Shear Wave Dispersion Research Articles

Efficient computational algorithms for modeling guided wave dispersion in arterial walls

Arterial stiffness is a well-known biomarker of early cardiovascular disease. Shear wave dispersion ultrasound vibrometry (SDUV) has emerged as a promising technique to estimate local arterial stiffness from the observed dispersion of guided waves. With the ultimate goal of developing real-time inversion for arterial stiffness from SDUV measurements, we develop and validate highly efficient and accurate computational algorithms that compute the wave dispersion in multi-layered immersed tubes. The proposed approach carefully combines Fourier transformation and one-dimensional finite-element discretization to accurately capture fully three-dimensional wave propagation. The method is several orders of magnitude more efficient than three-dimensional finite element simulation, and eliminates other complexities such as the need for absorbing boundary conditions. The method is validated using SDUV experiments on tissue-mimicking phantoms. The validation exercise uncovered an important detail that is often overlooked—the dispersion curve captured through SDUV experiments does not correspond to a single dispersion curve, but a combination of multiple dispersion curves. This implies that proper identification of the dispersion curves could be critical to estimating the arterial stiffness. In this talk, we present the details of the proposed method including formulation, computational complexity, verification and validation.Arterial stiffness is a well-known biomarker of early cardiovascular disease. Shear wave dispersion ultrasound vibrometry (SDUV) has emerged as a promising technique to estimate local arterial stiffness from the observed dispersion of guided waves. With the ultimate goal of developing real-time inversion for arterial stiffness from SDUV measurements, we develop and validate highly efficient and accurate computational algorithms that compute the wave dispersion in multi-layered immersed tubes. The proposed approach carefully combines Fourier transformation and one-dimensional finite-element discretization to accurately capture fully three-dimensional wave propagation. The method is several orders of magnitude more efficient than three-dimensional finite element simulation, and eliminates other complexities such as the need for absorbing boundary conditions. The method is validated using SDUV experiments on tissue-mimicking phantoms. The validation exercise uncovered an important detail that is often overlo...

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.

Acoustic Radiation Force-Induced Creep-Recovery (ARFICR): A Noninvasive Method to Characterize Tissue Viscoelasticity.

Ultrasound shear wave elastography is a promising noninvasive, low cost, and clinically viable tool for liver fibrosis staging. Current shear wave imaging technologies on clinical ultrasound scanners ignore shear wave dispersion and use a single group velocity measured over the shear wave bandwidth to estimate tissue elasticity. The center frequency and bandwidth of shear waves induced by acoustic radiation force depend on the ultrasound push beam (push duration, -number, etc.) and the viscoelasticity of the medium, and therefore are different across scanners from different vendors. As a result, scanners from different vendors may give different tissue elasticity measurements within the same patient. Various methods have been proposed to evaluate shear wave dispersion to better estimate tissue viscoelasticity. A rheological model such as the Kelvin-Voigt model is typically fitted to the shear wave dispersion to solve for the elasticity and viscosity of tissue. However, these rheological models impose strong assumptions about frequency dependence of elasticity and viscosity. Here, we propose a new method called Acoustic Radiation Force Induced Creep-Recovery (ARFICR) capable of quantifying rheological model-independent measurements of elasticity and viscosity for more robust tissue health assessment. In ARFICR, the creep-recovery time signal at the focus of the push beam is used to calculate the relative elasticity and viscosity (scaled by an unknown constant) over a wide frequency range. Shear waves generated during the ARFICR measurement are also detected and used to calculate the shear wave velocity at its center frequency, which is then used to calibrate the relative elasticity and viscosity to absolute elasticity and viscosity. In this paper, finite-element method simulations and experiments in tissue mimicking phantoms are used to validate and characterize the extent of viscoelastic quantification of ARFICR. The results suggest that ARFICR can measure tissue viscoelasticity reliably. Moreover, the results showed the strong frequency dependence of viscoelastic parameters in tissue mimicking phantoms and healthy liver.

Effect of Ultrafast Imaging on Shear Wave Visualization and Characterization: An Experimental and Computational Study in a Pediatric Ventricular Model

Plane wave imaging in Shear Wave Elastography (SWE) captures shear wave propagation in real-time at ultrafast frame rates. To assess the capability of this technique in accurately visualizing the underlying shear wave mechanics, this work presents a multiphysics modeling approach providing access to the true biomechanical wave propagation behind the virtual image. This methodology was applied to a pediatric ventricular model, a setting shown to induce complex shear wave propagation due to geometry. Phantom experiments are conducted in support of the simulations. The model revealed that plane wave imaging altered the visualization of the shear wave pattern in the time (broadened front and negatively biased velocity estimates) and frequency domain (shifted and/or decreased signal frequency content). Furthermore, coherent plane wave compounding (effective frame rate of 2.3 kHz) altered the visual appearance of shear wave dispersion in both the experiment and model. This mainly affected stiffness characterization based on group speed, whereas phase velocity analysis provided a more accurate and robust stiffness estimate independent of the use of the compounding technique. This paper thus presents a versatile and flexible simulation environment to identify potential pitfalls in accurately capturing shear wave propagation in dispersive settings.

Influence of Tissue Microstructure on Shear Wave Speed Measurements in Plane Shear Wave Elastography: A Computational Study in Lossless Fibrotic Liver Media.

Shear wave elastography (SWE) has been used to measure viscoelastic properties for characterization of fibrotic livers. In this technique, external mechanical vibrations or acoustic radiation forces are first transmitted to the tissue being imaged to induce shear waves. Ultrasonically measured displacement/velocity is then utilized to obtain elastographic measurements related to shear wave propagation. Using an open-source wave simulator, k-Wave, we conducted a case study of the relationship between plane shear wave measurements and the microstructure of fibrotic liver tissues. Particularly, three different virtual tissue models (i.e., a histology-based model, a statistics-based model, and a simple inclusion model) were used to represent underlying microstructures of fibrotic liver tissues. We found underlying microstructures affected the estimated mean group shear wave speed (SWS) under the plane shear wave assumption by as much as 56%. Also, the elastic shear wave scattering resulted in frequency-dependent attenuation coefficients and introduced changes in the estimated group SWS. Similarly, the slope of group SWS changes with respect to the excitation frequency differed as much as 78% among three models investigated. This new finding may motivate further studies examining how elastic scattering may contribute to frequency-dependent shear wave dispersion and attenuation in biological tissues.

Viscoelastic properties of normal rat liver measured by ultrasound elastography: Comparison with oscillatory rheometry.

Ultrasound elastography has been widely used to measure liver stiffness. However, the accuracy of liver viscoelasticity obtained by ultrasound elastography has not been well established. To assess the accuracy of ultrasound elastography for measuring liver viscoelasticity and compare to conventional rheometry methods. In addition, to determine if combining these two methods could delineate the rheological behavior of liver over a wide range of frequencies. The phase velocities of shear waves were measured in livers over a frequency range from 100 to 400 Hz using the ultrasound elastography method of shearwave dispersion ultrasound vibrometry (SDUV), while the complex shear moduli were obtained by rheometry over a frequency range of 1 to 30 Hz. Three rheological models, Maxwell, Voigt, and Zener, were fit to the measured data obtained from the two separate methods and from the combination of the two methods. The elasticity measured by SDUV was in good agreement with that of rheometry. However, the viscosity measured by SDUV was significantly different from that of rheometry. The results indicate that the high frequency components of the dispersive data play a much more important role in determining the dispersive pattern or the viscous value than the low frequency components. It was found that the Maxwell model is not as appropriate as the Voigt and Zener models for describing the rheological behavior of liver.

Characterization of Viscoelasticity Due to Shear Wave Propagation: a Comparison of Existing Methods Based on Computational Simulation and Experimental Data

Shear wave propagation causes microvibrations within a medium; measuring the wave attenuation coefficient, α, and phase velocity, cs, the medium shear modulus, μ, and shear viscosity, η, are determined based on a viscoelastic model that includes both cs and α. The present work compares the performances of nine processing methods, based on cross-correlation and quadrature demodulation, used to extract the motion waveform from a sequence of radio-frequency (RF) echo signals from the medium. Kalman filtering determined the amplitude and the phase of the extracted motion waveform. The comparisons were done with regard to computational simulation and experiments with a gel phantom. Estimates obtained for μ and η of the medium considered different conditions for the vibration amplitude and the signal-to-noise ratio (SNR) of the RF echo signals and the waveform extracted by means of single frequency and shear wave dispersion ultrasound vibration (SDUV) methods. According to the simulated results, the cross-correlation-based processing techniques are more precise and accurate in comparison to quadrature demodulation techniques. The results for cs, α, μ and η of the phantom and those obtained under the same setup conditions for experimental and computational tests agree with each other. Comparing the estimates based on single frequency and SDUV techniques, they presented similar performances at high SNR of the RF echo signal. On the other hand, the former technique prevailed for low SNR.

Analysis of dispersion and absorption characteristics of shear waves in sinusoidally corrugated elastic medium with void pores

This theoretical work reports the dispersion and absorption characteristics of horizontally polarized shear wave (SH-wave) in a corrugated medium with void pores sandwiched between two dissimilar half-spaces. The dispersion and absorption equations have been derived in a closed form using the method of separation of variables. It has been established that there are two different kinds of wavefronts propagating in the proposed media. One of the wavefronts depends on the modulus of rigidity of elastic matrix of the medium and satisfies the dispersion equation of SH-waves. The second wavefront depends on the changes in volume fraction of the pores. Numerical computation of the obtained relations has been performed and the results are depicted graphically. The influence of corrugation, sandiness on the phase velocity and the damped velocity of SH-wave has been studied extensively.

A magneto-motive ultrasound platform designed for pre-clinical and clinical applications

Abstract Introduction Magneto-motive ultrasound (MMUS) combines magnetism and ultrasound (US) to detect magnetic nanoparticles in soft tissues. One type of MMUS called shear-wave dispersion magneto-motive ultrasound (SDMMUS) analyzes magnetically induced shear waves (SW) to quantify the elasticity and viscosity of the medium. The lack of an established presets or protocols for pre-clinical and clinical studies currently limits the use of MMUS techniques in the clinical setting. Methods This paper proposes a platform to acquire, process, and analyze MMUS and SDMMUS data integrated with a clinical ultrasound equipment. For this purpose, we developed an easy-to-use graphical user interface, written in C++/Qt4, to create an MMUS pulse sequence and collect the ultrasonic data. We designed a graphic interface written in MATLAB to process, display, and analyze the MMUS images. To exemplify how useful the platform is, we conducted two experiments, namely (i) MMUS imaging to detect magnetic particles in the stomach of a rat, and (ii) SDMMUS to estimate the viscoelasticity of a tissue-mimicking phantom containing a spherical target of ferrite. Results The developed software proved to be an easy-to-use platform to automate the acquisition of MMUS/SDMMUS data and image processing. In an in vivo experiment, the MMUS technique detected an area of 6.32 ± 1.32 mm2 where magnetic particles were heterogeneously distributed in the stomach of the rat. The SDMMUS method gave elasticity and viscosity values of 5.05 ± 0.18 kPa and 2.01 ± 0.09 Pa.s, respectively, for a tissue-mimicking phantom. Conclusion Implementation of an MMUS platform with addressed presets and protocols provides a step toward the clinical implementation of MMUS imaging equipment. This platform may help to localize magnetic particles and quantify the elasticity and viscosity of soft tissues, paving a way for its use in pre-clinical and clinical studies.

超音波Shear Wave Dispersion Imagingによる肝の弾性と粘性の測定

To investigate the value of shear wave (SW) speed (m/s) and dispersion slope ([m/s]/kHz), which is related to viscosity obtained by a prototype ultrasound elastography system in rat livers with various degrees of inflammation and fibrosis. SW speed was significantly higher in the fibrosis model rats (G3) than in the inflammation model rats (G1). Dispersion slope was significantly higher in the inflammation model rats (G2) than in the fibrosis model rats (G4). These results indicate that SW speed is more effective than dispersion slope in assessing the degree of fibrosis and also suggest that dispersion slope is more effective than SW speed in assessing the degree of inflammation. Dispersion slope measurements may provide additional pathophysiological insights into liver tissue.

Model-dependent and model-independent approaches for evaluating hepatic fibrosis in rat liver using shearwave dispersion ultrasound vibrometry

This study assesses gradations of hepatic fibrosis in rat livers using both model-dependent and model-independent approaches. Liver fibrosis was induced in 37 rats using carbon tetrachloride (CCl4); 6 rats served as the controls. Shear wave velocity as a function of frequency, referred to as velocity dispersion, was measured in vitro by an ultrasound elastography method called shearwave dispersion ultrasound vibrometry (SDUV). For the model-dependent approach, the velocity dispersion data were fit to the Voigt model to solve the viscoelastic modulus. For the model-independent approach, the pattern of the velocity dispersion data was analyzed by linear regression to extract the slope and intercept features. The parameters obtained by both approaches were evaluated separately using a receiver operating characteristic (ROC) curve analysis. The results show that, of all the parameters for differentiating between grade F0–F1 and grade F2–F4 fibrosis, the intercept had the greatest value for the area under the ROC curve. This finding suggests that the model-independent approach may provide an alternative method to the model-dependent approach for staging liver fibrosis.

Dispersion of shear wave in a pre-stressed hetrogeneous orthotropic layer over a pre-stressed anisotropic porous half-space with self-weight

The purpose of this study is to illustrate the propagation of the shear waves (SH-waves) in a prestressed hetrogeneous orthotropic media overlying a pre-stressed anisotropic porous half-space with self weight. It is considered that the compressive initial stress, mass density and moduli of rigidity of the upper layer are space dependent. The proposed model is solved to obtain the different dispersion relations for the SH-wave in the elastic-porous medium of different properties. The effects of compressive and tensile stresses along with the heterogeneity, porosity, Biot‟s gravity parameter on the dispersion of SH-wave are shown numerically. The wave analysis further indicates that the technical parameters of upper and lower half-space affect the wave velocity significantly. The results may be useful to understand the nature of seismic wave propagation in geophysical applications and in the field of earthquake and material science engineering.

Blind Source Separation - Based Motion Detector for Sub-Micrometer, Periodic Displacement in Ultrasonic Imaging.

Sub-micrometer, periodic motion detection using blind source separation (BSS) via principal component analysis (PCA) is presented in the context of magnetomotive ultrasound (MMUS) imaging and Shearwave Dispersion Ultrasound Vibrometry (SDUV). In MMUS, an oscillating external magnetic field displaces tissue loaded with superparamagnetic iron oxide (SPIO) particles, whereas in SDUV, periodic tissue motion is induced using acoustic radiation force (ARF) to measure visco-elastic properties. BSS motion detection performance in MMUS imaging and SDUV was compared against frequency-phase locked (FPL) and normalized cross-correlation (NCC) motion detectors, respectively, in silico and in experimental phantoms. Parametric MMUS phantom images constructed using the BSS method had nearly twice the SNR of the corresponding images constructed using FPL method when a 0.043 mm or smaller kernel size was used. In FEM models of SDUV, the error in the BSS-estimated viscoelastic properties of simulated materials was < 10%, whereas the error was > 20% using NCC when the simulated SNR was 15 dB. In a calibrated elasticity phantom, the amplitude of the motion was ≤ 0.5 μm for a scanner power level ≤ 20%. The median percent error in BSS-derived shear modulus of the phantom was -6.8%, -1.55%, -17.11% for power level of 20%, 15%, and 10%, respectively. The corresponding NCC-derived errors were 29.90%, 127.1%, and 244.70%. These results suggest the relevance of using BSS for the detection of sub-micrometer, periodic motion in MMUS and SDUV imaging, particularly when SNR is less than 15 dB and/or induced displacements are less than 0.5 μm.

Shear wave dispersion behaviors of soft, vascularized tissues from the microchannel flow model

The frequency dependent behavior of tissue stiffness and the dispersion of shear waves in tissue can be measured in a number of ways, using integrated imaging systems. The microchannel flow model, which considers the effects of fluid flow in the branching vasculature and microchannels of soft tissues, makes specific predictions about the nature of dispersion. In this paper we introduce a more general form of the 4 parameter equation for stress relaxation based on the microchannel flow model, and then derive the general frequency domain equation for the complex modulus. Dispersion measurements in liver (ex vivo) and whole perfused placenta (post-delivery) correspond to the predictions from theory, guided by independent stress relaxation measurements and consideration of the vascular tree structure.

Quantitative evaluation of rock brittleness and fracability based on elastic-wave velocity variation around borehole

Abstract Brittleness and fracability are two important rock properties in hydraulic fracturing of unconventional reservoirs. Based on the variation of compressional and shear velocity around borehole using acoustic measurement, an effective technique is developed to estimate these parameters to guide reservoir-fracturing. During drilling, when the rock is broken, a significant amount of drilling induced cracks will occur in the formation around the borehole, reducing elastic wave velocity around borehole and causing the wave velocity variation away from borehole. The radial variation of compressional and shear velocities of formation rocks surrounding a borehole were respectively obtained from P-wave travel time tomography and dipole shear-wave dispersion inversion. By integrating the two variation profiles along the radial direction, the brittleness-fracability index is obtained to estimate the brittleness and fracability of formation rocks. The index shows fairly good consistency and correlation with rock brittleness and fracability, which demonstrates the practicability and effectiveness of the proposed approach. Well log data analysis examples are presented to demonstrate the effectiveness of our technique.

In vivo quantification of the shear modulus of the human Achilles tendon during passive loading using shear wave dispersion analysis

The shear wave velocity dispersion was analyzed in the Achilles tendon (AT) during passive dorsiflexion using a phase velocity method in order to obtain the tendon shear modulus (C55). Based on this analysis, the aims of the present study were (i) to assess the reproducibility of the shear modulus for different ankle angles, (ii) to assess the effect of the probe locations, and (iii) to compare results with elasticity values obtained with the supersonic shear imaging (SSI) technique. The AT shear modulus (C55) consistently increased with the ankle dorsiflexion (N = 10, p < 0.05). Furthermore, the technique showed a very good reproducibility (all standard error of the mean values <10.7 kPa and all coefficient of variation (CV) values ⩽0.05%). In addition, independently from the ankle dorsiflexion, the shear modulus was significantly higher in the proximal location compared to the more distal one. The shear modulus provided by SSI was always lower than C55 and the difference increased with the ankle dorsiflexion. However, shear modulus values provided by both methods were highly correlated (R = 0.84), indicating that the conventional shear wave elastography technique (SSI technique) can be used to compare tendon mechanical properties across populations. Future studies should determine the clinical relevance of the shear wave dispersion analysis, for instance in the case of tendinopathy or tendon tear.

Shear-wave elasticity imaging of a liver fibrosis mouse model using high-frequency ultrasound.

The objective of this study was to develop a high-frequency imaging platform for evaluating liver fibrosis in mice based on shear-wave elasticity imaging (SWEI). Although SWEI has been used to diagnose hepatic fibrosis clinically, it is performed at relatively low frequencies (<20 MHz). For preclinical ultrasound imaging in small animals, a high-frequency (>30 MHz) single-element transducer with mechanical scanning is often used. In this study we developed a new SWEI system based on a 40-MHz single-element transducer for imaging and a separate 20-MHz excitation transducer for producing the radiation force and the associated shear waves. Liver fibrosis was induced in ten C57BL/6 (B6) mice using carbon tetrachloride; the other ten mice served as the control group. Synchronizing the excitation beam (i.e., the beam from the excitation transducer) and the detection beam sequence (i.e., the beam from the imaging transducer) allows this mechanical-scanning setup to analyze the shear-wave dispersion relation. The liver viscoelastic properties were determined in vivo by measuring the shear-wave dispersion curve followed by fitting to the Voigt model. The mice were then killed and the fibrosis stage was evaluated (from F0 to F4) based on the METAVIR score. The measured mean values of liver elasticity and viscosity, respectively, ranged from 1.06 to 1.89 kPa and from 1.29 to 1.75 Pa∙s for normal F0 and fibrosis stages of F3 and F4. The Spearman coefficients for the correlations between the measured elasticity and viscosity at various fibrosis stages as assessed by the METAVIR score were 0.73 (p < 0.001) and 0.634 (p = 0.0013), respectively. We also found that the collagen content in the liver was linearly correlated with the measured elasticity (r(2) = 0.54, p < 0.001) and less strongly with the viscosity (r2 = 0.26, p = 0.022). Finally, the diagnosis performance of high-frequency SWEI was evaluated using multivariate receiver operating characteristic curve (ROC) analysis. The areas under the multivariate ROC curve for diagnosing fibrosis stages of F ≥ 3, F = 4, F0 vs. F3, F0 vs. F4, and F3 vs. F4 were 0.9, 0.98, 0.83, 1.0, and 0.96, respectively. Compared with traditional ROC analysis, an improved diagnosis performance was found for diagnosing fibrosis stages of F ≥ 3 and F0 vs. F3. These results demonstrate that the developed high-frequency SWEI platform can yield quantitative viscoelastic properties for diagnosing various fibrosis stages in mice. It is a promising tool for studying the progression of liver fibrosis in preclinical animal models both noninvasively and quantitatively.

Modelling the impulse diffraction field of shear waves in transverse isotropic viscoelastic medium

The generation of shear waves from an ultrasound focused beam has been developed as a major concept for remote palpation using shear wave elastography (SWE). For muscular diagnostic applications, characteristics of the shear wave profile will strongly depend on characteristics of the transducer as well as the orientation of muscular fibers and the tissue viscoelastic properties. The numerical simulation of shear waves generated from a specific probe in an anisotropic viscoelastic medium is a key issue for further developments of SWE in fibrous soft tissues. In this study we propose a complete numerical tool allowing 3D simulation of a shear wave front in anisotropic viscoelastic media. From the description of an ultrasonic transducer, the shear wave source is simulated by using Field’s II software and shear wave propagation described by using the Green’s formalism. Finally, the comparison between simulations and experiments are successively performed for both shear wave velocity and dispersion profile in a transverse isotropic hydrogel phantom, in vivo forearm muscle and in vivo biceps brachii.

New parameters in shear wave elastography

In the field of shear wave elastography, a specific technique called Supersonic Shear Imaging (SSI) was developed since almost 15 years. This technique is based on two concepts: By means of the acoustic radiation pressure phenomena shear waves are generated directly within tissues. Then, shear wave propagation is caught in real time by using an ultrafast ultrasound device (up to 20,000 frames/s). As shear wave speed is directly related to stiffness of tissues, such a concept allows to recover elastic maps of organs. Nevertheless, stiffness is not always only sufficient to better understand organs pathologies and behaviors. So, there is a need to add new parameters for a better characterization. In this context, SSI technique can be extended in order to reach new mechanical parameters, which can potentially help physicians. By looking at the shear wave dispersion, viscosity of tissues can be retrieved by using the right rheological model. Elastic anisotropy is recovered by rotating the probe at the surface of the investigated organ. For each position, the shear wave speed is calculated allowing to deduce orientation of fibers. At last, the change in tissue stiffness as a function of the pressure applied over medium, also called acoustoelasticity theory, allows the assessment of the nonlinear elastic properties. The combination of all these new parameters, viscosity, anisotropy, and nonlinearity, with stiffness offer new possibilities of diagnosis for physicians to better understand organs pathologies.

What Do We Know About Shear Wave Dispersion in Normal and Steatotic Livers?

A number of new approaches to measure the viscoelastic properties of the liver are now available to clinicians, many involving shear waves. However, we are at an early stage in understanding the physical processes that govern shear wave propagation in normal liver, with more unknowns added when pathologies such as steatosis are present. This technical note focuses on what is known about the characterization of normal and steatotic (or fatty) livers, with a particular focus on dispersion. Some studies in phantoms and mouse livers support the hypothesis that, starting with a normal liver, increasing accumulations of micro- and macrosteatosis will increase the lossy viscoelastic properties of shear waves in a medium. This results in an increased dispersion (or slope) of shear wave speed and attenuation in the steatotic livers. Theoretical and empirical findings across a number of studies are summarized.