On the effects of reflected waves in transient shear wave elastography

In recent years, novel quantitative techniques have been developed to provide noninvasive and quantitative stiffness images based on shear wave propagation. Using radiation force and ultrafast ultrasound imaging, the supersonic shear imaging technique allows one to remotely generate and follow a transient plane shear wave propagating in vivo in real time. The tissue shear modulus, i.e., its stiffness, can then be estimated from the shear wave local velocity. However, because the local shear wave velocity is estimated using a time-of- flight approach, reflected shear waves can cause artifacts in the estimated shear velocity because the incident and reflected waves propagate in opposite directions. Such effects have been reported in the literature as a potential drawback of elastography techniques based on shear wave speed, particularly in the case of high stiffness contrasts, such as in atherosclerotic plaque or stiff lesions. In this letter, we present our implementation of a simple directional filter, previously used for magnetic resonance elastography, which separates the forward- and backward-propagating waves to solve this problem. Such a directional filter could be applied to many elastography techniques based on the local estimation of shear wave speed propagation, such as acoustic radiation force imaging (ARFI), shearwave dispersion ultrasound vibrometry (SDUV), needle-based elastography, harmonic motion imaging, or crawling waves when the local propagation direction is known and high-resolution spatial and temporal data are acquired.     

3-D FDTD simulation of shear waves for evaluation of complex modulus imaging

The Navier equation describing shear wave propagation in 3-D viscoelastic media is solved numerically with a finite differences time domain (FDTD) method. Solutions are formed in terms of transverse scatterer velocity waves and then verified via comparison to measured wave fields in heterogeneous hydrogel phantoms. The numerical algorithm is used as a tool to study the effects on complex shear modulus estimation from wave propagation in heterogeneous viscoelastic media. We used an algebraic Helmholtz inversion (AHI) technique to solve for the complex shear modulus from simulated and experimental velocity data acquired in 2-D and 3-D. Although 3-D velocity estimates are required in general, there are object geometries for which 2-D inversions provide accurate estimations of the material properties. Through simulations and experiments, we explored artifacts generated in elastic and dynamic-viscous shear modulus images related to the shear wavelength and average viscosity.     

层状无砟轨道结构脱层缺陷超声成像

无砟轨道是典型的层状混凝土结构,脱层缺陷是其最常见的损伤形式,影响着高速列车的安全运行。传统的合成孔径聚焦成像方法是基于恒定声速的超声检测方法,忽略层间的声阻抗差异以及声波在层间界面处的折射,导致声束难以在缺陷处聚焦,声波在层状结构中传播的时间误差较大。鉴于此,提出了一种多层结构合成孔径聚焦成像方法,充分考虑多层结构中的层间声速差异,采用射线追踪方法准确获取声波在多层结构中的传播时间。在此基础上,分析了不同入射波模式以及不同激发频率对多层结构合成孔径聚焦成像结果的影响。结果表明：采用多层结构合成孔径聚焦成像方法,使用频率为50 kHz的横波入射成像分辨率更高,对无砟轨道脱层缺陷检测效果更好。该研究为该类缺陷检测提供了理论支撑。     

Pure modes for elastic waves in crystals: mathematical modeling and search

A universal search method of pure longitudinal and pure transverse modes for elastic wave propagation in crystals, in general piezoelectrics, is presented. A mathematical model of pure modes for elastic waves based on adiabatic state equations for an arbitrary anisotropic piezoelectric medium and its equation of motion under elastic deformations in the rotated Cartesian coordinates is constructed. The condition for longitudinal normals is that all non-diagonal matrix elements of the effective elastic stiffness coefficients in the corresponding wave equation are equal to zero. Equating to zero non-diagonal elements only in one row of this matrix, one can obtain the condition for transverse normals. A computer program is prepared which allows to find the pure modes for elastic waves in crystals and to calculate their characteristics when symmetry class, elastic, piezoelectric, dielectric constants, and crystal density are known.     

Minimum variance ultrasonic imaging applied to an in situ sparse guided wave array

Ultrasonic guided wave imaging with a sparse, or spatially distributed, array can detect and localize damage over large areas. Conventional delay-and-sum images from such an array typically have a relatively high noise floor, however, and contain artifacts that often cannot be discriminated from damage. Considered here is minimum variance distortionless response (MVDR) imaging, which is a variation of delay-and-sum imaging whereby weighting coefficients are adaptively computed at each pixel location. Utilization of MVDR significantly improves image quality compared with delay-and-sum imaging, and additional improvements are obtained from incorporation of a priori scattering information in the MVDR method, use of phase information, and instantaneous windowing. Simulated data from a through-hole scatterer are used to illustrate performance improvements, and a performance metric is proposed that allows for quantitative comparisons of images from a known scatterer. Experimental results from a through-hole scatterer are also provided that illustrate imaging efficacy.     

Chaotic scattering of waves from nonlinear scatterers

Summary Two examples of the effect of nonlinearities on the scattering of nondispersive waves are presented. It is shown that nonlinear boundary conditions can lead to broadband, chaotic scattered waves when the scatterer is excited by a single wavelength plane wave. One of the examples treats a spherical scatterer in a linear elastic medium. A number of modern techniques in nonlinear analysis is used to diagnose the chaotic dynamics including Poincaré maps, fractal dimensions and Lyapunov exponents.     

Energy focusing and the shapes of wave fronts in anisotropic fluid-saturated porous media

Summary The purpose of this paper is to investigate the energy focusing pattern evolution in the parameter space while the wave fronts propagate in the anisotropic fluid-saturated porous media. Firstly, the bifurcation conditions for a general anisotropic fluid-saturated porous material are deduced. Then, by choosing the material parameters as control variables, the influence of the anisotropy of the solid skeleton and pore fluid parameters on the development characteristics of energy focusing patterns is discussed, and the three-dimensional configurations for the focusing structures are explored. The results indicate that the energy focusing also exists on the wave fronts of the slow waves, which is a particular propagation characteristic for the slow waves in anisotropic fluid-saturated porous media. The distinct trends for the slow wave energy focusing are revealed. This has significant meaning in further understanding the roles of the fluid phase in the dynamic response of the fluid-saturated porous media.     

Propagation properties of longitudinal leaky surface waves on lithium tetraborate

Theoretical and experimental results of longitudinal leaky surface waves with a higher phase velocity than that of ordinary leaky surface waves and a low propagation loss on lithium tetraborate (LBO) are investigated in detail. They propagate along the surface with a phase velocity close to that of longitudinal bulk wave, slightly radiating two kinds of shear bulk waves (or one shear bulk wave in the case that one of two shear wave terms is uncoupled) into the solid. Most surface components of the mode consist of a longitudinal wave term and an electromagnetic wave term. The detailed propagation properties of the longitudinal leaky surface waves on LBO with the Euler angles (phi, theta, 90 degrees ) are investigated theoretically and experimentally. The (011) cut of LBO was found to be desirable for higher frequency SAW devices. One of the reasons why that mode on LBO has a low propagation loss is also discussed.     

Existence of longitudinal and transverse waves in anisotropic thermoelastic media

Four waves propagate in an anisotropic thermoelastic medium. The fastest among them is a quasi-longitudinal wave. The slowest of them is a thermal wave. The remaining two are called quasi-transverse waves. The prefix ‘quasi’ refers to their polarizations being nearly, but not exactly, parallel or perpendicular to the direction of propagation. The polarizations of these four waves are not mutually orthogonal. Hence, unlike anisotropic elastic media, the existence of a longitudinal wave may not imply the existence of a transverse wave, by default. The existence of a purely longitudinal wave in an anisotropic thermoelastic medium is ensured by the stationary characters of three expressions. These expressions involve components of phase direction with elastic (stiffness and coupling) and thermal coefficients of the thermoelastic medium. The existence of a purely transverse wave is ensured by the two equations restricting the choice of thermoelastic (stiffness and coupling) coefficients. The existence of longitudinal and transverse waves along the coordinate axes and in the coordinate planes are discussed for general anisotropy. The discussion is extended to orthotropic materials, and the existence of pure phases is explored along few specific phase directions.     

Existence of longitudinal waves in anisotropic poroelastic solids

In anisotropic fluid-saturated porous solids, four waves can propagate along a general phase direction. However, solid particles in different waves may not vibrate in mutually orthogonal directions. In the propagation of each of these waves, the displacement of pore–fluid particles may not be parallel to that of solid particles. The polarization for a wave is the direction of aggregate displacement of the particles of the two constituents of a porous aggregate. These polarizations, for different waves, are not mutually orthogonal. Out of the four waves in anisotropic poroelastic medium, two are termed as quasi-longitudinal waves. The prefix ‘quasi’ refers to their polarization being nearly, but not exactly, parallel to the direction of propagation. The existence of purely longitudinal waves in an anisotropic poroelastic medium is ensured by the stationary characters of two expressions. These expressions involve the elastic (stiffness and coupling) coefficients of a porous aggregate and the components of phase direction. Necessary and sufficient conditions for the existence of longitudinal waves are discussed for different anisotropic symmetries. Conditions are also discussed for the existence of the apparent longitudinal waves, i.e., the propagation of wave motion with the particle displacement parallel to the ray direction instead of the phase direction. A graphical solution of a numerical example is shown to check the existence of these apparent longitudinal waves for general directions of phase propagation.     

Thermo-acoustical waves in linear thermo-elastic materials

Summary Coupled waves of thermal and mechanical jumps in linear thermo-elastic materials are analysed. General linear anisotropic constitutive equations of thermo-elastic materials are derived from the Clausius-Duhem inequality and Vernotte's heat conduction law is adopted. The waves are defined to have jumps in acceleration and in temperature rate and the four-dimensional thermo-acoustical propagation condition is obtained. The differential equations which govern the variation of the wave amplitudes are obtained. For waves in linear isotropic thermo-elastic materials, there are four principal waves. Two shear waves are purely mechanical and propagate with constant amplitude, while two thermo-longitudinal waves have different propagation velocities: one is larger and other smaller than the purely mechanical longitudinal wave velocity, and their amplitudes decay, in general, exponentially in time.     

Second harmonic generation of shear waves in crystals

Nonlinear self-interaction of shear waves in electro-elastic crystals is investigated based on the rotationally invariant state function. Theoretical analyses are conducted for cubic, hexagonal, and trigonal crystals. The calculations show that nonlinear self-interaction of shear waves has some characteristics distinctly different from that of longitudinal waves. First, the process of self-interaction to generate its own second harmonic wave is permitted only in some special wave propagation directions for a shear wave. Second, the geometrical nonlinearity originated from finite strain does not contribute to the second harmonic generation (SHG) of shear waves. Therefore, unlike the case of longitudinal wave, the second-order elastic constants do not involve in the nonlinear parameter of the second harmonic generation of shear waves. Third, unlike the nonlinearity parameter of the longitudinal waves, the nonlinear parameter of the shear wave exhibits strong anisotropy, which is directly related to the symmetry of the crystal. In the calculations, the electromechanical coupling nonlinearity is considered for the 6 mm and 3 m symmetry crystals. Complement to the SHG of longitudinal waves already in use, the SHG of shear waves provides more measurements for the determination of third-order elastic constants of solids. The method is applied to a Z-cut lithium niobate (LiNbO/sub 3/) crystal, and its third-order elastic constant c/sub 444/ is determined.     

识别薄板中兰姆波和体波的阶梯板方法

斜探头在某些频率下激励出的兰姆波,其群速度与体波的传播速度相近,所以通过判断传播速度不易区分出兰姆波和体波。通过数值模拟和实验,分别研究了激励频率为2 MHz的纵波和S0模态兰姆波在阶梯板上的反射特性,发现:在阶梯板上入射S0模态兰姆波时,有反射回波;而入射纵波时,无反射回波。基于这种反射特性的差别,提出了一种利用阶梯板区别薄板中兰姆波和体波的方法,该方法可用于确认探头的激励特性。     

A method for multidimensional wave propagation analysis via component‐wise partition of longitudinal and shear waves

An explicit integration algorithm for computations of discontinuous wave propagation in two‐dimensional and three‐dimensional solids is presented, which is designed to trace extensional and shear waves in accordance with their respective propagation speeds. This has been possible by an orthogonal decomposition of the total displacement into extensional and shear components, leading to two decoupled equations: one for the extensional waves and the other for shear waves. The two decoupled wave equations are integrated with their CFL time step sizes and then reconciled to a common step size by employing a previously developed front‐shock oscillation algorithm that is proven to be effective in mitigating spurious oscillations. Numerical experiments have demonstrated that the proposed algorithm for two‐dimensional and three‐dimensional wave propagation problems traces the stress wave fronts with high‐fidelity compared with existing conventional algorithms. Copyright © 2013 John Wiley & Sons, Ltd.     

医用线列阵声场计算方法

用指向性函数分别描述了医用线列阵单频波和宽带波声场。讨论了应用电子聚焦处理、幅度加权变迹处理和孔径变迹处理的方法来改善波束特性；论述了在实际中应用较多的宽带波声场的计算。通过分析表明，宽带波持续时间愈长，宽带波声场就愈接近于单频波声场。     

Ultrasonic beam steering through inhomogeneous layers with a timereversal mirror

Adaptive time delay focusing techniques allow an efficient correction of the effects due to an inhomogeneous layer close to the transducer array. If the layer is far from the array, these techniques are no longer appropriate to correct the diffraction effects between the layer and the transducer array. This problem was overcome by the use of acoustic time reversal mirrors. In this technique, the Green's function of a dominant scatterer available in the medium is recorded in digital memories and used to focus on the scatterer in both transmit and receive modes. We present in this paper an extension of this technique to focus, in the presence of an aberrating layer, not only on the dominant scatterer, but also around it in order to image the surrounding zone. From the knowledge of the Green's function needed to focus on the initial scatterer, we calculate the new Green's function matched to the new point of interest. The algorithm uses the concept of time reversal propagation, and we shall present here theoretical and experimental results obtained with this technique. Finally, the knowledge of each Green's function matched to each new desired focal point allows the realization of a B-scan image of the zone surrounding the reflector     

Universal space-time properties of X waves

Exact results concerning spatiotemporal universal features of three-dimensional propagation-invariant solutions of the wave equation (X waves) are derived. In particular, relations connecting the pulse transverse extension to the longitudinal coordinate and the propagation velocity to the spatial field distribution are obtained for the whole class of X waves.     

Kinematics of failure waves in glasses

A new method for observation of the failure waves in glasses is proposed which allows this phenomenon to be reliably and reproducibly monitored, the failure wave propagation velocity to be measured, and an increase in the longitudinal stress to be determined. Using this method, the stresses produced by an elastic shock compression pulse propagating from the entrance of a stack of glass plates to the exit from this stack were experimentally measured. The compression wave exhibits splitting at each interface between adjacent glass plates in the stack, which leads to the formation of transmitted and reflected failure waves and is accompanied by decreasing stress in the leading elastic wave.     

Influence of couple stresses on the propagation of elastic waves in a micropolar cubically anisotropic medium

Expressions for the phase and radial velocities of propagation of three-dimensional fronts of quasilongitudinal and quasitransverse elastic waves in a micropolar cubically anisotropic medium have been obtained. An analysis of the influence of the micropolar elastic constant on the dependence of the wave velocities on the angle of inclination of the normal to the wave surface has been made. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 2, pp. 178–182, March–April, 2006.