A Frequency-Shift Method to Measure Shear-Wave Attenuation in Soft Tissues

A method of enhanced shear wave elastography based on Chirp coded excitation

Shear Wave Elastography (SWE) is an imaging technique that detects shear waves generated by tissue excited by Acoustic Radiation Force (ARF), and characterizes the mechanical properties of soft tissue by analyzing the propagation velocity of shear wave. ARF induces a change in energy density through the nonlinear propagation of ultrasound waves, which drives the tissue to generate shear waves. However, the amplitude of shear waves generated by ARF is weak, and the shear waves are strongly attenuated in vivo. Furthermore, the shear waves are usually drowned out by noise at deep locations, which presents a challenge in the detection of shear waves and low signal-to-noise ratios. In this paper, we investigate the feasibility of applying the Chirp coded signal for shear wave excitation (Chirp-SWE) in ARF-based shear wave elastography. The use of Chirp coded excitation of push waveforms was employed to enhance the action of ARF, thereby effectively exciting shear waves. Comparative experiments were carried out with conventional sine long pulses (SWE) and the Barker coded signal (Barker-SWE). The analysis of theoretical and simulation results revealed that Chirp-SWE could increase the excitation energy by approximately 10% compared to conventional SWE and Barker-SWE. The results of the elastic phantom experiments demonstrated that the average peak axial particle velocity obtained by Chirp-SWE was approximately 30%-50% higher, which facilitated the formation of a more stable shear wave. Additionally, it exhibited a higher signal-to-noise ratio during elasticity measurements. The in vitro liver experiments further validated the feasibility of implementing Chirp-SWE in tissues. The results demonstrated the feasibility and advantages of Chirp coded excitation of push waveforms in improving shear wave elastography results. It is expected that this will enhance the accuracy and robustness of soft tissue elastography.

Ultrasound shear wave viscoelastography to characterize liver nodules

Purpose. To investigate the diagnostic performance of ultrasound (US)-based shear wave speed (SWS), shear wave attenuation (SWA), and combination of them as shear wave viscoelastography (SWVE) methods in patients undergoing US to characterize focal liver nodules.Materials and methods. In this prospective cross-sectional study, 70 patients with 72 nodules were enrolled. Investigational US and clinical magnetic resonance imaging (MRI) examinations were performed in all participants. The composite reference standard included MRI or histopathology to differentiate benign and malignant nodules. A linear discriminant analysis (LDA) was used to assess the combination of SWVE methods. Analyzes included Mann-WhitneyUtest, receiver operating characteristic analysis, and computation of sensitivity and specificity at the point that maximized the Youden index.Results. Mean SWS was significantly higher in malignant than benign nodules (2.49 ± 0.76 m s-1vs. 1.72 ± 0.70,p< 0.001), whereas SWA was lower (0.56 ± 0.30 vs. 1.10 ± 0.43 Np/m/Hz,p< 0.001). To differentiate between malignant and benign nodules, SWS with a threshold of 2.43 m s-1achieved a sensitivity of 0.54 (95% confidence interval (CI): 0.38-0.69) and a specificity of 0.88 (CI: 0.74-0.95). SWA with a threshold of 0.81 Np/m/Hz yielded a sensitivity of 0.81 (CI: 0.66-0.90) and a specificity of 0.74 (CI: 0.58-0.86). Combining these SWVE methods using a LDA resulted in a sensitivity of 0.81 (CI: 0.66-0.91) and a specificity of 0.86 (CI: 0.71-0.94).Conclusion. Malignant nodules had higher SWS and lower SWA than benign ones. The combination of SWS and SWA in a LDA classification algorithm increased the diagnostic performance.

Shear wave elastography primer for the abdominal radiologist

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSION

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

Rapid wideband characterization of viscoelastic material properties by Bessel function-based time harmonic ultrasound elastography (B-THE)

Elastography is an emerging diagnostic technique that uses conventional imaging modalities such as sonography or magnetic resonance imaging to quantify tissue stiffness. However, different elastography methods provide different stiffness values, which require calibration using well-characterized phantoms or tissue samples. A comprehensive, fast, and cost-effective elastography technique for phantoms or tissue samples is still lacking. Therefore, we propose ultrasound Bessel-fit-based time harmonic elastography (B-THE) as a novel tool to provide rapid feedback on stiffness-related shear wave speed (SWS) and viscosity-related wave penetration rate (PR) over a wide range of harmonic vibration frequencies. The method relies on external induction and B-mode capture of cylindrical shear waves that satisfy the Bessel wave equation for efficient fit-based parameter recovery. B-THE was demonstrated in polyacrylamide phantoms in the frequency range of 20-200 Hz and was cross-validated by magnetic resonance elastography (MRE) using clinical 3-T MRI and compact 0.5-T tabletop MRI scanners. Frequency-independent material parameters were derived from rheological models and validated by numerical simulations. B-THE quantified frequency-resolved SWS and PR 13 to 176 times faster than more expensive clinical MRE and tabletop MRE and have a good accuracy (relative deviation to reference: 6 %, 10 % and 4 % respectively). Simulations of liver-mimicking material phantoms showed that a simultaneous fit of SWS and PR based on the fractional Maxwell rheological model outperformed a fit on PR solely. B-THE provides a comprehensive and fast elastography technique for the quantitative characterization of the viscoelastic behavior of soft tissue mimicking materials.

Between-Visit Reproducibility of Shear Wave Viscoelastography in Volunteers and Patients With Metabolic Dysfunction-Associated Steatotic Liver Disease

OBJECTIVE

To assess the reproducibility of six ultrasound (US)-determined shear wave (SW) viscoelastography parameters for assessment of mechanical properties of the liver in volunteers and patients with biopsy-proven metabolic dysfunction-associated steatotic liver disease (MASLD) or metabolic dysfunction-associated steatohepatitis (MASH).

METHODS

This prospective, cross-sectional, institutional review board-approved study included 10 volunteers and 20 patients with MASLD or MASH who underwent liver US elastography twice, at least 2 weeks apart. SW speed (SWS), Young's modulus (E), shear modulus (G), SW attenuation (SWA), SW dispersion (SWD), and viscosity were computed from radiofrequency data recorded on a research US scanner. Linear mixed models were used to consider the sonographer on duty as a confounder. The reproducibility of measurements was assessed by intraclass correlation coefficient (ICC), coefficient of variation (CV), reproducibility coefficient (RDC), and Bland-Altman analyses.

RESULTS

The sonographer performing the exam had no impact on viscoelastic parameters (P > .05). ICCs of SWS, E, G, SWA, SWD, and viscosity were, respectively, 0.89 (95% confidence intervals [CI]: 0.79-0.95), 0.81 (95% CI: 0.79-0.95), 0.90 (95% CI: 0.80-0.95), 0.96 (95% CI: 0.93-0.98), 0.78 (95% CI: 0.60-0.89), and 0.90 (95% CI: 0.80-0.95); CVs were 11.9, 23.3, 24.2, 10.1, 29.0, and 32.2%; RDCs were 33.0, 64.5, 66.9, 27.7, 80.3, and 89.2%, and Bland-Altman mean biases and 95% limits of agreement were -0.05 (-0.45, 0.35) m/s, -0.61 (-5.33, 4.10) kPa, -0.25 (-2.06, 1.56) kPa, -0.01 (-0.27, 0.26) Np/m/Hz, -0.09 (-7.09, 6.91) m/s/kHz, and -0.33 (-2.60, 1.94) Pa/s, between the two visits.

CONCLUSION

US-determined viscoelastography parameters can be measured with high reproducibility and consistency between two visits 2 weeks apart on the same ultrasound machine.

Quantitative Ultrasound and Ultrasound-Based Elastography for Chronic Liver Disease: Practical Guidance, From the AJR Special Series on Quantitative Imaging

Quantitative ultrasound (QUS) and ultrasound-based elastography techniques are emerging as non-invasive effective methods for assessing chronic liver disease. They are more accurate than B-mode imaging alone and more accessible than MRI as alternatives to liver biopsy. Early detection and monitoring of diffuse liver processes such as steatosis, inflammation, and fibrosis play an important role in guiding patient management. The most widely available and validated techniques are attenuation-based QUS techniques and shear-wave elastography techniques that measure shear-wave speed. Other techniques are supported by a growing body of evidence and are increasingly commercialized. This review explains general physical concepts of QUS and ultrasound-based elastography techniques for evaluating chronic liver disease. The first section describes QUS techniques relying on attenuation, backscatter, and speed of sound. The second section discusses ultrasound-based elastography techniques analyzing shear-wave speed, shear-wave dispersion, and shear-wave attenuation. With an emphasis on clinical implementation, each technique's diagnostic performance along with thresholds for various clinical applications are summarized, to provide guidance on analysis and reporting for radiologists. Measurement methods, advantages, and limitations are also discussed. The third section explores developments in quantitative contrast-enhanced and vascular ultrasound that are relevant to chronic liver disease evaluation.

Characterizing dispersion in bovine liver using ARFI-based shear wave rheometry

Background:Dispersion presents both a challenge and a diagnostic opportunity in shear wave elastography (SWE).Shear Wave Rheometry(SWR) is an inversion technique for processing SWE data acquired using an acoustic radiation force impulse (ARFI) excitation. The main advantage of SWR is that it can characterize the shear properties of homogeneous soft media over a wide frequency range. Assumptions associated with SWR include tissue homogeneity, tissue isotropy, and axisymmetry of the ARFI excitation).Objective:Evaluate the validity of the SWR assumptions in ex vivo bovine liver.Approach:SWR was used to measure the shear properties of bovine liver tissue as function of frequency over a large frequency range. Assumptions associated with SWR (tissue homogeneity, tissue isotropy, and axisymmetry of the ARFI excitation) were evaluated through measurements performed at multiple locations and probe orientations. Measurements focused on quantities that would reveal violations of the assumptions.Main results:Measurements of shear properties were obtained over the 25-250 Hz range, and showed a 4-fold increase in shear storage modulus (from 1 to 4 kPa) and over a 10-fold increase in the loss modulus (from 0.2 to 3 kPa) over that decade-wide frequency range. Measurements under different conditions were highly repeatable, and model error was low in all cases.Significance and Conclusion:SWR depends on modeling the ARFI-induced shear wave as a full vector viscoelastic shear wave resulting from an axisymmetric source; it is agnostic to any specific rheological model. Despite this generality, the model makes three main simplifying assumptions. These results show that the modeling assumptions used in SWR are valid in bovine liver over a wide frequency band.

Ultrasound Viscoelastography by Acoustic Radiation Force: A State-of-the-Art Review

Ultrasound elastography (USE) is a promising tool for tissue characterization as several diseases result in alterations of tissue structure and composition, which manifest as changes in tissue mechanical properties. By imaging the tissue response to an applied mechanical excitation, USE mimics the manual palpation performed by clinicians to sense the tissue elasticity for diagnostic purposes. Next to elasticity, viscosity has recently been investigated as an additional, relevant, diagnostic biomarker. Moreover, since biological tissues are inherently viscoelastic, accounting for viscosity in the tissue characterization process enhances the accuracy of the elasticity estimation. Recently, methods exploiting different acquisition and processing techniques have been proposed to perform ultrasound viscoelastography. After introducing the physics describing viscoelasticity, a comprehensive overview of the currently available USE acquisition techniques is provided, followed by a structured review of the existing viscoelasticity estimators classified according to the employed processing technique. These estimators are further reviewed from a clinical usage perspective, and current outstanding challenges are discussed.

Effect of rt-PA on Shear Wave Mechanical Assessment and Quantitative Ultrasound Properties of Blood Clot Kinetics In Vitro

OBJECTIVE

The consequences associated with blood clots are numerous and are responsible for many deaths worldwide. The assessment of treatment efficacy is necessary for patient follow-up and to detect treatment-resistant patients. The aim of this study was to characterize the effect of treatment on blood clots in vitro using quantitative ultrasound parameters.

METHODS

Blood from 10 pigs was collected to form three clots per pig in gelatin phantoms. Clots were subjected to 1) no treatment, 2) rt-PA (recombinant tissue plasminogen activator) treatment after 20 minutes of clotting, and 3) rt-PA treatment after 60 minutes of clotting. Clots were weighted before and after the experiment to assess the treatment effect by the mass loss. The clot kinetics was studied over 100 minutes using elastography (Young's modulus, shear wave dispersion, and shear wave attenuation). Homodyne K-distribution (HKD) parameters derived from speckle statistics were also studied during clot formation and dissolving (diffuse-to-total signal power ratio and intensity parameters).

RESULTS

Treated clots loosed significantly more mass than non-treated ones (P < .005). A significant increase in Young's modulus was observed over time (P < .001), and significant reductions were seen for treated clots at 20 or 60 minutes compared with untreated ones (P < .001). The shear wave dispersion differed for treated clots at 60 minutes versus no treatments (P < .001). The shear wave attenuation decreased over time (P < .001), and was different for clots treated at 20 minutes versus no treatments (P < .031). The HKD intensity parameter varied over time (P < .032), and was lower for clots treated at 20 and 60 minutes than those untreated (P < .001 and P < .02).

CONCLUSION

The effect of rt-PA treatment could be confirmed by a decrease in Young's modulus and HKD intensity parameter. The shear wave dispersion and shear wave attenuation were sensitive to late and early treatments, respectively. The Young's modulus, shear wave attenuation, and HKD intensity parameter varied over time despite treatment.

Resonance, Velocity, Dispersion, and Attenuation of Ultrasound-Induced Shear Wave Propagation in Blood Clot In Vitro Models

OBJECTIVE

Improve the characterization of mechanical properties of blood clots. Parameters derived from shear wave (SW) velocity and SW amplitude spectra were determined for gel phantoms and in vitro blood clots.

METHODS

Homogeneous phantoms and phantoms with gel or blood clot inclusions of different diameters and mechanical properties were analyzed. SW amplitude spectra were used to observe resonant peaks. Parameters derived from those resonant peaks were related to mimicked blood clot properties. Three regions of interest were tested to analyze where resonances occurred the most. For blood experiments, 20 samples from different pigs were analyzed over time during a 110-minute coagulation period using the Young modulus, SW frequency dispersion, and SW attenuation.

RESULTS

The mechanical resonance was manifested by an increase in the number of SW spectral peaks as the inclusion diameter was reduced (P < .001). In blood clot inclusions, the Young modulus increased over time during coagulation (P < .001). Descriptive spectral parameters (frequency peak, bandwidth, and distance between resonant peaks) were linearly correlated with clot elasticity values (P < .001) with R2  = .77 for the frequency peak, .60 for the bandwidth, and .48 for the distance between peaks. The SW dispersion and SW attenuation reflecting the viscous behavior of blood clots decreased over time (P < .001), mainly in the early stage of coagulation (first minutes).

CONCLUSION

The confined soft inclusion configuration favored SW mechanical resonances potentially challenging the computation of spectral-based parameters, such as the SW attenuation. The impact of resonances can be reduced by properly selecting the region of interest for data analysis.

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.

Feasibility of Phase Velocity Imaging Using Multi Frequency Oscillation-Shear Wave Elastography

OBJECTIVE

To assess viscoelasticity, a pathologically relevant biomarker, shear wave elastography (SWE) generally uses phase velocity (PV) dispersion relationship generated via pulsed acoustic radiation force (ARF) excitation pulse. In this study, a multi-frequency oscillation (MFO)- excitation pulse with higher weight to higher frequencies is proposed to generate PV images via the generation of motion with energy concentrated at the target frequencies in contrast to the broadband frequency motion generated in pulsed SWE (PSWE).

METHODS

The feasibility of MFO-SWE to generate PV images at 100 to 1000 Hz in steps of 100 Hz was investigated by imaging 6 and 70 kPa inclusions with 6.5 and 10.4 mm diameter and ex vivo bovine liver with and without the presence of an aberration layer and chicken muscle ex vivo, and 4T1 mouse breast tumor, in vivo with comparisons to PSWE.

RESULTS

MFO-SWE-derived CNR was statistically higher than PSWE for 6 kPa (both with and without aberration) and 70 kPa (with aberration) inclusions and derived SNR of the liver was statistically higher than PSWE at higher frequency (600-1000 Hz). Quantitatively, at 600-1000 Hz, MFO-SWE improved CNR of inclusions (without and with) aberration on an average by (8.2 and 156)% and of the tumor by 122%, respectively, and improved SNR of the liver (without and with) aberration by (20.2 and 51.5)% and of chicken muscle by 72%, respectively compared to the PSWE.

CONCLUSIONS AND SIGNIFICANCE

These results indicate the advantages of MFO-SWE to improve PV estimation at higher frequencies which could improve viscoelasticity quantification and feature delineation.

Ultrasound Shear Wave Attenuation Imaging for Grading Liver Steatosis in Volunteers and Patients With Non-alcoholic Fatty Liver Disease: A Pilot Study

OBJECTIVE

The aims of the work described here were to assess shear wave attenuation (SWA) in volunteers and patients with non-alcoholic fatty liver disease (NAFLD) and compare its diagnostic performance with that of shear wave dispersion (SWD), magnetic resonance imaging (MRI) proton density fat fraction (PDFF) and biopsy.

METHODS

Forty-nine participants (13 volunteers and 36 NAFLD patients) were enrolled. Ultrasound and MRI examinations were performed in all participants. Biopsy was also performed in patients. SWA was used to assess histopathology grades as potential confounders. The areas under curves (AUCs) of SWA, SWD and MRI-PDFF were assessed in different steatosis grades by biopsy. Youden's thresholds of SWA were obtained for steatosis grading while using biopsy or MRI-PDFF as the reference standard.

RESULTS

Spearman's correlations of SWA with histopathology (steatosis, inflammation, ballooning and fibrosis) were 0.89, 0.73, 0.62 and 0.31, respectively. Multiple linear regressions of SWA confirmed the correlation with steatosis grades (adjusted R2 = 0.77, p < 0.001). The AUCs of MRI-PDFF, SWA and SWD were respectively 0.97, 0.99 and 0.94 for S0 versus ≥S1 (p > 0.05); 0.94, 0.98 and 0.78 for ≤S1 versus ≥S2 (both MRI-PDFF and SWA were higher than SWD, p < 0.05); and 0.90, 0.93 and 0.68 for ≤S2 versus S3 (both SWA and MRI-PDFF were higher than SWD, p < 0.05). SWA's Youden thresholds (Np/m/Hz) (sensitivity, specificity) for S0 versus ≥S1, ≤S1 versus ≥S2 and ≤S2 versus S3 were 1.05 (1.00, 0.92), 1.37 (0.96, 0.96) and 1.51 (0.83, 0.87), respectively. These values were 1.16 (1.00, 0.81), 1.49 (0.91, 0.82) and 1.67 (0.87, 0.92) when considering MRI-PDFF as the reference standard.

CONCLUSION

In this pilot study, SWA increased with increasing steatosis grades, and its diagnostic performance was higher than that of SWD but equivalent to that of MRI-PDFF.

Shear wave elastography can stratify rectal cancer response to short-course radiation therapy

Rectal cancer is a deadly disease typically treated using neoadjuvant chemoradiotherapy followed by total mesorectal excision surgery. To reduce the occurrence of mesorectal excision surgery for patients whose tumors regress from the neoadjuvant therapy alone, conventional imaging, such as computed tomography (CT) or magnetic resonance imaging (MRI), is used to assess tumor response to neoadjuvant therapy before surgery. In this work, we hypothesize that shear wave elastography offers valuable insights into tumor response to short-course radiation therapy (SCRT)-information that could help distinguish radiation-responsive from radiation-non-responsive tumors and shed light on changes in the tumor microenvironment that may affect radiation response. To test this hypothesis, we performed elastographic imaging on murine rectal tumors (n = 32) on days 6, 10, 12, 16, 18, 20, 23, and 25 post-tumor cell injection. The study revealed that radiation-responsive and non-radiation-responsive tumors had different mechanical properties. Specifically, radiation-non-responsive tumors showed significantly higher shear wave speed SWS (p < 0.01) than radiation-responsive tumors 11 days after SCRT. Furthermore, there was a significant difference in shear wave attenuation (SWA) (p < 0.01) in radiation-non-responsive tumors 16 days after SCRT compared to SWA measured just one day after SCRT. These results demonstrate the potential of shear wave elastography to provide valuable insights into tumor response to SCRT and aid in exploring the underlying biology that drives tumors' responses to radiation.

Full waveform inversion for arterial viscoelasticity

Objective. Arterial viscosity is emerging as an important biomarker, in addition to the widely used arterial elasticity. This paper presents an approach to estimate arterial viscoelasticity using shear wave elastography (SWE).Approach. While dispersion characteristics are often used to estimate elasticity from SWE data, they are not sufficiently sensitive to viscosity. Driven by this, we develop a full waveform inversion (FWI) methodology, based on directly matching predicted and measured wall velocity in space and time, to simultaneously estimate both elasticity and viscosity. Specifically, we propose to minimize an objective function capturing the correlation between measured and predicted responses of the anterior wall of the artery.Results. The objective function is shown to be well-behaving (generally convex), leading us to effectively use gradient optimization to invert for both elasticity and viscosity. The resulting methodology is verified with synthetic data polluted with noise, leading to the conclusion that the proposed FWI is effective in estimating arterial viscoelasticity.Significance. Accurate estimation of arterial viscoelasticity, not just elasticity, provides a more precise characterization of arterial mechanical properties, potentially leading to a better indicator of arterial health.

Investigation of the relationship between tensile viscoelasticity and unloaded ultrasound shear wave measurements in ex vivo tendon

Mechanical properties of biological tissues are of key importance for proper function and in situ methods for mechanical characterization are sought after in the context of both medical diagnosis as well as understanding of pathophysiological processes. Shear wave elastography (SWE) and accompanying physical modelling methods provide valid estimates of stiffness in quasi-linear viscoelastic, isotropic tissue but suffer from limitations in assessing non-linear viscoelastic or anisotropic material, such as tendon. Indeed, mathematical modelling predicts the longitudinal shear wave velocity to be unaffected by the tensile but rather the shear viscoelasticity. Here, we employ a heuristic experimental testing approach to the problem to assess the most important potential confounders, namely tendon mass density and diameter, and to investigate associations between tendon tensile viscoelasticity with shear wave descriptors. Small oscillatory testing of animal flexor tendons at two baseline stress levels over a large frequency range comprehensively characterized tensile viscoelastic behavior. A broad set of shear wave descriptors was retrieved on the unloaded tendon based on high frame-rate plane wave ultrasound after applying an acoustic deformation impulse. Tensile modulus and strain energy dissipation increased logarithmically and linearly, respectively, with the frequency of the applied strain. Shear wave descriptors were mostly unaffected by tendon diameter but were highly sensitive to tendon mass density. Shear wave group and phase velocity showed no association with tensile elasticity or strain rate-stiffening but did show an association with tensile strain energy dissipation. The longitudinal shear wave velocity may not characterize tensile elasticity but rather tensile viscous properties of transversely isotropic collagenous tissues.

Improved two-point frequency shift power method for measurement of shear wave attenuation

Quantitative assessment of mechanical properties of biological soft tissues is frequently evaluated using a noninvasive modality, called ultrasound shear wave elastography (SWE). SWE typically exerts an acoustic radiation force (ARF) to produce shear waves propagating in the lateral direction for which velocities and attenuations are measured. The tissue viscoelasticity is commonly studied by investigating the shear wave phase velocity curves. Viscoelastic tissue properties can also be characterized through utilizing various shear wave attenuation techniques. In this study, we propose an improved method for measuring the shear wave attenuation, called two-point frequency shift power (2P-FSP), which is an improved version of the two-point frequency shift (2P-FS) method. The technique is fully data driven and does not use a rheological model for mathematical modeling. The 2P-FSP method utilizes the power spectra frequency shift of shear waves measured at two spatial positions, which provides robustness to noise. The conceptual basis for the 2P-FSP is provided and tested with numerical and experimental data. We investigated how the location of the first signal and the distance interval between the two locations influence the shear wave attenuation measurement in the 2P-FSP technique. We utilized the 2P-FSP method on numerical phantom data generated using a finite-difference-based method in tissue-mimicking viscoelastic media. Moreover, we tested the 2P-FSP method with data from custom-made tissue-mimicking viscoelastic phantom experiments, and ex vivo porcine liver. We compared results from the proposed technique with results from 2P-FS and analytical values in the case of simulations. The results showed that the 2P-FSP method provides improved results over the 2P-FS technique for lower signal-to-noise ratio (SNR) and locations farther from the push location considered, and can be used to measure attenuation of viscoelastic soft tissues.

Comprehensive experimental assessments of rheological models' performance in elastography of soft tissues

Elastography researchers have utilized several rheological models to characterize soft tissue viscoelasticity over the past thirty years. Due to the frequency-dependent behavior of viscoelastic parameters as well as the different techniques and frequencies employed in various studies of soft tissues, rheological models have value in standardizing disparate techniques via explicit mathematical representations. However, the important question remains: which of the several available models should be considered for widespread adoption within a theoretical framework? We address this by evaluating the performance of three well established rheological models to characterize ex vivo bovine liver tissues: the Kelvin-Voigt (KV) model as a 2-parameter model, and the standard linear solid (SLS) and Kelvin-Voigt fractional derivative (KVFD) models as 3-parameter models. The assessments were based on the analysis of time domain behavior (using stress relaxation tests) and frequency domain behavior (by measuring shear wave speed (SWS) dispersion). SWS was measured over a wide range of frequency from 1 Hz to 1 kHz using three different tests: (i) harmonic shear tests using a rheometer, (ii) reverberant shear wave (RSW) ultrasound elastography scans, and (iii) RSW optical coherence elastography scans, with each test targeting a distinct frequency range. Our results demonstrated that the KVFD model produces the only mutually consistent rendering of time and frequency domain data for liver. Furthermore, it reduces to a 2-parameter model for liver (correspondingly to a 2-parameter "spring-pot" or power-law model for SWS dispersion) and provides the most accurate predictions of the material viscoelastic behavior in time (>98% accuracy) and frequency (>96% accuracy) domains. STATEMENT OF SIGNIFICANCE: Rheological models are applied in quantifying tissues viscoelastic properties. This study is unique in presenting comprehensive assessments of rheological models.

The Revisited Frequency-Shift Method for Shear Wave Attenuation Computation and Imaging

Ultrasound (US) shear wave (SW) elastography has been widely studied and implemented on clinical systems to assess the elasticity of living organs. Imaging of SW attenuation reflecting viscous properties of tissues has received less attention. A revisited frequency shift (R-FS) method is proposed to improve the robustness of SW attenuation imaging. Performances are compared with the FS method that we originally proposed and with the two-point frequency shift (2P-FS) and attenuation measuring US SW elastography (AMUSE) methods. In the proposed R-FS method, the shape parameter of the gamma distribution fitting SW spectra is assumed to vary with distance, in contrast to FS. Second, an adaptive random sample consensus (A-RANSAC) line fitting method is used to prevent outlier attenuation values in the presence of noise. Validation was made on ten simulated phantoms with two viscosities (0.5 and 2 Pa [Formula: see text]) and different noise levels (15 to -5 dB), two experimental homogeneous gel phantoms, and six in vivo liver acquisitions on awake ducks (including three normal and three fatty duck livers). According to the conducted experiments, R-FS revealed mean reductions in coefficients of variation (CV) of 62.6% on simulations, 62.5% with phantoms, and 62.3% in vivo compared with FS. Corresponding reductions compared with 2P-FS were 45.4%, 77.1%, and 62.0%, respectively. Reductions in normalized root-mean-square errors for simulations were 63.9% and 48.7% with respect to FS and 2P-FS, respectively.

Broadband-excitation-based mechanical spectroscopy of highly viscous tissue-mimicking phantoms

Standard rheometers assess mechanical properties of viscoelastic samples up to 100 Hz, which often hinders the assessment of the local-scale dynamics. We demonstrate that high-frequency analysis can be achieved by inducing broadband waves and monitoring their media-dependent propagation using optical coherence tomography. Here, we present a new broadband wave analysis based on two-dimensional Fourier transformation. We validated this method by comparing the mechanical parameters to monochromatic excitation and a standard oscillatory test data. Our method allows for high-frequency mechanical spectroscopy, which could be used to investigate the local-scale dynamics of different biological tissues and the influence of diseases on their microstructure.

Nonlinear Characterization of Tissue Viscoelasticity With Acoustoelastic Attenuation of Shear Waves

Shear-wave elastography (SWE) measures shear-wave speed (SWS), which is related to the underlying shear modulus of soft tissue. SWS in soft tissue changes depending on the amount of external strain that soft tissue is subjected to due to the acoustoelastic (AE) phenomenon. In the literature, variations of SWS as a function of applied uniaxial strain were used for nonlinear characterization, assuming soft tissues to be elastic, although soft tissues are indeed viscoelastic in nature. Hence, nonlinear characterization using SWS alone is insufficient. In this work, we use SWS together with shear-wave attenuation (SWA) during incremental quasi-static compressions in order to derive biomechanical characterization based on the AE theory in terms of well-defined storage and loss moduli. As part of this study, we also quantify the effect of applied strain on measurements of SWS and SWA since such confounding effects need to be taken into account when using SWS and/or SWA, e.g., for staging a disease state, while such effects can also serve as an additional imaging biomarker. Our results from tissue-mimicking phantoms with varying oil percentages and ex vivo porcine liver experiments demonstrate the feasibility of our proposed methods. In both experiments, SWA was observed to decrease with applied strain. For 10% compression in ex vivo livers, shear-wave attenuation decreased, on average, by 28% (93 Np/m), while SWS increased, on average, by 20% (0.26 m/s).

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

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

Phase Velocity Estimation With Expanded Bandwidth in Viscoelastic Phantoms and Tissues

Ultrasound shear wave elastography (SWE) is a technique used to measure mechanical properties to evaluate healthy and pathological soft tissues. SWE typically employs an acoustic radiation force (ARF) to generate laterally propagating shear waves that are tracked in the spatiotemporal domains, and algorithms are used to estimate the wave velocity. The tissue viscoelasticity is often examined through analyzing the shear wave phase velocity dispersion curves, which is the variation of phase velocity with frequency or wavelength. A number of available methods to estimate dispersion exist, which can differ in resolution and variance. Moreover, most of these techniques reconstruct dispersion curves for a limited frequency band. In this work, we propose a novel method used for dispersion curve calculation. Our unique approach uses a generalized Stockwell transformation combined with a slant frequency-wavenumber analysis (GST-SFK). We tested the GST-SFK method on numerical phantom data generated using a finite-difference-based method in tissue-mimicking viscoelastic media. In addition, we evaluated the method on numerical shear wave motion data with different amounts of white Gaussian noise added. Additionally, we performed tests on data from custom-made tissue-mimicking viscoelastic phantom experiments, ex vivo porcine liver measurements, and in vivo liver tissue experiments. We compared results from our method with two other techniques used for estimating shear wave phase velocity: the two-dimensional Fourier transform (2D-FT) and the eigenvector (EV) method. Tests carried out revealed that the GST-SFK method provides dispersion curve estimates with lower errors over a wider frequency band in comparison to the 2D-FT and EV methods. In addition, the GST-SFK provides expanded bandwidth by a factor of two or more to be used for phase velocity estimation, which is meaningful for a tissue dispersion analysis in vivo.

Viscoelastic parameter estimation using simulated shear wave motion and convolutional neural networks

Ultrasound shear wave elastography (SWE) techniques have been very useful for the analysis of tissue rheological properties, but there are still obstacles for robust evaluation of viscoelastic tissue properties. In this proof-of-concept study, we investigate whether convolutional neural networks (CNN) are capable of retrieving the elasticity and viscosity parameters from simulated shear wave motion images. Staggered-grid finite difference simulations based on a Kelvin-Voigt rheological model were used to generate data for this study. The wave motion datasets were created using Kelvin-Voigt shear elasticity values ranging from 1 to 25 kPa, shear viscosities ranging from 0 to 10 Pa⋅s, and two different push profiles using f-numbers of 1 and 2. The CNN architectures, optimized using mean squared error loss, were then trained to retrieve a specific viscoelastic parameter. Both elasticity and viscosity values were successfully retrieved, with regression R² values above 0.99 when correlating the estimated mechanical properties versus the true mechanical properties. The CNN performance was also compared to estimation of shear elasticity and viscosity from fitting dispersion curves estimated from two-dimensional Fourier transform analysis. The results demonstrated that the CNN models were robust to noise, vertical position and partially to f-number. The architecture was proven to be robust to multiple push profiles if trained properly. The CNN results showed higher accuracy over the full viscoelastic parameter range compared to the Fourier-based analysis. The overall results showed the CNNs' potential to be an alternative to complex mathematical analyses such as Fourier analysis and dispersion curve estimation used currently for shear wave viscoelastic parameter estimation.

Multiparametric in vivo ultrasound shear wave viscoelastography on farm-raised fatty duck livers: human radiology imaging applied to food sciences

Nine mulard ducks that were being raised for foie gras (steatosis) production went through in vivo shear wave (SW) elastography imaging of their liver during the force-feeding period to investigate changes in liver tissue characteristics. A total of 4 imaging sessions at an interval of 3 to 4 d were conducted at the farm on each animal. Three ducks were sacrificed at the second, third, and fourth imaging sessions for histopathology analysis of all animals at these time points. Six SW elastography parameters were evaluated: SW speed, SW attenuation, SW dispersion, Young's modulus, viscosity, and shear modulus. Shear waves of different frequencies propagate with different phase velocities. Thus, SW speed and other dependent parameters such as Young's modulus, viscosity, and shear modulus were computed at 2 frequencies: 75 and 202 Hz. Each parameter depicted a statistically significant trend along the force-feeding process (P-values between 0.001 and 0.0001). The fat fraction of the liver increased over the 12-day period of feeding. All parameters increased monotonically over time at 75 Hz, whereas modal relations were seen at 202 Hz. Shear wave dispersion measured between 75 and 202 Hz depicted a plateau from day 5. Based on this validation, proposed imaging methods are aimed to be used in the future on naturally fed ducks and geese.

Comprehensive Viscoelastic Characterization of Tissues and the Inter-relationship of Shear Wave (Group and Phase) Velocity, Attenuation and Dispersion

We report shear wave phase and group velocity, dispersion and attenuation in oil-in-gelatin viscoelastic phantoms and in vivo liver data. Moreover, we measured the power law coefficient from each dispersion curve and used it, together with the shear wave velocity, to calculate an approximate value for attenuation that agrees with independent attenuation measurements. Results in phantoms exhibit good agreement for all parameters with respect to independent mechanical measurements. For in vivo data, the livers of 20 patients were scanned. Results were compared with pathology scores obtained from liver biopsies. Across these cases, increases in shear wave dispersion and attenuation were related to increased steatosis score. It was found that shear wave dispersion and attenuation are experimentally linked, consistent with simple predictions based on the rheology of tissues, and can be used individually or jointly to assess tissue viscosity. Thus, this study indicates the possible utility of using shear wave dispersion and attenuation to non-invasively and quantitatively assess steatosis.

In vivo Ultrafast Quantitative Ultrasound and Shear Wave Elastography Imaging on Farm-Raised Duck Livers during Force Feeding

Shear wave elastography (speed and dispersion), local attenuation coefficient slope and homodyned-K parametric imaging were used for liver steatosis grading. These ultrasound biomarkers rely on physical interactions between shear and compression waves with tissues at both macroscopic and microscopic scales. These techniques were applied in a context not yet studied with ultrasound imaging, that is, monitoring steatosis of force-fed duck livers from pre-force-fed to foie gras stages. Each estimated feature presented a statistically significant trend along the feeding process (p values <10^-3). However, whereas a monotonic increase in the shear wave speed was observed along the process, most quantitative ultrasound features exhibited an absolute maximum value halfway through the process. As the liver fat fraction in foie gras is much higher than that seen clinically, we hypothesized that a change in the ultrasound scattering regime is encountered for high-fat fractions, and consequently, care has to be taken when applying ultrasound biomarkers to grading of severe states of steatosis.

Viscoelastic Response Ultrasound Derived Relative Elasticity and Relative Viscosity Reflect True Elasticity and Viscosity: In Silico and Experimental Demonstration

Viscoelastic response (VisR) ultrasound characterizes the viscoelastic properties of tissue by fitting acoustic radiation force (ARF)-induced displacements in the region of ARF excitation to a 1-D mass-spring-damper (MSD) model. Elasticity and viscosity are calculated separately but relative to the applied ARF amplitude. We refer to these parameters as "relative elasticity (RE)" and "relative viscosity (RV)." We herein test the hypothesis that RE and RV linearly correlate to true elasticity and viscosity in tissue. VisR imaging was simulated in 144 homogeneous viscoelastic materials with varying elasticities and viscosities. Derived RE linearly correlated with material elasticity and varied by an average of 2.52% when the material viscosity changed from 0.1 to 1.3 Pa · s. Derived RV linearly correlated with material viscosity but varied by an average of 102.5% when material elasticity changed from 3.33 to 20 kPa. The effect of elasticity on RV measurement was compensated using the slope of the linear relationship between RV and natural frequency ( ωtextn ). After compensation, RV [Formula: see text] (elasticity compensated RV) linearly correlated with material viscosity and varied by less than 1.00% on average when the modeled shear elastic modulus changed from 3.3 to 20 kPa. In addition to elasticity compensation, variation in ARF amplitude over depth was compensated, yielding REDC and [Formula: see text]. REDC and [Formula: see text] successfully contrasted elastic and viscous inclusions, respectively, in three simulated phantoms. Experimentally, in the homogeneous oil-in-gelatin phantoms and excised livers, REDC linearly correlated with shear wave dispersion ultrasound vibrometry (SDUV) derived shear elastic modulus, and [Formula: see text] linearly correlated with SDUV-derived shear viscosity. In excised livers containing viscoelastic oil-in-gelatin inclusions, the inclusions were successfully contrasted from the liver background by both REDC and [Formula: see text]. These results suggest that RE and RV are relevant for qualitatively assessing the elastic and viscous properties of tissue.

Two-Point Frequency Shift Method for Shear Wave Attenuation Measurement

Ultrasound shear wave elastography (SWE) is an increasingly used noninvasive modality for quantitative evaluation of tissue mechanical properties. SWE typically uses an acoustic radiation force to produce laterally propagating shear waves that are tracked in the spatial and temporal domains, in order to obtain the wave velocity. One of the ways to study the viscoelasticity is through studying the shear wave phase velocity dispersion curves. Shear wave attenuation can be also characterized in viscoelastic tissues with methods that use multiple lateral data samples. In this article, we present an alternative method for measuring the shear wave attenuation without using a rheological model two-point frequency shift (2P-FS). The technique uses information related to the amplitude spectra FS of shear waves measured at only two lateral locations. The theoretical basis for the 2P-FS is derived and validated. We examined how the first signal position and the distance between the two locations affect the shear wave attenuation estimation in the 2P-FS method. We tested this new method on digital phantom data created using the local interaction simulation approach (LISA) in viscoelastic media. Moreover, we tested data acquired from custom-made tissue-mimicking viscoelastic phantom experiments and ex vivo porcine liver measurements. We compared results from the 2P-FS method with the other two techniques used for assessing a shear wave attenuation: the FS-based method and the attenuation-measuring ultrasound shear wave elastography (AMUSE) technique. In addition, we evaluated the 2P-FS algorithm with different levels of added white Gaussian noise to the shear wave particle velocity using numerical phantoms. Tests conducted showed that the 2P-FS method gives robust results based on only two measurements and can be used to measure attenuation of viscoelastic soft tissues.

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.

Distributing Synthetic Focusing Over Multiple Push-Detect Events Enhances Shear Wave Elasticity Imaging Performance

Plane wave (PW) imaging is a commonly used method for tracking waves during shear wave elasticity imaging (SWEI), but its unfocused transmission beam reduces tracking accuracy and precision. Coherent compounding minimizes this problem, but SWEI's stringent frame rate requirement and the coarse pitch of most clinical transducers limit its effectiveness. Synthetic aperture imaging (SAI) is an alternate ultrasound imaging approach with a much tighter focus than PW imaging, but its lower transmission power has deterred researchers from using SAI in SWEI. Hadamard-encoded multielement SAI can overcome this limitation. However, only a limited number of subapertures (3-5) can be transmitted in a single push-detect event. We have developed methods to distribute more subapertures or more compounding angles over multiple push-detect events. In this paper, we report the results of experiments conducted on phantoms to assess SWEI's performance when using Hadamard-encoded distributed-multielement synthetic aperture (HDMSA) imaging or distributed plane wave compounding (DPWC) to track shear waves. Tracking shear waves with HDMSA improved the elastographic signal-to-noise ratio (SNR_e) by 61.6%-89.5% depending on the phantom employed. Similarly, DPWC tracking improved SNR_e by 56.2%-93.3% for the same group of phantoms. Compared to focused ultrasound tracking (at the focus), SNR_e improved by 28.6% and 32.5% when tracking shear waves with HDMSA and DPWC, respectively. Long acquisitions could introduce decoding errors that decrease the performance when performing HDMSA tracking within the clinical setting. Nevertheless, the results of studies performed on the bicep muscle of three healthy volunteers demonstrate that for stationary organs, tracking shear waves with HDMSA yielded repeatable elastograms that offer better elastographic performance than those produced with current tracking methods.

Reconstruction of Viscosity Maps in Ultrasound Shear Wave Elastography

Change in viscoelastic properties of biological tissues may often be symptomatic of a dysfunction that can be correlated to tissue pathology. Shear wave elastography is an imaging method mainly used to assess stiffness but with the potential to measure viscoelasticity of biological tissues. This can enable tissue characterization; and thus, can be used as a marker to improve diagnosis of pathological lesions. In this study, a frequency-shift method based framework is presented for the reconstruction of viscosity by analyzing the spectral properties of acoustic radiation force-induced shear waves. The aim of the study was to investigate the feasibility of viscosity reconstruction maps in homogeneous as well as heterogeneous samples. Experiments were performed in four in vitro phantoms, two ex vivo porcine liver samples, two ex vivo fatty duck liver samples, and one in vivo fatty goose liver. Successful viscosity maps were reconstructed in homogeneous and heterogeneous phantoms with embedded mechanical inclusions having different geometries. Quantitative values of viscosity obtained for two porcine liver tissues, two fatty duck liver samples, and one goose fatty liver were (mean ± SD) 0.61 ± 0.21, 0.52 ± 0.35; 1.28 ± 0.54, 1.36 ± 0.73, and 1.67 ± 0.70 Pa.s, respectively.

Attenuation of Shear Waves in Normal and Steatotic Livers

Shear wave propagation in the liver has been a robust subject of research, with shear wave speed receiving the most attention. The correlation between increased shear wave speed and increased fibrosis in the liver has been established as a useful diagnostic tool. In comparison, the precise mechanisms of shear wave attenuation, and its relation to diseased states of the liver, are less well-established. This study focused on the hypothesis that steatosis adds a viscous (lossy) component to the liver, which increases shear wave attenuation. Twenty patients' livers were scanned with ultrasound and with induced shear wave propagation, and the resulting displacement profiles were analyzed using recently developed estimators to derive both the speed and attenuation of the shear waves within 6-cm² regions of interest. The results were compared with pathology scores obtained from liver biopsies taken under ultrasound guidance. Across these cases, increases in shear wave attenuation were linked to increased steatosis score. This preliminary study supports the hypothesis and indicates the possible utility of the measurements for non-invasive and quantitative assessment of steatosis.

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 resonance elastography of coagulating blood: theoretical viscoelasticity modeling and ex-vivo experimentation

Deep vein thrombosis is a common vascular disease that can lead to pulmonary embolism and death. The early diagnosis and clot age staging are important parameters for reliable therapy planning. This article presents an acoustic radiation force induced resonance elastography method for the viscoelastic characterization of clotting blood. The physical concept of this method relies on the mechanical resonance of the blood clot occurring at specific frequencies. Resonances are induced by focusing ultrasound beams inside the sample under investigation. Coupled to an analytical model of wave scattering, the ability of the proposed method to characterize the viscoelasticity of a mimicked venous thrombosis in the acute phase is demonstrated. Experiments with a gelatin-agar inclusion sample of known viscoelasticity are performed for validation and establishment of the proof of concept. In addition, an inversion method is applied in-vitro for the kinetic monitoring of the blood coagulation process of six human blood samples obtained from two volunteers. The computed elasticity and viscosity values of blood samples at the end of the 90 min kinetics were estimated at 411 ± 71 Pa and 0.25 ± 0.03 Pa.s for volunteer #1, and 387 ± 35 Pa and 0.23 ± 0.02 Pa.s for volunteer #2, respectively. The proposed method allowed reproducible time-varying thrombus viscoelastic measurements from samples having physiological dimensions.

Ultrafast imaging of cell elasticity with optical microelastography

In wave physics, and especially seismology, uncorrelated vibrations could be exploited using “noise correlation” tools to reconstruct images of a medium. By using a high-frequency vibration, a high-speed tracking device, and a reconstruction technique based on temporal correlations of travelling waves we conceptualized an optical microelastography technique to map elasticity of internal cellular structures. This technique, unlike other methods, can provide an elasticity image in less than a millisecond, thus opening the possibility of studying dynamic cellular processes and elucidating new mechanocellular properties. We call this proposed technique “cell quake elastography.”

Elasticity is a fundamental cellular property that is related to the anatomy, functionality, and pathological state of cells and tissues. However, current techniques based on cell deformation, atomic force microscopy, or Brillouin scattering are rather slow and do not always accurately represent cell elasticity. Here, we have developed an alternative technique by applying shear wave elastography to the micrometer scale. Elastic waves were mechanically induced in live mammalian oocytes using a vibrating micropipette. These audible frequency waves were observed optically at 200,000 frames per second and tracked with an optical flow algorithm. Whole-cell elasticity was then mapped using an elastography method inspired by the seismology field. Using this approach we show that the elasticity of mouse oocytes is decreased when the oocyte cytoskeleton is disrupted with cytochalasin B. The technique is fast (less than 1 ms for data acquisition), precise (spatial resolution of a few micrometers), able to map internal cell structures, and robust and thus represents a tractable option for interrogating biomechanical properties of diverse cell types.

Forward and inverse viscoelastic wave scattering by irregular inclusions for shear wave elastography

Inversion methods in shear wave elastography use simplifying assumptions to recover the mechanical properties of soft tissues. Consequently, these methods suffer from artifacts when applied to media containing strong stiffness contrasts, and do not provide a map of the viscosity. In this work, the shear wave field recorded inside and around an inclusion was used to estimate the viscoelastic properties of the inclusion and surrounding medium, based on an inverse problem approach assuming local homogeneity of both media. An efficient semi-analytical method was developed to model the scattering of an elastic wave by an irregular inclusion, based on a decomposition of the field by Bessel functions and on a decomposition of the boundaries as Fourier series. This model was validated against finite element modeling. Shear waves were experimentally induced by acoustic radiation force in soft tissue phantoms containing stiff and soft inclusions, and the displacement field was imaged at a high frame rate using plane wave imaging. A nonlinear least-squares algorithm compared the model to the experimental data and adjusted the geometrical and mechanical parameters. The estimated shear storage and loss moduli were in good agreement with reference measurements, as well as the estimated inclusion shape. This approach provides an accurate estimation of geometry and viscoelastic properties for a single inclusion in a homogeneous background in the context of radiation force elastography.