Longitudinal Shear Wave Research Articles

In situ elastic constant determination of unidirectional CFRP composites via backwall reflected multi-mode ultrasonic bulk waves using a linear array probe

The determination of elastic constants of a transversely isotropic carbon fiber reinforced plastic (CFRP) composite is the prerequisite of mechanical strength calculation, material degradation evaluation, ultrasonic non-destructive testing for main load-bearing CFRP structures both after manufacturing and in service. Conventional ultrasonic methods request extra sample preparation, water immersion condition or special designed goniometric devices to rotate the test structures, making the elastic constants measurement expensive, inconvenient and not in situ. In this paper, a novel ultrasonic method that enables in situ determination of elastic constants via backwall reflection method (BRM) using a linear array probe is proposed. The BRM can achieve single sided measurement of ultrasonic travel times in various directions including the fiber direction using different pairs of transmitter and receiver array elements. Both quasi longitudinal and quasi shear waves are captured via the mode conversions from the multiple surface reflections. All elastic constants are determined through the particle swarm optimization by minimizing the sum of the squared deviations between the BRM measured and theoretically calculated multi-mode bulk wave travel times in the fiber orthogonal and parallel planes. This method is experimentally verified on a 4.45 mm thick unidirectional T700 carbon fiber/epoxy CFRP composite. The BRM measured Young's modulus in the fiber direction agrees well with that measured by tensile test, with a small deviation of −4.58%. This work proves that the proposed method is single sided, easy to operate, without the necessity of sample preparation, water immersion and extra rotation device, and can determine all elastic constants with high precision, which is therefore promising for in situ applications.

Longitudinal shear wave elasticity measurements of millimeter-sized biomaterials using a single-element transducer platform.

Temporal variations of the extracellular matrix (ECM) stiffness profoundly impact cellular behaviors, possibly more significantly than the influence of static stiffness. Three-dimensional (3D) cell cultures with tunable matrix stiffness have been utilized to characterize the mechanobiological interactions of elasticity-mediated cellular behaviors. Conventional studies usually perform static interrogations of elasticity at micro-scale resolution. While such studies are essential for investigations of cellular mechanotransduction, few tools are available for depicting the temporal dynamics of the stiffness of the cellular environment, especially for optically turbid millimeter-sized biomaterials. We present a single-element transducer shear wave (SW) elasticity imaging system that is applied to a millimeter-sized, ECM-based cell-laden hydrogel. The single-element ultrasound transducer is used both to generate SWs and to detect their arrival times after being reflected from the side boundaries of the sample. The sample’s shear wave speed (SWS) is calculated by applying a time-of-flight algorithm to the reflected SWs. We use this noninvasive and technically straightforward approach to demonstrate that exposing 3D cancer cell cultures to X-ray irradiation induces a temporal change in the SWS. The proposed platform is appropriate for investigating in vitro how a group of cells remodels their surrounding matrix and how changes to their mechanical properties could affect the embedded cells in optically turbid millimeter-sized biomaterials.

A New Design of the Dual-Mode and Pure Longitudinal EMAT by Using a Radial-Flux-Focusing Magnet.

An electromagnetic acoustic transducer (EMAT) is suitable for measuring the propagation time more accurately without causing abrasion to the transducer during testing due to the principle of its excitation. This work designs a flux-concentrating EMAT with a radial-flux-focusing permanent magnet to significantly enhance static magnetic field strength. Through theoretical analysis and finite element simulation, two kinds of coils are designed according to the concentration areas of the horizontal and vertical components of the magnetic field. One is used to generate pure longitudinal waves, and the other is used to generate both longitudinal waves and shear waves. The experimental comparison shows that the amplitudes of the pure longitudinal wave and the dual-mode wave excited by the two kinds of coils with the radial-flux-focusing magnet are more than two times higher than those with the ordinary magnet. Therefore, the flux-concentrating EMAT with the appropriate coil provides an insight into realizing more accurate detection where longitudinal wave detection is required.

Stress state near the cracks coming out from the ends of a thin rigid inclusion that is caused by the action of longitudinal shear waves

Stress state near the cracks coming out from the ends of a thin rigid inclusion that is caused by the action of longitudinal shear waves

An Iterative Method for Solving the Problem of Diffraction of Longitudinal Shear Waves on A System of Thin Rigid Inclusions

An Iterative Method for Solving the Problem of Diffraction of Longitudinal Shear Waves on A System of Thin Rigid Inclusions

Vibration and acoustic insulation properties of generalized phononic crystals

Based on the previous studies, the concept of generalized phononic crystals (GPCs) is further introduced into the cylindrical shell structures, and a type of cylindrical shells of generalized phononic crystals (CS-GPCs) is constructed. Subsequently, the structure field and acoustic-structural coupled field of that composite cylindrical shells are examined respectively in this paper. Considering the Bloch theorem is not capable of explaining the generalized periodic situation existing in this structure field, a new analysis method involving transferring matrix eigenvalue based on the mechanical state vector is proposed to calculate the energy band structure. Through observing the energy band structure, an obvious wave band gap is obtained when the elastic wave propagates in the CS-GPCs for modes with different order, whose forming mechanism includes two aspects, i.e., the wave front expansion effect and the Bragg scattering effect. In addition, we further explore the related influences of the longitudinal wave mode and shear wave mode in structure on these band gaps, and some conclusions are illustrated. For acoustic-structural coupled field, the expressions of the acoustic transmission coefficients for different modes are built, and the frequency responses are numerically calculated to verify the band gap characteristics of the CS-GPCs. Furthermore, the acoustic pressure distribution of the internal and external acoustic fields is also analyzed in detail, and the influence laws of the parameters (offset distance and frequency) of the line source on acoustical pressure distribution and its directivity are explored.

Characterizing Rayleigh wave and longitudinal shear wave propagation for measurements of elastic moduli using optical coherence elastography

Optical coherence elastography based on the measurements of elastic wave speeds can quantify elastic moduli in the wave propagation directions and provide high-resolution elasticity maps for tissue. Here, we simultaneously visualized a longitudinal shear wave propagating along the depth and a Rayleigh wave propagating in the lateral direction, and analyzed the propagation characteristics of the elastic waves, including group speeds, frequency spectra, and frequency-dependent wave speeds. The analysis of the propagation characteristics demonstrates the reliability of the elasticity quantification by measuring different types of speeds of the elastic waves.

Propagation characteristics of longitudinal wave, shear wave and bending wave in porous circular nanoplates

On the basis of nonlocal strain gradient theory, considering the material properties of porous FGM changing with thickness and the influence of moment of inertia, the wave equation of FG nano circular plate is derived by using the first-order shear deformation plate theory, by introducing dimensionless parameters, we transform the equations into dimensionless wave equations, and the dispersion relations of bending wave, shear wave and longitudinal wave are obtained by Laplace and Hankel integral transformation method. The influence of nonlocal parameter, porosity volume fraction, strain gradient parameters and power law index on the propagation characteristics of bending wave, shear wave and longitudinal wave in FG nano circular plate.

Repetitive optical coherence elastography measurements with blinking nanobombs.

Excitation of dye-loaded perfluorocarbon nanoparticles (nanobombs) can generate highly localized axially propagating longitudinal shear waves (LSW) that can be used to quantify tissue mechanical properties without transversal scanning of the imaging beam. In this study, we used repetitive excitations of dodecafluoropentane (C5) and tetradecafluorohexane (C6) nanobombs by a nanosecond-pulsed laser to produce multiple LSWs from a single spot in a phantom. A 1.5 MHz Fourier-domain mode-locked laser in combination with a phase correction algorithm was used to perform elastography. Multiple nanobomb activations were also monitored by detecting photoacoustic signals. Our results demonstrate that C6 nanobombs can be used for repetitive generation of LSW from a single spot for the purpose of material elasticity assessment. This study opens new avenues for continuous quantification of tissue mechanical properties using single delivery of the nanoparticles.

Parameter Recognition of Mode-Converted Wave in Single-Source Ultrasound Using Gabor Transform for Bolt Axial Stress Evaluation

In this paper, a novel parameter recognition method of mode-converted wave in single-source ultrasound is put forward and applied to the estimation of axial stresses in bolts. To overcome the distortion and aliasing of the mode-converted wave in single-source ultrasonic signal, a time-frequency parameter recognition method based on the Gabor transform is introduced to recognize the accurate time of flight (TOF) of the mode-converted wave. Based on the mode conversion of the single-source longitudinal ultrasound, a new nonlinear evaluation model based on acoustoelastic equation is derived to determine the axial stress of bolt. The performance of the proposed method is evaluated by comparing it with the commonly used TOF ratio method of longitudinal wave and shear wave (L-S). The experiment result shows that the proposed method is more effective in detecting the connection status of bolted joints than the traditional L-S method.

Modeling wavefields in saturated elastic porous media based on thermodynamically compatible system theory for two-phase solid-fluid mixtures

A two-phase model and its application to wavefields numerical simulation are discussed in the context of modeling of compressible fluid flows in elastic porous media. The derivation of the model is based on a theory of thermodynamically compatible systems and on a model of nonlinear elastoplasticity combined with a two-phase compressible fluid flow model. The governing equations of the model include phase mass conservation laws, a total momentum conservation law, an equation for the relative velocities of the phases, an equation for mixture distortion, and a balance equation for porosity. They form a hyperbolic system of conservation equations that satisfy the fundamental laws of thermodynamics. Two types of phase interaction are introduced in the model: phase pressure relaxation to a common value and interfacial friction. Inelastic deformations also can be accounted for by source terms in the equation for distortion. The thus formulated model can be used for studying general compressible fluid flows in a deformable elastoplastic porous medium, and for modeling wave propagation in a saturated porous medium. Governing equations for small-amplitude wave propagation in a uniform porous medium saturated with a single fluid are derived. They form a first-order hyperbolic PDE system written in terms of stress and velocities and, like in Biot’s model, predict three type of waves existing in real fluid-saturated porous media: fast and slow longitudinal waves and shear waves. For the numerical solution of these equations, an efficient numerical method based on a staggered-grid finite difference scheme is used. The results of solving some numerical test problems are presented and discussed.

Characterization of soft tissue tumours with ultrasound, shear wave elastography and MRI.

To predict accurately whether a soft tissue mass was benign or malignant and to characterize its type using ultrasound, shear wave elastography and MRI. We hypothesized that with the addition of shear wave elastography, it would be possible to determine a threshold velocity value to classify a lesion as benign or malignant. A total of 151 consecutive, consenting adult patients were prospectively recruited to this study in a tertiary referral musculoskeletal oncology centre. All lesions were assessed with ultrasound, including B mode, Doppler and shear wave elastography measurements. One hundred thirty-eight patients also underwent MRI of the lesion. A histological diagnosis was obtained for all lesions. Malignant lesions were larger than benign lesions and had a greater Doppler activity. There was no useful threshold shear wave velocity to differentiate between benign and malignant lesions. Longitudinal and transverse shear wave velocities were strongly positively correlated with each other. An inverse correlation was shown with lesion size and depth, regardless of whether it was benign or malignant. A logistic regression model combining the ultrasound and MRI characteristics did not confidently classify a lesion as benign or malignant and was inferior to expert opinion. The strongest predictors of malignancy are large lesion size and high vascularity. The combination of all ultrasound characteristics (including shear wave elastography) and MRI features does not confidently classify a lesion as benign or malignant, and histological diagnosis remains the gold standard.

Statistical and Texture Descriptors of Symptomatic Plantar Fasciitis Using Ultrasound Shear Wave Elastography

Plantar fasciitis (PFis) is a common cause of heel pain. This study aims to assess the plantar fascia (PF) quantitatively by using feature descriptors and seek valuable imaging biomarkers that can reliably diagnose PFis. A total of 63 participants underwent B-mode and longitudinal shear wave elastography (SWE) on unilateral plantar fasciae. To characterize the statistical and spatial texture features of the PF, ten statistical descriptors of the shear modulus in the standardized region of interest in PF and twenty texture descriptors in the SWE measurement window (in both horizontal and vertical directions) are proposed. Four statistical quantities ( mode, avg, med, qG ) and four texture descriptors ( autoc, sosvh, savgh svarh ) showed potential for diagnosing PFis, based on significant differences between the PFis and the healthy groups. Receiver operating characteristic (ROC) curve analysis revealed that the statistical descriptors have area under the curve (AUC) of approximately 0.9 (likelihood ratio >6.798) and the texture descriptors have AUC of approximately 0.85 (likelihood ratio >3.195). Combinations of statistical and texture descriptors can achieve higher AUCs~0.968. In addition, these descriptors were related to the clinical indices (body mass index and visual analogue scale) with Spearman’s correlation coefficient of $r=-0$ .5~−0.4( $p ). The proposed statistical and texture descriptors showed valuable potential if applied to clinical shear wave elastography for the diagnosis of PFis. This work lays the foundation of using ultrasound shear wave image features for describing symptomatic PFis.

Effects of Adhesive Parameters on Dispersion Characteristics of Ultrasonic Guided Waves in Composite Pipes

The aim of the investigation presented here was to understand how the viscosity parameters of an adhesive layer affect group velocity and attenuation of the double-layer adhered pipe. Various parameter combinations (attenuation of longitudinal wave and shear wave, pαL and qαT; thickness, d; and density, nρ) were utilized in order to generate different uncured degrees of the adhesive layer. In the frequency range 0∼500 kHz, the group velocity dispersion curves and attenuation dispersion curves were obtained from these models. Then, the group velocity and attenuation of the two commonly used modes, L0,2 and T0,1, were compared and analyzed. The results have shown that it is important to remark that little effect on group velocity was caused, and significant linear increases of attenuation occur with increase in q, d, and n. However, variable p had little effect on attenuation; more modes emerged when d increased or n decreased, causing difficulties on mode identification and signal processing. The numerical results provided a useful way to evaluate bonding quality by measuring the group velocity and attenuation in the pipelines.

The logging recognition of solid bitumen and its effect on physical properties, AC, resistivity and NMR parameters

Abstract Solid bitumen not only strongly damages the reservoir properties, but it is easily confused with oil and gas in the conventional classification logging interpretation, which seriously affects the effective recognition of oil and gas. Thus, it leads to a deceptive estimation of the reserve. Focusing on the above problems, this study takes Jurassic solid bitumen-containing reservoirs from the Santai-Northern Santai area in the Junggar Basin as an example, and aims to quantitatively evaluate the impact of solid bitumen on the porosity, permeability, resistivity, AC (Acoustic) and NMR (Nuclear Magnetic Resonance), with a comparison between the values of these parameters before and after core bitumen dissolution, as well as to establish an NMR identification method for solid bitumen. The results show that solid bitumen can damage the pore structure of the reservoir and cause a reduction of porosity and permeability. The content of solid bitumen is linearly correlated with the change of porosity and permeability. After solid bitumen dissolved, the resistivity decreased, the longitudinal wave time difference (Vp) and shear wave time difference (Vs) increased, and the shear wave time difference changed noticeably. The content of solid bitumen is exponentially correlated with the change of resistivity, and linearly correlated with the change of longitudinal wave time difference and shear wave time difference. Solid bitumen had a short transverse relaxation time and a response range of 10–1000 μs (Peak 1) on the T2 map. Bitumen-containing sandstone had 3 peaks on the T2 map. Peak 1 decreased, while Peaks 2 and 3 increased after the solid bitumen dissolved. Solid bitumen can be characterized by a typical short time lag of the transverse wave, a bigger density porosity than the NMR porosity and small values of T1LM and T2LM, which led to an effective recognition of the layers of solid bitumen. The results are significant for the exploration and development of oilfields.

Longitudinal shear waves for elastic characterization of tissues in optical coherence elastography

In dynamic optical coherence elastography (OCE), surface acoustic waves are the predominant perturbations. They constrain the quantification of elastic modulus to the direction of wave propagation only along the surface of tissues, and disregard elasticity gradients along depth. Longitudinal shear waves (LSW), on the other hand, can be generated at the surface of the tissue and propagate through depth with desirable properties for OCE: (1) LSW travel at the shear wave speed and can discriminate elasticity gradients along depth, and (2) the displacement of LSW is longitudinally polarized along the direction of propagation; therefore, it can be measured by a phase-sensitive optical coherence tomography system. In this study, we explore the capabilities of LSW generated by a circular glass plate in contact with a sample using numerical simulations and tissue-mimicking phantom experiments. Results demonstrate the potential of LSW in detecting an elasticity gradient along axial and lateral directions simultaneously. Finally, LSW are used for the elastography of ex vivo mouse brain and demonstrate important implications in in vivo and in situ measurements of local elasticity changes in brain and how they might correlate with the onset and progression of degenerative brain diseases.

Longitudinal elastic wave imaging using nanobomb optical coherence elastography.

Wave-based optical coherence elastography (OCE) is a rapidly emerging technique for elasticity assessment of tissues having high displacement sensitivity and simple implementation. However, most current noncontact wave excitation techniques are unable to target a specific tissue site in 3D and rely on transversal scanning of the imaging beam. Here, we demonstrate that dye-loaded perfluorocarbon nanoparticles (nanobombs) excited by a pulsed laser can produce localized axially propagating longitudinal shear waves while adhering to the laser safety limit. A phase-correction method was developed and implemented to perform sensitive nanobomb elastography using a ∼1.5 MHz Fourier domain mode-locking laser. The nanobomb activation was also monitored by detecting photoacoustic signals. The highly localized elastic waves detected by the nanobomb OCE suggest the possibility of high-resolution 3D elastographic imaging.

Interaction of Harmonic Longitudinal Shear Waves with V-Shaped Inclusions

We solve the problem of determination of the stressed state in the vicinity of a tunnel rigid inclusion whose cross section consists of two segments originating out from the same point. The inclusion is placed in an infinite elastic medium with propagating plane harmonic longitudinal shear waves. The problem is reduced to the solution of a system of two singular integral equations with fixed singularities. For the approximate solution of this system, we apply a numerical method that takes into account the true asymptotics of the unknown functions and is based on the use of special quadrature formulas for the evaluation of singular integrals.

Impacts of the murine skull on high-frequency transcranial photoacoustic brain imaging.

Non-invasive photoacoustic tomography (PAT) of mouse brains with intact skulls has been a challenge due to the skull's strong acoustic attenuation, aberration, and reverberation, especially in the high-frequency range (>15 MHz). In this paper, we systematically investigated the impacts of the murine skull on the photoacoustic wave propagation and on the PAT image reconstruction. We studied the photoacoustic acoustic wave aberration due to the acoustic impedance mismatch at the skull boundaries and the mode conversion between the longitudinal wave and shear wave. The wave's reverberation within the skull was investigated for both longitudinal and shear modes. In the inverse process, we reconstructed the transcranial photoacoustic computed tomography (PACT) and photoacoustic microscopy (PAM) images of a point target enclosed by the mouse skull, showing the skull's different impacts on both modalities. Finally, we experimentally validated the simulations by imaging an in vitro mouse skull phantom using representative transcranial PAM and PACT systems. The experimental results agreed well with the simulations and confirmed the accuracy of our forward and inverse models. We expect that our results will provide better understanding of the impacts of the murine skull on transcranial photoacoustic brain imaging and pave the ways for future technical improvements.

Numerical simulation and machine learning based analysis of the ultrasonic waveform propagating in bone tissue

Since bone has a complex structure, it is difficult to analytically understand the behavior of the ultrasound although it is useful for bone quality diagnosis. Our group, therefore, had been working on simulating ultrasound propagation inside bone models. In this paper, the results of the neural network based bone analysis using waveforms derived by the 3-D elastic FDTD (finite-difference time domain) simulation will be presented as well as its basis and some representative results of the FDTD method applied for the bone assessment. Since the FDTD simulation only requires the 3-D geometry of the model and the acoustic parameters (density, speed of longitudinal wave and shear wave) of the media, it has been very useful for evaluating each effect of a certain acoustic parameter or the bone geometry such as bone density, respectively, in addition to the purpose of visually understanding the wave behavior inside the model including the propagation path. Moreover, thanks to the recent powerful computational resource, it is now realized to prepare a huge number of waveforms for machine learning by using FDTD method. As a result, it was shown that the neural network can estimate the bone density better than the traditional method. (Grant: JSPS KAKENHI 16K01431.)