Shear Wave Propagation Research Articles

How well does shear wave elastography predict elevated filling pressures? a comparison to the current guideline algorithm

Abstract Funding Acknowledgements Type of funding sources: Public hospital(s). Main funding source(s): University Hospitals (Uz) Leuven Background The assessment of left ventricular diastolic function is complex, as there is no single invasive parameter that provides a direct measurement of myocardial compliance, myocardial relaxation, or – as a surrogate - LV filling pressure. A combination of several parameters is therefore used to estimate the diastolic function. Shear wave (SW) elastography is a novel method based on high frame rate echocardiography. SWs occur after mechanical excitation of the myocardium, e.g. after mitral valve closure (MVC), and their propagation velocity is directly related to myocardial stiffness (MS). The propagation velocity of SWs is directly related to myocardial stiffness and could be used for estimating left ventricular diastolic pressures. Purpose The aim of this study was to investigate if the MS at mid-diastole or end-diastole and the velocities of natural shear waves are related and, thus, could be used to estimate left ventricular end-diastolic pressures (LVEDP) as marker of diastolic function. Methods We prospectively enrolled 70 patients with a wide range of diastolic function, scheduled for heart catheterization so that LV mid diastolic filling pressures (LVMDP) and enddiastolic filling pressures (LVEDP) could be invasively measured (Panel B). Patients with dysfunction in the anteroseptal wall or regional myocardial abnormalities, as well as severe aortic stenosis, and a more than moderate mitral regurgitation were excluded. Echocardiography was performed immediately after catheterization. SW elastography in parasternal long axis views of the left ventricle (LV) was performed using an experimental scanner (HD-PULSE) at 1050 ± 220 frames per second. Tissue acceleration maps were extracted from an anatomical M-mode line along the midline of the LV septum. The SW propagation velocity at MVC was measured as the slope on the M-mode acceleration map (Panel A). Standard echocardiographic parameters of diastolic function were obtained with a high end ultrasound machine. The Algorithm for evaluating diastolic dysfunction as recommended by the European Association of Cardiovascular Imaging Guidelines 2016 was used for estimating LVMDP. Results SW Velocity correlated better with LVMDP (AUC = 0.8, Sensitivity = 0.84, Specificity= 0.80; =0.26; Panels C,E) than the Guideline approach (AUC = 0.67, Sensitivity = 0.33, Specificity = 1.00, Panel G). SWV showed the best results in predicting LVEDP (AUC = 0.94, Sensitivity = 0.92, Specificity = 0.89 and =0.56 (Panels D,F)). Conclusions Shear wave velocities, detected by high frame rate elastography, have a strong correlation with the end-diastolic filling pressure and allowed significantly better to differentiate normal from elevated filling pressure that current guideline recommended algorithms. This suggests a potential clinical value of the new method for the non-invasive assessment of diastolic function. Abstract Figure. Abstract Figure.

Transcranial Ultrasound Estimation of Viscoelasticity and Fluidity of the Soft Matter

In the fields of geology, materials and biomedical engineering, the noninvasive and accurate estimation of the dynamic mechanical properties of the soft matter enclosed in a rigid shell induced by a low-frequency vibration is worthy of exploration. The addition of fluidity on the basis of viscoelasticity to describe the properties of the soft matter, especially when containing a large amount of water, may be of great value in the detection of crustal movement, material structure, and early cerebral diseases. In the biomedical field, since the influence of the skull on ultrasound is unknown for viewing the propagation of the transcranial shear wave, it is challenging to obtain the mechanical properties of the brain tissue with the skull using the transcranial ultrasound. In this study, the propagations of the transcranial shear wave within the brain tissue induced by an external low-frequency vibration are presented by finite-element-method simulation. This experiment achieved a transcranial ultrasound estimation and differentiation of viscoelasticity and fluidity of brain phantoms enclosed in the skull using the low-frequency vibration and Kelvin-Voigt fractional derivative modeling, and the estimation results are consistent with the nontranscranial ones. These results represent a great potential in the estimation of viscoelasticity and fluidity of the soft matter under different boundary constraints in various areas.

Anisotropy in small-strain shear modulus of granular materials: Effects of particle properties and experimental conditions

Granular soils display directional diversity in stiffness at small strains, which is essential for geotechnical engineering design and can be reflected by the anisotropy of small-strain shear modulus G0. However, the understanding of the stiffness anisotropy of soils is still limited. This contribution presents a series of shear (S-) wave propagation tests using cubical specimens and planer piezoelectric transducers, and discusses the effects of the intrinsic particle properties and experimental conditions on the G0 anisotropy. Four granular materials: spherical glass beads, Toyoura sand, basmati rice, and wild rice are prepared densely in a dry condition and tested under both K0 and isotropic stress states. The experimental results reveal that the particle shape and particle orientation after deposition can affect the anisotropy of the S-wave velocities (Vs), and thus, G0. Tests with different granular materials show that a more elongated particle shape can induce larger anisotropy in G0. From the results of tests on the wild rice specimens, Vs is found to be higher when the major axes of the particles coincide with the direction of the wave propagation, compared to the situation when the major axes are parallel to the oscillation direction of the S-wave. Among the six components in the principal directions, the S-waves neither propagating nor oscillating along the particle orientation are the slowest. Considering the experimental conditions, a mix of flexible (membrane) and rigid boundaries tends to induce larger anisotropy in G0 and a measurable difference between symmetric shear moduli Ghv and Gvh, while the effect of the specimen aspect ratio is less significant.

ROLE OF SHEAR WAVE ELASTOGRAPHY IN CHARACTERIZATION OF BREAST MASSES USING HISTOPATHOLOGY AS GOLD STANDARD

Background: More recent ultrasound technique like SWE have led to better degrees of breast mass characterization by estimating tissue stiffness based on the acoustically generated shear wave propagation speed through the tissue. To nd out the sensitivity and Aims and Objectives: specicity of shear wave elastography in characterizing palpable breast masses using histopathology as gold standard. Materials and methods: This prospective, cross-sectional study was from may 2020 to June 2021. All patients underwent B-mode ultrasound, SWE and USG guided core biopsy of breast mass, BI-RADS on USG with modications by SWE assigned, cut-off values for qualitative and quantitative variables of SWE for differentiation between benign and malignant masses were estimated. SWE ndings were corelated with histopathology. Results: On histopathology amongst 55 patients 27 (49%) were benign and 28 (51%) were malignant. On USG, 19 were BI-RADS3 and 36 were BI-RADS 4 (4a, n = 18; 4b, n = 14; 4c, n = 4) leading to 78.57% sensitivity and 48.15% specicity. On modied BI-RADS' using E-color and Emean/E-max, specicity improved to 66.67% and 77.78% respectively. Addition of SWE to ul Conclusion: trasound improves characterization of BI-RADS 3 and 4a masses. E-max, E-mean and E-color are the most useful SWE parameters to differentiate between malignant and benign breast masses

POS-772 SHEAR WAVE BASED ELASTOGRAPHY POINT QUALIFICATION IN THE EVALUATION OF RENAL PARENCHYMA STIFFNESS IN KIDNEY TRANSPLANT RECIPIENTS UNDERGOING GRAFT BIOPSY

Shear wave elastography (SWE) is an ultrasound technique that measures tissue stiffness non-invasively. In SWE, a real-time short-duration acoustic push pulse generates shear waves travelling perpendicular to the main US beam. Renal biopsy remains the gold standard in assessing rejection and chronicity in kidney transplantation. However, biopsy remains imperfect, with limitations and inherent risks, including sampling errors, allograft trauma with multiple needle pass attempts, and significant interobserver variation in interpreting biopsy samples among pathologists.

Discrete element modeling of shear wave propagation in carbonate precipitate–cemented particles

Discrete element modeling of shear wave propagation in carbonate precipitate–cemented particles

Performance of Shear Wave Speed Measurements by Using Reverberant Optical Coherence Elastography

Elasticity of biological tissue is important to understand its properties, which could play important role in medical diagnosis and treatment, especially in its early stage of pathology. Optical Coherence Elastography (OCE) has been intensively developed for mapping the elasticity contrast of various biological tissues. OCE techniques based on tracking of shear vibrational wave propagation is one of the most popular techniques. The high speed of shear wave propagation in biological media leads to challenges in both data acquisition and data processing. Recently, the concept of reverberant shear wave fi eld has been applied to OCE, called Rev3D-OCE. In this work, we experimentally investigate the performance of Rev3D-OCE to differentiate gelatin phantoms with a slight difference of elasticity. We verifi ed that Rev3D-OCE can differentiate different shear wave speeds associated with different concentrations of gelatin phantoms, where higher shear wave speed was observed in a higher concentration of the phantom as expected. The average shear wave speed of gelatin with 3 wt% and 4 wt% concentrations were measured as 1.3 ± 0.2 m/s and 1.5 ± 0.1 m/s with about 11% and 14% of errors as compared with that obtained by standard mechanical testing, respectively. In addition, the spatial resolution of Rev3D-OCE as determined from the edge response measurement at the boundary between two gelatins of 3 wt% and 4 wt% concentrations was measured to be 0.3 millimeters.

Physical Principles of Elastography: A Primer for Radiologists

AbstractElastography is the noninvasive method of qualitative and quantitative evaluation of strain and elastic modulus distribution in soft tissues. In simpler terms, elastography is the science of measuring tissue stiffness, the deviation of which correlates with pathology of the tissue/organs being evaluated. Whereas, elasticity, refers to the property of solid matter to return to their original shape and size after removal of the deforming forces. In all forms of elastography, irrespective of the types of deforming forces or moduli, the deformation of tissue occurs in the form of shear deformation. The velocity of shear waves in the deformed tissue depends on its density and on the shear modulus. The direction of propagation of shear wave is perpendicular to the inciting mechanical or acoustic wave. The shear wave is then subsequently tracked using multiple tracking pulses, which measures tissue displacement in response to the passing shear wave. The calculated speed of the shear wave is then converted to conventional Young's modulus for the purpose of computing the tissue stiffness.The currently used elastography techniques are static or quasi-static elastography and dynamic elastography. Strain elastography (a form of static or quasi-static elastography) is based on the principle of acquisition of radio-frequency (RF) signals before and after the application of a deforming force in the form of slight compression of tissue by a transducer. RF signals are compared between the pre-compression image data set and the post-compression image data set and correlated between the two data sets.Dynamic elastography may be either ultrasound (US) based or magnetic resonance (MR) based. The types of dynamic US elastography are: acoustic radiation force impulse imaging (ARFI), transient elastography (TE), point shear wave elastography (pSWE), and shear wave elastography (SWE). ARFI uses a standard transducer to produce and propagate rapid bursts of long focused ultrasound pulses, also called as “push pulses” which cause tissue deformity, the propagation of which is tracked using radio-frequency echo tracking. In TE, a probe mounted on a vibrator is used to produce a small thump by piston like motion of transducer. The shear wave which arises from the edges of the transducer is tracked using high pulse repetition frequency tissue Doppler and computed using M-mode for display of quantitative parameters. Point shear wave, also known as quantitative ARFI, uses shear waves generated using transient tissue displacement caused by ARFI and are subsequently subjected to tracking by Doppler. Shear wave elastography is based on the principles of imaging shear wave speed. An acoustic radiation force impulse is transmitted along the acoustic axis to produce tissue displacement and deformation at points of acoustic axis. The generated shear wave is imaged using RF echo tracking over a grid of points, which is translated into a real time image. MR elastography is a dynamic technique and the basic principles of MR elastography are the same as other forms of dynamic elastography. MR elastography has limited utility in iron-overload states and in addition, due to the large amount of time required for acquisition, the technique is not suitable for unstable patients.This review presents a simplified summary of the principles of elastography along with definition of the terms and the types of elastography which are currently available to radiologists for clinical application and concludes with a brief on the newer developments for the future.

Controllable Angle Shear Wavefront Reconstruction Based on Image Fusion Method for Shear Wave Elasticity Imaging.

The generation and measurement of shear waves are critical in ultrasonic elasticity imaging. Generally, the resulting wavefront direction is very important for accurately measuring the shear speed and estimating the medium elasticity. In this article, the proposed method can generate a compound shear wavefront with the same direction as speed reconstruction and zero angles between the wavefront and the focus direction, which can improve the estimation accuracy of shear wave velocity. Also, this method, called time-division multipoint excitation image fusion (TDMPEIF), can reconstruct the shear wave propagation images acquired at different depths of a medium according to the frame sequence to produce the shear waves front with a regulable angle. Moreover, the shear wave speed and the elasticity of a medium can be mapped quantitatively with this method. The results demonstrate that the TDMPEIF can improve the quality of the shear wave velocity images, which has wide application value and good promotion prospects for quantitative evaluation of tissue elasticity.

Seismic site characterization with shear wave (SH) reflection and refraction methods

Reflection and critically refracted seismic methods use traveltime measurements of body waves propagating between a source and a series of receivers on the ground surface to calculate subsurface velocities. Body wave energy is refracted or reflected at boundaries where there is a change in seismic impedance, defined as the product of material density and seismic velocity. This article provides practical guidance on the use of horizontally propagating shear wave (SH-wave) refraction and reflection methods to determine shear wave velocity as a function of depth for near-surface seismic site characterizations. Method principles and the current state of engineering practice are reviewed, along with discussions of limitations and uncertainty assessments. Typical data collection procedures are described using basic survey equipment, along with information on more advanced applications and emerging technologies. Eight case studies provide examples of the techniques in real-world seismic site characterizations performed in a variety of geological settings.

Transition of gap-graded soil fabric – shear wave measurements and dispersion relation

The dynamic response of gap-graded soils is complex; it requires massive experimental and theoretical investigation in order for a sound understanding to be developed. The complexity of the behaviour of such soils arises partially due to the presence of many influential parameters, such as the finer sand/silt content (Fs), size ratio (Rd), and void ratio (e). In this contribution, experiments are conducted on a series of gap-graded soil mixtures, where the coarser sand is mixed with four different finer sands or non-plastic silt with different sizes, namely various Rd, and one well-graded material is also tested. The S-wave velocity (Vs) and low-pass threshold frequency (flp) are measured in the isotropic stress state using a triaxial apparatus equipped with planar piezoelectric transducers. The experimental results reveal that, for a given e or relative density (Dr), both flp and Vs decrease at a low Fs, but increase at a high Fs. The slope of the linear regression between flp and Vs appears to capture this transitional behaviour, depending on Fs and Rd, which can then be used to correlate the physical state of the gap-graded soil fabric. The transitional behaviour is more noticeable at a larger Rd, which is in line with the existing literature. To understand the effect of the Rd on the shear wave propagation at a low Fs, the particle-scale dispersion relation for binary chains is newly introduced and correlated with accompanying experimental observations.

2D Shear Wave Imaging in Gaussian Noise and Reflection Media

Shear wave imaging (SWI) is a rapid and convenient method of collecting images of tissues in the region of interest. SWI is based on the mechanical properties of soft tissues named the complex shear modulus (CSM). The complex shear modulus consisting of the elasticity and the viscosity, is useful for diagnosing pathological tissue conditions. Previous studies have not fully exploited the estimation of CSM in the medium containing Gaussian noise and the shear wave's reflection phenomenon. In this study, we focused on the model of shear wave propagation in the 2D environment by the time domain finite difference method (FDTD), taking into account the effect of Gaussian noise and reflected shear wave. We then reduced the noise of the measured particle velocity using a designed least mean square filter. Finally, for direct estimation of CSM, Helmholtz algebraic inverse transformation algorithm was used. Reflected waves significantly affect the estimation of CSM, especially the tissue's viscosity, which is demonstrated by numerical simulation results.

Analysis of generated shear wave due to stress discontinuity in a monoclinic layered structure

The present study articulates the generation of SH-wave due to sudden stress discontinuity which moves at the monoclinic crustal layer of finite thickness overlying a monoclinic half-space. Free surface displacement field are obtained in exact form by the method due to Cagniard which is modified by De Hoop for different cases of stress discontinuities at the interface of the layered structure, i.e. when the stress discontinuity is created at certain point and then expands with uniform velocity U in z-direction (i.e. Case I); when a dynamic region of discontinuous stress moves with uniform velocity (i.e. Case II); when the stress discontinuity is created in a static region and then expands with uniform velocity (i.e. Case III); and when an impulsive stress discontinuity occurs only at point z = Ut (i.e. Case IV). The numerical calculations and graphical illustrations have been carried out in order to reveal the effect of anisotropy (monoclinic and transversely isotropic) on the free surface displacement field which give some peculiar results and serve as major highlights of the present study. Additionally, as a special case, the deduced results are matched with the isotropic case, which validates the undertaken work.

Physically intuitive continuum mechanics model for quartz crystal microbalance: Viscoelasticity of rubbery polymers at MHz frequencies

AbstractEmploying a quartz crystal microbalance (QCM) as a MHz‐viscoelastic sensor requires extracting information from higher harmonics beyond the Sauerbrey limit, which can be problematic for rubbery polymer films that are highly dissipative because of the onset of anharmonic side bands and film resonance. Data analysis for QCM can frequently obscure the underlying physics or involve approximations that tend to break down at higher harmonics. In this study, modern computational tools are leveraged to solve a continuum physics model for the QCM's acoustic shear wave propagation through a polymer film with zero approximations, retaining the physical intuition of how the experimental signal connects to the shear modulus of the material. The resulting set of three coupled equations are solved numerically to fit experimental data for the resonance frequency Δfn and dissipation ΔΓn shifts as a function of harmonic number n, over an extended harmonic range approaching film resonance. This allows the frequency‐dependent modulus of polymer films at MHz frequencies, modeled as linear on a log–log scale, to be determined for rubbery polybutadiene (PB) and polydimethylsiloxane (PDMS) films, showing excellent agreement with time–temperature shifted rheometry data from the literature.

A mathematical modelling of multiphysics-based propagation characteristics of surface wave in piezoelectric - hydrogel layer on an elastic substrate

This paper presents a mathematical modelling of a novel multiphysics (electro-mechanic coupling) problem of the shear wave propagation in laminated structures (piezoelectric - hydrogel - elastic substrate) using the wave mode method while finding the general solution for each medium. A dynamic mechanical equilibrium equation (for transverse deflection) and Maxwell equation (for electric potential) are solved in a coupled manner over each domain resulting a general closed-form solution. A specific analytical solution is then obtained enforcing the boundary conditions at the top of piezoelectric layer and the interface continuity requirements between each layer and the elastic half-space. A novel approach, to uncouple the coupled equations, is presented resulting in a final systematic solution. The effect of x coordinate (thickness) on the field variables is carefully examined for the electrically open and short cases. The jump in the stress and electric displacement components (causing delamination due to shearing mode of fracture) is present across all the interfaces due to the different bulk material constants. The key contribution of the current work is demonstrating the influence of fixed-charge concentration inside the hydrogel layer on the shear wave propagation. The present study thus provides a new concept for adjusting and controlling the elastic wave propagation in the composite structures, and provides a proper theoretical understanding of wave propagation in the damage tolerance-based design of piezotronics devices.

Sensitivity of the shear wave speed-stress relationship to soft tissue material properties and fiber alignment

The use of shear wave propagation to noninvasively measure material properties and loading in tendons and ligaments is a growing area of interest in biomechanics. Prior models and experiments suggest that shear wave speed primarily depends on the apparent shear modulus (i.e., shear modulus accounting for contributions from all constituents) at low loads, and then increases with axial stress when axially loaded. However, differences in the magnitudes of shear wave speeds between ligaments and tendons, which have different substructures, suggest that the tissue's composition and fiber alignment may also affect shear wave propagation. Accordingly, the objectives of this study were to (1) characterize changes in the apparent shear modulus induced by variations in constitutive properties and fiber alignment, and (2) determine the sensitivity of the shear wave speed-stress relationship to variations in constitutive properties and fiber alignment. To enable systematic variations of both constitutive properties and fiber alignment, we developed a finite element model that represented an isotropic ground matrix with an embedded fiber distribution. Using this model, we performed dynamic simulations of shear wave propagation at axial strains from 0% to 10%. We characterized the shear wave speed-stress relationship using a simple linear regression between shear wave speed squared and axial stress, which is based on an analytical relationship derived from a tensioned beam model. We found that predicted shear wave speeds were both in-range with shear wave speeds in previous in vivo and ex vivo studies, and strongly correlated with the axial stress (R2 = 0.99). The slope of the squared shear wave speed-axial stress relationship was highly sensitive to changes in tissue density. Both the intercept of this relationship and the apparent shear modulus were sensitive to both the shear modulus of the ground matrix and the stiffness of the fibers' toe-region when the fibers were less well-aligned to the loading direction. We also determined that the tensioned beam model overpredicted the axial tissue stress with increasing load when the model had less well-aligned fibers. This indicates that the shear wave speed increases likely in response to a load-dependent increase in the apparent shear modulus. Our findings suggest that researchers may need to consider both the material and structural properties (i.e., fiber alignment) of tendon and ligament when measuring shear wave speeds in pathological tissues or tissues with less well-aligned fibers.

Nonlinear Behaviour of Concrete Buttress Dams under High-Frequency Excitations Taking into Account Topographical Amplifications

Concrete buttress dams could potentially be susceptible to high-frequency vibrations, especially in the cross-stream direction, due to their slender design. Previous studies have mainly focused on low-frequency vibrations in stream direction using a simplified foundation model with the massless method, which does not consider topographic amplifications. This paper therefore investigates the nonlinear behaviour of concrete buttress dams subjected to high-frequency excitations, considering cross-stream vibrations. For comparison, the effect of low-frequency excitations is also investigated. The influence of the irregular topography of the foundation surface on the amplification of seismic waves at the foundation surface and thus in the dam is considered by a rigorous method based on the domain-reduction method using the direct finite element method. The sensitivity of the calculated response of the dam to the free-field modelling approach is investigated by comparing the result with analyses using an analytical method based on one-dimensional wave propagation theory and a massless approach. Available deconvolution software is based on the one-dimensional shear wave propagation to transform the earthquake motion from the foundation surface to the corresponding input motion at depth. Here, a new deconvolution method for both shear and pressure wave propagation is developed based on an iterative time-domain procedure using a one-dimensional finite element column. The examples presented showed that topographic amplifications of high-frequency excitations have a significant impact on the response of this type of dam. Cross-stream vibrations reduced the safety of the dam due to the opening of the joints and the increasing stresses. The foundation modelling approach had a significant impact on the calculated response of the dam. The massless method produced unreliable results, especially for high-frequency excitations. The free-field modelling with the analytical method led to unreliable joint openings. It is therefore recommended to use an accurate approach for foundation modelling, especially in cases where nonlinearity is considered.

Incomplete soil‐foundation contact and foundation input motion: From numerical analysis to field evidence

AbstractThis paper presents how incomplete wall contact between the foundation side‐walls and the surrounding soil alters the foundation input motion (FIM) of rectangular rigid boxes. The foundations are considered to have square sections embedded in a homogeneous linear half‐space. The free‐field motion (FFM) is assumed to be a vertical propagating shear wave. The foundation inputs in three translational and three rotational degrees of freedom (DOFs) were calculated using finite element analysis. Three additional net translational inputs were also introduced to cover movements along all six DOFs and remove the complexity of dealing with the rotational motions. Numerous models with incomplete soil‐foundation contacts were constructed and related FIMs were examined numerically. The key results show that an incomplete contact can activate all six DOFs, even under translational FFM. In some cases, the net input motion reaches ordinates of four times the peak value counterpart in the FFM. This ratio, in perpendicular horizontal and, also, vertical directions, reaches 0.7 and 0.2, respectively. Given the field evidence observations, it is concluded that the odd trends reported in the literature for kinematic transfer functions (TFs), which have not been justified to date, may be caused by a partial soil‐foundation contact.

High-temperature EMAT with double-coil configuration generates shear and longitudinal wave modes in paramagnetic steel

The non-contact nature of electromagnetic acoustic transducers (EMATs) allows a continuous operation at high temperatures without physical coupling. The existing high-temperature EMATs are mainly shear-wave EMATs, and there are few reports on shear-longitudinal wave or longitudinal-wave EMATs due to the low intensity of the horizontal magnetic field. However, a desirable EMAT design characteristic is the possibility of selecting to generate different acoustic wave modes for various engineering applications. In this paper, a high-temperature EMAT with a double-coil configuration on waveform generation in paramagnetic steel was studied. By adjusting the configuration relationship between the electromagnetic coil and the EMAT eddy-current coil, the selective generation of shear-wave, longitudinal-wave, and shear-longitudinal wave modes was realized. According to quantitative analysis of shear and longitudinal waves generated by the double-coil EMAT, the amplitude ratio of shear and longitudinal waves was about 1 when the diameter of the EMAT eddy-current coil was equal to the inner diameter of the electromagnetic coil. Furthermore, shear-wave mode and shear-longitudinal wave mode high-temperature EMATs were designed and fabricated. The EMAT was placed in a high-temperature environment to continuously measure the paramagnetic steel SUS304. The amplitudes of the shear wave and longitudinal wave at 500 °C decreased by 10.2 times and 3.8 times, respectively, compared with that at 25 °C. The designed EMAT can selectively generate and receive different bulk acoustic wave modes at high temperatures.

Low-frequency (105 Hz) shear modulus of nanosuspension

The low-frequency shear wave propagation in a suspension of silica nanoparticles in a polyethylsiloxane liquid was studied. The shear wave length was measured on ultrasonic interferometer, and it is equal to 55 μm. The value of the tangent of the mechanical losses angle is determined to be 0.18. These parameters were used to calculate the shear modulus of the investigated colloidal suspension; its value is 0.15‒105 Pa. The results obtained are in quite agreement with the data obtained by another way of the acoustic resonance method.