Frequency Shear Wave Research Articles

Seismic stability of obliquely loaded circular plate anchors

The vertical uplift resistance of obliquely loaded circular plate anchors buried in sand subjected to seismic loadings has been obtained in this paper. The pseudo-dynamic approach based on kinematic theorem of limit analysis has been applied for performing the analysis in which the nonlinear acceleration distributions are incorporated considering standing shear (S) and primary (P) wave propagations within the soil medium. Results are obtained in terms of seismic uplift factor (Fγs) due to soil self-weight component for a wide range of parameters. Through a parametric study, the effects of different parameters including normalized frequencies of Shear (S) and Primary (P) waves and damping ratio (ξ) of soil are highlighted. On account of amplified accelerations effects, the value of Fγs has been found to drastically reduce with an increase in load inclination (θ), horizontal and vertical seismic acceleration coefficients (kh and kv). The results show that the influence of damping ratio (ξ) of soil becomes more dominant particularly for frequencies close to the fundamental frequency of P wave.

Finite deformation elastography of articular cartilage and biomaterials based on imaging and topology optimization

Tissues and engineered biomaterials exhibit exquisite local variation in stiffness that defines their function. Conventional elastography quantifies stiffness in soft (e.g. brain, liver) tissue, but robust quantification in stiff (e.g. musculoskeletal) tissues is challenging due to dissipation of high frequency shear waves. We describe new development of finite deformation elastography that utilizes magnetic resonance imaging of low frequency, physiological-level (large magnitude) displacements, coupled to an iterative topology optimization routine to investigate stiffness heterogeneity, including spatial gradients and inclusions. We reconstruct 2D and 3D stiffness distributions in bilayer agarose hydrogels and silicon materials that exhibit heterogeneous displacement/strain responses. We map stiffness in porcine and sheep articular cartilage deep within the bony articular joint space in situ for the first time. Elevated cartilage stiffness localized to the superficial zone is further related to collagen fiber compaction and loss of water content during cyclic loading, as assessed by independent T2 measurements. We additionally describe technical challenges needed to achieve in vivo elastography measurements. Our results introduce new functional imaging biomarkers, which can be assessed nondestructively, with clinical potential to diagnose and track progression of disease in early stages, including osteoarthritis or tissue degeneration.

Recent advances in the physics of polymer systems

Recent advances in the physics of polymer systems

Preliminary clinical experience with shear wave dispersion (SWD) imaging of the liver

Quantifying the extent of liver fibrosis is important in the management of patients with chronic liver disease. Liver biopsy is the gold standard for diagnosis and grading of liver fibrosis. However, liver biopsy is costly, invasive and may have associated complications. Liver biopsy may also be limited by sampling variability due to the heterogeneous nature of liver fibrosis. Liver biopsy limitations have led to the development of non-invasive techniques for the evaluation of and monitoring of liver fibrosis. These include transient elastography (TE) (Fibroscan©), shear wave elastography (SWE) and magnetic resonance elastography (MRE). These technologies use algorithms for quantifying liver elasticity and have all shown promising results for non-invasive fibrosis staging. However, both TE and SWE have limitations including in patients with inflammation (hepatitis) and/or steatosis. Liver diseases such as non-alcoholic steatohepatitis (NASH), non-alcoholic fatty liver disease (NAFLD) and acute hepatitis have been reported to increase liver viscosity. It is proposed that these alterations in liver viscosity alter the propagation of shear waves, and that a more accurate assessment would be obtained by assessing both the elasticity and viscosity i.e. viscoelastic properties in the liver. Shear wave dispersion (SWD) is a new imaging technology software that has been developed on the Canon Aplio i-series for assessing the dispersion of the shear wave. In viscoelastic tissue, shear wave speed undergoes frequency dispersion i.e. change in the shear wave speed dependent on the shear wave frequency. The units of measurement are m/s/kHz. In perfectly elastic tissue, shear wave speed is constant regardless of the shear wave frequency. However, in viscoelastic tissue, shear wave speed varies depending on the shear wave frequency i.e. shear wave dispersion. We present the initial findings of using this new liver imaging tool in a sequential group of patients referred for liver biopsy in a tertiary level hospital. The indications were for the assessment of chronic liver disease, with exclusion of patients with suspected or confirmed malignancy. In this group, the manufacturer recommended SWD reference value was compared to liver biopsy findings to identify whether it could discriminate between patients with, and without inflammation (hepatitis).

Particle paths in nonlinear Schrödinger models in the presence of linear shear currents

We investigate the effect of constant-vorticity background shear on the properties of wavetrains in deep water. Using the methodology of Fokas (A Unified Approach to Boundary Value Problems, 2008, SIAM), we derive a higher-order nonlinear Schrödinger equation in the presence of shear and surface tension. We show that the presence of shear induces a strong coupling between the carrier wave and the mean-surface displacement. The effects of the background shear on the modulational instability of plane waves is also studied, where it is shown that shear can suppress instability, although not for all carrier wavelengths in the presence of surface tension. These results expand upon the findings of Thomas et al. (Phys. Fluids, vol. 24 (12), 2012, 127102). Using a modification of the generalized Lagrangian mean theory in Andrews & McIntyre (J. Fluid Mech., vol. 89, 1978, pp. 609–646) and approximate formulas for the velocity field in the fluid column, explicit, asymptotic approximations for the Lagrangian and Stokes drift velocities are obtained for plane-wave and Jacobi elliptic function solutions of the nonlinear Schrödinger equation. Numerical approximations to particle trajectories for these solutions are found and the Lagrangian and Stokes drift velocities corresponding to these numerical solutions corroborate the theoretical results. We show that background currents have significant effects on the mean transport properties of waves. In particular, certain combinations of background shear and carrier wave frequency lead to the disappearance of mean-surface mass transport. These results provide a possible explanation for the measurements reported in Smith (J. Phys. Oceanogr., vol. 36, 2006, pp. 1381–1402). Our results also provide further evidence of the viability of the modification of the Stokes drift velocity beyond the standard monochromatic approximation, such as recently proposed in Breivik et al. (J. Phys. Oceanogr., vol. 44, 2014, pp. 2433–2445) in order to obtain a closer match to a range of complex ocean wave spectra.

Elastic instabilities and shear waves in hyperelastic composites with various periodic fiber arrangements

We investigate the influence of fiber arrangement on elastic instabilities and shear wave propagation in hyperelastic 3D fiber composites (FCs) with periodic rectangular arrays of cylindrical fibers. We show that elastic instabilities and shear waves propagating along the fibers in uniaxially deformed FCs can be tuned through the choice of the periodicity of fiber arrangements (or periodic unit cell aspect ratio b/a) of FCs. In particular, we find that the range of deformations, where FCs are mechanically stable, decreases with an increase in the periodicity aspect ratio. Moreover, we identify the bounds for the critical stretches in FCs with periodic rectangular arrays of fibers. We find that the FC critical stretches are bounded by the critical values for corresponding 3D laminates (upper bound) and FCs with square arrays of fibers (lower bound). In FCs with large volume fractions of fibers (e.g. 25%), the polarization directions of the long shear waves start rotating upon approaching critical deformation. This indicates that fibers develop buckling shapes in non-principal planes. In FCs with small volume fractions of fibers (e.g. 5%), polarizations of the shear waves (of the lowest frequencies) barely changes the direction upon attaining the critical deformation; hence, buckling of fibers initially develops in one of the principal planes, depending on the periodicity aspect ratio of FCs.

Using surface wave amplitude spectra to estimate the source depth of Sichuan Jiuzhaigou <italic>M</italic>7.0 earthquake

The accurate source depth of earthquake is important for understanding plate-tectonic processes and structure of seismic faults, identifying natural earthquake and non-natural earthquake. The amplitude formula of seismic surface wave shows that the amplitude of surface wave is closely related to the focal mechanism, the azimuth from epicenter to station and the source depth. When the focal mechanism and the observation position are determined, the excitation energy of surface wave is sensitive to source depth. The surface wave amplitude spectrum can be applied to determine the focal depth. The amplitude energy of shallow earthquake shows the “notch” phenomenon in band of frequency between 0.01 and 0.08 Hz in amplitude spectra, i.e. the attenuation of amplitude energy. The position of the frequency-dependent “notch” is related to the source depth. In this study, the relationship between the position of the “notch” and the source depth is analyzed by theoretical seismogram. We obtain the amplitude spectrums of the far-field at different source depths and then locate the source depth by means of comparing with observed seismic waveforms. By the amplitude spectrum of theoretical surface wave, small changes in the source depth can cause the variation of the amplitude spectrum so that the source depth of shallow earthquake can be accurately determined. The focal mechanism is coupled with the source depth. In order to analyze the influence of the disturbance of source mechanism to source depth determination, the focal mechanism of Jiuzhaigou earthquake was inversed, with disturbance of 10 degrees to strike, dip and rake. The results show only rather small changes in locating depth. In order to eliminate the influence of low frequency noise, shear wave and surface wave of short-period on amplitude spectra, this study adopts the AK135 velocity model to remove the dispersion. In this study, the seismic source depth of the Jiuzhaigou M 7.0 earthquake of 8 August 2017 in Sichuan province, China, was determined at 8.2 km by the energy attenuation characteristics of Rayleigh amplitude spectrum.

Rayleigh-type wave in a nonlocal elastic solid with voids

Abstract The present work is concerned with propagation of surface waves in an isotropic homogeneous nonlocal elastic solid half-space with voids. Dispersion relation for Rayleigh-type surface wave has been derived, which is found to be complex in nature. The variation of phase speed and corresponding attenuation of Rayleigh-type wave against frequency, nonlocality and void parameters is computed for a specific model and presented graphically. It is shown that only one mode of Rayleigh-type wave exists, which faces a critical frequency same as the critical frequency of shear wave. The dispersion arises due to the presence of voids and nonlocality in the medium. The particle motion is elliptical and a tilt in the plane of particle motion occurs due to the presence of void parameter ‘τ’ in the medium. In the low frequency range, the variation in ellipticity is due to the presence of voids in the medium. Some particular cases have been deduced from the present formulation.

Acoustic Radiation Force-Induced Creep-Recovery (ARFICR): A Noninvasive Method to Characterize Tissue Viscoelasticity.

Ultrasound shear wave elastography is a promising noninvasive, low cost, and clinically viable tool for liver fibrosis staging. Current shear wave imaging technologies on clinical ultrasound scanners ignore shear wave dispersion and use a single group velocity measured over the shear wave bandwidth to estimate tissue elasticity. The center frequency and bandwidth of shear waves induced by acoustic radiation force depend on the ultrasound push beam (push duration, -number, etc.) and the viscoelasticity of the medium, and therefore are different across scanners from different vendors. As a result, scanners from different vendors may give different tissue elasticity measurements within the same patient. Various methods have been proposed to evaluate shear wave dispersion to better estimate tissue viscoelasticity. A rheological model such as the Kelvin-Voigt model is typically fitted to the shear wave dispersion to solve for the elasticity and viscosity of tissue. However, these rheological models impose strong assumptions about frequency dependence of elasticity and viscosity. Here, we propose a new method called Acoustic Radiation Force Induced Creep-Recovery (ARFICR) capable of quantifying rheological model-independent measurements of elasticity and viscosity for more robust tissue health assessment. In ARFICR, the creep-recovery time signal at the focus of the push beam is used to calculate the relative elasticity and viscosity (scaled by an unknown constant) over a wide frequency range. Shear waves generated during the ARFICR measurement are also detected and used to calculate the shear wave velocity at its center frequency, which is then used to calibrate the relative elasticity and viscosity to absolute elasticity and viscosity. In this paper, finite-element method simulations and experiments in tissue mimicking phantoms are used to validate and characterize the extent of viscoelastic quantification of ARFICR. The results suggest that ARFICR can measure tissue viscoelasticity reliably. Moreover, the results showed the strong frequency dependence of viscoelastic parameters in tissue mimicking phantoms and healthy liver.

Cut-off frequencies of circumferential horizontal shear waves in various functionally graded cylinder shells

In this study, cut-off frequencies of the circumferential SH waves in functionally graded piezoelectric-piezomagnetic material (FGPPM) cylinder shells with traction free, electrical and magnetic open boundary conditions are investigated analytically. The Wentzel-Kramers-Brillouin (WKB) method is employed for solving differential equations with variable coefficients for general cases. For comparison, Bessel functions and Kummer functions are used for solving cut-off frequency problems in homogenous and ideal FGPPM cylinder shells. It is shown that the WKB solution for the cut-off frequencies has good precise. The set of cut-off frequencies is a series of approximate arithmetic progressions, for which the difference is a function of the density and the effective elastic parameter. The relationship between the difference and the gradient coefficient is described. These results provide theoretical guidance for the non-destructive evaluation of curved shells based on the cut-off frequencies.

Are rapid changes in brain elasticity possible?

Elastography of the brain is a topic of clinical and preclinical research, motivated by the potential for viscoelastic measures of the brain to provide sensitive indicators of pathological processes, and to assist in early diagnosis. To date, studies of the normal brain and of those with confirmed neurological disorders have reported a wide range of shear stiffness and shear wave speeds, even within similar categories. A range of factors including the shear wave frequency, and the age of the individual are thought to have a possible influence. However, it may be that short term dynamics within the brain may have an influence on the measured stiffness. This hypothesis is addressed quantitatively using the framework of the microchannel flow model, which derives the tissue stiffness, complex modulus, and shear wave speed as a function of the vascular and fluid network in combination with the elastic matrix that comprise the brain. Transformation rules are applied so that any changes in the fluid channels or the elastic matrix can be mapped to changes in observed elastic properties on a macroscopic scale. The results are preliminary but demonstrate that measureable, time varying changes in brain stiffness are possible simply by accounting for vasodynamic or electrochemical changes in the state of any region of the brain. The value of this preliminary exploration is to identify possible mechanisms and order-of-magnitude changes that may be testable in vivo by specialized protocols.

Development of a Non-collinear Nonlinear Ultrasonic-Based Technique for the Assessment of Crack Tip Deformation

Non-collinear nonlinear ultrasonic (NCNLU) wave mixing technique has been established to study the localized plastic deformation at the crack tip during fatigue. A pair of ultrasonic shear wave was mixed non-collinearly to obtain a longitudinal wave of frequency equal to the sum of the two shear wave frequencies under a resonant condition. Experiments were carried out on notched 9Cr-1Mo 3-point bend specimen during high-cycle fatigue. The variation of the NCNLU parameter with the stress accumulation at the crack tip during the fatigue crack initiation and propagation and mapping of the deformation zone around the crack tip are described in this paper.

Shear wave velocity in sand considering the effects of frequency based on particle contact theory

Since the shear waves involved in in-situ and laboratory measurement methods vary significantly in terms of the frequency range, it is necessary to consider the effects of frequency on the shear wave velocity. In this study, sand particles are assumed to be spherical solid particles with an equal radius and identical material properties, and sand skeletons are regarded as granular aggregations generated through the random packing of sand particles. It is also assumed that the sand particles only undergo elastic deformation during shear wave propagation. Based on a spherical particle model, a formula is obtained for calculating the shear wave velocity in sand, with the shear wave frequency as an extra influencing parameter. The quantitative calculations demonstrate that the shear wave velocity decreases with an increase of sand porosity, and accelerates with increases of vertical effective stress and elastic modulus of the sand particles. It is also indicated that both the particle density and Poisson’s ratio of the sand particles have negligible effects on the shear wave propagation. The frequency dispersion characteristics of shear wave propagating in sand are also discussed. Moreover, the critical frequency is defined and its analytical expression is derived. The calculation results obtained using the proposed equations agree well with the in-situ measurement results and bender element test data.

Cardiac Shear Wave Velocity Detection in the Porcine Heart

Cardiac muscle stiffness can potentially be estimated non-invasively with shear wave elastography. Shear waves are present on the septal wall after mitral and aortic valve closure, thus providing an opportunity to assess stiffness in early systole and early diastole. We report on the shear wave recordings of 22 minipigs with high-frame-rate echocardiography. The waves were captured with 4000 frames/s using a programmable commercial ultrasound machine. The wave pattern was extracted from the data through a local tissue velocity estimator based on one-lag autocorrelation. The wave propagation velocity was determined with a normalized Radon transform, resulting in median wave propagation velocities of 2.2 m/s after mitral valve closure and 4.2 m/s after aortic valve closure. Overall the velocities ranged between 0.8 and 6.3 m/s in a 95% confidence interval. By dispersion analysis we found that the propagation velocity only mildly increased with shear wave frequency.

Breast Cancer Imaging by Color Doppler Shear Wave Elastography

In shear wave elastography, complicated shear wave wave-front caused by the reflection, refraction, and diffraction at the tissue boundary degrades the accuracy of velocity measurement. If the shear wave wave-front is visualized in real-time, the accuracy increases because the velocity is estimated along the shear wave propagation direction. Moreover, observed wave-front pattern provides valuable information about tissue structure, which makes the detection of the stiff part easier. We have proposed a novel shear wave elastography (Color Doppler Shear Wave Imaging: CD SWI) [Y.Yamakoshi, et al. IEEE tans on UFFC. 64, 340 (2017)]. Continuous shear wave of a frequency that is n/4 (n being an odd number) times the PRF is introduced from the tissue surface. Then, the shear wave wave-front appears simultaneously as a stripe pattern on conventional ultrasound color Doppler image. This cost-effective shear wave elastography is implemented on ACUSON S3000 (Siemens). The shear wave frequency is 235.3Hz. Shear wave velocity measured by CD SWI was compared with that by ARFI for breast phantom. Shear wave velocities by two methods showed good correlation, but the standard deviation of CD SWI was 42% of that of ARFI. Malignant lesions were imaged by CD SWI as an area with high shear wave velocity. Inherent shear wave propagation around a malignant lesion was also observed. It is suggested that a combination of shear wave image of CD SWI and B-mode image improves the sensitivity in detection of malignant lesions in breast tissue.

Shear Wave Imaging of Breast Tissue by Color Doppler Shear Wave Elastography.

Shear wave elastography is a distinctive method to access the viscoelastic characteristic of the soft tissue that is difficult to obtain by other imaging modalities. This paper proposes a novel shear wave elastography [color Doppler shear wave imaging (CD SWI)] for breast tissue. Continuous shear wave is produced by a small lightweight actuator, which is attached to the tissue surface. Shear wave wavefront that propagates in tissue is reconstructed as a binary pattern that consists of zero and the maximum flow velocities on color flow image (CFI). Neither any modifications of the ultrasound color flow imaging instrument nor a high frame rate ultrasound imaging instrument is required to obtain the shear wave wavefront map. However, two conditions of shear wave displacement amplitude and shear wave frequency are needed to obtain the map. However, these conditions are not severe restrictions in breast imaging. This is because the minimum displacement amplitude is [Formula: see text] for an ultrasonic wave frequency of 12 MHz and the shear wave frequency is available from several frequencies suited for breast imaging. Fourier analysis along time axis suppresses clutter noise in CFI. A directional filter extracts shear wave, which propagates in the forward direction. Several maps, such as shear wave phase, velocity, and propagation maps, are reconstructed by CD SWI. The accuracy of shear wave velocity measurement is evaluated for homogeneous agar gel phantom by comparing with the acoustic radiation force impulse method. The experimental results for breast tissue are shown for a shear wave frequency of 296.6 Hz.

Color Doppler shear wave imaging and its application to breast imaging

Imaging of continuous shear wave (CSW) induced by a small mechanical vibrator attached on tissue surface is low-cost and easy-to-use elastography. A problem of CSW is shear wave's reflection and refraction at tissue boundary, which degrade the accuracy of shear wave velocity estimation. We propose a novel shear wave elastography of CSW (Color Doppler Shear Wave Imaging: CD-SWI). Shear wave’s propagation in soft tissue is reconstructed directly without adding any function to conventional color flow imaging instrument. Two conditions for shear wave frequency and displacement amplitude are required to obtain maps. However, they are not severe restrictions because frequency is chosen among several frequencies suited for elastography and the required displacement amplitude is a few tens of microns. Both Fourier analysis along time axis and a directional filter on wave-number vector space improve image quality. Accuracy and image quality of CD-SWI are evaluated by comparing with ARFI method. CD-SWI is applied to breast in vivo and shear wave propagation in breast (f = 297 Hz) is observed. Inherent shear wave propagation in soft tissue reconstructed by CD-SWI, such as diffraction and refraction around tissue with different stiffness as well as shear wave velocity, may give novel information in tissue characterization by shear wave.

Ultrasonic method to characterize shear wave propagation in micellar fluids.

Viscoelastic micellar fluid characteristics have been measured with mechanically generated shear waves and showed good agreement to shear oscillatory methods. In this paper, shear waves in wormlike micellar fluids using ultrasound were successfully generated and detected. Micellar fluids of different concentrations (100, 200, 300, and 400 mM) were studied with ultrasound-based and conventional rheology methods. The measured micellar fluid complex modulus from oscillatory shear tests between 0.001 and 15.91 Hz was characterized with an extended Maxwell fluid model. The elastic and viscous parameters found using rheological testing were used to estimate shear wave phase velocity over a frequency range from 100 to 500 Hz, and compared to shear wave velocity measured with ultrasound-based methods with a mean absolute error 0.02 m/s. The shear wave frequency content was studied and an increase in shear wave center frequency was found as a function of micellar fluid concentration. Moreover, the bias found in the shear wave group velocity with respect to rheological measurement is attributed to the micellar fluid viscous component. Finally, the shear wave phase velocity evaluated at the center frequency agreed well with the rheological measurements.

Particulate damping media and isolation of ground-borne vibrations

Ground borne vibration can be dissipated by attenuation, absorption, frictional, and viscous damping before being transmitted to the buildings, by means of a suitable particulate media below the structure. We show that the band-pass behavior of particulate media for mechanical vibrations can also result in significant attenuation of vibrations for frequencies on either side of the pass-band. Sample particulate structures are subjected experimentally to the longitudinal and shear waves of different amplitude and frequencies, generated by electro-mechanical shakers vibrating in different directions. The amount of vibration damping by attenuation, resonance absorption, frictional and viscous dissipations are determined experimentally. The pressure wave and shear-waves, generated experimentally by the electro-mechanical shakers, are combined to simulate realistic ground borne vibrations. Damping media consisting of composite materials with different elastic properties are tested as tuned absorbers. The goal is to determine the damping characteristics for most efficient absorption of vibration, of different intensity and frequency. The results can be used to design tuned dampers for specific ground borne vibrations and determine material characteristics for dissipation of ground borne vibrations at large scale.

Seismic Active Earth Pressure on Walls Using a New Pseudo-Dynamic Approach

Seismic active soil thrust, soil pressure distribution and overturning moment are obtained in closed form using a new pseudo-dynamic approach based on standing shear and primary waves propagating on a visco-elastic backfill overlying rigid bedrock subjected to both harmonic horizontal and vertical acceleration. Seismic waves respect the zero stress boundary condition at the soil surface, backfill is modeled as a Kelvin–Voigt medium and a planar failure surface is assumed in the analysis. Effects of a wide range of parameters such as amplitude of base accelerations, soil shear resistance angle, soil wall friction angle, damping ratio are discussed. Results of the parametric study indicate that amplitude of the horizontal base acceleration and soil shear resistance angle are the factors most influencing active pressure distribution whereas the presence of the vertical acceleration always results in a quite small increase in seismic active thrust. Damping ratio is important mainly close to the fundamental frequency of shear wave where seismic active thrust is maximum. Unlike the original pseudo-dynamic approach the effect of a different frequency for S-wave and P-wave is considered in the analysis. Seismic active thrust is found to increase when the frequency of P-wave is greater than that of S-wave. The results obtained by the proposed approach are found to be in agreement with previous studies, provided that the seismic input is adapted to include amplification effects.