Capturing the Shear and Secondary Compression Waves: High-Frame-Rate Ultrasound Imaging in Saturated Foams.

We experimentally observe the shear and secondary compression waves inside soft porous water-saturated melamine foams by high-frame-rate ultrasound imaging. Both wave speeds are supported by the weak frame of the foam. The first and second compression waves show opposite polarity, as predicted by Biot theory. Our experiments have direct implications for medical imaging: melamine foams exhibit a similar microstructure as lung tissue. In the future, combined shear wave and slow compression wave imaging might provide new means of distinguishing malignant and healthy pulmonary tissue.

Longitudinal shear wave and transverse dilatational wave in solids.

Dilatation wave involves compression and extension and is known as the curl-free solution of the elastodynamic equation. Shear wave on the contrary does not involve any change in volume and is the divergence-free solution. This letter seeks to examine the elastodynamic Green's function through this definition. By separating the Green's function in divergence-free and curl-free terms, it appears first that, strictly speaking, the longitudinal wave is not a pure dilatation wave and the transverse wave is neither a pure shear wave. Second, not only a longitudinal shear wave but also a transverse dilatational wave exists. These waves are shown to be a part of the solution known as coupling terms. Their special motion is carefully described and illustrated.

Imaging of shear waves induced by Lorentz force in soft tissues.

This study presents the first observation of elastic shear waves generated in soft solids using a dynamic electromagnetic field. The first and second experiments of this study showed that Lorentz force can induce a displacement in a soft phantom and that this displacement was detectable by an ultrasound scanner using speckle-tracking algorithms. For a 100 mT magnetic field and a 10 ms, 100 mA peak-to-peak electrical burst, the displacement reached a magnitude of 1 µm. In the third experiment, we showed that Lorentz force can induce shear waves in a phantom. A physical model using electromagnetic and elasticity equations was proposed. Computer simulations were in good agreement with experimental results. The shear waves induced by Lorentz force were used in the last experiment to estimate the elasticity of a swine liver sample.

Near-field effects in Green's function retrieval from cross-correlation of elastic fields: experimental study with application to elastography.

In a lossless system, the causal and acausal Green's function for elastic waves can be retrieved by cross-correlating the elastic field at two positions. This field, composed of converging and diverging waves, is interpreted in the frame of a time-reversal process. In this work, the near-field effects on the spatio-temporal focusing of elastic waves are analyzed through the elastodynamic Green's function. Contrary to the scalar field case, the spatial focusing is not symmetric preserving the directivity pattern of a simple source. One important feature of the spatial asymmetry is its dependency on the Poisson ratio of the solid. Additionally, it is shown that the retrieval of the bulk wave speed values is affected by diffraction. The correction factor depends on the relative direction between the source and the observed field. Experimental verification of the analysis is carried out on the volume of a soft-solid. A low-frequency diffuse-like field is generated by random impacts at the sample's free surface. The displacement field is imaged using ultrasound by a standard speckle tracking technique. One important application of this work is in the estimation of the shear elastic modulus in soft biological tissues, whose quantification can be useful in non-invasive diagnosis of various diseases.

Shear wave elastography biases in abdominal wall layers characterization.

Ventral incisional hernia repair is one of the most common surgical procedures. The characterization of the abdominal wall layer mechanical properties is the first step towards personalized treatment. This study investigates the capability of elastography to assess these properties using anin vivoandin vitromodel of abdominal wall layers. Two experiment approaches are considered: shear wave elastography imaging and guided wave dispersion characterization, where the latter is used as a reference. Results show measurement biases in the shear wave elastography approach in such a layer structure configuration. Methods to overcome these biases are suggested to improve and to correct the elastography approach for abdominal wall layers and similar anatomical structures.

Passive elastography of the esophagus: from model to preliminaryin-vivoexperiments using diameter measurements.

Numerous diseases alter the esophagus elasticity, such as eosinophilic esophagitis and esophageal motility disorders like achalasia. The possibility to measure these modifications using minimally invasive techniques is a key issue for the diagnosis of such pathologies. The commercially available EndoflipTM(endoluminal functional lumen imaging probe) can be used to measure the luminal cross-sectional diameter of the esophagus at different points and over time, and is used in clinical routine to assess esophageal distensibility. We used this probe to track the propagation of shear waves similar to those that are produced naturally by natural waves, to compute wavelength of the esophagus using passive elastography algorithms. To assess the feasibility of such measurements, we compared the wavelengths obtained with the probe in polyvinyl alcohol (PVA) gel tubes to those obtained for the same tubes with optical tracking of their edges using a camera. We first compared the wavelength obtained with homogeneous gel tubes with both techniques, and then used paired gel tubes of different elasticities to investigate the possibility to measure different wavelengths. Although, the wavelength computed using the probe and the camera showed some small differences, qualitative differentiation of the tubes was achieved when using paired tubes with different elasticities. Using the camera, a wavelength of 61 mm was measured for the hard tube, and 35 mm for the soft tube. Using the probe, wavelengths of 61 mm and 38 mm were measured, respectively. Therefore, we demonstrate here the feasibility of using this probe to track wave propagation and to determine the wavelengths in gel tubes of different stiffnesses. This analysis was also taken to a preliminaryin-vivostudy that allowed tracking of natural waves in the esophagus using the luminal probe, which indicates that this technique can also be usedin vivoto measure the stiffness of the esophagus.

Characterization of muscle belly elastic properties during passive stretching using transient elastography.

Passive muscle stretching can be used in vivo to assess the viscoelastic properties of the entire musculo-articular complex, but does not allow the specific determination of the muscle or tendon viscoelasticity. In this respect, the local muscle hardness (LMH) of the gastrocnemius medialis (GM) belly was measured during a passive ankle stretching of 10 subjects using transient elastography. A Biodex isokinetic dynamometer was used to stretch ankle plantar flexors, to measure ankle angle, and the passive torque developed by the ankle joint in resistance to the stretch. Results show that the LMH increased during the stretching protocol, with an averaged ratio between maximal LMH and minimal LMH of 2.62+/-0.46. Furthermore, LMH-passive torque relationships were nicely fitted using a linear model with mean correlation coefficients (R(2)) of 0.828+/-0.099. A good reproducibility was found for the maximal passive torque (ICC=0.976, SEM=2.9Nm, CV=5.5%) and the y-intercept of the LMH-passive torque relationship (ICC=0.893, SEM=105Pa, CV=7.8%). However, the reproducibility was low for the slope of this relationship (ICC=0.631, SEM=10.35m(-2), CV=60.4%). The y-intercept of the LMH-passive torque relationship was not significantly changed after 10min of static stretching. This result confirms the finding of a previous study indicating that changes in passive torque following static stretching could be explained by an acute increase in muscle length without any changes in musculo-articular intrinsic mechanical properties.

Shear elasticity estimation from surface wave: the time reversal approach.

In this work the shear elasticity of soft solids is measured from the surface wave speed estimation. An external source creates mechanical waves which are detected using acoustic sensors. The surface wave speed estimation is extracted from the complex reverberated elastic field through a time-reversal analysis. Measurements in a hard and a soft gelatin-based phantom are validated by independent transient elastography estimations. In contrast with other elasticity assessment methods, one advantage of the present approach is its low sound technology cost. Experiments performed in cheese and soft phantoms allows one to envision applications in the food industry and medicine.

Multiple sources array controls shear-wave field in soft tissue using time reversal.

In most elastography experiments, shear waves are generated using a single source on the surface with a shaker, or in the bulk with radiation pressure of ultrasound. However, emitting controlled shear waves from multiple sources is a good way to improve the signal to-noise-ratio for shear-wave elastography. The experiments are conducted using six shakers with independent driving electronics in gelatin-graphite to mimic the tissue. Based on time reversal, our approach shows the feasibility of controlling shear-wave field in space with multiple focal spots at chosen locations, and in time with a chosen delay between each focusing. Improved by 10 dB compared to the use of a single source, the signal-to-noise ratio demonstrates that time-reversal as an adaptive filter is a good method to deliver maximum energy vibrations toward deep regions. Furthermore, this adaptive approach allows controlled vibrations to be delivered through bone conduction: a shear-wave focal spot is experimentally observed in a soft brain tissue-mimicking phantom using the multiple sources array applied to a skull model.

Simulation of nonlinear transient elastography: finite element model for the propagation of shear waves in homogeneous soft tissues.

In this study, visco-hyperelastic Landau's model, which is widely used in acoustical physic field, is introduced into a finite element formulation. It is designed to model the nonlinear behaviour of finite amplitude shear waves in soft solids, typically, in biological tissues. This law is used in finite element models based on elastography, experiments reported in Jacob et al, the simulations results show a good agreement with the experimental study: It is observed in both that a plane shear wave generates only odd harmonics and a nonplane wave generates both odd and even harmonics in the spectral domain. In the second part, a parametric study is performed to analyse the influence of different factors on the generation of odd harmonics of plane wave. A quantitative relation is fitted between the odd harmonic amplitudes and the non-linear elastic parameter of Landau's model, which provides a practical guideline to identify the non-linearity of homogeneous tissues using elastography experiment.

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.

In vivo breast tumor detection using transient elastography.

This paper presents first in vivo experiments for breast tumor detection using transient elastography. This technique has been developed for detection and quantitative mapping of hard lesions in soft tissues. It consists in following the propagation inside soft tissues of very low-frequency shear waves (approximately 60 Hz) generated by a vibrating system located at the body surface. Because transient shear waves propagate through the medium in less than 0.1 s, the shear propagation imaging is performed with an ultrafast echographic scanner able to reach frame rates up to 6000 Hz. The local shear wave speed is directly linked to the local shear Young's modulus of the medium. The shear elasticity map of the medium can then be computed using an inversion algorithm. In vivo experiments were conducted on 15 women who had palpable breast lesions. For clinical adaptability reasons, shear waves were generated by the surface of the ultrasound (US) imaging transducer itself, which was linked to a mechanical vibrator. Our preliminary in vivo results demonstrate the clinical applicability of the transient elastography technique for breast lesion detection.

Diffraction field of a low frequency vibrator in soft tissues using transient elastography.

For the last 10 years, interest has grown in low frequency shear waves that propagate in the human body. However, the generation of shear waves by acoustic vibrators is a relatively complex problem, and the directivity patterns of shear waves produced by the usual vibrators are more complicated than those obtained for longitudinal ultrasonic transducers. To extract shear modulus parameters from the shear wave propagation in soft tissues, it is important to understand and to optimize the directivity pattern of shear wave vibrators. This paper is devoted to a careful study of the theoretical and the experimental directivity pattern produced by a point source in soft tissues. Both theoretical and experimental measurements show that the directivity pattern of a point source vibrator presents two very strong lobes for an angle around 35 degrees . This paper also points out the impact of the near field in the problem of shear wave generation.

Assessment of muscle hardness changes induced by a submaximal fatiguing isometric contraction.

Transient elastography consists of measuring the transverse local shear elastic modulus defined as local muscle hardness (LMH). It has previously been shown that LMH is correlated to muscle activity level during non-fatiguing contractions. The aim of this study was to describe how LMH and muscle activity level change during a submaximal fatiguing constant-torque protocol. Changes in gastrocnemius medialis LMH and in surface electromyographic activities (sEMG) of plantar flexors induced by a submaximal isometric plantar flexion (40% of the maximal isometric torque) until exhaustion were quantified. During the contraction, sEMG of each muscle increased (P<0.001) whereas LMH remained constant (P>0.05). Active LMH assessed during the contraction did not parallel muscle activity level changes during this type of submaximal fatigue protocol. Interestingly, LMH at rest assessed in passive conditions was higher prior to the fatiguing effort (P<0.05), rather than that assessed immediately after. Muscle and tendon viscous behaviors could imply a creep phenomenon during a prolonged isometric contraction, and our results in LMH at rest could indicate that this phenomenon induces changes in muscle intrinsic mechanical properties. Further studies are needed to examine whether it could have an influence on muscle activity levels during the contraction.

Time reversal of elastic waves in soft solids.

When a scalar far-field wave is time reversed, it starts to converge toward its initial point source location, then collapses and finally diverges. Without evanescent waves, the symmetric focus spot is limited by the Rayleigh criterion. We present an experimental observation of a time-reversal elastic wave in a soft solid cavity using the transient elastography technique. It is observed that the time-reversed far field wave collapses and gives birth to near fieldlike effects. Elastodynamic Green's functions computation confirms the experimental conclusions: the diffraction limit implies a direction dependant Rayleigh criterion.

Imaging anisotropic and viscous properties of breast tissue by magnetic resonance-elastography.

MR-elastography is a new technique for assessing the viscoelastic properties of tissue. One current focus of elastography is the provision of new physical parameters for improving the specificity in breast cancer diagnosis. This analysis describes a technique to extend the reconstruction to anisotropic elastic properties in terms of a so-called transversely isotropic model. Viscosity is treated as being isotropic. The particular model chosen for the anisotropy is appealing because it is capable of describing elastic shear anisotropy of parallel fibers. The dependence of the reconstruction on the particular choice of Poisson's ratio is eliminated by extracting the compressional displacement contribution using the Helmholtz-Hodge decomposition. Results are presented for simulations, a polyvinyl alcohol breast phantom, excised beef muscle, and measurements in two patients with breast lesions (invasive ductal carcinoma and fibroadenoma). The results show enhanced anisotropic and viscous properties inside the lesions and an indication for preferred fiber orientation.

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.

Observation of shock transverse waves in elastic media.

We report the first experimental observation of a shock transverse wave propagating in an elastic medium. This observation was possible because the propagation medium, a soft solid, allows one to reach a very high Mach number. In this extreme configuration, the shock formation is observed over a distance of less than a few wavelengths, thanks to a prototype of an ultrafast scanner (that acquires 5000 frames per second). A comparison of these new experimental data with theoretical predictions, based on a modified Burger's equation, shows good agreement.

Measurement of elastic nonlinearity of soft solid with transient elastography.

Transient elastography is a powerful tool to measure the speed of low-frequency shear waves in soft tissues and thus to determine the second-order elastic modulus mu (or the Young's modulus E). In this paper, it is shown how transient elastography can also achieve the measurement of the nonlinear third-order elastic moduli of an Agar-gelatin-based phantom. This method requires speed measurements of polarized elastic waves measured in a statically stressed isotropic medium. A static uniaxial stress induces a hexagonal anisotropy (transverse isotropy) in solids. In the special case of uniaxially stressed isotropic media, the anisotropy is not caused by linear elastic coefficients but by the third-order nonlinear elastic constants, and the medium recovers its isotropic properties as soon as the uniaxial stress disappears. It has already been shown how transient elastography can measure the elastic (second-order) moduli in a media with transverse isotropy such as muscles. Consequently this method, based on the measurement of the speed variations of a low-frequency (50-Hz) polarized shear strain waves as a function of the applied stress, allows one to measure the Landau moduli A, B, C that completely describe the third-order nonlinearity. The several orders of magnitude found among these three constants can be justified from the theoretical expression of the internal energy.