Shear Wave Propagation Research Articles

The effect of microfabric heterogeneity on shear wave properties in fine-grained sediments

The water-sediment interface is highly susceptible to physical, biological, and chemical processes, which can create significant levels of heterogeneity in sediment biogeoacoustic properties at various spatial scales that affect transmission and scattering of elastic waves. Using a suite of microscopy, spectroscopy, and medical sonoelastography techniques, relationships between heterogeneity in the sediment microfabric and shear wave speed can be investigated at spatial scales ranging from centimeters to micrometers. Here, we study fine-grained sediments extracted from two unique intertidal mudflats in the Great Bay Estuary, New Hampshire, USA. Shear waves were excited via acoustic radiation force and external vibration in the 50–200 Hz frequency band, and particle velocity was sensed in the top 2 centimeters of sediment at approximately 0.5-micrometer spatial resolution using a research-grade medical imaging array. By directly imaging the propagating shear wave, spatial heterogeneity of shear wave speed was directly measured. Next, subsamples were extracted and prepared for microscopy, where volume fraction and orientation of organic, mineral, and aqueous components were studied at various spatial scales. A comparison of between shear wave speed and microfabric parameters will be presented. [Work sponsored by ONR.]

Comparative Studies between Frequency Domain Analysis and Time Domain Analysis on Free-Field One-Dimensional Shear Wave Propagation

In Korea, the underground silo structure for low- and intermediate-level radioactive waste disposal facilities has been constructed and operated since 2014. Large-scale earthquakes occurred in 2016 and 2017, respectively, in Gyeongju and Pohang areas near the underground silo structures, and interest in the stability of the underground silo increased significantly. In this paper, one-dimensional free-field analyses have been carried out before the three-dimensional silo dynamic analyses subjected to earthquake loadings. As an additional study, a new form of the finite element equilibrium equation is derived in terms of relative motions, which is essentially the same equation expressed in terms of total motions where the base shear force is applied to the earthquake load. The accuracy of conventional finite element solutions is evaluated by directly comparing them with closed-form solutions by frequency domain analysis such as SHAKE91.

FUNCTIONAL ASSESSMENT OF WAVE PROPAGATION IN IMPERFECT CYLINDER MATERIALS

This work provides a theoretical framework to investigate the shear wave propagation properties within an Electrostrictive cylindrical layered structure. The structure is made up of a concentric, Functionally Assessed Electrostrictive Material (FAEM) cylindrical layer of limited width and an inadequately bonded Electrostrictive material cylinder. The FAEM layer has a constant functional gradient in the radial direction, and flaws at the interface are taken seriously, mirroring actual circumstances involving structural and electrical degradation. The fundamental electromechanical connected Bessel's equations are used to simplify field differential equations by mathematical modifications. Relationships for shear wave propagation under electrically short and open circumstances are established analytically. The acquired findings are verified against predefined standards and a particular issue instance. The impact of variables on the phase velocity of shear waves, including functional range and imperfection parameters, is shown through numerical simulations and graphical displays. The research also establishes boundaries for electrically short and open circumstances, taking into account the shear defect that exists between the inner and outer cylindrical layers.

Liver Magnetic Resonance Elastography: Focus on Methodology, Technique, and Feasibility.

Magnetic resonance elastography (MRE) is an imaging technique that combines low-frequency mechanical vibrations with magnetic resonance imaging to create visual maps and quantify liver parenchyma stiffness. As in recent years, diffuse liver diseases have become highly prevalent worldwide and could lead to a chronic condition with different stages of fibrosis. There is a strong necessity for a non-invasive, highly accurate, and standardised quantitative assessment to evaluate and manage patients with different stages of fibrosis from diagnosis to follow-up, as the actual reference standard for the diagnosis and staging of liver fibrosis is biopsy, an invasive method with possible peri-procedural complications and sampling errors. MRE could quantitatively evaluate liver stiffness, as it is a rapid and repeatable method with high specificity and sensitivity. MRE is based on the propagation of mechanical shear waves through the liver tissue that are directly proportional to the organ's stiffness, expressed in kilopascals (kPa). To obtain a valid assessment of the real hepatic stiffness values, it is mandatory to obtain a high-quality examination. To understand the pearls and pitfalls of MRE, in this review, we describe our experience after one year of performing MRE from indications and patient preparation to acquisition, quality control, and image analysis.

Emerging technologies and advanced analyses for non-invasive near-surface site characterization

The in-situ small-strain shear modulus of soil and rock materials is a parameter of paramount importance in geotechnical modeling. It can be derived from non-invasive geophysical surveys, which provide the possibility of testing the subsurface in its natural and undisturbed condition by inferring the velocity of propagation of shear waves. In addition, for soil dynamics and earthquake engineering applications, the small-strain damping ratio plays a relevant role, yet its estimation is still challenging, lacking consolidated approaches for its in-situ evaluation. Recent advancements in instrumentation, such as distributed acoustic sensing (DAS), combined with advanced analysis methodologies for the interpretation of seismic wave propagation (e.g., machine learning and full waveform inversion), open new frontiers in site characterization. This paper presents and compares some advanced applications of measuring 1D and 2D variations in shear wave velocity and attenuation in-situ with reference to a specific case history.

Focused Shear Wave Beam Propagation in Tissue-Mimicking Phantoms.

Ultrasound transient elastography (TE) technologies for liver stiffness measurement (LSM) utilize vibration of small, flat pistons, which generate shear waves that lack directivity. The most common cause for LSM failure in practice is insufficient shear wave signal at the needed depths. We propose to increase shear wave amplitude by focusing the waves into a directional beam. Here, we demonstrate the generation and propagation of focused shear wave beams (fSWBs) in gelatin. Directional fSWBs are generated by vibration at 200-400 Hz of a concave piston embedded near the surface of gelatin phantoms and measured with high-frame-rate ultrasound imaging. Five phantoms with a range of stiffnesses are employed. Shear wave speeds assessed by fSWBs are compared with those by radiation-force-based methods (2D SWE). fSWB amplitudes are compared to predictions using an analytical model. fSWB-derived shear wave speeds are in good agreement with 2D SWE. The amplitudes of fSWBs are localized to the LSM region and are significantly greater than unfocused shear waves. Overall agreement with theory is observed, with some discrepancies in the theoretical source condition. Focusing shear waves can increase the signal in the LSM region for TE. Challenges for translation include coupling piston vibration with the patient skin and increased attenuation in vivo compared to the phantoms employed here. Fibrosis is the most predictive measure of patient outcome in non-alcoholic fatty liver disease. Increased shear wave amplitude in the LSM region can reduce fibrosis assessment failure rates by TE, thus reducing the need for invasive methods like biopsy.

Seismic Anisotropy of Mafic Blueschists: EBSD‐Based Constraints From the Exhumed Rock Record

AbstractSeismic anisotropy constitutes a useful tool for imaging the structure along the plate interface in subduction zones, but the seismic properties of mafic blueschists, a common rock type in subduction zones, remain poorly constrained. We applied the technique of electron backscatter diffraction (EBSD) based petrofabric analysis to calculate the seismic anisotropies of 14 naturally deformed mafic blueschists at dry, ambient conditions. The ductilely deformed blueschists were collected from terranes with inferred peak P‐T conditions applicable to subducting slabs at or near the plate interface in active subduction zones. Epidote blueschists display the greatest P wave anisotropy range (AVp ∼7%–20%), while lawsonite blueschist AVp ranges from ∼2% to 10%. S wave anisotropies generate shear wave splitting delay times up to ∼0.1 s over a thickness of 5 km. AVp magnitude increases with glaucophane abundance (from areal EBSD measurements), decreases with increasing epidote or lawsonite abundance, and is enhanced by glaucophane crystallographic preferred orientation (CPO) strength. Two‐phase rock recipe models provide further evidence of the primary role of glaucophane, epidote, and lawsonite in generating blueschist seismic anisotropy. The symmetry of P wave velocity patterns reflects the deformation‐induced CPO type in glaucophane—an effect previously observed for hornblende on amphibolite P wave anisotropy. The distinctive seismic properties that distinguish blueschist from other subduction zone rock types and the strong correlation between anisotropy magnitude/symmetry and glaucophane CPO suggest that seismic anisotropy may be a useful tool in mapping the extent and deformation of blueschists along the interface, and the blueschist‐eclogite transition in active subduction zones.

A Study on the Potential of Sand Liquefaction Hazard at Chukai Sentral, Terengganu Using Plaxis 2D

An earthquake is classified as a natural disaster of mother nature. Sometimes, it cannot be predicted when it will occur and difficult to estimate the striking force values and the period of incident. The effect of the earthquake may catastrophic if the magnitude is more than 6 Richter. It had been proved by previous event, an earthquake could cause a huge impact towards the soil condition especially when the saturated soil is soft or loose since the propagation of shear wave and compression could induced the soil liquefaction and gave an effect towards excess pore pressure and effective stress of the soil that may affect the stability of infrastructure such as dam, embankment, and bridge. This study was conducted to analyse the horizontal displacement of soil due to earthquake and to evaluate the possibility of liquefaction at Chukai Sentral, Kemaman, Terengganu, Malaysia. The study was conducted using Plaxis-2D software based on Mohr-Coulomb soil model at magnitude of 5.4 Richter. The Mohr-Coulomb model was selected as its failure occurs when the shear stress acting on the soil reaches a critical value and the shear strength is related to the effective stress acting on it. The analysis was concentrated on the mesh deformation and horizontal displacement. The result shows the mesh deformation and horizontal displacement obtained in the boreholes not more than 6 mm. It is considered as a small deformation and will not trigger to the potential of liquefaction to that area. It can be concluded that the earthquake magnitude of 5.4 Richter is unable to disturb the natural resistance of the soil and structure due to their stiff layer proportion.

Photoacoustic elastography based on laser-excited shear wave

Elastography can be used as a diagnostic method for quantitative characterization of tissue hardness information and thus, differential changes in pathophysiological states of tissues. In this study, we propose a new method for shear wave elastography (SWE) based on laser-excited shear wave, called photoacoustic shear wave elastography (PASWE), which combines photoacoustic (PA) technology with ultrafast ultrasound imaging. By using a focused laser to excite shear waves and ultrafast ultrasonic imaging for detection, high-frequency excitation of shear waves and noncontact elastic imaging can be realized. The laser can stimulate the tissue with the light absorption characteristic to produce the thermal expansion, thus producing the shear wave. The frequency of shear wave induced by laser is higher and the frequency band is wider. By tracking the propagation of shear wave, Young’s modulus of tissue is reconstructed in the whole shear wave propagation region to further evaluate the elastic information of tissue. The feasibility of the method is verified by experiments. Compared with the experimental results of supersonic shear imaging (SSI), it is proved that the method can be used for quantitative elastic imaging of the phantoms. In addition, compared with the SSI method, this method can realize the noncontact excitation of the shear wave, and the frequency of the shear wave excited by the laser is higher than that of the acoustic radiation force (ARF), so the spatial resolution is higher. Compared to the traditional PA elastic imaging method, this method can obtain a larger imaging depth under the premise of ensuring the imaging resolution, and it has potential application value in the clinical diagnosis of diseases requiring noncontact quantitative elasticity.

Shear Waves in an Elastic Plate with a Hole Resting on a Rough Base

The article is devoted to the analytical and numerical study of the pattern of propagation and attenuation, due to Coulomb friction, of shear waves in an infinite elastic thin plate with a circular orifice of radius r0 lying on a rough base. Considering the friction forces and their influence on the sample of wave propagation in extended rods or thin plates is important for calculating the stress–strain state in them and the size of the area of motion. An exact analytical solution of a nonlinear boundary value problem for tangential stresses and velocities is obtained in quadratures by the Laplace transform, with respect to time. It turned out that the complete exhaustion of the wave front of a strong rupture occurs at a finite distance r* from the center of the orifice, and an elementary formula is given for this distance (the case of tangential shock stresses suddenly applied to the orifice boundary is considered). For various ratios of the magnitude of the limiting friction force to the amplitude of the applied load, the stopping (trailing) wave fronts are calculated. After passing them, a state of static equilibrium between the elastic and friction forces with a nonlinear distribution of residual stresses is established in the region r0≤r≤r*. For the first time, a precise analytical solution was obtained for the boundary value problem of the propagation of elastic shear waves in an infinite isotropic space with a cylindrical cavity, when a tangential shock load is set on its surface.

High-speed ultrasound imaging of bubbly flows and shear waves in soft matter.

In this methods paper, we explore the capabilities of high-speed ultrasound imaging (USI) to study fast varying and complex multi-phase structures in liquids and soft materials. Specifically, we assess the advantages and the limitations of this imaging technique through three distinct experiments involving rapid dynamics: the underwater flow induced by an external jet, the dissolution of sub-micron bubbles in water, and the propagation of shear waves in a soft elastic material. The phenomena were simultaneously characterized using optical microscopy and USI. In water, we use compounded USI for tracking a multi-phase flow produced by a jetting bubble diving into a liquid pool at speeds around 20 m s-1. These types of jets are produced by focusing a single laser pulse below the liquid surface. Upon breakup, they create a bubbly flow that exhibits high reflectivity to the ultrasound signal, enabling the visualization of the subsequent turbulent flow. In a second experiment, we demonstrate the potential of USI for recording the diffusive shrinkage of micro- and nanobubbles in water that could not be optically resolved. Puncturing an elastic material with a liquid jet creates shear waves that can be utilized for elastography measurements. We analysed the shape and speed of shear waves produced by different types of jetting bubbles in industrial gelatin. The wave characteristics were simultaneously determined by implementing particle velocimetry in optical and ultrasound measurements. For the latter, we employed a novel method to create homogeneously distributed micro- and nanobubbles in gelatin by illuminating it with a collimated laser beam.

Small-strain stiffness of liquefiable sands: A comparison between bender elements and resonant-column tests

Soil stiffness can be estimated by geophysical and dynamic testing methods. In the laboratory, the most common methods to measure the small-strain stiffness are the bender elements (BE) and resonant-column (RC) tests. This paper focuses on the comparison between the results of the small-strain stiffness of sands by BE and RC tests. For this purpose, an experimental program involving three liquefiable sandy soils (i.e., NB, TP-Lisbon and Toyoura sands) was carried out. Such program covered the measurement of the small-strain stiffness of these soils by BE in triaxial and RC apparatuses for different mean effective stress conditions. All tests were carried out on saturated soil specimens, which were remoulded using the air pluviation method for various relative densities. The experimental results were interpreted in terms of shear-wave velocity (Vs) and maximum shear modulus (Gmax) to derive the stress-dependency laws of these parameters. The experimental results revealed differences between Vs obtained from BE and RC tests, evidencing a clear effect of relative density on the shear-wave propagation. However, such a variation may be significantly reduced when a normalisation of Gmax in terms of a void ratio function F(e) is applied. As a result, this study demonstrated and validated the importance of accounting for the soil state conditions, for adequate compatibility of BE and RC tests in the estimate of the small-strain stiffness of liquefiable sands.

Full-wave Image Reconstruction in Transcranial Photoacoustic Computed Tomography using a Finite Element Method.

Transcranial photoacoustic computed tomography presents challenges in human brain imaging due to skull-induced acoustic aberration. Existing full-wave image reconstruction methods rely on a unified elastic wave equation for skull shear and longitudinal wave propagation, therefore demanding substantial computational resources. We propose an efficient discrete imaging model based on finite element discretization. The elastic wave equation for solids is solely applied to the hard-tissue skull region, while the soft-tissue or coupling-medium region that dominates the simulation domain is modeled with the simpler acoustic wave equation for liquids. The solid-liquid interfaces are explicitly modeled with elastic-acoustic coupling. Furthermore, finite element discretization allows coarser, irregular meshes to conform to object geometry. These factors significantly reduce the linear system size by 20 times to facilitate accurate whole-brain simulations with improved speed. We derive a matched forward-adjoint operator pair based on the model to enable integration with various optimization algorithms. We validate the reconstruction framework through numerical simulations and phantom experiments.

Displacement Tracking Techniques in Ultrasound Elastography: From Cross Correlation to Deep Learning.

Ultrasound elastography is a noninvasive medical imaging technique that maps viscoelastic properties to characterize tissues and diseases. Elastography can be divided into two classes in a broad sense: strain elastography (SE), which relies on Hooke's law to delineate strain as a surrogate for elasticity, and shear-wave elastography (SWE), which tracks the propagation of shear waves (SWs) in tissues to estimate the elasticity. As tracking the displacement field in the temporal or spatial domain is an inevitable step of both SE and SWE, the success is contingent on the displacement estimation accuracy. Recent reviews mostly focused on clinical applications of elastography, disregarding advances in displacement tracking algorithms. Here, we comprehensively review the recently proposed displacement estimation algorithms applied to both SE and SWE. In addition to cross correlation, block-matching-based (i.e., window-based), model-based, energy-based, and deep learning-based tracking techniques, we review large and lateral displacement tracking, adaptive beamforming, data enhancement, and noise-suppression algorithms facilitating better displacement estimation. We also discuss the simulation models for displacement tracking validation, clinical translation and validation of displacement tracking methods, performance evaluation metrics, and publicly available codes and data for displacement tracking in elastography. Finally, we provide experiential opinions on different tracking algorithms, list the limitations of the current state of elastographic tracking, and comment on possible future research.

Four-dimensional (4D) Ultrasound Shear Wave Elastography Using Sequential Excitation.

Current shear wave elastography methods primarily focus on 2D imaging. To explore mechanical properties of biological tissues in 3D, a four-dimensional (4D, x, y, z, t) ultrasound shear wave elastography is required. However, 4D ultrasound shear wave elastography is still challenging due to the limitation of the hardware of standard ultrasound acquisition systems. In this study, we introduce a novel method to achieve 4D shear wave elastography, named sequential-based excitation shear wave elastography (SE-SWE). This method can achieve 4D elastography implemented by a 1024-element 2D array with a standard ultrasound 256-channel system. The SE-SWE method employs sequential excitation to generate shear waves, and utilizes a 2D array, dividing it into four sub-sections, to capture shear waves across multiple planes. This process involves sequentially exciting each sub-section to capture shear waves, followed by compounding the acquired data from these subsections. The phantom studies showed strong concordance between the shear wave speeds (SWS) measured by SE-SWE and expected values, confirming the accuracy of this method and potential to differentiate tissues by stiffness. In ex vivo chicken breast experiments, SE-SWE effectively distinguished between orientations relative to muscle fibers, highlighting its ability to capture the anisotropic properties of tissues. The SE-SWE method advances shear wave elastography significantly by using a 2D array divided into four subsections and sequential excitation, achieving high-resolution volumetric imaging at 1.6mm resolution. The SE-SWE method offers a straightforward and effective approach for 3D shear volume imaging of tissue biological properties.

Impact of loosely bounded interfaces between three-layered media on shear wave propagation

Impact of loosely bounded interfaces between three-layered media on shear wave propagation

A study of Griffith crack in nonlocal infinite magneto-elastic media

The main objective of this article is to study how a finite crack interacts with horizontally polarized shear (SH) waves in a nonlocal isotropic medium when a magnetic field is present. The study aims to understand the effects of various parameters, including the magnetic field, non-locality, frequency of SH waves, on the behavior of the crack. Here, we are concerned with Griffith’s theory of a brittle fracture crack mechanism. The article starts by formulating the governing equations for the propagation of SH waves in the given medium. These equations are converted into dual integral equations using Fourier transformation. Subsequently, an Abel transformation is applied to obtain a Fredholm integral equation of the second kind. Daubechies wavelet family has been used to find an approximate solution for the integral equation. The article aims to determine specific physical quantities including stress intensity factor (SIF), shear stress, and crack energy related to the behavior of the crack. These parameters are essential in understanding how the crack responds to the external conditions. The application of Daubechies wavelets in this context is a relatively new and innovative approach. The study performed a comprehensive analysis of the effects of various factors on the crack behavior. The findings are presented in graphical form to help illustrate the conclusions. To assess the accuracy of the proposed method, the obtained results are compared with known results from the literature for local media. This is an important step in demonstrating the reliability and effectiveness of the proposed approach.

Development of broad modulus profile upon polymer-polymer interface formation between immiscible glassy-rubbery domains.

Interfaces of glassy materials such as thin films, blends, and composites create strong unidirectional gradients to the local heterogeneous dynamics that can be used to elucidate the length scales and mechanisms associated with the dynamic heterogeneity of glasses. We focus on bilayer films of two different polymers with very different glass transition temperatures ([Formula: see text]) where previous work has demonstrated a long-range (∼200 nm) profile in local [Formula: see text] is established between immiscible glassy and rubbery polymer domains when the polymer-polymer interface is formed to equilibrium. Here, we demonstrate that an equally long-ranged gradient in local modulus [Formula: see text] is established when the polymer-polymer interface ([Formula: see text]5 nm) is formed between domains of glassy polystyrene (PS) and rubbery poly(butadiene) (PB), consistent with previous reports of a broad [Formula: see text] profile in this system. A continuum physics model for the shear wave propagation caused by a quartz crystal microbalance across a PB/PS bilayer film is used to measure the viscoelastic properties of the bilayer during the evolution of the PB/PS interface showing the development of a broad gradient in local modulus [Formula: see text] spanning [Formula: see text]180 nm between the glassy and rubbery domains of PS and PB. We suggest these broad profiles in [Formula: see text] and [Formula: see text] arise from a coupling of the spectrum of vibrational modes across the polymer-polymer interface as a result of acoustic impedance matching of sound waves with [Formula: see text] nm during interface broadening that can then trigger density fluctuations in the neighboring domain.

Rotational 3D shear wave elasticity imaging: Effect of knee flexion on 3D shear wave propagation in in vivo vastus lateralis

Skeletal muscle is a complex tissue, exhibiting not only direction-dependent material properties (commonly modeled as a transversely isotropic material), but also changes in observed material properties due to factors such as contraction and passive stretch. In this work, we evaluated the effect of muscle passive stretch on shear wave propagation along and across the muscle fibers using a rotational 3D shear wave elasticity imaging system and automatic analysis methods. We imaged the vastus lateralis of 10 healthy volunteers, modulating passive stretch by imaging at 8 different knee flexion angles (controlled by a BioDex system). In addition to demonstrating the ability of this acquisition and automatic processing system to estimate muscle shear moduli over a range of values, we evaluated potential higher order biomarkers for muscle health that capture the change in muscle stiffness along and across the fibers with changing knee flexion. The median within-subject variability of these biomarkers is found to be <16%, suggesting promise as a repeatable clinical metric. Additionally, we report an unexpected observation: that shear wave signal amplitude along the fibers increases with increasing flexion and muscle stiffness, which is not predicted by transversely isotropic (TI) material simulations. This observation may point to an additional potential biomarker for muscle health or inform other material modeling choices for muscle.

Resonance, Velocity, Dispersion, and Attenuation of Ultrasound-Induced Shear Wave Propagation in Blood Clot In Vitro Models.

Improve the characterization of mechanical properties of blood clots. Parameters derived from shear wave (SW) velocity and SW amplitude spectra were determined for gel phantoms and in vitro blood clots. Homogeneous phantoms and phantoms with gel or blood clot inclusions of different diameters and mechanical properties were analyzed. SW amplitude spectra were used to observe resonant peaks. Parameters derived from those resonant peaks were related to mimicked blood clot properties. Three regions of interest were tested to analyze where resonances occurred the most. For blood experiments, 20 samples from different pigs were analyzed over time during a 110-minute coagulation period using the Young modulus, SW frequency dispersion, and SW attenuation. The mechanical resonance was manifested by an increase in the number of SW spectral peaks as the inclusion diameter was reduced (P < .001). In blood clot inclusions, the Young modulus increased over time during coagulation (P < .001). Descriptive spectral parameters (frequency peak, bandwidth, and distance between resonant peaks) were linearly correlated with clot elasticity values (P < .001) with R2 = .77 for the frequency peak, .60 for the bandwidth, and .48 for the distance between peaks. The SW dispersion and SW attenuation reflecting the viscous behavior of blood clots decreased over time (P < .001), mainly in the early stage of coagulation (first minutes). The confined soft inclusion configuration favored SW mechanical resonances potentially challenging the computation of spectral-based parameters, such as the SW attenuation. The impact of resonances can be reduced by properly selecting the region of interest for data analysis.