Detection of tissue harmonic motion induced by ultrasonic radiation force using pulse-echo ultrasound and Kalman filter

A method using pulse echo ultrasound and the Kalman filter is developed for detecting submicron harmonic motion induced by ultrasonic radiation force. The method estimates the amplitude and phase of the motion at desired locations within a tissue region with high sensitivity. The harmonic motion generated by the ultrasound radiation force is expressed as extremely small oscillatory Doppler frequency shifts in the fast time (A-line) of ultrasound echoes, which are difficult to estimate. In slow time (repetitive ultrasound echoes) of the echoes, the motion also is presented as oscillatory phase shifts, from which the amplitude and phase of the harmonic motion can be estimated with the least mean squared error by Kalman filter. This technique can be used to estimate the traveling speed of a harmonic shear wave by tracking its phase changes during propagation. The shear wave propagation speed can be used to solve for the elasticity and viscosity of tissue as reported in our earlier study. Validation and in vitro experiments indicate that the method provides excellent estimations for very small (submicron) harmonic vibrations and has potential for noninvasive and quantitative stiffness measurements of tissues such as artery.     

Noninvasive method for estimation of complex elastic modulus of arterial vessels

Pulse wave velocity (PWV) is widely used for estimating the stiffness of an artery. It is well-known that a stiffened artery can be associated with various diseases and with aging. Usually, PWV is measured using the "foot-to-foot" method in which the travel time of the wave is measured over a distance. The "foot" of the pressure wave is not clear due to reflected waves and blood noise. Also, PWV is an average indicator of artery stiffness between the two measuring points and, therefore, does not identify local stiffness variations. We propose producing a bending wave in the arterial wall using low-frequency, localized ultrasound radiation force and measuring the wave velocity along the arterial wall. The wave velocity can be measured accurately over a few millimeters. A mathematical model for wave propagation along the artery is developed with which the Young's modulus of the artery can be determined from measured wave velocities. Experiments were conducted on a pig carotid artery cast in a tissue-mimicking gelatin. The wave velocity was measured by the phase change at a known distance for a given frequency. The measured wave velocity is about 3 m/s at 100 Hz and 6.5 m/s at 500 Hz. The real part of complex elastic modulus of the artery is estimated to be 300 kPa.     

Narrowband shear wave generation by a Finite-Amplitude radiation force: The fundamental component

A highly localized source of low-frequency shear waves can be created by the modulated radiation force resulting from two intersecting quasi-continuous-wave ultrasound beams of slightly different frequencies. In contrast to most other radiation force-based methods, these shear waves can be narrowband. Consequently, different frequency-dependent effects will not significantly affect their spectrum as they propagate within a viscoelastic medium, thereby enabling the viscoelastic shear properties of the medium to be determined at any given modulation frequency. This can be achieved by tracking the shear wave phase delay and change in amplitude over a specific distance. In this paper we explore the properties of short duration (dynamic) low-frequency shear wave propagation and study how the shear displacement field depends on the excitation conditions. Our investigations make use of the approximate Green's functions for viscoelastic media, and the evolution of such waves is studied in the spatiotemporal domain from a theoretical perspective. Although nonlinearities are included in our confocal source model, just the properties of the fundamental shear component are examined in this paper. We examine how the shear wave propagation is affected by the shear viscosity, the coupling wave, the spatial distribution of the force, the shear speed, and the duration of the modulated wave. A method is proposed for estimating the shear viscosity of a viscoelastic medium. In addition, it is shown how the Voigt model paremeters can be extracted from the frequency-dependent speed and attenuation.     

Imaging feedback of histotripsy treatments using ultrasound shear wave elastography

Histotripsy is a cavitation-based ultrasound therapy that mechanically fractionates soft solid tissues into fluid-like homogenates. This paper investigates the feasibility of imaging the tissue elasticity change during the histotripsy process as a tool to provide feedback for the treatments. The treatments were performed on agar tissue phantoms and ex vivo kidneys using 3-cycle ultrasound pulses delivered by a 750-kHz therapeutic array at peak negative/positive pressure of 17/108 MPa and a repetition rate of 50 Hz. Lesions with different degrees of damage were created with increasing numbers of therapy pulses from 0 to 2000 pulses per treatment location. The elasticity of the lesions was measured with ultrasound shear wave elastography, in which a quasi-planar shear wave was induced by acoustic radiation force generated by the therapeutic array, and tracked with ultrasound imaging at 3000 frames per second. Based on the shear wave velocity calculated from the sequentially captured frames, the Young's modulus was reconstructed. Results showed that the lesions were more easily identified on the shear wave velocity images than on B-mode images. As the number of therapy pulses increased from 0 to 2000 pulses/location, the Young's modulus decreased exponentially from 22.1 ± 2.7 to 2.1 ± 1.1 kPa in the tissue phantoms (R2 = 0.99, N = 9 each), and from 33.0 ± 7.1 to 4.0 ± 2.5 kPa in the ex vivo kidneys (R2 = 0.99, N = 8 each). Correspondingly, the tissues transformed from completely intact to completely fractionated as examined via histology. A good correlation existed between the lesions' Young's modulus and the degree of tissue fractionation as examined with the percentage of remaining structurally intact cell nuclei (R2 = 0.91, N = 8 each). These results indicate that lesions produced by histotripsy can be detected with high sensitivity using shear wave elastography. Because the decrease in the tissue elasticity corresponded well with the morphological and histological change, this study provides a basis for predicting the local treatment outcomes from tissue elasticity change.     

Dynamic mechanical response of elastic spherical inclusions to impulsive acoustic radiation force excitation

Acoustic radiation force impulse imaging has been used clinically to study the dynamic response of lesions relative to their background material to focused, impulsive acoustic radiation force excitations through the generation of dynamic displacement field images. Dynamic displacement data are typically displayed as a set of parametric images, including displacement immediately after excitation, maximum displacement, time to peak displacement, and recovery time from peak displacement. To date, however, no definitive trends have been established between these parametric images and the tissues' mechanical properties. This work demonstrates that displacement magnitude, time to peak displacement, and recovery time are all inversely related to the Young's modulus in homogeneous elastic media. Experimentally, pulse repetition frequency during displacement tracking limits stiffness resolution using the time to peak displacement parameter. The excitation pulse duration also impacts the time to peak parameter, with longer pulses reducing the inertial effects present during impulsive excitations. Material density affects tissue dynamics, but is not expected to play a significant role in biological tissues. The presence of an elastic spherical inclusion in the imaged medium significantly alters the tissue dynamics in response to impulsive, focused acoustic radiation force excitations. Times to peak displacement for excitations within and outside an elastic inclusion are still indicative of local material stiffness; however, recovery times are altered due to the reflection and transmission of shear waves at the inclusion boundaries. These shear wave interactions cause stiffer inclusions to appear to be displaced longer than the more compliant background material. The magnitude of shear waves reflected at elastic lesion boundaries is dependent on the stiffness contrast between the inclusion and the background material, and the stiffness and size of the inclusion dictate when shear wave reflections within the lesion will interfere with one another. Jitter and bias associated with the ultrasonic displacement tracking also impact the estimation of a tissue's dynamic response to acoustic radiation force excitation.     

Assessment of viscous and elastic properties of sub-wavelength layered soft tissues using shear wave spectroscopy: theoretical framework and in vitro experimental validation

In elastography, quantitative imaging of soft tissue elastic properties is provided by local shear wave speed estimation. Shear wave imaging in a homogeneous medium thicker than the shear wavelength is eased by a simple relationship between shear wave speed and local shear modulus. In thin layered organs, the shear wave is guided and thus undergoes dispersive effects. This case is encountered in medical applications such as elastography of skin layers, corneas, or arterial walls. In this work, we proposed and validated shear wave spectroscopy as a method for elastic modulus quantification in such layered tissues. Shear wave dispersion curves in thin layers were obtained by finite-difference simulations and numerical solving of the boundary conditions. In addition, an analytical approximation of the dispersion equation was derived from the leaky Lamb wave theory. In vitro dispersion curves obtained from phantoms were consistent with numerical studies (deviation <1.4%). The least-mean-squares fitting of the dispersion curves enables a quantitative and accurate (error < 5% of the transverse speed) assessment of the elasticity. Dispersion curves were also found to be poorly influenced by shear viscosity. This phenomenon allows independent recovery of the shear modulus and the viscosity, using, respectively, the dispersion curve and the attenuation estimation along the propagation axis.     

Propagation of shear waves generated by a modulated finite amplitude radiation force in a viscoelastic medium

An effective way to generate localized narrow-band low-frequency shear waves within tissue noninvasively, is by the modulated radiation force, resulting from the interference of two confocal quasi-CW ultrasound beams of slightly different frequencies. By using approximate viscoelastic Green's functions, investigations of the properties of the propagated shear-field component at the fundamental modulation frequency were previously reported by our group. However, high-amplitude source excitations may be needed to increase the signal-to-noise-ratio for shear-wave detection in tissue. This paper reports a study of the generation and propagation of dynamic radiation force components at harmonics of the modulation frequency for conditions that generally correspond to diagnostic safety standards. We describe the propagation characteristics of the resulting harmonic shear waves and discuss how they depend on the parameters of nonlinearity, focusing gain, and absorption. For conditions of high viscosity (believed to be characteristic of soft tissue) and higher modulation frequencies, the approximate shear wave Green's function is inappropriate. A more exact viscoelastic Green's function is derived in k-space, and using this, it is shown that the lowpass and dispersive effects, associated with a Voigt model of tissue, are more accurately represented. Finally, it is shown how the viscoelastic properties of the propagating medium can be estimated, based on several spectral components of the shear wave spectrum.     

Application of 1-D transient elastography for the shear modulus assessment of thin-layered soft tissue: comparison with supersonic shear imaging technique

Elasticity estimation of thin-layered soft tissues has gained increasing interest propelled by medical applications like skin, corneal, or arterial wall shear modulus assessment. In this work, the authors propose one-dimensional transient elastography (1DTE) for the shear modulus assessment of thin-layered soft tissue. Experiments on three phantoms with different elasticities and plate thicknesses were performed. First, using 1DTE, the shear wave speed dispersion curve inside the plate was obtained and validated with finite difference simulation. No dispersive effects were observed and the shear wave speed was directly retrieved from time-of-flight measurements. Second, the supersonic shear imaging (SSI) technique (considered to be a gold standard) was performed. For the SSI technique, the propagating wave inside the plate is guided as a Lamb wave. Experimental SSI dispersion curves were compared with finite difference simulation and fitted using a generalized Lamb model to retrieve the plate bulk shear wave speed. Although they are based on totally different mechanical sources and induce completely different diffraction patterns for the shear wave propagation, the 1DTE and SSI techniques resulted in similar shear wave speed estimations. The main advantage of the 1DTE technique is that bulk shear wave speed can be directly retrieved without requiring a dispersion model.     

Monitoring of thermal therapy based on shear modulus changes: I. shear wave thermometry

The clinical applicability of high-intensity focused ultrasound (HIFU) for noninvasive therapy is today hampered by the lack of robust and real-time monitoring of tissue damage during treatment. The goal of this study is to show that the estimation of local tissue elasticity from shear wave imaging (SWI) can lead to the 2-D mapping of temperature changes during HIFU treatments. This new concept of shear wave thermometry is experimentally implemented here using conventional ultrasonic imaging probes. HIFU treatment and monitoring were, respectively, performed using a confocal setup consisting of a 2.5-MHz single-element transducer focused at 30 mm on ex vivo samples and an 8-MHz ultrasound diagnostic probe. Thermocouple measurements and ultrasound-based thermometry were used as a gold standard technique and were combined with SWI on the same device. The SWI sequences consisted of 2 successive shear waves induced at different lateral positions. Each wave was created using 100-μs pushing beams at 3 depths. The shear wave propagation was acquired at 17,000 frames/s, from which the elasticity map was recovered. HIFU sonications were interleaved with fast imaging acquisitions, allowing a duty cycle of more than 90%. Elasticity and temperature mapping was achieved every 3 s, leading to realtime monitoring of the treatment. Tissue stiffness was found to decrease in the focal zone for temperatures up to 43°C. Ultrasound-based temperature estimation was highly correlated to stiffness variation maps (r2 = 0.91 to 0.97). A reversible calibration phase of the changes of elasticity with temperature can be made locally using sighting shots. This calibration process allows for the derivation of temperature maps from shear wave imaging. Compared with conventional ultrasound-based approaches, shear wave thermometry is found to be much more robust to motion artifacts.     

Improving thermal ablation delineation with electrode vibration elastography using a bidirectional wave propagation assumption

Thermal ablation procedures are commonly used to treat hepatic cancers and accurate ablation representation on shear wave velocity images is crucial to ensure complete treatment of the malignant target. Electrode vibration elastography is a shear wave imaging technique recently developed to monitor thermal ablation extent during treatment procedures. Previous work has shown good lateral boundary delineation of ablated volumes, but axial delineation was more ambiguous, which may have resulted from the assumption of lateral shear wave propagation. In this work, we assume both lateral and axial wave propagation and compare wave velocity images to those assuming only lateral shear wave propagation in finite element simulations, tissue-mimicking phantoms, and bovine liver tissue. Our results show that assuming bidirectional wave propagation minimizes artifacts above and below ablated volumes, yielding a more accurate representation of the ablated region on shear wave velocity images. Area overestimation was reduced from 13.4% to 3.6% in a stiff-inclusion tissue-mimicking phantom and from 9.1% to 0.8% in a radio-frequency ablation in bovine liver tissue. More accurate ablation representation during ablation procedures increases the likelihood of complete treatment of the malignant target, decreasing tumor recurrence.     

Monitoring of thermal therapy based on shear modulus changes: II. Shear wave imaging of thermal lesions

The clinical applicability of high-intensity focused ultrasound (HIFU) for noninvasive therapy is currently hampered by the lack of robust and real-time monitoring of tissue damage during treatment. The goal of this study is to show that the estimation of local tissue elasticity from shear wave imaging (SWI) can lead to a precise mapping of the lesion. HIFU treatment and monitoring were respectively performed using a confocal setup consisting of a 2.5-MHz single element transducer focused at 34 mm on ex vivo samples and an 8-MHz ultrasound diagnostic probe. Ultrasound-based strain imaging was combined with shear wave imaging on the same device. The SWI sequences consisted of 2 successive shear waves induced at different lateral positions. Each wave was created with pushing beams of 100 μs at 3 depths. The shear wave propagation was acquired at 17,000 frames/s, from which the elasticity map was recovered. HIFU sonications were interleaved with fast imaging acquisitions, allowing a duty cycle of more than 90%. Thus, elasticity and strain mapping was achieved every 3 s, leading to real-time monitoring of the treatment. When thermal damage occurs, tissue stiffness was found to increase up to 4-fold and strain imaging showed strong shrinkages that blur the temperature information. We show that strain imaging elastograms are not easy to interpret for accurate lesion characterization, but SWI provides a quantitative mapping of the thermal lesion. Moreover, the concept of shear wave thermometry (SWT) developed in the companion paper allows mapping temperature with the same method. Combined SWT and shear wave imaging can map the lesion stiffening and temperature outside the lesion, which could be used to predict the eventual lesion growth by thermal dose calculation. Finally, SWI is shown to be robust to motion and reliable in vivo on sheep muscle.     

Optical imaging with a directional detector

We demonstrate a new optical imaging technique based on a directional detector that measures the intensity of light waves that propagate only in a narrow angular window around a specific direction. Light waves that propagate in other directions do not significantly affect the detector output. The directional detector is obtained by illuminating the interrogated object with a high-coherence light source and measuring the interference between the light wave reflected from the object and a reference wave. By measuring the intensity of the interference pattern with an optical detector that has a finite width and moving the object by use of a rotation stage, one can obtain the angular directionality of the filter. The use of coherent detection in the directional detector makes it possible to increase the sensitivity of the system. The directional detector was analyzed theoretically and demonstrated experimentally for a Gaussian beam scattered from a conducting cylinder. The interference enabled us to theoretically increase the angular resolution by a factor of approximately 10 and experimentally by a factor of 8.5. A configuration for using a directional detector array to reconstruct a two-dimensional object is suggested. Since the directional detector makes it possible to reduce the effect of diffraction and scattering, reconstruction techniques based on nondiffracting sources, as implemented in x-ray tomography, may be used.     

Shearwave dispersion ultrasound vibrometry (SDUV) for measuring tissue elasticity and viscosity

Characterization of tissue elasticity (stiffness) and viscosity has important medical applications because these properties are closely related to pathological changes. Quantitative measurement is more suitable than qualitative measurement (i.e., mapping with a relative scale) of tissue viscoelasticity for diagnosis of diffuse diseases where abnormality is not confined to a local region and there is no normal background tissue to provide contrast. Shearwave dispersion ultrasound vibrometry (SDUV) uses shear wave propagation speed measured in tissue at multiple frequencies (typically in the range of hundreds of Hertz) to solve quantitatively for both tissue elasticity and viscosity. A shear wave is stimulated within the tissue by an ultrasound push beam and monitored by a separate ultrasound detect beam. The phase difference of the shear wave between 2 locations along its propagation path is used to calculate shear wave speed within the tissue. In vitro SDUV measurements along and across bovine striated muscle fibers show results of tissue elasticity and viscosity close to literature values. An intermittent pulse sequence is developed to allow one array transducer for both push and detect function. Feasibility of this pulse sequence is demonstrated by in vivo SDUV measurements in swine liver using a dual transducer prototype simulating the operation of a single array transducer.     

Shear modulus imaging with 2-D transient elastography

In previous work, we have shown that time-resolved 2-D transient elastography is a promising technique for characterizing the elasticity of soft tissues. It involves the measurement of the displacements induced by the propagation of low frequency (LF) pulsed shear waves in biological tissues. In this paper, we present a novel apparatus that contains a LF vibrating device surrounding a linear array of 128 ultrasonic transducers that performs ultrafast ultrasonic imaging (up to 10,000 frames/s) and that is able to follow in real time the propagation of a LF shear wave in the human body. The vibrating device is made of two rods, fixed to electromagnetic vibrators, that produce in the ultrasonic image area a large amplitude shear wave. The geometry has been chosen both to enhance the sensitivity and to create a quasi linear shear wave front in the imaging plane. An inversion algorithm is used to recover the shear modulus map from the spatio-temporal data, and the first experimental results obtained from tissue-equivalent materials are presented.     

The stiffening of arteries by the tissue-mimicking gelatin

Pulse wave velocity (PWV) is widely used for estimating the stiffness of an artery. PWV is measured by the time of travel of the "foot" of the pressure wave over a known distance. This technique has a low time resolution and is an average measurement of artery stiffness between the two measuring sites. The elastic modulus of the artery can be estimated with PWV, but the surrounding tissue effects are not considered. In this paper an external short pulse wave is generated noninvasively in the arterial wall by the radiation force of ultrasound. The pulse wave velocity in the artery is measured by a scanning technique with high-time resolution. The effect of tissue-mimicking gelatin on the artery is analyzed by measuring the wave velocity of the artery without and embedded in gelatin. It is found that the tissue-mimicking gelatin significantly stiffens the rubber tube and the artery if they are embedded in gelatin.     

A composite high-frame-rate system for clinical cardiovascular imaging

High frame-rate ultrasound RF data acquisition has been proved to be critical for novel cardiovascular imaging techniques, such as high-precision myocardial elastography, pulse wave imaging (PWI), and electromechanical wave imaging (EWI). To overcome the frame-rate limitations on standard clinical ultrasound systems, we developed an automated method for multi-sector ultrasound imaging through retrospective electrocardiogram (ECG) gating on a clinically used open architecture system. The method achieved both high spatial (64 beam density) and high temporal resolution (frame rate of 481 Hz) at an imaging depth up to 11 cm and a 100% field of view in a single breath-hold duration. Full-view imaging of the left ventricle and the abdominal aorta of healthy human subjects was performed using the proposed technique in vivo. ECG and ultrasound RF signals were simultaneously acquired on a personal computer (PC). Composite, full-view frames both in RF- and B-mode were reconstructed through retrospective combination of seven small (20%) juxtaposed sectors using an ECG-gating technique. The axial displacement of the left ventricle, in both long-axis and short-axis views, and that of the abdominal aorta, in a long-axis view, were estimated using a RF-based speckle tracking technique. The electromechanical wave and the pulse wave propagation were imaged in a cineloop using the proposed imaging technique. Abnormal patterns of such wave propagation can serve as indicators of early cardiovascular disease. This clinical system could thus expand the range of applications in cardiovascular elasticity imaging for quantitative, noninvasive diagnosis of myocardial ischemia or infarction, arrhythmia, abdominal aortic aneurysms, and early-stage atherosclerosis.     

Propagation of solitary waves in 2D granular media: A numerical study

The impact-induced wave propagation in a model granular material composed of closely packed linearly elastic spherical particles interacting through Hertzian contact is investigated numerically using a specially adapted molecular dynamics framework. Of particular interest is the effect of the stiffness and density mismatch between main and interstitial beads on the anisotropic nature and speed of propagation of the primary compressive wave generated by a localized impact event in an extended square-packed granular medium. Two propagation regimes are observed in the numerical simulations: the first one described by a solitary wave pattern emanating from the point of impact, and the other characterized by a directional propagation of the impact energy in the principal directions of the pack. A simple model is proposed to describe the bounds between these two propagation regimes in the parametric space defined by the mass and stiffness ratios between main and interstitial particles. Maps of the normalized maximum compressive force and wave speed are presented to quantify the anisotropy of the wave propagation response.     

Waves in a rotating elastic solid

Wave propagation in a uniformly rotating elastic solid is discussed based on displacement equations in a moving frame. The time-harmonic Green’s dyadic for a point body force is obtained in closed form. It is reconfirmed that two quasi dilatational and shear waves are coupled to each other, and the deformation decomposition into the dilatation and rotation is not possible for the rotating solid. Further, it is also confirmed that the velocity of the Rayleigh surface wave depends not only on the rotational velocity but also on its direction and that the Rayleigh wave vanishes when the rotational velocity approaches the Rayleigh wave velocity of the immovable solid.     

A new ultrasonic method for stress determination in textured materials

Non-destructive measurement of stress using ultrasonics often fails because of texture in the analysed material: texture as well as stress influences the wave velocity and reliable methods are needed to separate the two effects. This contribution briefly reviews earlier approaches and presents a new method to separate texture and stress effects by measuring the velocity dispersion of polarized shear waves. The techniques is based upon recently published theoretical work on wave propagation in polycrystalline quasi-isotropic as well as textured materials. Experimental results are in general agreement with the theoretical data.     

Air-coupled guided waves combined with thermography for monitoring fatigue in biaxially loaded composite tubes

Non-destructive methodologies for remote monitoring of fatigue induced by mechanical load in fibre reinforced plastics are presented. Hollow cylinders (glass fibre winding) were stepwise biaxially fatigued and measured in single-sided access configurations. Based on conversion of air-coupled ultrasound to guided waves, it is shown that accumulated fatigue damage is accompanied by decrease in phase velocity and increase in attenuation. The change in wave velocity caused by fatigue is shown to correlate closely with measurements of stiffness degradation of the composite. The attenuation of guided waves is affected by crack density which is visually traceable in the transparent composite. Monitoring of cyclic loading of the specimens by thermal imaging and a high-speed camera revealed that the initiation of final failure in the specimens coincides with spots of increased temperature. Air-coupled guided wave area scans allow for observing the development of these areas and other local damage in the composite.