Two-Point Frequency Shift Method for Shear Wave Attenuation Measurement

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.

Ultrasound Shear Elastography With Expanded Bandwidth (USEWEB): A Novel Method for 2D Shear Phase Velocity Imaging of Soft Tissues

Ultrasound shear wave elastography (SWE) is a noninvasive approach for evaluating mechanical properties of soft tissues. In SWE either group velocity measured in the time-domain or phase velocity measured in the frequency-domain can be reported. Frequency-domain methods have the advantage over time-domain methods in providing a response for a specific frequency, while time-domain methods average the wave velocity over the entire frequency band. Current frequency-domain approaches struggle to reconstruct SWE images over full frequency bandwidth. This is especially important in the case of viscoelastic tissues, where tissue viscoelasticity is often studied by analyzing the shear wave phase velocity dispersion. For characterizing cancerous lesions, it has been shown that considerable biases can occur with group velocity-based measurements. However, using phase velocities at higher frequencies can provide more accurate evaluations. In this paper, we propose a new method called Ultrasound Shear Elastography with Expanded Bandwidth (USEWEB) used for two-dimensional (2D) shear wave phase velocity imaging. We tested the USEWEB method on data from homogeneous tissue-mimicking liver fibrosis phantoms, custom-made viscoelastic phantom measurements, phantoms with cylindrical inclusions experiments, and in vivo renal transplants scanned with a clinical scanner. We compared results from the USEWEB method with a Local Phase Velocity Imaging (LPVI) approach over a wide frequency range, i.e., up to 200-2000 Hz. Tests carried out revealed that the USEWEB approach provides 2D phase velocity images with a coefficient of variation below 5% over a wider frequency band for smaller processing window size in comparison to LPVI, especially in viscoelastic materials. In addition, USEWEB can produce correct phase velocity images for much higher frequencies, up to 1800 Hz, compared to LPVI, which can be used to characterize viscoelastic materials and elastic inclusions.

Effect of rt-PA on Shear Wave Mechanical Assessment and Quantitative Ultrasound Properties of Blood Clot Kinetics In Vitro

OBJECTIVE

The consequences associated with blood clots are numerous and are responsible for many deaths worldwide. The assessment of treatment efficacy is necessary for patient follow-up and to detect treatment-resistant patients. The aim of this study was to characterize the effect of treatment on blood clots in vitro using quantitative ultrasound parameters.

METHODS

Blood from 10 pigs was collected to form three clots per pig in gelatin phantoms. Clots were subjected to 1) no treatment, 2) rt-PA (recombinant tissue plasminogen activator) treatment after 20 minutes of clotting, and 3) rt-PA treatment after 60 minutes of clotting. Clots were weighted before and after the experiment to assess the treatment effect by the mass loss. The clot kinetics was studied over 100 minutes using elastography (Young's modulus, shear wave dispersion, and shear wave attenuation). Homodyne K-distribution (HKD) parameters derived from speckle statistics were also studied during clot formation and dissolving (diffuse-to-total signal power ratio and intensity parameters).

RESULTS

Treated clots loosed significantly more mass than non-treated ones (P < .005). A significant increase in Young's modulus was observed over time (P < .001), and significant reductions were seen for treated clots at 20 or 60 minutes compared with untreated ones (P < .001). The shear wave dispersion differed for treated clots at 60 minutes versus no treatments (P < .001). The shear wave attenuation decreased over time (P < .001), and was different for clots treated at 20 minutes versus no treatments (P < .031). The HKD intensity parameter varied over time (P < .032), and was lower for clots treated at 20 and 60 minutes than those untreated (P < .001 and P < .02).

CONCLUSION

The effect of rt-PA treatment could be confirmed by a decrease in Young's modulus and HKD intensity parameter. The shear wave dispersion and shear wave attenuation were sensitive to late and early treatments, respectively. The Young's modulus, shear wave attenuation, and HKD intensity parameter varied over time despite treatment.

Ultrasound Shear Wave Propagation Modeling in General Tissue-Like Viscoelastic Materials

OBJECTIVE

This study aims to present an approach for the simulation of ultrasound elastic waves propagation in a diverse range of heterogeneous tissue-like viscoelastic materials, including, but not limited to, Kelvin-Voigt, Zener, Maxwell, Burger's, and Maxwell-Wiechert models, while also allowing for modeling highly viscous fluids.

METHODS

Ultrasound shear wave elastography (SWE) serves as a cost-effective modality for noninvasive, quantitative assessment of soft tissue viscoelastic mechanical properties. To explore tissue viscoelasticity, measuring the shear wave phase velocity in the frequency domain is a common method. In this paper, we employ modeling and numerical simulations to enhance the development of SWE methods. The study employs the staggered grid finite difference (SGFD) method along with recursive calculations of convolution integrals pertinent to linear viscoelastic models.

RESULTS

The presented numerical method demonstrates its capability to simulate the propagation of ultrasound elastic waves, both longitudinal and shear, across a broad spectrum of tissue-like viscoelastic heterogeneous materials. The approach successfully accommodates various viscoelastic models without requiring additional modifications in the numerical model, thus enabling a comprehensive exploration of different viscoelastic behaviors commonly observed in diverse tissue types.

CONCLUSION

The developed combination of the SGFD method and recursive calculation of convolution integrals presents a novel and versatile approach in modeling linear viscoelastic tissue-like materials for SWE applications. This method eliminates the need for model-specific adaptations in numerical simulations, thereby offering flexibility for exploring and understanding diverse viscoelastic behaviors inherent in different heterogeneous tissue types, contributing significantly to the advancement of ultrasound SWE for diagnostic purposes.

Resonance, Velocity, Dispersion, and Attenuation of Ultrasound-Induced Shear Wave Propagation in Blood Clot In Vitro Models

OBJECTIVE

Improve the characterization of mechanical properties of blood clots. Parameters derived from shear wave (SW) velocity and SW amplitude spectra were determined for gel phantoms and in vitro blood clots.

METHODS

Homogeneous phantoms and phantoms with gel or blood clot inclusions of different diameters and mechanical properties were analyzed. SW amplitude spectra were used to observe resonant peaks. Parameters derived from those resonant peaks were related to mimicked blood clot properties. Three regions of interest were tested to analyze where resonances occurred the most. For blood experiments, 20 samples from different pigs were analyzed over time during a 110-minute coagulation period using the Young modulus, SW frequency dispersion, and SW attenuation.

RESULTS

The mechanical resonance was manifested by an increase in the number of SW spectral peaks as the inclusion diameter was reduced (P < .001). In blood clot inclusions, the Young modulus increased over time during coagulation (P < .001). Descriptive spectral parameters (frequency peak, bandwidth, and distance between resonant peaks) were linearly correlated with clot elasticity values (P < .001) with R2  = .77 for the frequency peak, .60 for the bandwidth, and .48 for the distance between peaks. The SW dispersion and SW attenuation reflecting the viscous behavior of blood clots decreased over time (P < .001), mainly in the early stage of coagulation (first minutes).

CONCLUSION

The confined soft inclusion configuration favored SW mechanical resonances potentially challenging the computation of spectral-based parameters, such as the SW attenuation. The impact of resonances can be reduced by properly selecting the region of interest for data analysis.

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.

Full waveform inversion for arterial viscoelasticity

Objective. Arterial viscosity is emerging as an important biomarker, in addition to the widely used arterial elasticity. This paper presents an approach to estimate arterial viscoelasticity using shear wave elastography (SWE).Approach. While dispersion characteristics are often used to estimate elasticity from SWE data, they are not sufficiently sensitive to viscosity. Driven by this, we develop a full waveform inversion (FWI) methodology, based on directly matching predicted and measured wall velocity in space and time, to simultaneously estimate both elasticity and viscosity. Specifically, we propose to minimize an objective function capturing the correlation between measured and predicted responses of the anterior wall of the artery.Results. The objective function is shown to be well-behaving (generally convex), leading us to effectively use gradient optimization to invert for both elasticity and viscosity. The resulting methodology is verified with synthetic data polluted with noise, leading to the conclusion that the proposed FWI is effective in estimating arterial viscoelasticity.Significance. Accurate estimation of arterial viscoelasticity, not just elasticity, provides a more precise characterization of arterial mechanical properties, potentially leading to a better indicator of arterial health.

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).

Acoustic Radiation Force: A Review of Four Mechanisms for Biomedical Applications

Radiation force is a universal phenomenon in any wave motion where the wave energy produces a static or transient force on the propagation medium. The theory of acoustic radiation force (ARF) dates back to the early 19th century. In recent years, there has been an increasing interest in the biomedical applications of ARF. Following a brief history of ARF, this article describes a concise theory of ARF under four physical mechanisms of radiation force generation in tissue-like media. These mechanisms are primarily based on the dissipation of acoustic energy of propagating waves, the reflection of the incident wave, gradients of the compressional wave speeds, and the spatial variations of energy density in standing acoustic waves. Examples describing some of the practical applications of ARF under each mechanism are presented. This article concludes with a discussion on selected ideas for potential future applications of ARF in biomedicine.

Phase Velocity Estimation With Expanded Bandwidth in Viscoelastic Phantoms and Tissues

Ultrasound shear wave elastography (SWE) is a technique used to measure mechanical properties to evaluate healthy and pathological soft tissues. SWE typically employs an acoustic radiation force (ARF) to generate laterally propagating shear waves that are tracked in the spatiotemporal domains, and algorithms are used to estimate the wave velocity. The tissue viscoelasticity is often examined through analyzing the shear wave phase velocity dispersion curves, which is the variation of phase velocity with frequency or wavelength. A number of available methods to estimate dispersion exist, which can differ in resolution and variance. Moreover, most of these techniques reconstruct dispersion curves for a limited frequency band. In this work, we propose a novel method used for dispersion curve calculation. Our unique approach uses a generalized Stockwell transformation combined with a slant frequency-wavenumber analysis (GST-SFK). We tested the GST-SFK method on numerical phantom data generated using a finite-difference-based method in tissue-mimicking viscoelastic media. In addition, we evaluated the method on numerical shear wave motion data with different amounts of white Gaussian noise added. Additionally, we performed tests on data from custom-made tissue-mimicking viscoelastic phantom experiments, ex vivo porcine liver measurements, and in vivo liver tissue experiments. We compared results from our method with two other techniques used for estimating shear wave phase velocity: the two-dimensional Fourier transform (2D-FT) and the eigenvector (EV) method. Tests carried out revealed that the GST-SFK method provides dispersion curve estimates with lower errors over a wider frequency band in comparison to the 2D-FT and EV methods. In addition, the GST-SFK provides expanded bandwidth by a factor of two or more to be used for phase velocity estimation, which is meaningful for a tissue dispersion analysis in vivo.

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.

Hydrophone Spatial Averaging Correction for Acoustic Exposure Measurements From Arrays-Part I: Theory and Impact on Diagnostic Safety Indexes

This article reports underestimation of mechanical index (MI) and nonscanned thermal index for bone near focus (TIB) due to hydrophone spatial averaging effects that occur during acoustic output measurements for clinical linear and phased arrays. TIB is the appropriate version of thermal index (TI) for fetal imaging after ten weeks from the last menstrual period according to the American Institute of Ultrasound in Medicine (AIUM). Spatial averaging is particularly troublesome for highly focused beams and nonlinear, nonscanned modes such as acoustic radiation force impulse (ARFI) and pulsed Doppler. MI and variants of TI (e.g., TIB), which are displayed in real-time during imaging, are often not corrected for hydrophone spatial averaging because a standardized method for doing so does not exist for linear and phased arrays. A novel analytic inverse-filter method to correct for spatial averaging for pressure waves from linear and phased arrays is derived in this article (Part I) and experimentally validated in a companion article (Part II). A simulation was developed to estimate potential spatial-averaging errors for typical clinical ultrasound imaging systems based on the theoretical inverse filter and specifications for 124 scanner/transducer combinations from the U.S. Food and Drug Administration (FDA) 510(k) database from 2015 to 2019. Specifications included center frequency, aperture size, acoustic output parameters, hydrophone geometrical sensitive element diameter, etc. Correction for hydrophone spatial averaging using the inverse filter suggests that maximally achievable values for MI, TIB, thermal dose ( t ₄₃ ), and spatial-peak-temporal-average intensity ( [Formula: see text]) for typical clinical systems are potentially higher than uncorrected values by (means ± standard deviations) 9% ± 4% (ARFI MI), 19% ± 15% (ARFI TIB), 50% ± 41% (ARFI t ₄₃ ), 43% ± 39% (ARFI [Formula: see text]), 7% ± 5% (pulsed Doppler MI), 15% ± 11% (pulsed Doppler TIB), 42% ± 31% (pulsed Doppler t ₄₃ ), and 33% ± 27% (pulsed Doppler [Formula: see text]). These values correspond to frequencies of 3.2 ± 1.3 (ARFI) and 4.1 ± 1.4 MHz (pulsed Doppler), and the model predicts that they would increase with frequency. Inverse filtering for hydrophone spatial averaging significantly improves the accuracy of estimates of MI, TIB, t ₄₃ , and [Formula: see text] for ARFI and pulsed Doppler signals.

Dispersion curve calculation in viscoelastic tissue-mimicking materials using non-parametric, parametric, and high-resolution methods

Ultrasound shear wave elastography is a modality used for noninvasive, quantitative evaluation of soft tissue mechanical properties. A common way of exploring the tissue viscoelasticity is through analyzing the shear wave velocity dispersion curves. The variation of phase velocity with frequency or wavelength is called the dispersion curve. An increase of the available spectrum to be used for phase velocity estimation is meaningful for a tissue dispersion analysis in vivo. A number of available methods for dispersion relation estimation exist which can give diffuse results due the presence of noise in the measured data. In this work we compare six selected methods used for dispersion curve calculation in viscoelastic materials. Non-parametric, parametric and high-resolution methods were examined and compared. We tested selected methods on digital phantom data created using finite-difference-based method in tissue-mimicking viscoelastic media as well as on the experimental custom tissue-mimicking phantoms. In addition, we evaluated the algorithms with different levels of added white Gaussian noise to the shear wave particle velocity from numerical phantoms. Tests conducted showed that more advanced methods can offer better frequency resolution, and less variance than the fast Fourier transform. In addition, the non-parametric Blackman-Tukey approach exhibits similar performance and can be interchangeably used for shear wave phase velocity dispersion curves calculation.

Hydrophone Spatial Averaging Artifacts for ARFI Beams from Array Transducers

This paper reports underestimation of peak compressional pressure (p _c), peak rarefactional pressure (p _r ), and pulse intensity integral (pii) due to hydrophone spatial averaging of acoustic radiation force impulse (ARFI) beams generated by clinical linear and phased arrays. Although a method exists for correcting for hydrophone spatial averaging for circularly-symmetric beams, there is presently no analogous method for rectangularly-symmetric beams generated by linear and phased arrays. Consequently, pressure parameters (p _c, p _r , and pii) from clinical arrays are often not corrected for spatial averaging. This can lead to errors in Mechanical Index (MI) and Thermal Index (TI), which are derived from pressure measurements and are displayed in real-time during clinical ultrasound scans. ARFI beams were generated using three clinical linear array transducers. Output pressure waveforms for all three transducers were measured using five hydrophones with geometrical sensitive element sizes (d_g) ranging from 85 to 1000 μm. Spatial averaging errors were found to increase with hydrophone sensitive element size. For example, if d_g = 500 μm (typical membrane hydrophone), frequency = 2.25 MHz and F/# = 1.5, then average errors are approximately -20% (p_c), -10% (p_r), and -25% (pii). Therefore, due to hydrophone spatial averaging, typical membrane hydrophones can exhibit significant underestimation of ARFI pressure measurements, which likely compromises exposure safety indexes.