. It provides theoretical and mathematical basis for the design of cushioning package.

OPTIMISED ABSORBING BOUNDARY CONDITIONS FOR ELASTIC-WAVE PROPAGATION

2001 ◽  
Vol 09 (03) ◽  
pp. 1005-1014
Author(s):  
A. LANGE ◽  
J. ZHOU ◽  
N. SAFFARI
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Elastic Wave ◽  
Normal Incidence ◽  
Absorbing Boundary Conditions ◽  
Elastic Wave Propagation ◽  
Reflection Coefficients ◽  
Absorbing Boundary ◽  
Wide Range ◽  
Complete Absorption

Second-order absorbing boundary conditions for numerical modeling of elastic-wave propagation are studied. The corresponding reflection coefficients are derived, from which a necessary and sufficient condition for complete absorption at normal incidence is deduced. We define a family of absorbing boundary conditions from symmetrically specified zero reflection incidences. Conditions to avoid singular reflection coefficients are given for this case, these ensure that the solutions of the elastic wave equation also satisfy the boundary conditions. These are then optimised over a wide range of materials, and absorbing boundary conditions that give an efficient absorption for the whole range are obtained. We also compare the results with absorbing boundary conditions developed from the least-squares solution of the system requiring complete absorption at all incidences. The best set of conditions are presented and compared with Clayton and Engquist6 (A2) condition.

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