A diffraction correction for storage and loss moduli imaging using radiation force based elastography

A Comprehensive Review on the Viscoelastic Parameters Used for Engineering Materials, Including Soft Materials, and the Relationships between Different Damping Parameters

Although the physical properties of a structure, such as stiffness, can be determined using some statical tests, the identification of damping parameters requires a dynamic test. In general, both theoretical prediction and experimental identification of damping are quite difficult. There are many different techniques available for damping identification, and each method gives a different damping parameter. The dynamic indentation method, rheometry, atomic force microscopy, and resonant vibration tests are commonly used to identify the damping of materials, including soft materials. While the viscous damping ratio, loss factor, complex modulus, and viscosity are quite common to describe the damping of materials, there are also other parameters, such as the specific damping capacity, loss angle, half-power bandwidth, and logarithmic decrement, to describe the damping of various materials. Often, one of these parameters is measured, and the measured parameter needs to be converted into another damping parameter for comparison purposes. In this review, the theoretical derivations of different parameters for the description and quantification of damping and their relationships are presented. The expressions for both high damping and low damping are included and evaluated. This study is considered as the first comprehensive review article presenting the theoretical derivations of a large number of damping parameters and the relationships among many damping parameters, with a quantitative evaluation of accurate and approximate formulas. This paper could be a primary resource for damping research and teaching.

Ultrasound Viscoelastography by Acoustic Radiation Force: A State-of-the-Art Review

Ultrasound elastography (USE) is a promising tool for tissue characterization as several diseases result in alterations of tissue structure and composition, which manifest as changes in tissue mechanical properties. By imaging the tissue response to an applied mechanical excitation, USE mimics the manual palpation performed by clinicians to sense the tissue elasticity for diagnostic purposes. Next to elasticity, viscosity has recently been investigated as an additional, relevant, diagnostic biomarker. Moreover, since biological tissues are inherently viscoelastic, accounting for viscosity in the tissue characterization process enhances the accuracy of the elasticity estimation. Recently, methods exploiting different acquisition and processing techniques have been proposed to perform ultrasound viscoelastography. After introducing the physics describing viscoelasticity, a comprehensive overview of the currently available USE acquisition techniques is provided, followed by a structured review of the existing viscoelasticity estimators classified according to the employed processing technique. These estimators are further reviewed from a clinical usage perspective, and current outstanding challenges are discussed.

Feasibility of Phase Velocity Imaging Using Multi Frequency Oscillation-Shear Wave Elastography

OBJECTIVE

To assess viscoelasticity, a pathologically relevant biomarker, shear wave elastography (SWE) generally uses phase velocity (PV) dispersion relationship generated via pulsed acoustic radiation force (ARF) excitation pulse. In this study, a multi-frequency oscillation (MFO)- excitation pulse with higher weight to higher frequencies is proposed to generate PV images via the generation of motion with energy concentrated at the target frequencies in contrast to the broadband frequency motion generated in pulsed SWE (PSWE).

METHODS

The feasibility of MFO-SWE to generate PV images at 100 to 1000 Hz in steps of 100 Hz was investigated by imaging 6 and 70 kPa inclusions with 6.5 and 10.4 mm diameter and ex vivo bovine liver with and without the presence of an aberration layer and chicken muscle ex vivo, and 4T1 mouse breast tumor, in vivo with comparisons to PSWE.

RESULTS

MFO-SWE-derived CNR was statistically higher than PSWE for 6 kPa (both with and without aberration) and 70 kPa (with aberration) inclusions and derived SNR of the liver was statistically higher than PSWE at higher frequency (600-1000 Hz). Quantitatively, at 600-1000 Hz, MFO-SWE improved CNR of inclusions (without and with) aberration on an average by (8.2 and 156)% and of the tumor by 122%, respectively, and improved SNR of the liver (without and with) aberration by (20.2 and 51.5)% and of chicken muscle by 72%, respectively compared to the PSWE.

CONCLUSIONS AND SIGNIFICANCE

These results indicate the advantages of MFO-SWE to improve PV estimation at higher frequencies which could improve viscoelasticity quantification and feature delineation.

Ultrasound Shear Wave Attenuation Imaging for Grading Liver Steatosis in Volunteers and Patients With Non-alcoholic Fatty Liver Disease: A Pilot Study

OBJECTIVE

The aims of the work described here were to assess shear wave attenuation (SWA) in volunteers and patients with non-alcoholic fatty liver disease (NAFLD) and compare its diagnostic performance with that of shear wave dispersion (SWD), magnetic resonance imaging (MRI) proton density fat fraction (PDFF) and biopsy.

METHODS

Forty-nine participants (13 volunteers and 36 NAFLD patients) were enrolled. Ultrasound and MRI examinations were performed in all participants. Biopsy was also performed in patients. SWA was used to assess histopathology grades as potential confounders. The areas under curves (AUCs) of SWA, SWD and MRI-PDFF were assessed in different steatosis grades by biopsy. Youden's thresholds of SWA were obtained for steatosis grading while using biopsy or MRI-PDFF as the reference standard.

RESULTS

Spearman's correlations of SWA with histopathology (steatosis, inflammation, ballooning and fibrosis) were 0.89, 0.73, 0.62 and 0.31, respectively. Multiple linear regressions of SWA confirmed the correlation with steatosis grades (adjusted R2 = 0.77, p < 0.001). The AUCs of MRI-PDFF, SWA and SWD were respectively 0.97, 0.99 and 0.94 for S0 versus ≥S1 (p > 0.05); 0.94, 0.98 and 0.78 for ≤S1 versus ≥S2 (both MRI-PDFF and SWA were higher than SWD, p < 0.05); and 0.90, 0.93 and 0.68 for ≤S2 versus S3 (both SWA and MRI-PDFF were higher than SWD, p < 0.05). SWA's Youden thresholds (Np/m/Hz) (sensitivity, specificity) for S0 versus ≥S1, ≤S1 versus ≥S2 and ≤S2 versus S3 were 1.05 (1.00, 0.92), 1.37 (0.96, 0.96) and 1.51 (0.83, 0.87), respectively. These values were 1.16 (1.00, 0.81), 1.49 (0.91, 0.82) and 1.67 (0.87, 0.92) when considering MRI-PDFF as the reference standard.

CONCLUSION

In this pilot study, SWA increased with increasing steatosis grades, and its diagnostic performance was higher than that of SWD but equivalent to that of MRI-PDFF.

Imaging of Single Transducer-Harmonic Motion Imaging-Derived Displacements at Several Oscillation Frequencies Simultaneously

Mapping of mechanical properties, dependent on the frequency of motion, is relevant in diagnosis, monitoring treatment response, or intra-operative surgical resection planning. While shear wave speeds at different frequencies have been described elsewhere, the effect of frequency on the "on-axis" acoustic radiation force (ARF)-induced displacement has not been previously investigated. Instead of generating single transducer-harmonic motion imaging (ST-HMI)-derived peak-to-peak displacement (P2PD) image at a particular frequency, a novel multi-frequency excitation pulse is proposed to generate P2PD images at 100-1000 Hz simultaneously. The performance of the proposed excitation pulse is compared with the ARFI by imaging 16 different inclusions (Young's moduli of 6, 9, 36, 70 kPa and diameters of 1.6, 2.5, 6.5, and 10.4 mm) embedded in an 18 kPa background. Depending on inclusion size and stiffness, the maximum CNR and contrast were achieved at different frequencies and were always higher than ARFI. The frequency, at which maximum CNR and contrast were achieved, increased with stiffness for fixed inclusion's size and decreased with size for fixed stiffness. In vivo feasibility is tested by imaging a 4T1 breast cancer mouse tumor on Day 6, 12, and 19 post-injection of tumor cells. Similar to phantoms, the CNR of ST-HMI images was higher than ARFI and increased with frequency for the tumor on Day 6. Besides, P2PD at 100-1000 Hz indicated that the tumor became stiffer with respect to the neighboring non-cancerous tissue over time. These results indicate the importance of using a multi-frequency excitation pulse to simultaneously generate displacement at multiple frequencies to better delineate inclusions or tumors.

Improved two-point frequency shift power method for measurement of shear wave attenuation

Quantitative assessment of mechanical properties of biological soft tissues is frequently evaluated using a noninvasive modality, called ultrasound shear wave elastography (SWE). SWE typically exerts an acoustic radiation force (ARF) to produce shear waves propagating in the lateral direction for which velocities and attenuations are measured. The tissue viscoelasticity is commonly studied by investigating the shear wave phase velocity curves. Viscoelastic tissue properties can also be characterized through utilizing various shear wave attenuation techniques. In this study, we propose an improved method for measuring the shear wave attenuation, called two-point frequency shift power (2P-FSP), which is an improved version of the two-point frequency shift (2P-FS) method. The technique is fully data driven and does not use a rheological model for mathematical modeling. The 2P-FSP method utilizes the power spectra frequency shift of shear waves measured at two spatial positions, which provides robustness to noise. The conceptual basis for the 2P-FSP is provided and tested with numerical and experimental data. We investigated how the location of the first signal and the distance interval between the two locations influence the shear wave attenuation measurement in the 2P-FSP technique. We utilized the 2P-FSP method on numerical phantom data generated using a finite-difference-based method in tissue-mimicking viscoelastic media. Moreover, we tested the 2P-FSP method with data from custom-made tissue-mimicking viscoelastic phantom experiments, and ex vivo porcine liver. We compared results from the proposed technique with results from 2P-FS and analytical values in the case of simulations. The results showed that the 2P-FSP method provides improved results over the 2P-FS technique for lower signal-to-noise ratio (SNR) and locations farther from the push location considered, and can be used to measure attenuation of viscoelastic soft tissues.

The Revisited Frequency-Shift Method for Shear Wave Attenuation Computation and Imaging

Ultrasound (US) shear wave (SW) elastography has been widely studied and implemented on clinical systems to assess the elasticity of living organs. Imaging of SW attenuation reflecting viscous properties of tissues has received less attention. A revisited frequency shift (R-FS) method is proposed to improve the robustness of SW attenuation imaging. Performances are compared with the FS method that we originally proposed and with the two-point frequency shift (2P-FS) and attenuation measuring US SW elastography (AMUSE) methods. In the proposed R-FS method, the shape parameter of the gamma distribution fitting SW spectra is assumed to vary with distance, in contrast to FS. Second, an adaptive random sample consensus (A-RANSAC) line fitting method is used to prevent outlier attenuation values in the presence of noise. Validation was made on ten simulated phantoms with two viscosities (0.5 and 2 Pa [Formula: see text]) and different noise levels (15 to -5 dB), two experimental homogeneous gel phantoms, and six in vivo liver acquisitions on awake ducks (including three normal and three fatty duck livers). According to the conducted experiments, R-FS revealed mean reductions in coefficients of variation (CV) of 62.6% on simulations, 62.5% with phantoms, and 62.3% in vivo compared with FS. Corresponding reductions compared with 2P-FS were 45.4%, 77.1%, and 62.0%, respectively. Reductions in normalized root-mean-square errors for simulations were 63.9% and 48.7% with respect to FS and 2P-FS, respectively.

Nonlinear Characterization of Tissue Viscoelasticity With Acoustoelastic Attenuation of Shear Waves

Shear-wave elastography (SWE) measures shear-wave speed (SWS), which is related to the underlying shear modulus of soft tissue. SWS in soft tissue changes depending on the amount of external strain that soft tissue is subjected to due to the acoustoelastic (AE) phenomenon. In the literature, variations of SWS as a function of applied uniaxial strain were used for nonlinear characterization, assuming soft tissues to be elastic, although soft tissues are indeed viscoelastic in nature. Hence, nonlinear characterization using SWS alone is insufficient. In this work, we use SWS together with shear-wave attenuation (SWA) during incremental quasi-static compressions in order to derive biomechanical characterization based on the AE theory in terms of well-defined storage and loss moduli. As part of this study, we also quantify the effect of applied strain on measurements of SWS and SWA since such confounding effects need to be taken into account when using SWS and/or SWA, e.g., for staging a disease state, while such effects can also serve as an additional imaging biomarker. Our results from tissue-mimicking phantoms with varying oil percentages and ex vivo porcine liver experiments demonstrate the feasibility of our proposed methods. In both experiments, SWA was observed to decrease with applied strain. For 10% compression in ex vivo livers, shear-wave attenuation decreased, on average, by 28% (93 Np/m), while SWS increased, on average, by 20% (0.26 m/s).

Shear wave imaging and classification using extended Kalman filter and decision tree algorithm

Shear wave ultrasound elastography is a quantitative imaging approach in soft tissues based on viscosity-elastic properties. Complex shear modulus (CSM) estimation is an effective solution to analyze tissues' physical properties for elasticity and viscosity based on the wavenumber and attenuation coefficient. CSM offers a way to detect and classify some types of soft tissues. However, CSM-based elastography inherits some obstacles, such as estimation precision and calculation complexity. This work proposes an approach for two-dimensional CSM estimation and soft tissue classification using the Extended Kalman Filter (EKF) and Decision Tree (DT) algorithm, named the EKF-DT approach. CSM estimation is obtained by applying EKF to exploit shear wave propagation at each spatial point. Afterward, the classification of tissues is done by a direct and efficient decision tree algorithm categorizing three types of normal, cirrhosis, and fibrosis liver tissues. Numerical simulation scenarios have been employed to illustrate the recovered quality and practicality of the proposed method's liver tissue classification. With the EKF, the estimated wave number and attenuation coefficient are close to the ideal values, especially the estimated wave number. The states of three liver tissue types were automatically classified by applying the DT coupled with two proposed thresholds of elasticity and viscosity: (2.310 kPa, 1.885 Pa.s) and (3.620 kPa 3.146 Pa.s), respectively. The proposed method shows the feasibility of CSM estimation based on the wavenumber and attenuation coefficient by applying the EKF. Moreover, the DT can automate the classification of liver tissue conditions by proposing two thresholds. The proposed EKF-DT method can be developed by 3D image reconstruction and empirical data before applying it in medical practice.

Plane wave elastography: a frequency-domain ultrasound shear wave elastography approach

In this paper, we propose plane wave elastography (PWE), a novel ultrasound shear wave elastography (SWE) approach. Currently, commercial methods for SWE rely on directional filtering based on the prior knowledge of the wave propagation direction, to remove complicated wave patterns formed due to reflection and refraction. The result is a set of decomposed directional waves that are separately analyzed to construct shear modulus fields that are then combined through compounding. Instead, PWE relies on a rigorous representation of the wave propagation using the frequency-domain scalar wave equation to automatically select appropriate propagation directions and simultaneously reconstruct shear modulus fields. Specifically, assuming a homogeneous, isotropic, incompressible, linear-elastic medium, we represent the solution of the wave equation using a linear combination of plane waves propagating in arbitrary directions. Given this closed-form solution, we formulate the SWE problem as a nonlinear least-squares optimization problem which can be solved very efficiently. Through numerous phantom studies, we show that PWE can handle complicated waveforms without prior filtering and is competitive with state-of-the-art that requires prior filtering based on the knowledge of propagation directions.

Viscoelastic parameter estimation using simulated shear wave motion and convolutional neural networks

Ultrasound shear wave elastography (SWE) techniques have been very useful for the analysis of tissue rheological properties, but there are still obstacles for robust evaluation of viscoelastic tissue properties. In this proof-of-concept study, we investigate whether convolutional neural networks (CNN) are capable of retrieving the elasticity and viscosity parameters from simulated shear wave motion images. Staggered-grid finite difference simulations based on a Kelvin-Voigt rheological model were used to generate data for this study. The wave motion datasets were created using Kelvin-Voigt shear elasticity values ranging from 1 to 25 kPa, shear viscosities ranging from 0 to 10 Pa⋅s, and two different push profiles using f-numbers of 1 and 2. The CNN architectures, optimized using mean squared error loss, were then trained to retrieve a specific viscoelastic parameter. Both elasticity and viscosity values were successfully retrieved, with regression R² values above 0.99 when correlating the estimated mechanical properties versus the true mechanical properties. The CNN performance was also compared to estimation of shear elasticity and viscosity from fitting dispersion curves estimated from two-dimensional Fourier transform analysis. The results demonstrated that the CNN models were robust to noise, vertical position and partially to f-number. The architecture was proven to be robust to multiple push profiles if trained properly. The CNN results showed higher accuracy over the full viscoelastic parameter range compared to the Fourier-based analysis. The overall results showed the CNNs' potential to be an alternative to complex mathematical analyses such as Fourier analysis and dispersion curve estimation used currently for shear wave viscoelastic parameter estimation.

Local Phase Velocity Based Imaging of Viscoelastic Phantoms and Tissues

Assessment of soft tissue elasticity and viscosity is of interest in several clinical applications. In this study, we present the feasibility of the local phase velocity based imaging (LPVI) method to create images of phase velocity and viscoelastic parameters in viscoelastic tissue-mimicking materials and soft tissues. In viscoelastic materials, it is necessary to utilize wave-mode isolation using a narrow bandpass filter combined with a directional filter in order to robustly reconstruct phase velocity images with LPVI in viscoelastic media over a wide range of frequencies. A pair of sequential focused acoustic radiation force push beams, focused once on the left-hand side and once on the right-hand side of the probe, was used to produce broadband propagating shear waves. The local shear wave phase velocity is then recovered in the frequency domain for multiple frequencies, for both acquired data sets. Then, a 2-D shear wave velocity map is reconstructed by combining maps from two separate acquisitions. By testing the method on simulated data sets and performing in vitro phantom and in vivo liver tissue experiments, we show the ability of the proposed technique to generate shear wave phase velocity maps at various frequencies in viscoelastic materials. Moreover, a nonlinear least-squares problem is solved in order to locally estimate elasticity and viscosity parameters. The LPVI method with added directional and wavenumber filters can produce phase velocity images, which can be used to characterize the viscoelastic materials.

Shear Wave Velocity Estimation Using the Real-Time Curve Tracing Method in Ultrasound Elastography

The estimation of shear wave velocity is very important in ultrasonic shear wave elasticity imaging (SWEI). Since the stability and accuracy of ultrasonic testing equipment have been greatly improved, in order to further improve the accuracy of shear wave velocity estimation and increase the quality of shear wave elasticity maps, we propose a novel real-time curve tracing (RTCT) technique to accurately reconstruct the motion trace of shear wave fronts. Based on the curve fitting of each frame shear wave, the propagation velocity of two-dimensional shear waves can be estimated. In this paper, shear wave velocity estimation and shear wave image reconstruction are implemented for homogeneous regions and stiff spherical inclusion regions with different elasticity, respectively. The experimental result shows that the proposed shear wave velocity estimation method based on the real-time curve tracing method has advantages in accuracy and anti-noise performance. Moreover, by eliminating artifacts of shear wave videos, the velocity map acquired can restore the shape of inclusions better. The real-time curve tracing method can provide a new idea for the estimation of shear wave velocity and elastic parameters.

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.

In vivo Ultrafast Quantitative Ultrasound and Shear Wave Elastography Imaging on Farm-Raised Duck Livers during Force Feeding

Shear wave elastography (speed and dispersion), local attenuation coefficient slope and homodyned-K parametric imaging were used for liver steatosis grading. These ultrasound biomarkers rely on physical interactions between shear and compression waves with tissues at both macroscopic and microscopic scales. These techniques were applied in a context not yet studied with ultrasound imaging, that is, monitoring steatosis of force-fed duck livers from pre-force-fed to foie gras stages. Each estimated feature presented a statistically significant trend along the feeding process (p values <10^-3). However, whereas a monotonic increase in the shear wave speed was observed along the process, most quantitative ultrasound features exhibited an absolute maximum value halfway through the process. As the liver fat fraction in foie gras is much higher than that seen clinically, we hypothesized that a change in the ultrasound scattering regime is encountered for high-fat fractions, and consequently, care has to be taken when applying ultrasound biomarkers to grading of severe states of steatosis.

Viscoelastic Response Ultrasound Derived Relative Elasticity and Relative Viscosity Reflect True Elasticity and Viscosity: In Silico and Experimental Demonstration

Viscoelastic response (VisR) ultrasound characterizes the viscoelastic properties of tissue by fitting acoustic radiation force (ARF)-induced displacements in the region of ARF excitation to a 1-D mass-spring-damper (MSD) model. Elasticity and viscosity are calculated separately but relative to the applied ARF amplitude. We refer to these parameters as "relative elasticity (RE)" and "relative viscosity (RV)." We herein test the hypothesis that RE and RV linearly correlate to true elasticity and viscosity in tissue. VisR imaging was simulated in 144 homogeneous viscoelastic materials with varying elasticities and viscosities. Derived RE linearly correlated with material elasticity and varied by an average of 2.52% when the material viscosity changed from 0.1 to 1.3 Pa · s. Derived RV linearly correlated with material viscosity but varied by an average of 102.5% when material elasticity changed from 3.33 to 20 kPa. The effect of elasticity on RV measurement was compensated using the slope of the linear relationship between RV and natural frequency ( ωtextn ). After compensation, RV [Formula: see text] (elasticity compensated RV) linearly correlated with material viscosity and varied by less than 1.00% on average when the modeled shear elastic modulus changed from 3.3 to 20 kPa. In addition to elasticity compensation, variation in ARF amplitude over depth was compensated, yielding REDC and [Formula: see text]. REDC and [Formula: see text] successfully contrasted elastic and viscous inclusions, respectively, in three simulated phantoms. Experimentally, in the homogeneous oil-in-gelatin phantoms and excised livers, REDC linearly correlated with shear wave dispersion ultrasound vibrometry (SDUV) derived shear elastic modulus, and [Formula: see text] linearly correlated with SDUV-derived shear viscosity. In excised livers containing viscoelastic oil-in-gelatin inclusions, the inclusions were successfully contrasted from the liver background by both REDC and [Formula: see text]. These results suggest that RE and RV are relevant for qualitatively assessing the elastic and viscous properties of tissue.

Fast Local Phase Velocity-Based Imaging: Shear Wave Particle Velocity and Displacement Motion Study

Fast and precise noninvasive evaluation of tissue mechanical properties is of high importance in ultrasound shear wave elastography. In this study, we present an updated, faster version of the local phase velocity-based imaging (LPVI) method used to create images of local phase velocity in soft tissues. The updated LPVI implementation uses 1-D Fourier transforms in spatial dimensions separately in comparison to its original implementation. A directional filter is applied upon the shear wave field to extract the left-to-right (LR) and right-to-left (RL) propagating shear waves. A local shear wave phase velocity map is recovered based on both LR and RL waves. Finally, a 2-D shear wave velocity map is reconstructed by combining the LR and RL phase velocity maps. LPVI performance for shear wave displacement and velocity-wave motion data is examined. A study of LPVI used for only one data acquisition with multiple focused ultrasound push beams is presented. The lesion placement with respect to the pushes and whether two sequential pushes provided different results from two simultaneous radiation force pushes was investigated. The addition of white Gaussian noise to the wave motion data was also tested to examine the LPVI method's performance. Robust and accurate shear wave phase velocity maps are reconstructed using the proposed LPVI method using numerical tissue-mimicking phantoms with inclusions. Results from the numerical phantom study showed that the reconstructed, asymmetric inclusions, for various axial locations, are better preserved for shear wave particle velocity signals compared with particle displacement motion data.

Two-Point Frequency Shift Method for Shear Wave Attenuation Measurement

Ultrasound shear wave elastography (SWE) is an increasingly used noninvasive modality for quantitative evaluation of tissue mechanical properties. SWE typically uses an acoustic radiation force to produce laterally propagating shear waves that are tracked in the spatial and temporal domains, in order to obtain the wave velocity. One of the ways to study the viscoelasticity is through studying the shear wave phase velocity dispersion curves. Shear wave attenuation can be also characterized in viscoelastic tissues with methods that use multiple lateral data samples. In this article, we present an alternative method for measuring the shear wave attenuation without using a rheological model two-point frequency shift (2P-FS). The technique uses information related to the amplitude spectra FS of shear waves measured at only two lateral locations. The theoretical basis for the 2P-FS is derived and validated. We examined how the first signal position and the distance between the two locations affect the shear wave attenuation estimation in the 2P-FS method. We tested this new method on digital phantom data created using the local interaction simulation approach (LISA) in viscoelastic media. Moreover, we tested data acquired from custom-made tissue-mimicking viscoelastic phantom experiments and ex vivo porcine liver measurements. We compared results from the 2P-FS method with the other two techniques used for assessing a shear wave attenuation: the FS-based method and the attenuation-measuring ultrasound shear wave elastography (AMUSE) technique. In addition, we evaluated the 2P-FS algorithm with different levels of added white Gaussian noise to the shear wave particle velocity using numerical phantoms. Tests conducted showed that the 2P-FS method gives robust results based on only two measurements and can be used to measure attenuation of viscoelastic soft tissues.

Attenuation Measuring Ultrasound Shearwave Elastography as a Method for Evaluating Pancreatic Viscoelasticity

Pancreatic cancer is the fourth most common cause of cancer-related fatalities as there are a limited number of tools to diagnose this disease in its early stages. Pancreatitis is characterized as an inflammation of the pancreatic tissue due to an excess amount of pancreatic enzymes remaining in the organ. Both of these diseases result in a stiffening of the tissue which makes them suitable for the use of elastography techniques as a diagnostic method. However, these methods typically assume that the tissue is purely elastic when biological tissue is inherently viscoelastic. The attenuation measuring ultrasound shear elastography (AMUSE) method, which measures both attenuation and shear wave velocity was used to characterize the viscoelasticity of pancreatic tissue. This method was tested in ex vivo normal porcine samples that were also stiffened in formalin and in vivo by conducting studies in healthy human subjects. Ex vivo testing showed ranges of phase velocity, group velocity, and phase attenuation values of 1.05 - 1.33 m/s, 0.83 - 1.12 m/s, and 183 - 210 Np/m. After immersing the ex vivo tissue in formalin there was a distinguishable difference between normal and stiffened tissue. This study produced percent difference ranges of phase velocity, group velocity, and phase attenuation from 0 to 100 minutes in formalin of 30.0% - 56.5%, 38.2% - 58.6%, and 55.8% - 64.8%, respectively. The ranges of phase velocity, group velocity, and phase attenuation results in human subjects were 1.53 - 1.60 m/s, 1.76 - 1.91 m/s, and 196 - 204 Np/m, respectively. These results were within a similar range reported by other elastography techniques. Further work with the AMUSE method in subjects with pancreatitis and cancer is needed to determine its effectiveness in showing a difference between healthy and diseased tissue in humans.

Distributing Synthetic Focusing Over Multiple Push-Detect Events Enhances Shear Wave Elasticity Imaging Performance

Plane wave (PW) imaging is a commonly used method for tracking waves during shear wave elasticity imaging (SWEI), but its unfocused transmission beam reduces tracking accuracy and precision. Coherent compounding minimizes this problem, but SWEI's stringent frame rate requirement and the coarse pitch of most clinical transducers limit its effectiveness. Synthetic aperture imaging (SAI) is an alternate ultrasound imaging approach with a much tighter focus than PW imaging, but its lower transmission power has deterred researchers from using SAI in SWEI. Hadamard-encoded multielement SAI can overcome this limitation. However, only a limited number of subapertures (3-5) can be transmitted in a single push-detect event. We have developed methods to distribute more subapertures or more compounding angles over multiple push-detect events. In this paper, we report the results of experiments conducted on phantoms to assess SWEI's performance when using Hadamard-encoded distributed-multielement synthetic aperture (HDMSA) imaging or distributed plane wave compounding (DPWC) to track shear waves. Tracking shear waves with HDMSA improved the elastographic signal-to-noise ratio (SNR_e) by 61.6%-89.5% depending on the phantom employed. Similarly, DPWC tracking improved SNR_e by 56.2%-93.3% for the same group of phantoms. Compared to focused ultrasound tracking (at the focus), SNR_e improved by 28.6% and 32.5% when tracking shear waves with HDMSA and DPWC, respectively. Long acquisitions could introduce decoding errors that decrease the performance when performing HDMSA tracking within the clinical setting. Nevertheless, the results of studies performed on the bicep muscle of three healthy volunteers demonstrate that for stationary organs, tracking shear waves with HDMSA yielded repeatable elastograms that offer better elastographic performance than those produced with current tracking methods.

Reconstruction of Viscosity Maps in Ultrasound Shear Wave Elastography

Change in viscoelastic properties of biological tissues may often be symptomatic of a dysfunction that can be correlated to tissue pathology. Shear wave elastography is an imaging method mainly used to assess stiffness but with the potential to measure viscoelasticity of biological tissues. This can enable tissue characterization; and thus, can be used as a marker to improve diagnosis of pathological lesions. In this study, a frequency-shift method based framework is presented for the reconstruction of viscosity by analyzing the spectral properties of acoustic radiation force-induced shear waves. The aim of the study was to investigate the feasibility of viscosity reconstruction maps in homogeneous as well as heterogeneous samples. Experiments were performed in four in vitro phantoms, two ex vivo porcine liver samples, two ex vivo fatty duck liver samples, and one in vivo fatty goose liver. Successful viscosity maps were reconstructed in homogeneous and heterogeneous phantoms with embedded mechanical inclusions having different geometries. Quantitative values of viscosity obtained for two porcine liver tissues, two fatty duck liver samples, and one goose fatty liver were (mean ± SD) 0.61 ± 0.21, 0.52 ± 0.35; 1.28 ± 0.54, 1.36 ± 0.73, and 1.67 ± 0.70 Pa.s, respectively.

Local Phase Velocity Based Imaging: A New Technique Used for Ultrasound Shear Wave Elastography

Ultrasound shear wave elastography is an imaging modality for noninvasive evaluation of tissue mechanical properties. However, many current techniques overestimate lesions dimension or shape especially when small inclusions are taken into account. In this paper, we propose a new method called local phase velocity-based imaging (LPVI) as an alternative technique to measure tissue elasticity. Two separate acquisitions with ultrasound push beams focused once on the left side and once on the right side of the inclusion were generated. A local shear wave velocity is then recovered in the frequency domain (for a single frequency or frequency band) for both acquired data sets. Finally, a two-dimensional shear wave velocity map is reconstructed by combining maps from two separate acquisitions. Robust and accurate shear wave velocity maps are reconstructed using the proposed LPVI method in calibrated liver fibrosis tissue mimicking homogeneous phantoms, a calibrated elastography phantom with stepped cylinder inclusions and a homemade gelatin phantom with ex vivo porcine liver inclusion. Results are compared with an existing phase velocity-based imaging approach and a group velocity-based method considered as the state of the art. Results from the phantom study showed that increased frequency improved the shape of the reconstructed inclusions and contrast-to-noise ratio between the target and background.

Application of a forward model of axisymmetric shear wave propagation in viscoelastic media to shear wave elastography

A simple but general solution of Navier's equation for axisymmetric shear wave propagation in a homogeneous isotropic viscoelastic medium is presented. It is well-suited for use as a forward model for some acoustic radiation force impulse based shear wave elastography applications because it does not require precise knowledge of the strength of the source, nor its spatial or temporal distribution. Instead, it depends on two assumptions: (1) the source distribution is axisymmetric and confined to a small region near the axis of symmetry, and (2) the propagation medium is isotropic and homogeneous. The model accounts for the vector polarization of shear waves and exactly represents geometric spreading of the shear wavefield, whether spherical, cylindrical, or neither. It makes no assumption about the frequency dependence of material parameters, i.e., it is material-model independent. Validation using measured shear wavefields excited by acoustic radiation force in a homogeneous gelatin sample show that the model accounts for well over 90% of the measured wavefield "energy." An optimal fit of the model to simulated shear wavefields with noise in a homogeneous viscoelastic medium enables estimation of both the shear storage modulus and shear wave attenuation to within 1%.

A 2D finite element model for shear wave propagation in biological soft tissues: Application to magnetic resonance elastography

Dynamic elastography is a virtual palpation tool that aims at investigating the mechanical response of biological soft tissues in vivo. The objective of this study is to develop a finite element model (FEM) with low computational cost for reproducing realistically wave propagation for magnetic resonance elastography in heterogeneous soft tissues. Based on the first-order shear deformation theory for moderately thick structures, this model is developed and validated through comparison with analytical formulations of wave propagating in heterogeneous, viscoelastic infinite medium. This 2D-FEM is then compared to experimental data and a 3D-FEM using a commercial software. Our FEM is a powerful promising tool for investigations of magnetic resonance elastography.

Characterization of Viscoelastic Materials Using Group Shear Wave Speeds

Recent investigations of viscoelastic properties of materials have been performed by observing shear wave propagation following localized, impulsive excitations, and Fourier decomposing the shear wave signal to parameterize the frequency-dependent phase velocity using a material model. This paper describes a new method to characterize viscoelastic materials using group shear wave speeds , , and determined from the shear wave displacement, velocity, and acceleration signals, respectively. Materials are modeled using a two-parameter linear attenuation model with phase velocity and dispersion slope at a reference frequency of 200 Hz. Analytically calculated lookup tables are used to determine the two material parameters from pairs of measured group shear wave speeds. Green's function calculations are used to validate the analytic model. Results are reported for measurements in viscoelastic and approximately elastic phantoms and demonstrate good agreement with phase velocities measured using Fourier analysis of the measured shear wave signals. The calculated lookup tables are relatively insensitive to the excitation configuration. While many commercial shear wave elasticity imaging systems report group shear wave speeds as the measures of material stiffness, this paper demonstrates that differences , , and of group speeds are first-order measures of the viscous properties of materials.

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.

Robust Phase Velocity Dispersion Estimation of Viscoelastic Materials Used for Medical Applications Based on the Multiple Signal Classification Method

Ultrasound shear wave elastography (SWE) is emerging as a promising imaging modality for the noninvasive evaluation of tissue mechanical properties. One of the ways to explore the viscoelasticity is through analyzing the shear wave velocity dispersion curves. To explore the dispersion, it is necessary to estimate the shear wave velocity at each frequency. An increase of the available spectrum to be used for phase velocity estimation is significant for a tissue dispersion analysis in vivo. A number of available methods suffer because the available spectrum that one can work with is limited. We present an alternative method to the classical 2-D Fourier transform (2D-FT) that uses the multiple signal classification (MUSIC) technique to provide robust estimation of the -space and phase velocity dispersion curves. We compared results from the MUSIC method with the 2D-FT technique twofold: by searching for maximum peaks and gradient-based strategy. We tested this method on digital phantom data created using finite-element methods (FEMs) in viscoelastic media as well as on the experimental phantoms used in the Radiological Society of North America Quantitative Imaging Biomarker Alliance effort for the standardization of shear wave velocity in liver fibrosis applications. In addition, we evaluated the algorithm with different levels of added noise for FEMs. The MUSIC algorithm provided dispersion curves estimation with lower errors than the conventional 2D-FT method. The MUSIC method can be used for the robust evaluation of shear wave velocity dispersion curves in viscoelastic media.

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.

Forward and inverse viscoelastic wave scattering by irregular inclusions for shear wave elastography

Inversion methods in shear wave elastography use simplifying assumptions to recover the mechanical properties of soft tissues. Consequently, these methods suffer from artifacts when applied to media containing strong stiffness contrasts, and do not provide a map of the viscosity. In this work, the shear wave field recorded inside and around an inclusion was used to estimate the viscoelastic properties of the inclusion and surrounding medium, based on an inverse problem approach assuming local homogeneity of both media. An efficient semi-analytical method was developed to model the scattering of an elastic wave by an irregular inclusion, based on a decomposition of the field by Bessel functions and on a decomposition of the boundaries as Fourier series. This model was validated against finite element modeling. Shear waves were experimentally induced by acoustic radiation force in soft tissue phantoms containing stiff and soft inclusions, and the displacement field was imaged at a high frame rate using plane wave imaging. A nonlinear least-squares algorithm compared the model to the experimental data and adjusted the geometrical and mechanical parameters. The estimated shear storage and loss moduli were in good agreement with reference measurements, as well as the estimated inclusion shape. This approach provides an accurate estimation of geometry and viscoelastic properties for a single inclusion in a homogeneous background in the context of radiation force elastography.