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

Estimation of the phase velocity dispersion curves for viscoelastic materials using Point Limited Shear Wave Elastography

Ultrasound shear wave elastography (SWE) is widely used in clinical applications for non-invasive measurements of soft tissue viscoelasticity. The study of tissue viscoelasticity often involves the analysis of shear wave phase velocity dispersion curves, which show how the phase velocity varies with frequency or wavelength. In this study, we propose an alternative method to the two-dimensional Fourier transform (2D-FT) and Phase Gradient (PG) methods for shear wave phase velocity estimation. We introduce a new method called Point Limited Shear Wave Elastography (PL-SWE), which aims to reconstruct phase velocity dispersion curves using a minimal number of measurement points in the spatial domain (as few as two signals can be utilized). We investigated how the positioning of the first signal and the distance between selected signals affect the shear wave velocity dispersion estimation in PL-SWE. The effectiveness of this novel approach was evaluated through the analysis of analytical phantom data in viscoelastic media, along with experimental data from custom-made tissue-mimicking elastic and viscoelastic phantoms, and in vivo renal transplant data. A comparative analysis with the 2D-FT technique revealed that PL-SWE provided phase velocity dispersion curve estimates with root mean squared percentage error (RMSPE) values of less than 1.61% for analytical phantom data, 1.58% for elastic phantoms, 4.29% for viscoelastic phantoms and 7.68% for in vivo data, while utilizing significantly fewer signals compared to 2D-FT. The results demonstrate that the PL-SWE method also outperforms the PG method. For the viscoelastic phantoms, the mean RMSPE values using PL-SWE ranged from 2.61% to 4.29%, while the PG method produced RMSPE values between 3.56% and 15%. In the case of in vivo data, PL-SWE yielded RMSPE values between 7.01% and 7.68%, while PG results ranged from 17% to 418%. These findings highlight the superior accuracy and reliability of the PL-SWE method, particularly when compared to the PG approach. Our tests demonstrate that PL-SWE can effectively measure the phase velocity of both elastic and viscoelastic materials and tissues using a limited number of signals. Utilizing a minimal number of spatial measurement points could enable accurate assessments even in cases with restricted field of view, thereby expanding the applicability of SWE across various patient populations.

Deep denoising approach to improve shear wave phase velocity map reconstruction in ultrasound elastography

BACKGROUND

Measurement noise often leads to inaccurate shear wave phase velocity estimation in ultrasound shear wave elastography. Filtering techniques are commonly used for denoising the shear wavefields. However, these filters are often not sufficient, especially in fatty tissues where the signal-to-noise ratio (SNR) can be very low.

PURPOSE

The purpose of this study is to develop a deep learning approach for denoising shear wavefields in ultrasound shear wave elastography. This may lead to improved reconstruction of shear wave phase velocity image maps.

METHODS

The study addresses noise by transforming particle velocity data into a time-frequency representation. A neural network with encoder and decoder convolutional blocks effectively decomposes the input and extracts the signal of interest, improving the SNR in high-noise scenarios. The network is trained on simulated phantoms with elasticity values ranging from 3  to 60 kPa. A total of 1 85 570 samples with 80%-20 % $\%$ split were used for training and validation. The approach is tested on experimental phantom and ex-vivo goat liver tissue data. Performance was compared with the traditional filtering methods such as bandpass, median, and wavelet filtering. Kruskal-Wallis one-way analysis of variance was performed to check statistical significance. Multiple comparisons were performed using the Mann-Whitney U test and Holm-Bonferroni adjustment ofp - values $p-{\rm values}$ .

RESULTS

The results are evaluated using SNR and the percentage of pixels that can be reconstructed in the phase velocity maps. The SNR levels in experimental data improved from -2 to 9.9 dB levels to 15.6 to 30.3 dB levels. Kruskal-Wallis one-way analysis showed statistical significance (p < 0.05 $p<0.05$ ). Multiple comparisons with p-value corrections also showed statistically significant improvement when compared to the bandpass and wavelet filtering scheme (p < 0.05 $p<0.05$ ). Smoother phase velocity maps were reconstructed after denoising. The coefficient of variation is less than5 % $5\%$ in CIRS phantom and less than18 % $18\%$ in ex-vivo goat liver tissue.

CONCLUSIONS

The proposed approach demonstrates improvement in shear wave phase velocity image map reconstruction and holds promise that deep learning methods can be effectively utilized to extract true shear wave signal from measured noisy data.

Twin Peak Method for Estimating Tissue Viscoelasticity using Shear Wave Elastography

Tissue viscoelasticity is becoming an increasingly useful biomarker beyond elasticity and can theoretically be estimated using shear wave elastography (SWE), by inverting the propagation and attenuation characteristics of shear waves. Estimating viscosity is often more difficult than elasticity because attenuation, the main effect of viscosity, leads to poor signal-to-noise ratio of the shear wave motion. In the present work, we provide an alternative to existing methods of viscoelasticity estimation that is robust against noise. The method minimizes the difference between simulated and measured versions of two sets of peaks (twin peaks) in the frequency-wavenumber domain, obtained first by traversing through each frequency and then by traversing through each wavenumber. The slopes and deviation of the twin peaks are sensitive to elasticity and viscosity respectively, leading to the effectiveness of the proposed inversion algorithm for characterizing mechanical properties. This expected effectiveness is confirmed through in silico verification, followed by ex vivo validation and in vivo application, indicating that the proposed approach can be effectively used in accurately estimating viscoelasticity, thus potentially contributing to the development of enhanced biomarkers.

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.

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.

Evaluation of Robustness of S-Transform Based Phase Velocity Estimation in Viscoelastic Phantoms and Renal Transplants

Ultrasound shear wave elastography (SWE) methods are being used to differentiate healthy versus diseased tissue on the basis of their viscoelastic mechanical properties. Tissue viscoelasticity is often studied by analyzing shear wave phase velocity dispersion curves, which is the variation of phase velocity with frequency or wavelength. Recently, a unique approach using a generalized Stockwell transformation (GST-SFK) was proposed for the calculation of dispersion curves in viscoelastic media over expanded frequency band. In this work, the method's robustness was evaluated on data from five custom-made viscoelastic tissue-mimicking phantoms and sixty in vivo renal transplants. For each phantom, 15 shear wave motion data acquisitions were taken, while 10-13 acquisitions were acquired for renal transplants measured in the renal cortex. For each data-set mean and standard deviation (SD) of estimated phase velocity dispersion curves were studied. In addition, the viscoelastic parameters of the Zener model were examined, which were preceded by a convergence analysis. For viscoelastic phantoms scanned with a research ultrasound scanner, and for the in vivo renal transplants scanned with a clinical scanner, the decisive advantage of the GST-SFK method over the standard two-dimensional Fourier transform (2D-FT) method was shown. The GST-SFK method provided dispersion curve estimates with lower SD over a wider frequency band in comparison to the 2D-FT method. These advantages are relevant to the analysis of the mechanical properties of tissues in clinical practice to discriminate healthy from diseased tissue.

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.

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.

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.

Multimodal guided wave inversion for arterial stiffness: methodology and validation in phantoms

Arterial stiffness is an important biomarker for many cardiovascular diseases. Shear wave elastography is a recent technique aimed at estimating local arterial stiffness using guided wave inversion (GWI), i.e. matching the computed and measured wave dispersion. This paper develops and validates a new GWI approach by synthesizing various recent observations and algorithms: (a) refinements to signal processing to obtain more accurate experimental dispersion curves; (b) an efficient forward model to compute theoretical dispersion curves for immersed, incompressible cylindrical waveguides; (c) an optimization framework based on the recent observation that the measured dispersion curve is multimodal, i.e. it matches for not one but two different wave modes in two different frequency ranges. The resulting inversion approach is validated using extensive experimental data from rubber tube phantoms, not only for modulus estimation but also to simultaneously estimate modulus and wall thickness. The observations indicate that the modulus estimates are best performed with the information on wall thickness. The approach, which takes less than half a minute to run, is shown to be accurate, with the modulus estimated with less than 4% error for 70% of the experiments.

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.

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.

Diffuse shear wave spectroscopy for soft tissue viscoelastic characterization

In order to limit and slow the development of diseases, they have to be diagnosed early as possible to treat patients in a better and more rapid manner. In this paper, we focus on a noninvasive and quick method based on diffuse fields in elastography to detect diseases that affect the stiffness of organs. To validate our method, a phantom experiment numerically pre-validated is designed. It consists of seven vibrators that generate white noises in a bandwidth of [80-300] Hz and then a complex acoustic field in a phantom. Waves are tracked by a linear ultrasound probe L11-4v linked to a Verasonics Vantage System and are converted into a particle velocity 2D map as a function of time. The phase velocity of the shear waves is calculated using a temporal and 2D spatial Fourier transform and an adapted signal-processing method. Shear wave velocity dispersion measurement in the frequency bandwidth of the vibrators enables one to characterize the dynamic hardness of the material through the viscoelastic parameters μ and η in an acquisition time shorter than a second (T_acq = 300 ms). With the aim of estimating the consistency of the method, the experiment is performed N = 10 times. The measured elastic modulus and viscous parameter that quantify the dynamic properties of the medium correspond to the expected values: μ = 1.23 ± 0.05 kPa and η = 0.51 ± 0.09 Pa∙s.

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.

A parametric evaluation of shear wave speeds estimated with time-of-flight calculations in viscoelastic media

Shear wave elasticity imaging (SWEI) uses an acoustic radiation force to generate shear waves, and then soft tissue mechanical properties are obtained by analyzing the shear wave data. In SWEI, the shear wave speed is often estimated with time-of-flight (TOF) calculations. To characterize the errors produced by TOF calculations, three-dimensional (3D) simulated shear waves are described by time-domain Green's functions for a Kelvin-Voigt model evaluated for multiple combinations of the shear elasticity and the shear viscosity. Estimated shear wave speeds are obtained from cross correlations and time-to-peak (TTP) calculations applied to shear wave particle velocities and shear wave particle displacements. The results obtained from these 3D shear wave simulations indicate that TTP calculations applied to shear wave particle displacements yield effective estimates of the shear wave speed if noise is absent, but cross correlations applied to shear wave particle displacements are more robust when the effects of noise and shear viscosity are included. The results also show that shear wave speeds estimated with TTP methods and cross correlations using shear wave particle velocities are more sensitive to increases in shear viscosity and noise, which suggests that superior estimates of the shear wave speed are obtained from noiseless or noisy shear wave particle displacements.

A parametric evaluation of shear wave speeds estimated with time-of-flight calculations in viscoelastic media

Shear wave elasticity imaging (SWEI) uses an acoustic radiation force to generate shear waves, and then soft tissue mechanical properties are obtained by analyzing the shear wave data. In SWEI, the shear wave speed is often estimated with time-of-flight (TOF) calculations. To characterize the errors produced by TOF calculations, three-dimensional (3D) simulated shear waves are described by time-domain Green's functions for a Kelvin-Voigt model evaluated for multiple combinations of the shear elasticity and the shear viscosity. Estimated shear wave speeds are obtained from cross correlations and time-to-peak (TTP) calculations applied to shear wave particle velocities and shear wave particle displacements. The results obtained from these 3D shear wave simulations indicate that TTP calculations applied to shear wave particle displacements yield effective estimates of the shear wave speed if noise is absent, but cross correlations applied to shear wave particle displacements are more robust when the effects of noise and shear viscosity are included. The results also show that shear wave speeds estimated with TTP methods and cross correlations using shear wave particle velocities are more sensitive to increases in shear viscosity and noise, which suggests that superior estimates of the shear wave speed are obtained from noiseless or noisy shear wave particle displacements.

Four-dimensional (4D) phase velocity optical coherence elastography in heterogeneous materials and biological tissue

The variations of mechanical properties in soft tissues are biomarkers used for clinical diagnosis and disease monitoring. Optical coherence elastography (OCE) has been extensively developed to investigate mechanical properties of various biological tissues. These methods are generally based on time-domain data and measure the time-of-flight of the localized shear wave propagations to estimate the group velocity. However, there is considerable information that can be obtained from examining the mechanical properties such as wave propagation velocities at different frequencies. Here we propose a method to evaluate phase velocity, wave velocity at various frequencies, in four-dimensional space (x, y, z, f), called 4D-OCE phase velocity. The method enables local estimates of the phase velocity of propagating mechanical waves in a medium. We acquired and analyzed data with this method from a homogeneous reference phantom, a heterogeneous phantom material with four different excitation cases, and ex vivo porcine kidney tissue. The 3D-OCE group velocity was also estimated to compare with 4D-OCE phase velocity. Moreover, we performed numerical simulation of wave propagations to illustrate the boundary behavior of the propagating waves. The proposed 4D-OCE phase velocity is capable of providing further information in OCE to better understand the spatial variation of mechanical properties of various biological tissues with respect to frequency.

Influence of Load and Transducer Bandwidth on the Repeatability of In Vivo Tendon Stiffness Evaluation Using Shear Wave Elastography

Objective:

To determine how different examination protocols with the use of transducers, of different bandwidths, and applied with varied tension to tendons would influence the sonographic study results.

Methods:

Thirty-one participants were divided into two groups, with one subject used for theoretical investigation (A) and the remaining participants (B = 30) forming the study cohort. Both sets of participants were examined with three different transducers (SL10–3, SL15–4, and SL18–7) as well as with variable loading on the Achilles tendon (relaxed, tensed, and loaded). The resulting coverage of the color map provided qualitative tendon stiffness and quantitative tendon stiffness values.

Results:

The estimated mean coverage extent, using elastographic color maps, produced by the three transducers was 98%, 98%, and 99%, respectively, in the relaxed state. Likewise, in the tensed state, mean coverage was 85%, 82%, and 77% in group A and 91%, 78%, and 71% in group B, respectively. Examining tendons that were loaded, the mean coverage was 68%, 42%, and 41%, respectively. The quantitative relaxed mean tendon elasticity values were 323, 366, and 393 kPa, respectively, in group A. Likewise, the relaxed mean values were 329, 341, and 358 kPa, respectively, in group B. The quantitative tensed mean tendon elasticity values were 413, 460, and 426 kPa, respectively, in group A. Likewise the tensed mean values were 412, 440, and 436 kPa, respectively, in group B.

Conclusions:

Varying the tendon loading significantly influenced the color map coverage, which governs the most reliable quantitative measurements on relaxed tendons. The best color map coverage was achieved using the transducer with the lowest frequency, regardless of the tension applied.

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.

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.

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.

Classification of Liver Diseases Based on Ultrasound Image Texture Features

This paper discusses using computer-aided diagnosis (CAD) to distinguish between hepatocellular carcinoma (HCC), i.e., the most common type of primary liver malignancy and a leading cause of death in people with cirrhosis worldwide, and liver abscess based on ultrasound image texture features and a support vector machine (SVM) classifier. Among 79 cases of liver diseases including 44 cases of liver cancer and 35 cases of liver abscess, this research extracts 96 features including 52 features of the gray-level co-occurrence matrix (GLCM) and 44 features of the gray-level run-length matrix (GLRLM) from the regions of interest (ROIs) in ultrasound images. Three feature selection models—(i) sequential forward selection (SFS), (ii) sequential backward selection (SBS), and (iii) F-score—are adopted to distinguish the two liver diseases. Finally, the developed system can classify liver cancer and liver abscess by SVM with an accuracy of 88.875%. The proposed methods for CAD can provide diagnostic assistance while distinguishing these two types of liver lesions.