Rotational 3D shear wave elasticity imaging: Effect of knee flexion on 3D shear wave propagation in in vivo vastus lateralis.

Skeletal muscle is a complex tissue, exhibiting not only direction-dependent material properties (commonly modeled as a transversely isotropic material), but also changes in observed material properties due to factors such as contraction and passive stretch. In this work, we evaluated the effect of muscle passive stretch on shear wave propagation along and across the muscle fibers using a rotational 3D shear wave elasticity imaging system and automatic analysis methods. We imaged the vastus lateralis of 10 healthy volunteers, modulating passive stretch by imaging at 8 different knee flexion angles (controlled by a BioDex system). In addition to demonstrating the ability of this acquisition and automatic processing system to estimate muscle shear moduli over a range of values, we evaluated potential higher order biomarkers for muscle health that capture the change in muscle stiffness along and across the fibers with changing knee flexion. The median within-subject variability of these biomarkers is found to be <16%, suggesting promise as a repeatable clinical metric. Additionally, we report an unexpected observation: that shear wave signal amplitude along the fibers increases with increasing flexion and muscle stiffness, which is not predicted by transversely isotropic (TI) material simulations. This observation may point to an additional potential biomarker for muscle health or inform other material modeling choices for muscle.

Repeatability of Rotational 3-D Shear Wave Elasticity Imaging Measurements in Skeletal Muscle.

Shear wave elasticity imaging (SWEI) usually assumes an isotropic material; however, skeletal muscle is typically modeled as a transversely isotropic material with independent shear wave speeds in the directions along and across the muscle fibers. To capture these direction-dependent properties, we implemented a rotational 3-D SWEI system that measures the shear wave speed both along and across the fibers in a single 3-D acquisition, with automatic detection of the muscle fiber orientation. We tested and examined the repeatability of this system's measurements in the vastus lateralis of 10 healthy volunteers. The average coefficient of variation of the measurements from this 3-D SWEI system was 5.3% along the fibers and 8.1% across the fibers. When compared with estimated respective 2-D SWEI values of 16.0% and 83.4%, these results suggest using 3-D SWEI has the potential to improve the precision of SWEI measurements in muscle. Additionally, we observed no significant difference in shear wave speed between the dominant and non-dominant legs along (p = 0.26) or across (p = 0.65) the muscle fibers.

Parametric Analysis of SV Mode Shear Waves in Transversely Isotropic Materials Using Ultrasonic Rotational 3-D SWEI.

Ultrasonic rotational 3-D shear wave elasticity imaging (SWEI) has been used to induce and evaluate multiple shear wave modes, including both the shear horizontal (SH) and shear vertical (SV) modes in in vivo muscle. Observations of both the SH and SV modes allow the muscle to be characterized as an elastic, incompressible, transversely isotropic (ITI) material with three parameters: the longitudinal shear modulus µL , the transverse shear modulus µT , and the tensile anisotropy χE . Measurement of the SV wave is necessary to characterize χE , but the factors that influence SV mode generation and characterization with ultrasonic SWEI are complicated. This work uses Green's function (GF) simulations to perform a parametric analysis to determine the optimal interrogation parameters to facilitate visualization and quantification of SV mode shear waves in muscle. We evaluate the impact of five factors: µL , µT , χE , fiber tilt angle [Formula: see text], and F-number of the push geometry on SV mode speed, amplitude, and rotational distribution. These analyses demonstrate that the following hold: 1) as µL increases, SV waves decrease in amplitude so are more difficult to measure in SWEI imaging; 2) as µT increases, the SV wave speeds increase; 3) as χE increases, the SV waves increase in speed and separate from the SH waves; 4) as fiber tilt angle [Formula: see text] increases, the measurable SV waves remain approximately the same speed, but change in strength and in rotational distribution; and 5) as the push beam geometry changes with F-number, the measurable SV waves remain approximately the same speed, but change in strength and rotational distribution. While specific SV mode speeds depend on the combinations of all parameters considered, measurable SV waves can be generated and characterized across the range of parameters considered. To maximize measurable SV waves separate from the SH waves, it is recommended to use an F/1 push geometry and [Formula: see text].

Phase and group velocities for shear wave propagation in an incompressible, hyperelastic material with uniaxial stretch.

Objective.Determining elastic properties of materials from observations of shear wave propagation is difficult in anisotropic materials because of the complex relations among the propagation direction, shear wave polarizations, and material symmetries. In this study, we derive expressions for the phase velocities of the SH and SV propagation modes as a function of propagation direction in an incompressible, hyperelastic material with uniaxial stretch.Approach.Wave motion is included in the material model by adding incremental, small amplitude motion to the initial, finite deformation. Equations of motion for the SH and SV propagation modes are constructed using the Cauchy stress tensor derived from the strain energy function of the material. Group velocities for the SH and SV propagation modes are derived from the angle-dependent phase velocities.Main results.Sample results are presented for the Arruda-Boyce, Mooney-Rivlin, and Isihara material models using model parameters previously determined in a phantom.Significance.Results for the Mooney-Rivlin and Isihara models demonstrate shear splitting in which the SH and SV propagation modes have unequal group velocities for propagation across the material symmetry axis. In addition, for sufficiently large stretch, the Arruda-Boyce and Isihara material models show cusp structures with triple-valued group velocities for the SV mode at angles of roughly 15° to the material symmetry axis.

Full Characterization of in vivo Muscle as an Elastic, Incompressible, Transversely Isotropic Material Using Ultrasonic Rotational 3D Shear Wave Elasticity Imaging.

Using a 3D rotational shear wave elasticity imaging (SWEI) setup, 3D shear wave data were acquired in the vastus lateralis of a healthy volunteer. The innate tilt between the transducer face and the muscle fibers results in the excitation of multiple shear wave modes, allowing for more complete characterization of muscle as an elastic, incompressible, transversely isotropic (ITI) material. The ability to measure both the shear vertical (SV) and shear horizontal (SH) wave speed allows for measurement of three independent parameters needed for full ITI material characterization: the longitudinal shear modulus µL , the transverse shear modulus µT , and the tensile anisotropy χE . Herein we develop and validate methodology to estimate these parameters and measure them in vivo, with µL = 5.77±1.00 kPa, µT = 1.93±0.41 kPa (giving shear anisotropy χµ = 2.11±0.92 ), and χE = 4.67±1.40 in a relaxed vastus lateralis muscle. We also demonstrate that 3D SWEI can be used to more accurately characterize muscle mechanical properties as compared to 2D SWEI.

Uniqueness of shear wave modeling in an incompressible, transversely isotropic (ITI) material.

Five material parameters are required to describe a transversely isotropic (TI) material including two Poisson's ratios that characterize the compressibility of the material. Both Poisson's ratios must be specified to model an incompressible, TI (ITI) material. However, a previous analysis of the procedure used to evaluate the incompressible limit in a two-dimensional (2D) space of Poisson's ratios has shown that elements of the stiffness tensor are not unique in this limit, and that an additional, fourth parameter is required to model these elements for an ITI material. In this study, we extend this analysis to the case of shear wave propagation in an ITI material. Shear wave signals are modeled using analytic Green's tensor methods to express the signals in terms of the phase velocity and polarization vectors of the shear horizontal (SH) and shear vertical (SV) propagation modes. In contrast to the previous result, the current analysis demonstrates that the phase velocity and polarization vectors are independent of the procedure used to evaluate the 2D limit of Poisson's ratios without the need to include an additional parameter. Thus, calculated shear wave signals are unique and can be used for comparison with experimental measurements to determine all three model parameters that characterize an ITI material.

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.

Analysis of multiple shear wave modes in a nonlinear soft solid: Experiments and finite element simulations with a tilted acoustic radiation force.

Tissue nonlinearity is conventionally measured in shear wave elastography by studying the change in wave speed caused by the tissue deformation, generally known as the acoustoelastic effect. However, these measurements have mainly focused on the excitation and detection of one specific shear mode, while it is theoretically known that the analysis of multiple wave modes offers more information about tissue material properties that can potentially be used to refine disease diagnosis. This work demonstrated proof of concept using experiments and finite element simulations in a uniaxially stretched phantom by tilting the acoustic radiation force excitation axis with respect to the material's symmetry axis. Using this unique set-up, we were able to visualize two propagating shear wave modes across the stretch direction for stretches larger than 140%. Complementary simulations were performed using material parameters determined from mechanical testing, which enabled us to convert the observed shear wave behavior into a correct representative constitutive law for the phantom material, i.e. the Isihara model. This demonstrates the potential of measuring shear wave propagation in combination with shear wave modeling in complex materials as a non-invasive alternative for mechanical testing.

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 required 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.

Characterization of Viscoelastic Materials Using Group Shear Wave Speeds.

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

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

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

Evaluating the Benefit of Elevated Acoustic Output in Harmonic Motion Estimation in Ultrasonic Shear Wave Elasticity Imaging.

Harmonic imaging techniques have been applied in ultrasonic elasticity imaging to obtain higher-quality tissue motion tracking data. However, harmonic tracking can be signal-to-noise ratio and penetration depth limited during clinical imaging, resulting in decreased yield of successful shear wave speed measurements. A logical approach is to increase the source pressure, but the in situ pressures used in diagnostic ultrasound have been subject to a de facto upper limit based on the Food and Drug Administration guideline for the mechanical index (MI <1.9). A recent American Institute of Ultrasound in Medicine report concluded that an in situ MI up to 4.0 could be warranted without concern for increased risk of cavitation in non-fetal tissues without gas bodies if there were a concurrent clinical benefit. This work evaluates the impact of using an elevated MI in harmonic motion tracking for hepatic shear wave elasticity imaging. The studies indicate that high-MI harmonic tracking increased shear wave speed estimation yield by 27% at a focal depth of 5 cm, with larger yield increase in more difficult-to-image patients. High-MI tracking improved harmonic tracking data quality by increasing the signal-to-noise ratio and decreasing jitter in the tissue motion data. We conclude that there is clinical benefit to use of elevated acoustic output in shear wave tracking, particularly in difficult-to-image patients.

Quantifying Image Quality Improvement Using Elevated Acoustic Output in B-Mode Harmonic Imaging.

Tissue harmonic imaging has been widely used in abdominal imaging because of its significant reduction in acoustic noise compared with fundamental imaging. However, tissue harmonic imaging can be limited by both signal-to-noise ratio and penetration depth during clinical imaging, resulting in decreased diagnostic utility. A logical approach would be to increase the source pressure, but the in situ pressures used in diagnostic ultrasound are subject to a de facto upper limit based on the U.S. Food and Drug Administration guideline for the mechanical index (<1.9). A recent American Institute of Ultrasound in Medicine report concluded that an effective mechanical index ≤4.0 could be warranted without concern for increased risk of cavitation in non-fetal tissues without gas bodies, but would only be justified if there were a concurrent improvement in image quality and diagnostic utility. This work evaluates image quality differences between normal and elevated acoustic output hepatic harmonic imaging using a transmit frequency of 1.8 MHz. The results indicate that harmonic imaging using elevated acoustic output leads to modest improvements (3%-7%) in contrast-to-noise ratio of hypo-echoic hepatic vessels and increases in imaging penetration depth on the order of 4 mm per mechanical index increase of 0.1 for a given focal depth. Difficult-to-image patients who suffer from poor ultrasound image quality exhibited larger improvements than easy-to-image study participants.

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

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

Ultrasonic Shear Wave Elasticity Imaging Sequencing and Data Processing Using a Verasonics Research Scanner.

Ultrasound elasticity imaging has been developed over the last decade to estimate tissue stiffness. Shear wave elasticity imaging (SWEI) quantifies tissue stiffness by measuring the speed of propagating shear waves following acoustic radiation force excitation. This paper presents the sequencing and data processing protocols of SWEI using a Verasonics system. The selection of the sequence parameters in a Verasonics programming script is discussed in detail. The data processing pipeline to calculate group shear wave speed (SWS), including tissue motion estimation, data filtering, and SWS estimation, is demonstrated. In addition, the procedures for calibration of beam position, scanner timing, and transducer face heating are provided to avoid SWS measurement bias and transducer damage.

On System-Dependent Sources of Uncertainty and Bias in Ultrasonic Quantitative Shear-Wave Imaging.

Ultrasonic quantitative shear-wave imaging methods have been developed over the last decade to estimate tissue elasticity by measuring the speed of propagating shear waves following acoustic radiation force excitation. This work discusses eight sources of uncertainty and bias arising from ultrasound system-dependent parameters in ultrasound shear-wave speed (SWS) measurements. Each of the eight sources of error is discussed in the context of a linear, isotropic, elastic, homogeneous medium, combining previously reported analyses with Field II simulations, full-wave 2-D acoustic propagation simulations, and experimental studies. Errors arising from both spatial and temporal sources lead to errors in SWS measurements. Arrival time estimation noise, speckle bias, hardware fluctuations, and phase aberration cause uncertainties (variance) in SWS measurements, while pulse repetition frequency (PRF) and beamforming errors, as well as coupling medium sound speed mismatch, cause biases in SWS measurements (accuracy errors). Calibration of the sources of bias is an important step in the development of shear-wave imaging systems. In a well-calibrated system, where the sources of bias are minimized, and averaging over a region of interest (ROI) is employed to reduce the sources of uncertainty, an SWS error can be expected.

Evaluating the Improvement in Shear Wave Speed Image Quality Using Multidimensional Directional Filters in the Presence of Reflection Artifacts.

Shear waves propagating through interfaces where there is a change in stiffness cause reflected waves that can lead to artifacts in shear wave speed (SWS) reconstructions. Two-dimensional (2-D) directional filters are commonly used to reduce in-plane reflected waves; however, SWS artifacts arise from both in- and out-of-imaging-plane reflected waves. Herein, we introduce 3-D shear wave reconstruction methods as an extension of the previous 2-D estimation methods and quantify the reduction in image artifacts through the use of volumetric SWS monitoring and 4-D-directional filters. A Gaussian acoustic radiation force impulse excitation was simulated in phantoms with Young's modulus (E) of 3 kPa and a 5-mm spherical lesion with E = 6, 12, or 18.75 kPa. The 2-D-, 3-D-, and 4-D-directional filters were applied to the displacement profiles to reduce in-and out-of-plane reflected wave artifacts. Contrast-to-noise ratio and SWS bias within the lesion were calculated for each reconstructed SWS image to evaluate the image quality. For 2-D SWS image reconstructions, the 3-D-directional filters showed greater improvements in image quality than the 2-D filters, and the 4-D-directional filters showed marginal improvement over the 3-D filters. Although 4-D-directional filters can further reduce the impact of large magnitude out-of-plane reflection artifacts in SWS images, computational overhead and transducer costs to acquire 3-D data may outweigh the modest improvements in image quality. The 4-D-directional filters have the largest impact in reducing reflection artifacts in 3-D SWS volumes.

An analytic, Fourier domain description of shear wave propagation in a viscoelastic medium using asymmetric Gaussian sources.

Recent measurements of shear wave propagation in viscoelastic materials have been analyzed by constructing the two-dimensional Fourier transform (2D-FT) of the spatial-temporal shear wave signal and using an analysis procedure derived under the assumption the wave is described as a plane wave, or as the asymptotic form of a wave expanding radially from a cylindrically symmetric source. This study presents an exact, analytic expression for the 2D-FT description of shear wave propagation in viscoelastic materials following asymmetric Gaussian excitations and uses this expression to evaluate the bias in 2D-FT measurements obtained using the plane or cylindrical wave assumptions. A wide range of biases are observed depending on specific values of frequency, aspect ratio R of the source asymmetry, and material properties. These biases can be reduced significantly by weighting the shear wave signal in the spatial domain to correct for the geometric spreading of the shear wavefront using a factor of x(p). The optimal weighting power p is found to be near the theoretical value of 0.5 for the case of a cylindrical source with R = 1, and decreases for asymmetric sources with R > 1.

Analyzing the Impact of Increasing Mechanical Index and Energy Deposition on Shear Wave Speed Reconstruction in Human Liver.

Shear wave elasticity imaging (SWEI) has found success in liver fibrosis staging. This work evaluates hepatic SWEI measurement success as a function of push pulse energy using two mechanical index (MI) values (1.6 and 2.2) over a range of pulse durations. Shear wave speed (SWS) was measured in the livers of 26 study subjects with known or potential chronic liver diseases. Each measurement consisted of eight SWEI sequences, each with different push energy configurations. The rate of successful SWS estimation was linearly proportional to the push energy. SWEI measurements with higher push energy were successful in patients for whom standard push energy levels failed. The findings also suggest that liver capsule depth could be used prospectively to identify patients who would benefit from elevated output. We conclude that there is clinical benefit to using elevated acoustic output for hepatic SWS measurement in patients with deeper livers.