A solution to diffraction biases in sonoelasticity: the acoustic impulse technique.

Several methods have been proposed to estimate the viscoelastic properties of soft biological tissues using forced low-frequency vibrations (10-500 Hz). Those methods are based on the measurement of phase velocity of the shear waves (approximately 5 m/s). It is shown in this article that the measurements of velocity as well as attenuation are subjected to biases. These biases are related to reflected waves created at boundaries, to the nonnegligible size of the piston source which causes diffraction effects and to the influence of a low-frequency compressional wave. Indeed, a theoretical analysis of the field radiated by a point source explains how mechanical vibrations of a piston generate a shear wave with a longitudinal component and how this component can interfere with a low-frequency compressional wave. However, by using a low-frequency transient excitation, these biases can be avoided. Then the precise numerical values of elasticity and viscosity can be deduced. Experiments in phantoms and beef muscles are shown. Moreover, a relative hardness imaging of a phantom composed of two media with different elasticities is presented.     

Effect of off-frequency sampling in magnetic resonance elastography

In magnetic resonance elastography (MRE), shear waves at a certain frequency are encoded through bipolar gradients that switch polarity at a controlled encoding frequency and are offset in time to capture wave propagation using a controlled sampling frequency. In brain MRE, there is a possibility that the mechanical actuation frequency is different from the vibration frequency, leading to a mismatch with encoding and sampling frequencies. This mismatch can occur in brain MRE from causes both extrinsic and intrinsic to the brain, such as scanner bed vibrations or active damping in the head. The purpose of this work was to investigate how frequency mismatch can affect MRE shear stiffness measurements. Experiments were performed on a dual-medium agarose gel phantom, and the results were compared with numerical simulations to quantify these effects. It is known that off-frequency encoding alone results in a scaling of wave amplitude, and it is shown here that off-frequency sampling can result in two main effects: (1) errors in the overall shear stiffness estimate of the material on the global scale and (2) local variations appearing as stiffer and softer structures in the material. For small differences in frequency, it was found that measured global stiffness of the brain could theoretically vary by up to 12.5% relative to actual stiffness with local variations of up to 3.7% of the mean stiffness. It was demonstrated that performing MRE experiments at a frequency other than that of tissue vibration can lead to artifacts in the MRE stiffness images, and this mismatch could explain some of the large-scale scatter of stiffness data or lack of repeatability reported in the brain MRE literature.     

Influence of composition of carbonyl iron particles on dynamic mechanical properties of magnetorheological elastomers

Magnetorheological elastomers (MRE) are known as smart materials. However, the magnetorheological (MR) effect of MRE is not high enough at present, which limits its engineering applications. Prior studies have shown that magneto-induced shear storage modulus and MR effect were mainly determined by the performance of the ferromagnetic particles. In this paper, MRE samples were prepared by carbonyl iron particles (CIP) of different compositions based on silicon rubber under external magnetic field. Their microstructures were observed using an optical digital microscope and a scanning electron microscope. The dynamic mechanical properties of MRE samples were measured using a modified dynamic mechanical analyzer under varying magnetic field strength and frequency. The results show that the carbon content of CIP have a greater impact on the dynamic mechanical properties of MRE. The magneto-induced shear storage modulus and MR effect can be increased by selecting CIP of low carbon content. In addition, the damping property is also significantly influenced by the carbon content of the CIP. This study is expected to provide guidance for fabrication of high performance MRE.     

A theoretical approach to local attenuation measurements of shear waves by MRE. Preliminary experimental results

An essential highlight of the presented method is the employment of Magnetic Resonance Elastography (MRE) for local measurements of the attenuation of elastic shear waves introduced into a biological sample. Such a measurement can be accomplished by combining the MRE method with those methods, in which collective displacement of spins is induced by external physical factors, such as variable electric field, strong magnetic field gradient or longitudinal elastic wave. A theoretical basis of the method involving external factors and results of preliminary experiments have been presented in this paper.     

Parametric scattering of high-frequency elastic waves by a small spherical cavity oscillating under the action of a Rayleigh wave

Scattering of high-frequency transverse and longitudinal plane waves incident on a spherical cavity located at a small depth under the surface of a half-space is considered. The cavity oscillates as a whole in the field of a low-frequency Rayleigh surface wave, the oscillation vectors of the longitudinal, transverse, and surface waves being coplanar. The cavity radius is assumed to be small compared to the wavelengths of the sounding wave and the pumping surface wave. The scattered compression and shear waves at the combination frequencies ω±Ω are calculated in the dipole approximation. Expressions obtained describe the qualitative behavior of the combination-frequency signal levels produced at the outputs of horizontally and vertically oriented geophones moving over the free surface of the elastic half-space.     

Electric fields in polymers during dynamic deformation

The transverse vibrations of a beam and the propagation of tension, compression, and shear deformation waves along the axis of a rod are studied by recording the electric field that appears under these conditions near the rod. Experiments are performed on samples made of various plastic materials in order to compare the effect of the properties of a material on the electric response during dynamic deformation, all other things being equal. Dynamic Young’s moduli are determined during bending vibrations and the propagation of longitudinal waves. It is shown that the location and type of antenna should be taken into account to adequately interpret a recorded signal and a dynamic mechanical process.     

Wave equations, dispersion relations, and van Hove singularities for applications of doublet mechanics to ultrasound propagation in bio- and nanomaterials

A fundamental mathematical framework for applications of Doublet Mechanics to ultrasound propagation in a discrete material is introduced. A multiscale wave equation, dispersion relation for longitudinal waves, and shear waves are derived. The van Hove singularities and corresponding highest frequency limits for the Mth-order wave equations of longitudinal and shear waves are determined for a widely used microbundle structure. Doublet Mechanics is applied to soft tissue and low-density polyethylene. The experimental dispersion data for soft tissue and low-density polyethylene are compared with results predicted by Doublet Mechanics and an attenuation model based on a Kramers-Kronig relation in classical continuum mechanics.     

声波测井技术的重要进展——偶极横波远探测测井

近年来单井反射声波远探测技术的一个重要进展是利用偶极声波探测仪器来发射和接收地层深部的反射信号。本文首先介绍了单井反射声波成像技术的研究进展。然后,从偶极横波成像原理、充液井孔中偶极远场辐射指向性、偶极声源激励下的井外声场分布、反射横波幅度和反射系数、偶极横波数据中的反射波分析和现场资料处理实例分析等方面详细论述了偶极声波远探测技术。最后,讨论了这门技术今后改进和发展的方向,通过本文读者可以了解偶极横波远探测技术的原理、方法、效果和应用前景。     

Temporal analysis of tissue displacement induced by a transient ultrasound radiation force

One of the stress sources that can be used in dynamic elastography imaging methods is the acoustic radiation force. However, displacements of the medium induced by this stress field are generally not fully understood in terms of spatial distribution and temporal evolution. A model has been developed based on the elastodynamic Green's function describing the different acoustic waves generated by focused ultrasound. The function is composed of three terms: two far-field terms, which correspond to a purely longitudinal compression wave and a purely transverse shear wave, and a coupling near-field term which has a longitudinal component and a transverse component. For propagation distances in the shear wavelength range, the predominant term is the near field term. The displacement duration corresponds to the propagation duration of the shear wave between the farthest source point and the observation point. This time therefore depends on the source size and the local shear modulus of the tissue. Evolution of the displacement/time curve profile, which is directly linked to spatial and temporal source profiles, is computed at different radial distances, for different durations of force applications and different shear elastic coefficients. Experimental results performed with an optical interferometric method in a homogeneous tissue-mimicking phantom agreed with the theoretical profiles.     

Feasibility of MR elastography of the intervertebral disc

Low back pain (LBP) is a costly and widely prevalent health disorder in the U.S. One of the most common causes of LBP is degenerative disc disease (DDD). There are many imaging techniques to characterize disc degeneration; however, there is no way to directly assess the material properties of the intervertebral disc (IVD) within the intact spine. Magnetic resonance elastography (MRE) is an MRI-based technique for non-invasively mapping the mechanical properties of tissues in vivo. The purpose of this study was to investigate the feasibility of using MRE to detect shear wave propagation in and determine the shear stiffness of an axial cross-section of an ex vivo baboon IVD, and compare with shear displacements from a finite element model of an IVD motion segment in response to harmonic shear vibration. MRE was performed on two baboon lumbar spine motion segments (L3–L4) with the posterior elements removed at a range of frequencies (1000–1500 Hz) using a standard clinical 1.5 T MR scanner. Propagating waves were visualized in an axial cross-section of the baboon IVDs in all three motion-encoding directions, which resembled wave patterns predicted using finite element modeling. The baboon nucleus pulposus showed an average shear stiffness of 79 ± 15 kPa at 1000 Hz. These results suggest that MRE is capable of visualizing shear wave propagation in the IVD, assessing the stiffness of the nucleus of the IVD, and can differentiate the nucleus and annulus regions.     

Longitudinal and lateral low frequency head wave analysis in soft media

This article studies the influence of the head wave in the lateral and longitudinal components of the displacements generated by the radiation of low-frequency elastic waves in an isotropic and homogeneous soft solid. Low-frequency shear waves are used to characterize elastic properties of soft tissues. In this context, it is useful to have a detailed study of the low-frequency wave field in this kind of material. A soft medium is characterized by the fact that the head wave is found in the source's axis. Even though its amplitude is small compared with the shear wave, it is possible to be observed experimentally by recording consecutive ultrasonic A-lines while the low-frequency wave propagates inside the medium. A standard one-dimensional speckle tracking technique is employed to measure the displacements. Experimental results were interpreted through the exact Green's function solution to the half-space problem. According to the theoretical and experimental analysis, the head wave and surface related terms in general contribute to the displacements in the low-frequency range. This article thoroughly analyzes and experimentally shows the contribution of the head wave for the lateral component, which is not fully addressed by the literature.     

Measurements of degree of sensitization (DoS) in aluminum alloys using EMAT ultrasound

Sensitization in 5XXX aluminum alloys is an insidious problem characterized by the gradual formation and growth of beta phase (Mg₂Al₃) at grain boundaries, which increases the susceptibility of alloys to intergranular corrosion (IGC) and intergranular stress-corrosion cracking (IGSCC). The degree of sensitization (DoS) is currently quantified by the ASTM G67 Nitric Acid Mass Loss Test, which is destructive and time consuming. A fast, reliable, and non-destructive method for rapid detection and the assessment of the condition of DoS in AA5XXX aluminum alloys in the field is highly desirable. In this paper, we describe a non-destructive method for measurements of DoS in aluminum alloys with an electromagnetic acoustic transducer (EMAT). AA5083 aluminum alloy samples were sensitized at 100 °C with processing times varying from 7 days to 30 days. The DoS of sensitized samples was first quantified with the ASTM 67 test in the laboratory. Both ultrasonic velocity and attenuation in sensitized specimens were then measured using EMAT and the results were correlated with the DoS data. We found that the longitudinal wave velocity was almost a constant, independent of the sensitization, which suggests that the longitudinal wave can be used to determine the sample thickness. The shear wave velocity and especially the shear wave attenuation are sensitive to DoS. Relationships between DoS and the shear velocity, as well as the shear attenuation have been established. Finally, we performed the data mining to evaluate and improve the accuracy in the measurements of DoS in aluminum alloys with EMAT.     

Numerical simulation of the process of wave separation of solid particles in resonance gas vibrations in the closed pipe

Drift of solid suspended particles under the action of longitudinal resonance vibrations of the gas column in a closed pipe is studied numerically. Nonlinear gas vibrations with the motion remaining to be laminar are considered. The gas velocity field contains periodic nonlinear waves and an acoustic flow, and the particles move under the action of the Stokes force. For the first, second, and third eigenfrequencies of the longitudinal gas column vibrations, distributions of light and heavy particles observed in the wave field of the closed pipe are obtained.     

Dynamic photoelastic study of the transient stress field in solids during shock wave lithotripsy

Photoelastic and shadowgraph imaging techniques were used to visualize the propagation and evolution of stress waves, and the resultant transient stress fields in solids during shock wave lithotripsy. In parallel, theoretical analysis of the wavefront evolution inside the solids was performed using a ray-tracing method. Excellent agreement between the theoretical prediction and experimental results was observed. Both the sample size and geometry were found to have a significant influence on the wave evolution and associated stress field produced inside the solid. In particular, characteristic patterns of spalling damage (i.e., transverse and longitudinal crack formation) were observed using plaster-of-Paris cylindrical phantoms of rectangular and circular cross sections. It was found that the leading tensile pulse of the reflected longitudinal wave is responsible for the initiation of microcracks in regions inside the phantom where high tensile stresses are produced. In addition, the transmitted shear wave was found to play a critical role in facilitating the extension and propagation of the microcrack.     

Convertible pneumatic actuator for magnetic resonance elastography of the brain

Here we present a novel pneumatic actuator design for brain magnetic resonance elastography (MRE). Magnetic resonance elastography is a phase contrast technique capable of tracing strain wave propagation and utilizing this information for the calculation of mechanical properties of materials and living tissues. In MRE experiments, the acoustic waves are generated in a synchronized way with respect to image acquisition, using various types of mechanical actuators. The unique feature of the design is its simplicity and flexibility, which allows reconfiguration of the actuator for different applications ranging from in vivo brain MRE to experiments with phantoms. Phantom and in vivo data are presented to demonstrate actuator performance.     

Simulation and analysis of magnetic resonance elastography wave images using coupled harmonic oscillators and Gaussian local frequency estimation.

New methods for simulating and analyzing Magnetic Resonance Elastography (MRE) images are introduced. To simulate a two-dimensional shear wave pattern, the wave equation is solved for a field of coupled harmonic oscillators with spatially varying coupling and damping coefficients in the presence of an external force. The spatial distribution of the coupling and the damping constants are derived from an MR image of the investigated object. To validate the simulation as well as to derive the elasticity modules from experimental MRE images, the wave patterns are analyzed using a Local Frequency Estimation (LFE) algorithm based on Gauss filter functions with variable bandwidths. The algorithms are tested using an Agar gel phantom with spatially varying elasticity constants. Simulated wave patterns and LFE results show a high agreement with experimental data. Furthermore, brain images with estimated elasticities for gray and white matter as well as for exemplary tumor tissue are used to simulate experimental MRE data. The calculations show that already small distributions of pathologically changed brain tissue should be detectable by MRE even within the limit of relatively low shear wave excitation frequency around 0.2 kHz.     

Ultrasonic shear wave properties of soft tissues and tissuelike materials

Determinations of shear wave speeds of sound and attenuation coefficients are reported for soft tissues, a silicone rubber reference material, and a gel used in manufacturing ultrasonically tissue-mimicking materials. Fresh bovine tissues were investigated, including calfskin, liver, cardiac muscle, and striated muscle. Because of the very large shear wave attenuation coefficients, reasonably accurate determinations of shear wave properties are difficult to make. The quantity measured directly was the complex reflection coefficient for shear waves at a planar interface between the sample and fused silica. Measurements were made at frequencies spanning the range 2-14 MHz. The shear wave attenuation coefficients increase with frequency and are of the order of 10(4) times the longitudinal wave attenuation coefficients. The shear wave speeds of sound also increase with frequency but are only a few percent of the longitudinal wave speeds of sound. The results are accurate enough to allow frequency dependencies to be proposed.     

DISCRETE HUYGENS' MODELLING APPROACH TO WAVE PROPAGATIONS IN A HOMOGENEOUS ELASTIC FIELD

The application of the discrete Huygens' modelling has been discussed for acoustic wave propagation problems, in which the scalar wave field problems have been focused. The present paper extends the application of the modelling to the elastic wave propagation in a homogeneous elastic medium in which two types of waves, the longitudinal wave and the shear wave, are independent except at the boundary. Each wave can be treated like a scalar wave until the two waves reach the boundary where they couple so as to satisfy the displacement or stress boundary condition. We propose the approach confining ourselves to the two-dimensional field. Some examples are demonstrated, whose solutions are compared with the vectorial wave modelling and finite difference modelling solutions whenever they are available.     

Acoustoelasticity in soft solids: assessment of the nonlinear shear modulus with the acoustic radiation force

The assessment of viscoelastic properties of soft tissues is enjoying a growing interest in the field of medical imaging as pathologies are often correlated with a local change of stiffness. To date, advanced techniques in that field have been concentrating on the estimation of the second order elastic modulus (mu). In this paper, the nonlinear behavior of quasi-incompressible soft solids is investigated using the supersonic shear imaging technique based on the remote generation of polarized plane shear waves in tissues induced by the acoustic radiation force. Applying a theoretical approach of the strain energy in soft solid [Hamilton et al., J. Acoust. Soc. Am. 116, 41-44 (2004)], it is shown that the well-known acoustoelasticity experiment allowing the recovery of higher order elastic moduli can be greatly simplified. Experimentally, it requires measurements of the local speed of polarized plane shear waves in a statically and uniaxially stressed isotropic medium. These shear wave speed estimates are obtained by imaging the shear wave propagation in soft media with an ultrafast echographic scanner. In this situation, the uniaxial static stress induces anisotropy due to the nonlinear effects and results in a change of shear wave speed. Then the third order elastic modulus (A) is measured in agar-gelatin-based phantoms and polyvinyl alcohol based phantoms.     

Reflection of elastic waves in a crystal of Heusler alloy Ni<Subscript>2</Subscript>MnGa in the phase transition range

The reflection of longitudinal and transverse acoustic waves from the free surface of the ferromagnetic shape memory alloy Ni₂MnGa that is located in the ranges of the premartensite and martensite phase transformations is considered. The propagation directions and amplitudes of the waves reflected in the (001) plane of the crystal are determined. They acquire the character of substantially quasi-longitudinal and quasi-transverse vibrations rather than being pure modes. The angles of wave reflection and conversion are shown to be effectively controlled by temperature and a magnetic field due to the colossal acoustic anisotropy of the crystal over the wide range of its phase transitions. Beginning from a certain critical angle of incidence of a quasi-transverse wave, the quasi-longitudinal wave having appeared upon reflection becomes an accompanying surface vibration, and it can be emitted into the bulk of the crystal when the phase transition point is approached. Two angles of full conversion of an incident quasi-longitudinal wave into a quasi-transverse wave are established, and their temperature dependences are found. Trivisonno’s experimental data for the ultrasound velocity and absorption in an Ni₂MnGa crystal are used to numerically estimate these acoustic effects.