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.

Imaging the Local Nonlinear Viscoelastic Properties of Soft Tissues: Initial Validation and Expected Benefits.

Imaging tissue mechanical properties has shown promise in noninvasive assessment of numerous pathologies. Researchers have successfully measured many linear tissue mechanical properties in laboratory and clinical settings. Currently, multiple complex mechanical effects such as frequency-dependence, anisotropy, and nonlinearity are being investigated separately. However, a concurrent assessment of these complex effects may enable more complete characterization of tissue biomechanics and offer improved diagnostic sensitivity. In this work, we report for the first time a method to map the frequency-dependent nonlinear parameters of soft tissues on a local scale. We recently developed a nonlinear elastography model that combines strain measurements from arbitrary tissue compression with radiation-force-based broadband shear wave speed (WS) measurements. Here, we extended this model to incorporate local measurements of frequency-dependent shear modulus. This combined approach provides a local frequency-dependent nonlinear parameter that can be obtained with arbitrary, clinically realizable tissue compression. Initial assessments using simulations and phantoms validate the accuracy of this approach. We also observed improved contrast in nonlinearity parameter at higher frequencies. Results from ex-vivo liver experiments show 32, 25, 34, and 38 dB higher contrast in elastograms than traditional linear elasticity, elastic nonlinearity, viscosity, and strain imaging methods, respectively. A lesion, artificially created by injection of glutaraldehyde into a liver specimen, showed a 59% increase in the frequency-dependent nonlinear parameter and a 17% increase in contrast ratio.

Enabling quantitative robot-assisted compressional elastography via the extended Kalman filter.

Compressional or quasi-static elastography has demonstrated the capability to detect occult cancers in a variety of tissue types, however it has a serious limitation in that the resulting elastograms are generally qualitative whereas other forms of elastography, such as shear-wave, can produce absolute measures of elasticity for histopathological classification. We address this limitation by introducing a stochastic method using an extended Kalman filter and robot-assistance to obtain quantitative elastograms which are resilient to measurement noise and system uncertainty. In this paper, the probabilistic framework is described, which utilizes many ultrasound acquisitions obtained from multiple palpations, to fuse data and uncertainty from a robotic manipulator's joint encoders and force/torque sensor directly into the inverse reconstruction of the elastogram. Quantitative results are demonstrated over homogeneous and inclusion gelatin phantoms using a seven degree of freedom manipulator for a range of initial elasticity assumptions. Results imply resilience to poorly assumed initial conditions as all trials were within 5 kPa of the elasticity measured by a mechanical testing system. Moreover, the presence or absence of an inclusion is clear in all reconstructed elastograms even when artifacts are present in displacement fields, indicating further robustness to measurement noise. The proposed stochastic method allows fusion of data from a robot's sensors directly into compressional elastography image reconstruction which may stabilize optimization and improve accuracy. This approach provides a mathematical framework to readily incorporate measurements from additional sensors in future applications which may extend the capabilities of compressional elastography beyond that of producing quantitative elasticity measurements.

Shear Wave Elasticity Imaging Using Nondiffractive Bessel Apodized Acoustic Radiation Force.

The acoustic radiation force impulse (ARFI) has been widely used in transient shear wave elasticity imaging (SWEI). For SWEI based on focused ARFI, the highest image quality exists inside the focal zone due to the limitation of the depth of focus and diffraction. Consequently, the areas outside the focal zone and in the near field present poor image quality. To address the limitations of the focused beam, we introduce Bessel apodized ARFI that enhances image quality and improves the depth of focus. The objective of this study is to evaluate the feasibility of SWEI based on Bessel ARF in simulation and experiment. We report measurements of elastogram image quality and depth of field in tissue-mimicking phantoms and ex vivo liver tissue. Our results demonstrate improved depth of field, image quality, and shear wave speed (SWS) estimation accuracy using Bessel push beams. As a result, Bessel ARF enlarges the field of view of elastograms. The signal-to-noise ratio (SNR) of Bessel SWEI is improved 26% compared with focused SWEI in homogeneous phantom. The estimated SWS by Bessel SWEI is closer to the measured SWS from a clinical scanner with an error of 0.3% compared to 2.4% with a focused beam. In heterogeneous phantoms, the contrast-to-noise ratios (CNRs) of shallow and deep inclusions are improved by 8.79 and 3.33 dB, respectively, under Bessel ARF. We also compare the results between Bessel SWEI and supersonic shear imaging (SSI), and the SNR of Bessel SWEI is improved by 8.1%. Compared with SSI, Bessel SWEI shows more accurate SWS estimates in high stiffness inclusions. Finally, Bessel SWEI can generate higher quality elastograms with less energy than conventional SSI.

Shear Induced Non-Linear Elasticity Imaging: Elastography for Compound Deformations.

The goal of non-linear ultrasound elastography is to characterize tissue mechanical properties under finite deformations. Existing methods produce high contrast non-linear elastograms under conditions of pure uni-axial compression, but exhibit bias errors of 10-50% when the applied deformation deviates from the uni-axial condition. Since freehand transducer motion generally does not produce pure uniaxial compression, a motion-agnostic non-linearity estimator is desirable for clinical translation. Here we derive an expression for measurement of the Non-Linear Shear Modulus (NLSM) of tissue subject to combined shear and axial deformations. This method gives consistent nonlinear elasticity estimates irrespective of the type of applied deformation, with a reduced bias in NLSM values to 6-13%. The method combines quasi-static strain imaging with Single-Track Location-Shear Wave Elastography (STL-SWEI) to generate local estimates of axial strain, shear strain, and Shear Wave Speed (SWS). These local values were registered and non-linear elastograms reconstructed with a novel nonlinear shear modulus estimation scheme for general deformations. Results on tissue mimicking phantoms were validated with mechanical measurements and multiphysics simulations for all deformation types with an error in NLSM of 6-13%. Quantitative performance metrics with the new compound-motion tracking strategy reveal a 10-15 dB improvement in Signal-to-Noise Ratio (SNR) for simple shear versus pure compressive deformation for NLSM elastograms of homogeneous phantoms. Similarly, the Contrast-to-Noise Ratio (CNR) of NLSM elastograms of inclusion phantoms improved by 25-30% for simple shear over pure uni-axial compression. Our results show that high fidelity NLSM estimates may be obtained at ~30% lower strain under conditions of shear deformation as opposed axial compression. The reduction in strain required could reduce sonographer effort and improve scan safety.

Intraocular Pressure-dependent Corneal Elasticity Measurement Using High-frequency Ultrasound.

Measurement of corneal biomechanical properties can aid in predicting corneal responses to diseases and surgeries. For delineation of spatially resolved distribution of corneal elasticity, high-resolution elastography system is required. In this study, we demonstrate a high-resolution elastography system using high-frequency ultrasound for ex-vivo measurement of intraocular pressure (IOP)-dependent corneal wave speed. Tone bursts of 500 Hz vibrations were generated on the corneal surface using an electromagnetic shaker. A 35-MHz single-element transducer was used to track the resulting anti-symmetrical Lamb wave in the cornea. We acquired spatially resolved wave speed images of the cornea at IOPs of 7, 11, 15, 18, 22, and 29 mmHg. The IOP dependence of corneal wave speed is apparent from these images. Statistical analysis of measured wave speed as a function of IOP revealed a linear relation between wave speed and IOP cs = 0.37 + 0.22 × IOP, with the coefficient of determination R2 = 0.86. We also observed depth-dependent variations of wave speed in the cornea, decreasing from anterior toward posterior. This depth dependence is more pronounced at higher IOP values. This study demonstrates the potential of high-frequency ultrasound elastography in the characterization of spatially resolved corneal biomechanical properties.

Nonlinear Shear Modulus Estimation With Bi-Axial Motion Registered Local Strain.

Nonlinear elasticity imaging provides additional information about tissue behavior that is potentially diagnostic and avoids errors inherent in applying a linear elastic model to tissue under large strains. Nonlinear elasticity imaging is challenging to perform due to the large deformations required to obtain sufficient tissue strain to elicit nonlinear behavior. This work uses a method of axial and lateral displacement tracking to estimate local axial strain with simultaneous measurement of shear modulus at multiple compression levels. By following the change in apparent shear modulus and the stress deduced from the strain maps, we are able to accurately quantify nonlinear shear modulus (NLSM). We have validated our technique with a mechanical NLSM measurement system. Our results demonstrate that 2-D tracking provides more consistent NLSM estimates than those obtained by 1-D (axial) tracking alone, especially where lateral motion is significant. The elastographic contrast-to-noise ratio in heterogeneous phantoms was 12.5%-60% higher using our method than that of 1-D tracking. Our method is less susceptible to mechanical variations, with deviations in mean elastic values of 2%-4% versus 5%-37% for 1-D tracking.

Plane-Wave Imaging Improves Single-Track Location Shear Wave Elasticity Imaging.

Single-track location shear wave elasticity imaging (STL-SWEI) is immune to speckle bias, but the quality of the images is depth dependent. We hypothesize that plane-wave imaging can reduce the depth dependence of STL-SWEI. To test this hypothesis, we developed a novel technique known as plane-wave STL-SWEI (pSTL-SWEI). To evaluate the pSTL-SWEI's potential, we performed studies on phantoms and excised murine pancreatic tumors. The mean shear wave speeds measured with STL-SWEI and pSTL-SWEI were similar. However, the elastographic signal-to-noise ratio (SNRe) of pSTL-SWEI elastograms was noticeably higher than that produced with STL-SWEI. Specifically, we observed an improvement in SNRe ranging from 39.9%-55.1%, depending on tissue stiffness. The spatial resolution of pSTL-SWEI elastograms was 2.7%-12.1% lower than that produced with STL-SWEI. pSTL-SWEI elastograms displayed higher contrast-to-noise ratio (CNRe) than those produced with STL-SWEI, especially when imaging was performed with low push pulse intensities and low pulse durations.

Measurement of Liver Stiffness Using Shear Wave Elastography in a Rat Model: Factors Impacting Stiffness Measurement with Multiple- and Single-Tracking-Location Techniques.

The clinical use of elastography for monitoring fibrosis progression is challenged by the subtle changes in liver stiffness associated with early-stage fibrosis and the comparatively large variance in stiffness estimates provided by elastography. Single-tracking-location (STL) shear wave elasticity imaging (SWEI) is an ultrasound elastography technique previously found to provide improved estimate precision compared with multiple-tracking-location (MTL) SWEI. Because of the improved precision, it is reasonable to expect that STL-SWEI would provide improved ability to differentiate liver fibrosis stage compared with MTL-SWEI. However, this expectation has not been previously challenged rigorously. In this work, the performance of STL- and MTL-SWEI in the setting of a rat model of liver fibrosis is characterized, and the advantages of STL-SWEI in staging fibrosis are explored. The purpose of this study was to determine what advantages, if any, arise from using STL-SWEI instead of MTL-SWEI in the characterization of fibrotic liver. Thus, the ability of STL-SWEI to differentiate livers at various METAVIR fibrosis scores, for ex vivo postmortem measurements, is explored. In addition, we examined the effect of the common confounding factor of fluid versus solid boundary conditions in SWEI experiments. Sprague-Dawley rats were treated with carbon tetrachloride over several weeks to produce liver disease of varying severity. STL and MTL stiffness measurements were performed ex vivo and compared with the METAVIR scores from histological analysis and the duration of treatment. A strong association was observed between liver stiffness and weeks of treatment with the liver toxin carbon tetrachloride. Direct comparison of STL- and MTL-SWEI measurements revealed no significant difference in ability to differentiate fibrosis stages based on SWEI mean values. However, image interquartile range was greatly improved in the case of STL-SWEI, compared with MTL-SWEI, at small beam spacing.

Shear Wave Speed Measurements Using Crawling Wave Sonoelastography and Single Tracking Location Shear Wave Elasticity Imaging for Tissue Characterization.

Elastography provides tissue stiffness information that attempts to characterize the elastic properties of tissue. However, there is still limited literature comparing elastographic modalities for tissue characterization. This study focuses on two quantitative techniques using different vibration sources that have not been compared to date: crawling wave sonoelastography (CWS) and single tracking location shear wave elasticity imaging (STL-SWEI). To understand each technique's performance, shear wave speed (SWS) was measured in homogeneous phantoms and ex vivo beef liver tissue. Then, the contrast, contrast-to-noise ratio (CNR), and lateral resolution were measured in an inclusion and two-layer phantoms. The SWS values obtained with both modalities were validated with mechanical measurements (MM) which serve as ground truth. The SWS results for the three different homogeneous phantoms (10%, 13%, and 16% gelatin concentrations) and ex vivo beef liver tissue showed good agreement between CWS, STL-SWEI, and MM as a function of frequency. For all gelatin phantoms, the maximum accuracy errors were 2.52% and 2.35% using CWS and STL-SWEI, respectively. For the ex vivo beef liver, the maximum accuracy errors were 9.40% and 7.93% using CWS and STL-SWEI, respectively. For lateral resolution, contrast, and CNR, both techniques obtained comparable measurements for vibration frequencies less than 300 Hz (CWS) and distances between the push beams ( ∆x ) between 3 mm and 5.31 mm (STL-SWEI). The results obtained in this study agree over an SWS range of 1-6 m/s. They are expected to agree in perfectly linear, homogeneous, and isotropic materials, but the SWS overlap is not guaranteed in all materials because each of the three methods have unique features.

Shear Wave Elastography in the Living, Perfused, Post-Delivery Placenta.

The placenta is the critical interface between the mother and the developing fetus and is essential for survival and growth. Despite the widespread use of ultrasound imaging and Doppler in obstetrics and gynecology and the recent growth of elastographic technologies, little is known about the biomechanical (elastic shear wave) properties of the placenta and the range of normal and pathologic parameters that are present. This study uses a well-developed protocol for perfusing whole placentas, post-delivery, to maintain tissue integrity and function for hours. In this model, the placenta is living, whole and maintained within normal physiologic parameters such as flow, arterial pressure and oxygen, throughout examination by ultrasound, Doppler and shear wave elastography. The preliminary results indicate that normal placental tissue on the fetal side has shear wave speeds on the order of 2 m/s, in a range similar to those of animal livers. Some abnormalities are found outside this range, and thus, elastographic measures of the placenta may provide useful assessments related to the state of the tissue.

Shear wave arrival time estimates correlate with local speckle pattern.

We present simulation and phantom studies demonstrating a strong correlation between errors in shear wave arrival time estimates and the lateral position of the local speckle pattern in targets with fully developed speckle. We hypothesize that the observed arrival time variations are largely due to the underlying speckle pattern, and call the effect speckle bias. Arrival time estimation is a key step in quantitative shear wave elastography, performed by tracking tissue motion via cross-correlation of RF ultrasound echoes or similar methods. Variations in scatterer strength and interference of echoes from scatterers within the tracking beam result in an echo that does not necessarily describe the average motion within the beam, but one favoring areas of constructive interference and strong scattering. A swept-receive image, formed by fixing the transmit beam and sweeping the receive aperture over the region of interest, is used to estimate the local speckle pattern. Metrics for the lateral position of the speckle are found to correlate strongly (r > 0.7) with the estimated shear wave arrival times both in simulations and in phantoms. Lateral weighting of the swept-receive pattern improved the correlation between arrival time estimates and speckle position. The simulations indicate that high RF echo correlation does not equate to an accurate shear wave arrival time estimate-a high correlation coefficient indicates that motion is being tracked with high precision, but the location tracked is uncertain within the tracking beam width. The presence of a strong on-axis speckle is seen to imply high RF correlation and low bias. The converse does not appear to be true-highly correlated RF echoes can still produce biased arrival time estimates. The shear wave arrival time bias is relatively stable with variations in shear wave amplitude and sign (-20 µm to 20 µm simulated) compared with the variation with different speckle realizations obtained along a given tracking vector. We show that the arrival time bias is weakly dependent on shear wave amplitude compared with the variation with axial position/ local speckle pattern. Apertures of f/3 to f/8 on transmit and f/2 and f/4 on receive were simulated. Arrival time error and correlation with speckle pattern are most strongly determined by the receive aperture.

Scholte wave generation during single tracking location shear wave elasticity imaging of engineered tissues.

The physical environment of engineered tissues can influence cellular functions that are important for tissue regeneration. Thus, there is a critical need for noninvasive technologies capable of monitoring mechanical properties of engineered tissues during fabrication and development. This work investigates the feasibility of using single tracking location shear wave elasticity imaging (STL-SWEI) for quantifying the shear moduli of tissue-mimicking phantoms and engineered tissues in tissue engineering environments. Scholte surface waves were observed when STL-SWEI was performed through a fluid standoff, and confounded shear moduli estimates leading to an underestimation of moduli in regions near the fluid-tissue interface.

Single tracking location acoustic radiation force impulse viscoelasticity estimation (STL-VE): A method for measuring tissue viscoelastic parameters.

Single tracking location (STL) shear wave elasticity imaging (SWEI) is a method for detecting elastic differences between tissues. It has the advantage of intrinsic speckle bias suppression compared with multiple tracking location variants of SWEI. However, the assumption of a linear model leads to an overestimation of the shear modulus in viscoelastic media. A new reconstruction technique denoted single tracking location viscosity estimation (STL-VE) is introduced to correct for this overestimation. This technique utilizes the same raw data generated in STL-SWEI imaging. Here, the STL-VE technique is developed by way of a maximum likelihood estimation for general viscoelastic materials. The method is then implemented for the particular case of the Kelvin-Voigt Model. Using simulation data, the STL-VE technique is demonstrated and the performance of the estimator is characterized. Finally, the STL-VE method is used to estimate the viscoelastic parameters of ex vivo bovine liver. We find good agreement between the STL-VE results and the simulation parameters as well as between the liver shear wave data and the modeled data fit.

Analysis and measurement of the modulation transfer function of harmonic shear wave induced phase encoding imaging.

Shear wave induced phase encoding (SWIPE) imaging generates ultrasound backscatter images of tissue-like elastic materials by using traveling shear waves to encode the lateral position of the scatters in the phase of the received echo. In contrast to conventional ultrasound B-scan imaging, SWIPE offers the potential advantages of image formation without beam focusing or steering from a single transducer element, lateral resolution independent of aperture size, and the potential to achieve relatively high lateral resolution with low frequency ultrasound. Here a Fourier series description of the phase modulated echo signal is developed, demonstrating that echo harmonics at multiples of the shear wave frequency reveal target k-space data at identical multiples of the shear wavenumber. Modulation transfer functions of SWIPE imaging systems are calculated for maximum shear wave acceleration and maximum shear constraints, and compared with a conventionally focused aperture. The relative signal-to-noise ratio of the SWIPE method versus a conventionally focused aperture is found through these calculations. Reconstructions of wire targets in a gelatin phantom using 1 and 3.5 MHz ultrasound and a cylindrical shear wave source are presented, generated from the fundamental and second harmonic of the shear wave modulation frequency, demonstrating weak dependence of lateral resolution with ultrasound frequency.

Design and validation of two optical beacons for guidewire localization in breast-conserving surgery.

Stereotactically placed guidewires are used for indicating the location of a nonpalpable carcinoma in breast-conserving surgery. Pathologists use the end of the embedded guidewire to guide sectioning during intraoperative margin assessment, but they do not currently have a tool to indicate the location of the guidewire end for informed sectioning. We present analysis and experimental testing of two optical methods for localizing the end of an embedded fiber-optic guidewire: the first uses irradiance emitted from the fiber to indicate the location of the guidewire end, while the second system uses the fiber optic to create a photoacoustic pulse for localization. Both systems locate the end of the guidewire within ±5 mm, which ensures that the lesion of interest is bisected during sectioning. The accuracy of the irradiance-based beacon is influenced by standard margin paints, so the photoacoustic beacon proved more useful under current tissue-handling protocols.

Single tracking location methods suppress speckle noise in shear wave velocity estimation.

In ultrasound-based elastography methods, the estimation of shear wave velocity typically involves the tracking of speckle motion due to an applied force. The errors in the estimates of tissue displacement, and thus shear wave velocity, are generally attributed to electronic noise and decorrelation due to physical processes. We present our preliminary findings on another source of error, namely, speckle-induced bias in phase estimation. We find that methods that involve tracking in a single location, as opposed to multiple locations, are less sensitive to this source of error since the measurement is differential in nature and cancels out speckle-induced phase errors.

Comparison of two methods for the generation of spatially modulated ultrasound radiation force.

Spatially modulated ultrasound radiation force (SMURF) imaging is an elastographic technique that involves generating a radiation force beam with a lateral intensity variation of a defined spatial frequency. This results in a shear wave of known wavelength. By using the displacements induced by the shear wave and standard Doppler or speckle-tracking methods, the shear wave frequency, and thus material shear modulus, is estimated. In addition to generating a pushing beam pattern with a specified lateral intensity variation, it is generally desirable to induce larger displacements so that the displacement data signal-to-noise ratio is higher. We provide an analysis of two beam forming methods for generating SMURF in an elastic material: the focal Fraunhofer and intersecting plane wave methods. Both techniques generate beams with a defined spatial frequency. However, as a result of the trade-offs associated with each technique, the peak acoustic intensity outputs in the region of interest differs for the same combinations of parameters (e.g., the focal depth, the width of the area of interest, and ultrasonic attenuation coefficient). Assuming limited transducer drive voltage, we provide a decision plot to determine which of the two techniques yields the greater pushing force for a specific configuration.

Shear-modulus estimation by application of spatially-modulated impulsive acoustic radiation force.

We present a method for determining the shear modulus of an elastic material wherein a spatially-modulated acoustic radiation force is used to generate a disturbance of known spatial frequency (wavelength). The propagation of this initial displacement as a shear wave is measured using ultrasound tracking methods and the temporal frequency of the shear wave is estimated. Given the known wavelength and material density and the measured estimate of temporal frequency, the shear modulus at the point of excitation may be calculated easily. Using this method, the shear moduli of two gelatin phantoms was estimated to be 1.4 and 5.8 kPa, in good agreement with 1.5 and 5.6 kPa values determined though quasistatic material testing.

Dynamic mechanical response of elastic spherical inclusions to impulsive acoustic radiation force excitation.

Acoustic radiation force impulse imaging has been used clinically to study the dynamic response of lesions relative to their background material to focused, impulsive acoustic radiation force excitations through the generation of dynamic displacement field images. Dynamic displacement data are typically displayed as a set of parametric images, including displacement immediately after excitation, maximum displacement, time to peak displacement, and recovery time from peak displacement. To date, however, no definitive trends have been established between these parametric images and the tissues' mechanical properties. This work demonstrates that displacement magnitude, time to peak displacement, and recovery time are all inversely related to the Young's modulus in homogeneous elastic media. Experimentally, pulse repetition frequency during displacement tracking limits stiffness resolution using the time to peak displacement parameter. The excitation pulse duration also impacts the time to peak parameter, with longer pulses reducing the inertial effects present during impulsive excitations. Material density affects tissue dynamics, but is not expected to play a significant role in biological tissues. The presence of an elastic spherical inclusion in the imaged medium significantly alters the tissue dynamics in response to impulsive, focused acoustic radiation force excitations. Times to peak displacement for excitations within and outside an elastic inclusion are still indicative of local material stiffness; however, recovery times are altered due to the reflection and transmission of shear waves at the inclusion boundaries. These shear wave interactions cause stiffer inclusions to appear to be displaced longer than the more compliant background material. The magnitude of shear waves reflected at elastic lesion boundaries is dependent on the stiffness contrast between the inclusion and the background material, and the stiffness and size of the inclusion dictate when shear wave reflections within the lesion will interfere with one another. Jitter and bias associated with the ultrasonic displacement tracking also impact the estimation of a tissue's dynamic response to acoustic radiation force excitation.