Impact of Acoustic Radiation Force Excitation Geometry on Shear Wave Dispersion and Attenuation Estimates

Shear wave elasticity imaging (SWEI) characterizes the mechanical properties of human tissues to differentiate healthy from diseased tissue. Commercial scanners tend to reconstruct shear wave speeds for a region of interest using time-of-flight methods reporting a single shear wave speed (or elastic modulus) to the end user under the assumptions that tissue is elastic and shear wave speeds are not dependent on the frequency content of the shear waves. Human tissues, however, are known to be viscoelastic, resulting in dispersion and attenuation. Shear wave spectroscopy and spectral methods have been previously reported in the literature to quantify shear wave dispersion and attenuation, commonly making an assumption that the acoustic radiation force excitation acts as a cylindrical source with a known geometric shear wave amplitude decay. This work quantifies the bias in shear dispersion and attenuation estimates associated with making this cylindrical wave assumption when applied to shear wave sources with finite depth extents, as commonly occurs with realistic focal geometries, in elastic and viscoelastic media. Bias is quantified using analytically derived shear wave data and shear wave data generated using finite-element method models. Shear wave dispersion and attenuation bias (up to 15% for dispersion and 41% for attenuation) is greater for more tightly focused acoustic radiation force sources with smaller depths of field relative to their lateral extent (height-to-width ratios <16). Dispersion and attenuation errors associated with assuming a cylindrical geometric shear wave decay in SWEI can be appreciable and should be considered when analyzing the viscoelastic properties of tissues with acoustic radiation force source distributions with limited depths of field.     

Analysis of Transient Shear Wave in Lossy Media

The propagation of shear waves from impulsive forces is an important topic in elastography. Observations of shear wave propagation can be obtained with numerous clinical imaging systems. Parameter estimations of the shear wave speed in tissues, and more generally the viscoelastic parameters of tissues, are based on some underlying models of shear wave propagation. The models typically include specific choices of the spatial and temporal shape of the impulsive force and the elastic or viscoelastic properties of the medium. In this work, we extend the analytical treatment of 2-D shear wave propagation in a biomaterial. The approach applies integral theorems relevant to the solution of the generalized Helmholtz equation, and does not depend on a specific rheological model of the tissue's viscoelastic properties. Estimators of attenuation and shear wave speed are derived from the analytical solutions, and these are applied to an elastic phantom, a viscoelastic phantom and in vivo liver using a clinical ultrasound scanner. In these samples, estimated shear wave group velocities ranged from 1.7?m/s in the liver to 2.5?m/s in the viscoelastic phantom, and these are lower-bounded by independent measurements of phase velocity.     

Comprehensive Viscoelastic Characterization of Tissues and the Inter-relationship of Shear Wave (Group and Phase) Velocity,Attenuation and Dispersion

We report shear wave phase and group velocity, dispersion and attenuation in oil-in-gelatin viscoelastic phantoms and in vivo liver data. Moreover, we measured the power law coefficient from each dispersion curve and used it, together with the shear wave velocity, to calculate an approximate value for attenuation that agrees with independent attenuation measurements. Results in phantoms exhibit good agreement for all parameters with respect to independent mechanical measurements. For in vivo data, the livers of 20 patients were scanned. Results were compared with pathology scores obtained from liver biopsies. Across these cases, increases in shear wave dispersion and attenuation were related to increased steatosis score. It was found that shear wave dispersion and attenuation are experimentally linked, consistent with simple predictions based on the rheology of tissues, and can be used individually or jointly to assess tissue viscosity. Thus, this study indicates the possible utility of using shear wave dispersion and attenuation to non-invasively and quantitatively assess steatosis.     

Two Point Method For Robust Shear Wave Phase Velocity Dispersion Estimation of Viscoelastic Materials

Ultrasound shear wave elastography (SWE) is an imaging modality used for noninvasive, quantitative evaluation of tissue mechanical properties. SWE uses an acoustic radiation force to produce laterally propagating shear waves that can be tracked in spatial and temporal domains in order to obtain the wave velocity. One of the ways to study the viscoelasticity is through examining the shear wave velocity dispersion curves. In this paper, we present an alternative method to two-dimensional Fourier transform (2D-FT). Our unique approach (2P-CWT) considers shear wave propagation measured in two lateral locations only and uses wavelet transformation analysis. We used the complex Morlet wavelet function as the mother wavelet to filter two shear waves at different locations. We examined how the first signal position and the distance between the two locations affect the shear wave velocity dispersion estimation in 2P-CWT. We tested this new method on a digital phantom data created using the local interaction simulation approach (LISA) in viscoelastic media with and without added white Gaussian noise to the wave motion. Moreover, we tested data acquired from custom made tissue mimicking viscoelastic phantom experiments and ex vivo porcine liver measurements. We compared results from 2P-CWT with the 2D-FT technique. 2P-CWT provided dispersion curves estimation with lower errors over a wider frequency band in comparison to 2D-FT. Tests conducted showed that the two-point technique gives results with better accuracy in simulation results and can be used to measure phase velocity of viscoelastic materials.     

Evaluation of Robustness of Local Phase Velocity Imaging in Homogenous Tissue-Mimicking Phantoms

Shear wave elastography (SWE) is a method of evaluating mechanical properties of soft tissues. Most current implementations of SWE report the group velocity for shear wave velocity, which assumes an elastic, isotropic, homogenous and incompressible tissue. Local phase velocity imaging (LPVI) is a novel method of phase velocity reconstruction that allows for accurate evaluation of shear wave velocity at specified frequencies. This method's robustness was evaluated in 11 elastic and 8 viscoelastic phantoms using linear and curvilinear arrays. We acquired data with acoustic radiation force push beams with different focal depths and F-numbers and reconstructed phase velocity images over a wide range of frequencies. Regardless of phantom, push beam focal depth and reconstruction frequency, an F-number around 3.0 was found to produce the largest usable area in the phase velocity reconstructions. For elastic phantoms scanned with a linear array, the optimal focal depth, frequency range and maximum region of interest (ROI) were 20–30 mm, 100–400 Hz and 2.70 cm², respectively. For viscoelastic phantoms scanned with a linear array, the optimal focal depth, frequency and maximum ROI were 20–30 mm, 100–300 Hz and 1.54 cm², respectively. For the curvilinear array in the same phantoms, optimal focal depth, frequency range and maximum ROIs were 45–60 mm, 100–400 and 100–300 Hz and 1.54 cm², respectively. In further work, LPVI reconstructions from inclusion phantoms will be evaluated to simulate non-homogeneous tissues. Additionally, LPVI will be evaluated in larger-volume phantoms to account for wave reflection from the containers when using the curvilinear array.     

Accounting for the Spatial Observation Window in the 2-D Fourier Transform Analysis of Shear Wave Attenuation

Recent measurements of shear wave propagation in viscoelastic materials have been analyzed by constructing the 2-D Fourier transform (2DFT) of the shear wave signal and measuring the phase velocity c(ω) and attenuation α(ω) from the peak location and full width at half-maximum (FWHM) of the 2DFT signal at discrete frequencies. However, when the shear wave is observed over a finite spatial range, the 2DFT signal is a convolution of the true signal and the observation window, and measurements using the FWHM can yield biased results. In this study, we describe a method to account for the size of the spatial observation window using a model of the 2DFT signal and a non-linear, least-squares fitting procedure to determine c(ω) and α(ω). Results from the analysis of finite-element simulation data agree with c(ω) and α(ω) calculated from the material parameters used in the simulation. Results obtained in a viscoelastic phantom indicate that the measured attenuation is independent of the observation window and agree with measurements of c(ω) and α(ω) obtained using the previously described progressive phase and exponential decay analysis.     

Shear wave dispersion measures liver steatosis

Crawling waves, which are interfering shear wave patterns, can be generated in liver tissue over a range of frequencies. Some important biomechanical properties of the liver can be determined by imaging the crawling waves using Doppler techniques and analyzing the patterns. We report that the dispersion of shear wave velocity and attenuation, that is, the frequency dependence of these parameters, are strongly correlated with the degree of steatosis in a mouse liver model, ex vivo. The results demonstrate the possibility of assessing liver steatosis using noninvasive imaging methods that are compatible with color Doppler scanners and, furthermore, suggest that liver steatosis can be separated from fibrosis by assessing the dispersion or frequency dependence of shear wave propagations.     

Correlation between Classical Rheometry and Supersonic Shear Wave Imaging in Blood Clots

The assessment of coagulating blood elasticity has gained importance as a result of several studies that have correlated it to cardiovascular pathologic conditions. In this study we use supersonic shear wave imaging (SSI) to measure viscoelastic properties of blood clots. At the same time, classical rheometry experiments were carried out on the same blood samples taken within the first few seconds of coagulation. Using SSI, phase velocities of the shear wave indicated increasing dispersion with time. In all cases, the frequency bandwidth of propagating shear waves changed from 20–50 Hz at the first few min of coagulation to around 300 Hz toward the end of experiments. Using the values of G′ and G″ from the rheometry studies, the theoretical shear wave velocities were calculated and correlated with SSI measurements. Results of the two techniques were in very good agreement, confirming that SSI provides accurate measurements of viscoelastic properties as corroborated by conventional rheometric measurements.     

Assessment of Structural Heterogeneity and Viscosity in the Cervix Using Shear Wave Elasticity Imaging: Initial Results from a Rhesus Macaque Model

Shear wave elasticity imaging has shown promise in evaluation of the pregnant cervix. Changes in shear wave group velocity have been attributed exclusively to changes in stiffness. This assumes homogeneity within the region of interest and purely elastic tissue behavior. However, the cervix is structurally/microstructurally heterogeneous and viscoelastic. We therefore developed strategies to investigate these complex tissue properties. Shear wave elasticity imaging was performed ex vivo on 14 unripened and 13 misoprostol-ripened cervix specimens from rhesus macaques. After tests of significant and uniform shear wave displacement, as well as reliability of estimates, group velocity decreased significantly from the distal (vaginal) to proximal (uterine) end of unripened, but not ripened, specimens. Viscosity was quantified by the slope of the phase velocity versus frequency. Dispersion was observed in both groups (median: 5.5 m/s/kHz, interquartile range: 1.5–12.0 m/s/kHz), also decreasing toward the proximal cervix. This work suggests that comprehensive assessment of complex tissues such as cervix requires consideration of structural heterogeneity and viscosity.     

Development of Tough Hydrogel Phantoms to Mimic Fibrous Tissue for Focused Ultrasound Therapies

Tissue-mimicking gels provide a cost-effective medium to optimize histotripsy treatment parameters with immediate feedback. Agarose and polyacrylamide gels are often used to evaluate treatment outcomes as they mimic the acoustic properties and stiffness of a variety of soft tissues, but they do not exhibit high toughness, a characteristic of fibrous connective tissue. To mimic pathologic fibrous tissue found in benign prostate hyperplasia (BPH) and other diseases that are potentially treatable with histotripsy, an optically transparent hydrogel with high toughness was developed that is a hybrid of polyacrylamide and alginate. The stiffness was established using shear wave elastography (SWE) and indentometry techniques and was found to be representative of human BPH ex vivo prostate tissue. Different phantom compositions and excised ex vivo BPH tissue samples were treated with a 700-kHz histotripsy transducer at different pulse repetition frequencies. Post-treatment, the hybrid gels and the tissue samples exhibited differential reduction in stiffness as measured by SWE. On B-mode ultrasound, partially treated areas were present as hyperechoic zones and fully liquified areas as hypoechoic zones. Phase contrast microscopy of the gel samples revealed liquefaction in regions consistent with the target lesion dimensions and correlated to findings identified in tissue samples via histology. The dose required to achieve liquefaction in the hybrid gel was similar to what has been observed in ex vivo tissue and greater than that of agarose of comparable or higher Young's modulus by a factor >10. These results indicate that the developed hydrogels closely mimic elasticities found in BPH prostate ex vivo tissue and have a similar response to histotripsy treatment, thus making them a useful cost-effective alternative for developing and evaluating different treatment protocols.     

Shear Wave Speed Estimation Using Reverberant Shear Wave Fields: Implementation and Feasibility Studies

Elastography is a modality that estimates tissue stiffness and, thus, provides useful information for clinical diagnosis. Attention has focused on the measurement of shear wave propagation; however, many methods assume shear wave propagation is unidirectional and aligned with the lateral imaging direction. Any deviations from the assumed propagation result in biased estimates of shear wave speed. To address these challenges, directional filters have been applied to isolate shear waves with different propagation directions. Recently, a new method was proposed for tissue stiffness estimation involving creation of a reverberant shear wave field propagating in all directions within the medium. These reverberant conditions lead to simple solutions, facile implementation and rapid viscoelasticity estimation of local tissue. In this work, this new approach based on reverberant shear waves was evaluated and compared with another well-known elastography technique using two calibrated elastic and viscoelastic phantoms. Additionally, the clinical feasibility of this technique was analyzed by assessing shear wave speed in human liver and breast tissues, in vivo. The results indicate that it is possible to estimate the viscoelastic properties in each scanned medium. Moreover, a better approach to estimation of shear wave speed was obtained when only the phase information was taken from the reverberant waves, which is equivalent to setting all magnitudes within the bandpass equal to unity: an idealization of a perfectly isotropic reverberant shear wave field.     

Congruence of imaging estimators and mechanical measurements of viscoelastic properties of soft tissues

Biomechanical properties of soft tissues are important for a wide range of medical applications, such as surgical simulation and planning and detection of lesions by elasticity imaging modalities. Currently, the data in the literature is limited and conflicting. Furthermore, to assess the biomechanical properties of living tissue in vivo, reliable imaging-based estimators must be developed and verified. For these reasons, we developed and compared two independent quantitative methods--crawling wave estimator (CRE) and mechanical measurement (MM) for soft tissue characterization. The CRE method images shear wave interference patterns from which the shear wave velocity can be determined and hence the Young's modulus can be obtained. The MM method provides the complex Young's modulus of the soft tissue from which both elastic and viscous behavior can be extracted. This article presents the systematic comparison between these two techniques on the measurement of gelatin phantom, veal liver, thermal-treated veal liver and human prostate. It was observed that the Young's moduli of liver and prostate tissues slightly increase with frequency. The experimental results of the two methods are highly congruent, suggesting CRE and MM methods can be reliably used to investigate viscoelastic properties of other soft tissues, with CRE having the advantages of operating in nearly real time and in situ.     

A fluorometric method for determination of C3b inactivator

A simple method for the determination of C3b inactivator in human plasma was investigated. Fluorescent-labeled C3, which was prepared by treatment with methylamine and a fluorescent thiol reagent, N-(dimethylamino-4-methylcoumarinyl)-maleimide, was used as the substrate. Diluted human plasma is incubated with fluorescent C3, reduced with 2-mercaptoethanol, and subjected to sodium dodecyl sulfate polyacrylamide gel electrophoresis. The fluorescent cleavage product is then determined by scanning the gels with a fluorospectrophotometer. This method is simple and sensitive enough to determine C3b inactivator activity in 1 μl of human plasma.     

Properties of ultrasonic waves in bovine bone marrow

We investigated the properties of ultrasonic waves in bovine bone marrow. Six bone marrow samples were obtained from different parts (proximal, middle and distal) of the shafts of two bovine femora without destruction. The measured frequency range was 3 to 10 MHz, and the temperature range was 15 to 40°C. Both wave velocity and attenuation coefficient in bone marrow always decreased as temperature increased. The velocity ranged from 1400 to 1610 m/s and attenuation coefficient ranged from 4 to 16 dB/cm. Wave velocities in bone marrow were similar to those in water, whereas the temperature dependences were different, and the wave attenuation coefficients were much higher than those in water. The dependence of velocity on temperature changed slightly around 23–24°C, where a transition from soft gel to oily liquid occurred. The transition temperature was confirmed by differential scanning calorimetry (DSC). Below this transition temperature, positive velocity dispersion was observed.     

Assessment of the Viscoelastic and Oscillation Properties of a Nano-engineered Multimodality Contrast Agent

Combinations of microbubbles (MBs) and superparamagnetic iron oxide nanoparticles (SPIONs) are used to fabricate dual contrast agents for ultrasound and MRI. This study examines the viscoelastic and oscillation characteristics of two MB types that are manufactured with SPIONs and either anchored chemically on the surface (MBs-chem) or physically embedded (MBs-phys) into a polymer shell. A linearized Church model was employed to simultaneously fit attenuation coefficients and phase velocity spectra that were acquired experimentally. The model predicted lower viscoelastic modulus values, undamped resonance frequencies and total damping ratios for MBs-chem. MBs-chem had a resonance frequency of approximately 13 MHz and a damping ratio of approximately 0.9; thus, MBs-chem can potentially be used as a conventional ultrasound contrast agent with the combined functionality of MRI detection. In contrast, MBs-phys had a resonance frequency and damping of 28 MHz and 1.2, respectively, and requires further modification of clinically available contrast pulse sequences to be visualized.     

Time-Aligned Plane Wave Compounding Methods for High-Frame-Rate Shear Wave Elastography: Experimental Validation and Performance Assessment on Tissue Phantoms

Shear wave elastography (SWE) is an ultrasonic technique able to quantitatively assess the mechanical properties of tissues by combining acoustic radiation force and ultrafast imaging. While utilizing coherent plane wave compounding enhances echo and shear wave motion signal-to-noise ratio (SNR), it also reduces the effective pulse repetition frequency (PRF_e), affecting the accuracy of the measurements of motion and, consequently, of material properties. It is important to maintain both high-motion SNR and PRF_e, particularly for the characterization of (material and/or geometrical) dispersive tissues such as arteries. This work proposes a method for SWE measurements with high SNR, while maintaining a high PRF_e, using conventional clinical ultrasound scanners. A time alignment process is applied after acquiring data from plane wave transmissions at different angles. The time alignment uses interpolation to obtain data points at higher frame rates, and the time-aligned data are compounded to increase the SNR. The method is used for SWE in tissue-mimicking phantoms of different stiffness and is compared with traditional plane wave compounding. Increases of 58% and 36% in spatial and temporal bandwidth compared with conventional plane wave compounding, respectively, can be achieved for SWE measurements of representative arterial stiffness values. Improvements in phase velocity accuracy and bandwidth in an arterial phantom are also described, to emphasize the beneficial advantage in dispersive cases.     

Absorption of longitudinal and shear waves and generation of heat in soft tissues

The author analysed the oblique incidence of a longitudinal plane wave and the generation of a shear wave at a boundary between a soft tissue and a gas, considering a viscoelastic model (Voigt solid) of the medium. From the data measured by Frizzell et al. (J. Acoust. Soc. Am. 60, 1409-1411) for shear waves, the average velocity 30 m/s and the average absorption coefficient 7.7 X 10(3) cm-1 at the frequency of 5 MHz were assumed for calculations. The amplitude and the intensity of the generated shear wave were obtained and hence the rate of heat production per unit volume was determined. At the boundary, this quantity was found to be of the same order of magnitude for the generated shear wave as for the incident longitudinal wave. In the case of the shear wave, which propagates almost perpendicularly to the boundary, it decreases rapidly with the distance. Therefore, the temperature increase caused by shear waves was negligible in respect to longitudinal waves in spite of the extremely high absorption coefficient. This conclusion could be confirmed by solving the inhomogeneous equation of heat conductivity for the case under consideration.     

Measurement of shear wave propagation and investigation of estimation of shear viscoelasticity for tissue characterization of the arterial wall

Purpose The aim of this study was to find an array of frequency components, ranging from 0 Hz (direct current) to several tens of hertz that comprise the small vibrations on the arterial wall using noninvasive in vivo experiments. These vibrations are caused mainly by blood flow. The viscoelasticity of the arterial wall was estimated from the frequency characteristics of these vibrations propagating from the intima to the adventitia.Methods Propagation of these frequencies in human tissue displays certain frequency characteristics. Based on the Voigt model, shear viscoelasticity can be estimated from the frequency characteristics of the propagating vibrations. Moreover, we estimated shear viscoelasticity from the measured frequency characteristics of shear wave attenuation.Results Shear wave propagation from the intima to the adventitia resulting from blood flow was explained theoretically based on the obtained measurements. Shear viscoelasticity was also estimated from the measured frequency characteristics of shear wave attenuation.Conclusions Based on the proposed method, shear viscoelasticity can be estimated from ultrasonographic measurements. These results have a novel potential for characterizing tissue noninvasively.     

Comparison of polyacrylamide and agarose gel thin-layer isoelectric focusing for the characterization of beta-lactamases

Plasmid-mediated beta-lactamases from strains of Escherichia coli and Pseudomonas aeruginosa were separated by isoelectric focusing on a 0.8-mm thin-layer agarose gel with a pH gradient of 3.5 to 9.5. Their banding patterns and isoelectric points were compared with those obtained with a 2.0-mm polyacrylamide gel as the support medium. The agarose method produced banding patterns and isoelectric points which corresponded to the polyacrylamide gel data for most samples. Differences were observed for HMS-1 and PSE-1 beta-lactamases. The HMS-1 sample produced two highly resolvable enzyme bands in agarose gels rather than the single faint enzyme band observed on polyacrylamide gels. The PSE-1 sample showed an isoelectric point shift of 0.2 pH unit between polyacrylamide and agarose gel (pI 5.7 and 5.5, respectively). The short focusing time, lack of toxic hazard, and ease of formulation make agarose a practical medium for the characterization of beta-lactamases.