Characterization of Viscoelastic Materials Using Group Shear Wave Speeds

Shear wave elastography primer for the abdominal radiologist

PURPOSE

Shear wave elastography (SWE) provides a means for adding information about the mechanical properties of tissues to a diagnostic ultrasound examination. It is important to understand the physics and methods by which the measurements are made to aid interpretation of the results as they relate to disease processes.

METHODS

The components of how ultrasound is used to generate shear waves and make measurements of the induced motion are reviewed. The physics of shear wave propagation are briefly described for elastic and viscoelastic tissues. Additionally, shear wave propagation in homogeneous and inhomogeneous cases is addressed.

RESULTS

SWE technology has been implemented by many clinical vendors with different capabilities. Various quality metrics are used to define valid measurements based on aspects of the shear wave signals or wave velocity estimates.

CONCLUSION

There are many uses for SWE in abdominal imaging, but it is important to understand how the measurements are performed to gauge their utility for diagnosis of different conditions. Continued efforts to make the technology robust in complex clinical situations are ongoing, but many applications actively benefit from added information about tissue mechanical properties for a more holistic view of the patient for diagnosis or assessment of prognosis and treatment management.

Fourier energy spectrum centroid: a robust and efficient approach for shear wave speed estimation inω-kspace

Objective.The propagation speed of a shear wave, whether externally or internally induced, in biological tissues is directly linked to the tissue's stiffness. The group shear wave speed (SWS) can be estimated using a class of time-of-flight (TOF) methods in the time-domain or phase speed-based methods in the frequency domain. However, these methods suffer from biased estimations or time-consuming computations, and they are especially prone to wave distortions inin vivocases. In this work, we present a parameter-free, robust, and efficient group SWS estimation method coined as Fourier energy spectrum centroid (FESC).Approach.The proposed FESC method is based on the center of mass inω-kspace. It was evaluated on data from computer simulations with additive Gaussian noise, a commercial elasticity phantom, anex vivopig liver, andin vivobiceps brachii muscles of three young healthy male subjects. The FESC method was compared with two 2D frequency-domain methods: Max-fre, which considers phase SWS at the peak ofk-space, and Fre-regre, which applies linear regression of phase SWS within a fixed bandwidth. Two additional benchmarks included time-domain methods based on cross-correlation (X-Corr) and radon sum transformation (RD).Main results.Statistical results showed that our FESC method and the RD method had comparable accuracy and robustness, outperforming the other benchmark methods. In the simulation and phantom studies, when the signal-to-noise ratio was higher than 25 dB, our FESC showed higher accuracy than RD. In thein vivostudy, our FESC method had better repeatability than RD. Furthermore, the proposed FESC method was 100 times faster than the runner-up method, X-Corr, and 3,000 times faster than the least efficient method, RD.Significance.All results indicated that our proposed Fourier-based method shows promise in reliably and efficiently providing reference values for group SWS in homogeneous bulk media.

Amplitude-Modulation Frequency Optimization for Enhancing Harmonic Motion Imaging Performance of Breast Tumors in the Clinic

OBJECTIVE

Elastography images tissue mechanical responses and infers the underlying properties to aid diagnosis and treatment response monitoring. The estimation of absolute or relative tumor properties may vary with dimensions even when the mechanical properties remain constant. Harmonic motion imaging (HMI) uses amplitude-modulated (AM) focused ultrasound to interrogate the targeted tissue's viscoelastic properties. In this study, effects of AM frequencies on HMI were investigated in terms of inclusion relative stiffness and size estimation.

METHODS

AM frequencies from 200 to 600 Hz in steps of 100 Hz were considered using a 5.3-kPa phantom with cylindrical inclusions (Young's modulus: 22, 31, 44, 56 kPa, and diameter: 4.8, 8.1, 13.6, 19.8 mm) to optimize the performance of HMI in characterizing tumors with the same mechanical properties and of different dimensions.

RESULTS

Consistent displacement ratios (DRs) (17.5% variation) of the inclusion to background were obtained with 200-Hz AM for breast-tumor-mimicking inclusions albeit a suboptimal inclusion size estimation obtained. 400-Hz was otherwise used for small and low-contrast inclusions (4.8 mm, 22 or 31 kPa). A linear relationship (R2 = 0.9043) was found between the inverse DR at these frequencies and the Young's modulus ratio. 400 Hz obtained the most accurate inclusion size estimation with an overall estimation error on the lateral dimension of 0.5 mm. In vivo imaging of breast cancer patients (n = 5) was performed at 200 or 400 Hz.

CONCLUSION

The results presented herein indicate that the HMI AM frequency could be optimized adaptively in cases of different applications, i.e., at 200 or 400 Hz, depending on whether aimed for consistent DR measurement for tumor response assessment or tumor margin delineation for surgical planning. HMI may thus be capable of predicting the pathologic endpoint of tumors in response to neoadjuvant chemotherapy (NACT) as early as 3 weeks into treatment.

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.

Influencing Factors, Reference Range and Repeatability of Salivary Gland Ultrasound Viscoelastic Imaging in Healthy Adults

OBJECTIVE

The study aimed to determine the influencing factors, reference range, the changes of salivary gland secretion function and repeatability of measurements taken from ultrasound (US) viscoelastic imaging in the salivary glands of healthy adults.

METHODS

From August 2023 to October 2023, 206 healthy adults were recruited. In November 2023, 50 healthy adults were recruited for acid stimulation testing. All volunteers underwent conventional and viscoelastic US of the salivary glands. The viscoelasticity values in different regions of interest (ROI), observers, genders, ages, body mass index (BMI) groups and before and after acid stimulation were compared separately. A two-sided 95% reference range was estimated accordingly.

RESULTS

There was no difference in the E-mean and V-mean values among different ROIs (p > 0.05). The intra-group correlation coefficient values between the different observers were all >0.908. Except for the influence of age on the E-mean value of the parotid gland, the V-mean of the parotid gland, the E-mean and V-mean of the submandibular gland were not affected by age, gender or BMI. Finally, differences were detected in the E-means and V-means of the parotid and submandibular glands before and after acid stimulation (p < 0.05).

CONCLUSION

US viscoelastic imaging is a simple and reliable technique for evaluating the stiffness and viscosity of salivary glands in healthy adults. It also can be used to dynamically evaluate the changes of salivary gland secretion function.

Development of a piezo stack - laser Doppler vibrometer sensing approach for characterizing shear wave dispersion and local viscoelastic property distributions

Laser Doppler vibrometry and wavefield analysis have recently shown great potential for nondestructive evaluation, structural health monitoring, and studying wave physics. However, there are limited studies on these approaches for viscoelastic soft materials, especially, very few studies on the laser Doppler vibrometer (LDV)-based acquisition of time-space wavefields of dispersive shear waves in viscoelastic materials and the analysis of these wavefields for characterizing shear wave dispersion and evaluating local viscoelastic property distributions. Therefore, this research focuses on developing a piezo stack-LDV system and shear wave time-space wavefield analysis methods for enabling the functions of characterizing the shear wave dispersion and the distributions of local viscoelastic material properties. Our system leverages a piezo stack to generate shear waves in viscoelastic materials and an LDV to acquire time-space wavefields. We introduced space-frequency-wavenumber analysis and least square regression-based dispersion comparison to analyze shear wave time-space wavefields and offer functions including extracting shear wave dispersion relations from wavefields and characterizing the spatial distributions of local wavenumbers and viscoelastic properties (e.g., shear elasticity and viscosity). Proof-of-concept experiments were performed using a synthetic gelatin phantom. The results show that our system can successfully generate shear waves and acquire time-space wavefields. They also prove that our wavefield analysis methods can reveal the shear wave dispersion relation and show the spatial distributions of local wavenumbers and viscoelastic properties. We expect this research to benefit engineering and biomedical research communities and inspire researchers interested in developing shear wave-based technologies for characterizing viscoelastic materials.

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.

Probing Tissue Viscoelasticity With STL Ultrasound Shearwave Spectroscopy Using Cole-Cole Diagrams

OBJECTIVE

Viscoelasticity is mapped by dispersion in shearwave elastography. Incomplete spectral information of shearwaves is therefore used to estimate mechanical stiffness. We propose capturing the "full-waveform-information" of the shear wave spectra to better resolve complex shear modulus μ* (ω). Approach is validated on phantom models, animal tissues, and feasibility demonstrated on human post-delivery placenta.

METHODS

We captured robust estimates of μ* in ex-vivo livers subjected to water bath ablation, glutaraldehyde exposure and in the placenta.

RESULTS

Complex modulus at 200 Hz is more reflective of tissue stiffness than cross-correlation estimate. Bias increased in phantoms with higher gelatin (G) (0.65: 6% G) and oil (O) (0.58: 6% G and 40% O) concentration, compared to elastic phantoms with low stiffness (0.33: 3% G). Actual tissues also reported higher bias in cross-correlation estimate (rabbit liver: 0.61, porcine liver: 2.20, and human placenta: 0.63). Stiffness is sensitive to ablation temperature, where the overall modulus changed from 3.02 KPa at 16 °C to 2.75 KPa at 56 °C in water bath. With exposure to Glutaraldehyde, the overall modulus increased from 2.37 to 9.03 KPa. Reconstruction errors in the loss modulus decreased by 68% with the power law compared to a Maxwell model in porcine livers with Cole-Cole inverse fitting.

CONCLUSION

Omitting Shear wave attenuation leads to bias. Reconstruction of rheological response with a model is sensitive to its architecture and also the framework.

SIGNIFICANCE

We use "full spectral information" in ultrasound shear wave elastography to better map μ*(ω) changes in viscoelastic tissues.

Systematic quantification of differences in shear wave elastography estimates between linear-elastic and viscoelastic material assumptionsa)

Quantitative, accurate, and standardized metrics are important for reliable shear wave elastography (SWE)-based biomarkers. For over two decades, the linear-elastic material assumption has been employed in SWE modes. In recent years, viscoelasticity estimation methods have been adopted in a few clinical systems. The current study aims to systematically quantify differences in SWE estimates obtained using linear-elastic and viscoelastic material assumptions. An acousto-mechanical simulation framework of acoustic radiation force impulse-based SWE was created to elucidate the effect of material viscosity and shear modulus on SWE estimates. Shear modulus estimates exhibited errors up to 72% when a numerical viscoelastic phantom was assessed as linearly elastic. Shear modulus estimates of polyvinyl alcohol phantoms between rheometry and SWE following the Kelvin-Voigt viscoelastic model assumptions were not significantly different. However, the percentage difference in shear modulus estimates between rheometry and SWE using the linear-elastic assumption was 50.1%-62.1%. In ex vivo liver, the percentage difference in shear modulus estimates between linear-elastic and viscoelastic methods was 76.1%. These findings provide a direct and systematic quantification of the potential error introduced when viscoelastic tissues are imaged with SWE following the linear-elastic assumption. This work emphasizes the need to utilize viscoelasticity estimation methods for developing robust quantitative imaging biomarkers.

Ultrasound Shear Wave Elastography in Cardiology

The advent of high-frame rate imaging in ultrasound allowed the development of shear wave elastography as a noninvasive alternative for myocardial stiffness assessment. It measures mechanical waves propagating along the cardiac wall with speeds that are related to stiffness. The use of cardiac shear wave elastography in clinical studies is increasing, but a proper understanding of the different factors that affect wave propagation is required to correctly interpret results because of the heart's thin-walled geometry and intricate material properties. The aims of this review are to give an overview of the general concepts in cardiac shear wave elastography and to discuss in depth the effects of age, hemodynamic loading, cardiac morphology, fiber architecture, contractility, viscoelasticity, and system-dependent factors on the measurements, with a focus on clinical application. It also describes how these factors should be considered during acquisition, analysis, and reporting to ensure an accurate, robust, and reproducible measurement of the shear wave.

Optimization of the Tracking Beam Sequence in Harmonic Motion Imaging

Harmonic motion imaging (HMI) is an ultrasound elastography technique that estimates the viscoelastic properties of tissues by inducing localized oscillatory motion using focused ultrasound (FUS). The resulting displacement, assumed to be inversely proportional to the tissue local stiffness, is estimated using an imaging array based on RF speckle tracking. In conventional HMI, this is accomplished with plane-wave (PW) imaging, which inherently suffers from low lateral resolution. Coherent PW compounding (PWC) leverages spatial and temporal resolution using synthetic focusing in transmit. In this study, we introduced focused imaging with parallel tracking in HMI and compared parallel tracking of various transmit F-numbers (F/2.6, 3, 4, and 5) qualitatively and quantitatively with PW and PWC imaging at various compounded angle ranges (6°, 12°, and 18°). An in silico model of a 56-kPa spherical inclusion (diameter: 3.6 mm) embedded in a 5.3-kPa background and a 5.3-kPa elastic phantom with cylindrical inclusions (Young's moduli: 22-56 kPa, diameters: 2.0-8.6 mm) were imaged to assess different tracking beam sequences. Speckle biasing in displacement estimation associated with parallel tracking was also investigated and concluded to be negligible in HMI. Parallel tracking in receive (Rx) resulted in 2%-7% and 8%-12% increase compared to PW imaging ( ) in HMI contrast and contrast-to-noise ratio in silico and phantoms. Focused imaging with parallel tracking in Rx was concluded to be most robust among PW and PWC imaging for displacement estimation, and its preclinical feasibility was demonstrated in postsurgical human cancerous breast tissue specimens and in vivo murine models of breast cancer.

Adjacent tissues modulate shear wave propagation in axially loaded tendons

Shear wave tensiometry is a noninvasive approach for gauging tendon loads based on shear wave speed. Transient shear waves are induced and tracked via sensors secured to the skin overlying a superficial tendon. Wave speeds measured in vivo via tensiometry modulate with tendon load but are lower than that predicted by a tensioned beam model of an isolated tendon, which may be due to the added inertia of adjacent tissues. The objective of this study was to investigate the effects of adjacent fat tissue on shear wave propagation measurements in axially loaded tendons. We created a layered, dynamic finite element model of an elliptical tendon surrounded by subcutaneous fat. Transient shear waves were generated via an impulsive excitation delivered across the tendon or through the subcutaneous fat. The layered models demonstrated dispersive behavior with phase velocity increasing with frequency. Group shear wave speed could be ascertained via dispersion analysis or time-to-peak measures at sequential spatial locations. Simulated wave speeds in the tendon and adjacent fat were similar and modulated with tendon loading. However, wave speed magnitudes were consistently lower in the layered models than in an isolated tendon. For all models, the wave speed-stress relationship was well described by a tensioned beam model after accounting for the added inertia of the adjacent tissues. These results support the premise that externally excited shear waves are measurable in subcutaneous fat and modulate with axial loading in the underlying tendon. The model suggests that adjacent tissues add inertia to the system, which in turn lowers shear wave speeds. This information must be considered when using tensiometry as a clinical or research tool to infer absolute tendon loading.

The impact of amplitude modulation frequency in harmonic motion imaging on inclusion characterization

OBJECTIVE

Ultrasound elasticity imaging techniques aim to provide a non-invasive characterization of tissue mechanical properties to detect pathological changes and monitor disease progression. Harmonic motion imaging (HMI) is an ultrasound-based elasticity imaging technique that utilizes an oscillatory acoustic radiation force to induce localized displacements and estimate relative tissue stiffness. Previous studies have applied a low amplitude modulation (AM) frequency of 25 or 50 Hz in HMI to assess the mechanical properties of different tissue types. In this study, we investigate the dependence of AM frequency in HMI and whether the frequency can be adjusted based on the size and mechanical properties of the underlying medium for enhanced image contrast and inclusion detection.

METHODS

A tissue-mimicking phantom with embedded inclusions at different sizes and stiffnesses was imaged within a range of AM frequencies from 25 to 250 Hz at 25-Hz step size.

DISCUSSION

The AM frequency at which the maximum contrast and CNR are achieved depends on the size and stiffness of the inclusions. A general trend shows that contrast and CNR peak at higher frequencies for smaller inclusions. In addition, for some inclusions with the same size but different stiffnesses, the optimized AM frequency increases with the stiffness of the inclusion. Nevertheless, there is a shift between the frequencies at which the contrast peaks and those with maximum CNR. Finally, in agreement with the phantom findings, imaging an ex-vivo human specimen with a 2.7-cm breast tumor at a range of AM frequencies showed that the highest contrast and CNR are achieved at the AM frequency of 50 Hz.

CONCLUSION

These findings indicate that the AM frequency can be optimized in different applications of HMI, especially in the clinic, for improved detection and characterization of tumors with different geometries and mechanical properties.

Comparing Myocardial Shear Wave Propagation Velocity Estimation Methods Based on Tissue Displacement, Velocity and Acceleration Data

Shear wave elastography (SWE) is a promising technique used to assess cardiac function through the evaluation of cardiac stiffness non-invasively. However, in the literature, SWE varies in terms of tissue motion data (displacement, velocity or acceleration); method used to characterize mechanical wave propagation (time domain [TD] vs. frequency domain [FD]); and the metric reported (wave speed [WS], shear or Young's modulus). This variety of reported methodologies complicates comparison of reported findings and sheds doubt on which methodology better approximates the true myocardial properties. We therefore conducted a simulation study to investigate the accuracy of various SWE data analysis approaches while varying cardiac geometry and stiffness. Lower WS values were obtained by the TD method compared with the FD method. Acceleration-based WS estimates in the TD were systematically larger than those based on velocity (∼10% difference). These observations were confirmed by TD analysis of 32 in vivo SWE mechanical wave measurements. In vivo data quality is typically too low for accurate FD analysis. Therefore, our study suggests using acceleration-based TD analysis for in vivo SWE to minimize underestimation of the true WS and, thus, to maximize the sensitivity of SWE to detect stiffness changes resulting from pathology.

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.

Shear wave speed measurement bias in a viscoelastic phantom across six ultrasound elastography systems: a comparative study with transient elastography and magnetic resonance elastography

Purpose

To quantify the bias of shear wave speed (SWS) measurements in a viscoelastic phantom across six different ultrasound (US) systems and to compare the SWS with those from transient elastography (TE) and magnetic resonance elastography (MRE).

Methods

A viscoelastic phantom of stiffness representing fibrotic liver or healthy thyroid was measured with nine (linear probe) and 10 (convex probe) modes of six different US-based shear wave elastography (SWE) systems using linear and convex probes. SWS measurements of three regions of interest were repeated thrice at two focal depths, coupling the probe to the phantom using a jig. An MRE system using three motion-encoding gradient frequencies of 60, 90, and 120 Hz and TE were also used to measure the stiffness of the phantom.

Results

The SWS from different SWE systems had mean coefficients of variation of 9.0–9.2% and 5.4–5.6% with linear and convex probes, respectively, in viscoelastic phantom measurement. The focal depth was a less significant source of SWS variability than the system. The total average SWS obtained with US-SWE systems was 19.9% higher than that obtained with MRE at 60 Hz, which is commonly used in clinical practice, and 31.5% higher than that obtained with TE using the M probe.

Conclusions

Despite the measurement biases associated with the SWE systems, biases were not necessarily consistent, and they changed with the probes used and depth measured. The SWS of the viscoelastic phantom obtained using different modalities increased according to the shear wave frequency used.

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.

Prostate Cancer Detection Using 3-D Shear Wave Elasticity Imaging

Transrectal ultrasound (TRUS) B-mode imaging provides insufficient sensitivity and specificity for prostate cancer (PCa) targeting when used for biopsy guidance. Shear wave elasticity imaging (SWEI) is an elasticity imaging technique that has been commercially implemented and is sensitive and specific for PCa. We have developed a SWEI system capable of 3-D data acquisition using a dense acoustic radiation force (ARF) push approach that leads to enhanced shear wave signal-to-noise ratio compared with that of the commercially available SWEI systems and facilitates screening of the entire gland before biopsy. Additionally, we imaged and assessed 36 patients undergoing radical prostatectomy using 3-D SWEI and determined a shear wave speed threshold separating PCa from healthy prostate tissue with sensitivities and specificities akin to those for multiparametric magnetic resonance imaging fusion biopsy. The approach measured the mean shear wave speed in each prostate region to be 4.8 m/s (Young's modulus E = 69.1 kPa) in the peripheral zone, 5.3 m/s (E = 84.3 kPa) in the central gland and 6.0 m/s (E = 108.0 kPa) for PCa with statistically significant (p < 0.0001) differences among all regions. Three-dimensional SWEI receiver operating characteristic analyses identified a threshold of 5.6 m/s (E = 94.1 kPa) to separate PCa from healthy tissue with a sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV) and area under the curve (AUC) of 81%, 82%, 69%, 89% and 0.84, respectively. Additionally, a shear wave speed ratio was assessed to normalize for tissue compression and patient variability, which yielded a threshold of 1.11 to separate PCa from healthy prostate tissue and was accompanied by a substantial increase in specificity, PPV and AUC, where the sensitivity, specificity, PPV, NPV and AUC were 75%, 90%, 79%, 88% and 0.90, respectively. This work illustrates the feasibility of using 3-D SWEI data to detect and localize PCa and demonstrates the benefits of normalizing for applied compression during data acquisition for use in biopsy targeting studies.

Viscoelasticity Imaging of Biological Tissues and Single Cells Using Shear Wave Propagation

Changes in biomechanical properties of biological soft tissues are often associated with physiological dysfunctions. Since biological soft tissues are hydrated, viscoelasticity is likely suitable to represent its solid-like behavior using elasticity and fluid-like behavior using viscosity. Shear wave elastography is a non-invasive imaging technology invented for clinical applications that has shown promise to characterize various tissue viscoelasticity. It is based on measuring and analyzing velocities and attenuations of propagated shear waves. In this review, principles and technical developments of shear wave elastography for viscoelasticity characterization from organ to cellular levels are presented, and different imaging modalities used to track shear wave propagation are described. At a macroscopic scale, techniques for inducing shear waves using an external mechanical vibration, an acoustic radiation pressure or a Lorentz force are reviewed along with imaging approaches proposed to track shear wave propagation, namely ultrasound, magnetic resonance, optical, and photoacoustic means. Then, approaches for theoretical modeling and tracking of shear waves are detailed. Following it, some examples of applications to characterize the viscoelasticity of various organs are given. At a microscopic scale, a novel cellular shear wave elastography method using an external vibration and optical microscopy is illustrated. Finally, current limitations and future directions in shear wave elastography are presented.

Radiological Society of North America/Quantitative Imaging Biomarker Alliance Shear Wave Speed Bias Quantification in Elastic and Viscoelastic Phantoms

OBJECTIVES

To quantify the bias of shear wave speed (SWS) measurements between different commercial ultrasonic shear elasticity systems and a magnetic resonance elastography (MRE) system in elastic and viscoelastic phantoms.

METHODS

Two elastic phantoms, representing healthy through fibrotic liver, were measured with 5 different ultrasound platforms, and 3 viscoelastic phantoms, representing healthy through fibrotic liver tissue, were measured with 12 different ultrasound platforms. Measurements were performed with different systems at different sites, at 3 focal depths, and with different appraisers. The SWS bias across the systems was quantified as a function of the system, site, focal depth, and appraiser. A single MRE research system was also used to characterize these phantoms using discrete frequencies from 60 to 500 Hz.

RESULTS

The SWS from different systems had mean difference 95% confidence intervals of ±0.145 m/s (±9.6%) across both elastic phantoms and ± 0.340 m/s (±15.3%) across the viscoelastic phantoms. The focal depth and appraiser were less significant sources of SWS variability than the system and site. Magnetic resonance elastography best matched the ultrasonic SWS in the viscoelastic phantoms using a 140 Hz source but had a - 0.27 ± 0.027-m/s (-12.2% ± 1.2%) bias when using the clinically implemented 60-Hz vibration source.

CONCLUSIONS

Shear wave speed reconstruction across different manufacturer systems is more consistent in elastic than viscoelastic phantoms, with a mean difference bias of < ±10% in all cases. Magnetic resonance elastographic measurements in the elastic and viscoelastic phantoms best match the ultrasound systems with a 140-Hz excitation but have a significant negative bias operating at 60 Hz. This study establishes a foundation for meaningful comparison of SWS measurements made with different platforms.

Measurement of Shear Wave Speed and Normalized Elastic Modulus of Human Skin with and without Dermal Striae Using Shear Wave Elastography

Supersonic shear imaging is a non-invasive technique used for detecting physiologic and pathologic changes in biological tissues. In this study, supersonic shear imaging was used to measure and compare shear wave speed (c_s) and normalized elastic modulus (E_N) values of skin with and skin without dermal striae (DS) in vivo. The values were measured at angles of 0°, 45°, 90° and 315° to the skin tension lines. In the presence of DS, a statistically significant reduction in the elasticity dermis was observed (p value <0.05). The mean values of c_s and E_N for STLs were higher in normal skin at 45° (4.26 ± 1.05 m/s and 56.23 ± 25.31 kPa) and 90° (4.26 ± 0.55 m/s and 54.91 ± 14.22 kPa), and those for DS were also higher at 45° (3.59 ± 0.72 m/s and 42.71 ± 27.97 kPa) and 90° (3.52 ± 0.65 m/s and 42.34 ± 31.68 kPa) than at other angles. Supersonic shear imaging was found to be a promising technique in the study of skin with DS. The data obtained in this study are expected to be relevant for future studies using shear wave elastography for the aforementioned purpose.

Shear wave dispersion as a potential biomarker for cervical remodeling during pregnancy: evidence from a non-human primate model

Shear wave dispersion (variation of phase velocity with frequency) occurs in tissues with layered and anisotropic microstructure and viscous components, such as the uterine cervix. This phenomenon, mostly overlooked in previous applications of cervical Shear Wave Elasticity Imaging (SWEI) for preterm birth risk assessment, is expected to change drastically during pregnancy due to cervical remodeling. Here we demonstrate the potential of SWEI-based descriptors of dispersion as potential biomarkers for cervical remodeling during pregnancy. First, we performed a simulation-based pre-selection of two SWEI-based dispersion descriptors: the ratio R of group velocities computed with particle-velocity and particle-displacement, and the slope S of the phase velocity vs. frequency. The pre-selection consisted of comparing the contrast-to-noise ratio (CNR) of dispersion descriptors in materials with different degrees of dispersion with respect to a low-dispersive medium. Shear waves induced in these media by SWEI were simulated with a finite-element model of Zener viscoelastic solids. The pre-selection also considered two denoising strategies to improve CNR: a low-pass filter with automatic frequency cutoff determination, and singular value decomposition of shear wave displacements. After pre-selection, the descriptor-denoising combination that produced the largest CNR was applied to SWEI cervix data from 18 pregnant Rhesus macaques acquired at weeks 10 (mid-pregnancy stage) and 23 (late pregnancy stage) of the 24.5-week full pregnancy. A maximum likelihood linear mixed-effects model (LME) was used to evaluate the dependence of the dispersion descriptor on pregnancy stage, maternal age, parity and other experimental factors. The pre-selection study showed that descriptor S combined with singular value decomposition produced a CNR 11.6 times larger than the other descriptor and denoising strategy combinations. In the Non-Human Primates (NHP) study, the LME model showed that descriptor S significantly decreased from mid to late pregnancy (-0.37 ± 0.07 m/s-kHz per week, p <0.00001) with respect to the base value of 15.5 ± 1.9 m/s-kHz. This change was more significant than changes in other SWEI features such as the group velocity previously reported. Also, S varied significantly between the anterior and posterior portions of the cervix (p =0.02) and with maternal age (p =0.008). Given the potential of shear wave dispersion to track cervical remodeling, we will extend its application to ongoing longitudinal human studies.

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.

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.

On the Challenges Associated with Obtaining Reproducible Measurements Using SWEI in the Median Nerve

This work discusses challenges we have encountered in acquiring reproducible measurements of shear wave speed (SWS) in the median nerve and suggests methods for improving reproducibility. First, procedural acquisition challenges are described, including nerve echogenicity, transducer pressure and transmit focal depth. Second, we present an iterative, radon sum-based algorithm that was developed specifically for measuring the SWS in median nerves. SWSs were measured using single track location shear wave elasticity imaging (SWEI) in the median nerves of six healthy volunteers and six patients diagnosed with carpal tunnel syndrome. Unsuccessful measurements were associated with several challenges including reverberation artifacts, low signal-to-noise ratio and temporal window limitations for tracking the velocity wave. To address these challenges, an iterative convergence algorithm was implemented to identify an appropriate temporal processing window that removed the reverberation artifacts while preserving shear wave signals. Algorithmically, it was important to consider the lateral regression kernel size and position and the temporal window. Procedurally, both nerve echogenicity and transducer compression were determined to impact the measured SWS. Shear waves were successfully measured in the median nerve proximal to the carpal tunnel, but SWEI measurements were significantly compromised within the carpal tunnel itself. The velocity-based SWSs were statistically significantly higher than the displacement SWSs (p < 0.0001), demonstrating for the first time dispersion in the median nerve in vivo using SWEI.

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.

Measurement of Viscoelastic Material Model Parameters Using Fractional Derivative Group Shear Wave Speeds in Simulation and Phantom Data

While ultrasound shear wave elastography originally focused on tissue stiffness under the assumption of elasticity, recent work has investigated the higher order, viscoelastic properties of the tissue. This article presents a method to use group shear wave speeds (gSWSs) at a series of derivative orders to characterize viscoelastic materials. This method uses a least squares fitting algorithm to match the experimental data to the calculated gSWS data, using an assumed material model and excitation geometry matched to the experimental imaging configuration. Building on a previous study that used particle displacement, velocity, and acceleration signals, this study extends the analysis to a continuous range of fractional derivative orders between 0 and 2. The method can be applied to any material model. Herein, material characterization was performed for three different two-parameter models and three different three-parameter models. This group speed-based method was applied to both shear wave simulations with ultrasonic tracking and experimental acquisitions in viscoelastic phantoms [similar to the Phase II Quantitative Imaging Biomarkers Alliance (QIBA) phantoms]. In both the cases, the group speed method produced more repeatable characterization overall than fitting the phase velocity results from the peak of the 2-D Fourier transform. Results suggest that the linear attenuation model is a better fit than the Voigt model for the viscoelastic QIBA phantoms.

Tractable calculation of the Green's tensor for shear wave propagation in an incompressible, transversely isotropic material

Assessing material properties from observations of shear wave propagation following an acoustic radiation force impulse (ARFI) excitation is difficult in anisotropic materials because of the complex relations among the propagation direction, shear wave polarizations, and material symmetries. In this paper, we describe a method to calculate shear wave signals using Green’s tensor methods in an incompressible, transversely isotropic (TI) material characterized by three material parameters. The Green’s tensor is written as the sum of an analytic expression for the SH propagation mode, and an integral expression for the SV propagation mode that can be evaluated by interpolation within precomputed integral functions with an efficiency comparable to the evaluation of a closed-form expression. By using parametrized integral functions, the number of requried numerical integrations is reduced by a factor of 10² − 10⁹ depending on the specific problem under consideration. Results are presented for the case of a point source positioned at the origin and a tall Gaussian source similar to an ARFI excitation. For an experimental configuration with a tilted material symmetry axis, results show that shear wave signals exhibit structures that are sufficiently complex to allow measurement of all three material parameters that characterize an incompressible, TI material.

Spatial localization of mechanical excitation affects spatial resolution, contrast, and contrast-to-noise ratio in acoustic radiation force optical coherence elastography

The notion that a spatially confined mechanical excitation would produce an elastogram with high spatial resolution has motivated the development of various elastography techniques with localized mechanical excitation. However, a quantitative investigation of the effects of spatial localization of mechanical excitation on the spatial resolution of elastograms is still lacking in optical coherence elastography (OCE). Here, we experimentally investigated the effect of spatial localization of acoustic radiation force (ARF) excitation on spatial resolution, contrast, and contrast-to-noise ratio (CNR) of dynamic uniaxial strain elastograms in dynamic ARF-OCE, based on a framework for analyzing the factors that influence the quality of the elastogram at different stages of the elastography workflow. Our results show that localized ARF excitation with a smaller acoustic focal spot size produced a strain elastogram with superior spatial resolution, contrast, and CNR. Our results also suggest that the spatial extent spanned by the displacement response in the sample may connect between the spatial localization of the mechanical excitation and the resulting elastogram quality. The elastography framework and experimental approach presented here may provide a basis for the quantitative analysis of elastogram quality in OCE that can be adapted and applied to different OCE systems and applications.

Towards a consensus on rheological models for elastography in soft tissues

A rising wave of technologies and instruments are enabling more labs and clinics to make a variety of measurements related to tissue viscoelastic properties. These instruments include elastography imaging scanners, rheological shear viscometers, and a variety of calibrated stress-strain analyzers. From these many sources of disparate data, a common step in analyzing results is to fit the measurements of tissue response to some viscoelastic model. In the best scenario, this places the measurements within a theoretical framework and enables meaningful comparisons of the parameters against other types of tissues. However, there is a large set of established rheological models, even within the class of linear, causal, viscoelastic solid models, so which of these should be chosen? Is it simply a matter of best fit to a minimum mean squared error of the model to several data points? We argue that the long history of biomechanics, including the concept of the extended relaxation spectrum, along with data collected from viscoelastic soft tissues over an extended range of times and frequencies, and the theoretical framework of multiple relaxation models which model the multi-scale nature of physical tissues, all lead to the conclusion that fractional derivative models represent the most succinct and meaningful models of soft tissue viscoelastic behavior. These arguments are presented with the goal of clarifying some distinctions between, and consequences of, some of the most commonly used models, and with the longer term goal of reaching a consensus among different sub-fields in acoustics, biomechanics, and elastography that have common interests in comparing tissue measurements.

Piecewise parabolic method for propagation of shear shock waves in relaxing soft solids: One-dimensional case

Shear shock waves can be generated spontaneously deep within the brain during a traumatic injury. This recently observed behavior could be a primary mechanism for the generation of traumatic brain injuries. However, shear shock wave physics and its numerical modeling are relatively unstudied. Existing numerical solvers used in biomechanics are not designed for the extremely large Mach numbers (greater than 1) observed in the brain. Furthermore, soft solids, such as the brain, have a complex nonclassical viscoleastic response, which must be accurately modeled to capture the nonlinear wave behavior. Here, we develop a 1D inviscid velocity-stress-like system to model the propagation of shear shock waves in a homogeneous medium. Then a generalized Maxwell body is used to model a relaxing medium that can describe experimentally determined attenuation laws. Finally, the resulting system is solved numerically with the piecewise parabolic method, a high-order finite volume method. The nonlinear and the relaxing components of this method are validated with theoretical predictions. Comparisons between numerical solutions obtained for the proposed model and the experiments of plane shear shock wave propagation based on high frame-rate ultrasound imaging and tracking are shown to be in excellent agreement.

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.