Shear wave spectroscopy for in vivo quantification of human soft tissues visco-elasticity

Ultrasound Shear Wave Simulation of Breast Tumor Using Nonlinear Tissue Elasticity

Shear wave elasticity imaging (SWEI) can assess the elasticity of tissues, but the shear modulus estimated in SWEI is often less sensitive to a subtle change of the stiffness that produces only small mechanical contrast to the background tissues. Because most soft tissues exhibit mechanical nonlinearity that differs in tissue types, mechanical contrast can be enhanced if the tissues are compressed. In this study, a finite element- (FE-) based simulation was performed for a breast tissue model, which consists of a circular (D: 10 mm, hard) tumor and surrounding tissue (soft). The SWEI was performed with 0% to 30% compression of the breast tissue model. The shear modulus of the tumor exhibited noticeably high nonlinearity compared to soft background tissue above 10% overall applied compression. As a result, the elastic modulus contrast of the tumor to the surrounding tissue was increased from 0.46 at 0% compression to 1.45 at 30% compression.

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

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

Quasi-plane shear wave propagation induced by acoustic radiation force with a focal line region: a simulation study

Shear wave propagation speed has been regarded as an attractive indicator for quantitatively measuring the intrinsic mechanical properties of soft tissues. While most existing techniques use acoustic radiation force (ARF) excitation with focal spot region based on linear array transducers, we try to employ a special ARF with a focal line region and apply it to viscoelastic materials to create shear waves. First, a two-dimensional capacitive micromachined ultrasonic transducer with 64 × 128 fully controllable elements is realised and simulated to generate this special ARF. Then three-dimensional finite element models are developed to simulate the resulting shear wave propagation through tissue phantom materials. Three different phantoms are explored in our simulation study using: (a) an isotropic viscoelastic medium, (b) within a cylindrical inclusion, and (c) a transverse isotropic viscoelastic medium. For each phantom, the ARF creates a quasi-plane shear wave which has a preferential propagation direction perpendicular to the focal line excitation. The propagation of the quasi-plane shear wave is investigated and then used to reconstruct shear moduli sequentially after the estimation of shear wave speed. In the phantom with a transverse isotropic viscoelastic medium, the anisotropy results in maximum speed parallel to the fiber direction and minimum speed perpendicular to the fiber direction. The simulation results show that the line excitation extends the displacement field to obtain a large imaging field in comparison with spot excitation, and demonstrate its potential usage in measuring the mechanical properties of anisotropic tissues.

Estimation of shear modulus in media with power law characteristics

Shear wave propagation in tissue generated by the radiation force is usually modeled by either a lossless or a classical viscoelastic equation. However, experimental data shows power law behavior which is not consistent with those approaches. It is well known that fractional derivatives results in power laws, therefore a time fractional wave equation, the Caputo equation, which can be derived from the fractional Kelvin-Voigt stress and strain relation is tested. This equation is solved using the finite difference method with experimental parameters obtained from the existing literature. The equation is characterized by a fractional order which is also the power law exponent of the frequency dependent shear modulus. It is shown that for fractional order between 0 and 1, the equation gives smaller shear modulus than the classical model. The opposite situation applies for fractional order greater than 1. The numerical simulation also shows that the shear wave velocity method is only reliable for small losses. In our case, this is only for a small fractional order. Based on the published values of fractional order from other studies, there is therefore a chance for biased estimation of the shear modulus.

Non-invasive and Non-destructive Characterization of Tissue Engineered Constructs Using Ultrasound Imaging Technologies: A Review

With the rapid expansion of biomaterial development and coupled efforts to translate such advances toward the clinic, non-invasive and non-destructive imaging tools to evaluate implants in situ in a timely manner are critically needed. The required multi-level information is comprehensive, including structural, mechanical, and biological changes such as scaffold degradation, mechanical strength, cell infiltration, extracellular matrix formation and vascularization to name a few. With its inherent advantages of non-invasiveness and non-destructiveness, ultrasound imaging can be an ideal tool for both preclinical and clinical uses. In this review, currently available ultrasound imaging technologies that have been applied in vitro and in vivo for tissue engineering and regenerative medicine are discussed and some new emerging ultrasound technologies and multi-modality approaches utilizing ultrasound are introduced.

Oestreicher and elastography

A sphere moving back and forth in tissue generates the kinds of complex displacement fields that are used in elastography. The analytical solution of Hans Oestreicher for this phenomenon [(1951). J. Acoust. Soc. Am. 23, 704-714] gives an understanding of the transverse and longitudinal, fast and slow waves that are generated. The results suggest several ways to determine the absorption coefficients of tissues, which together with phase velocity permit the computation of both the real shear modulus and the shear viscosity as functions of frequency.

Assessment of Substantial Liver Fibrosis by Real-time Shear Wave Elastography in Methotrexate-Treated Patients With Rheumatoid Arthritis

OBJECTIVES

A concern about methotrexate (MTX)-related liver fibrosis in patients with rheumatoid arthritis (RA) is still unresolved. This study investigated the correlation between liver stiffness and the cumulative MTX dose and the risk factors associated with substantial liver fibrosis assessed by real-time shear wave elastography (SWE), a recently introduced technique to evaluate liver stiffness in patients with RA.

METHODS

Data from 185 patients with RA were prospectively collected. Patients were divided into 3 groups according to cumulative MTX dose (group 1, total dose <1500 mg; group 2, 1500-4000 mg, and group 3, >4000 mg) and compared with healthy control participants. A Pearson correlation analysis was performed to evaluate correlations between liver stiffness and other clinical and laboratory variables. Substantial liver fibrosis was defined as liver stiffness of greater than 8.6 kPa by SWE. Associated factors were tested in a multivariate logistic analysis.

RESULTS

The mean liver stiffness value in healthy controls was significantly lower than in patients with RA treated with MTX (P< .006), but there was no significant difference among the MTX groups. Liver stiffness and the cumulative MTX dose was not correlated. Substantial liver fibrosis was detected only in 9 patients (4.9%). Multivariate analysis adjusted by age and sex revealed that only a high body mass index (odds ratio, 1.79; 95% confidence interval, 1.34-2.39; P < .001) was associated with liver stiffness of greater than 8.6 kPa.

CONCLUSIONS

Substantial liver fibrosis on SWE was observed in about 5% of MTX-treated patients with RA and was associated with only a high body mass index but not with the cumulative MTX dose, suggesting that other comorbidities might have a more important role in liver fibrosis.

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

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

Frequency adaptation for enhanced radiation force amplitude in dynamic elastography

In remote dynamic elastography, the amplitude of the generated displacement field is directly related to the amplitude of the radiation force. Therefore, displacement improvement for better tissue characterization requires the optimization of the radiation force amplitude by increasing the push duration and/or the excitation amplitude applied on the transducer. The main problem of these approaches is that the Food and Drug Administration (FDA) thresholds for medical applications and transducer limitations may be easily exceeded. In the present study, the effect of the frequency used for the generation of the radiation force on the amplitude of the displacement field was investigated. We found that amplitudes of displacements generated by adapted radiation force sequences were greater than those generated by standard nonadapted ones (i.e., single push acoustic radiation force impulse and supersonic shear imaging). Gains in magnitude were between 20 to 158% for in vitro measurements on agar-gelatin phantoms, and 170 to 336% for ex vivo measurements on a human breast sample, depending on focus depths and attenuations of tested samples. The signal-to-noise ratio was also improved more than 4-fold with adapted sequences. We conclude that frequency adaptation is a complementary technique that is efficient for the optimization of displacement amplitudes. This technique can be used safely to optimize the deposited local acoustic energy without increasing the risk of damaging tissues and transducer elements.

Quantitative evaluation of atrial radio frequency ablation using intracardiac shear-wave elastography

PURPOSE

Radio frequency catheter ablation (RFCA) is a well-established clinical procedure for the treatment of atrial fibrillation (AF) but suffers from a low single-procedure success rate. Recurrence of AF is most likely attributable to discontinuous or nontransmural ablation lesions. Yet, despite this urgent clinical need, there is no clinically available imaging modality that can reliably map the lesion transmural extent in real time. In this study, the authors demonstrated the feasibility of shear-wave elastography (SWE) to map quantitatively the stiffness of RFCA-induced thermal lesions in cardiac tissues in vitro and in vivo using an intracardiac transducer array.

METHODS

SWE was first validated in ex vivo porcine ventricular samples (N = 5). Both B-mode imaging and SWE were performed on normal cardiac tissue before and after RFCA. Areas of the lesions were determined by tissue color change with gross pathology and compared against the SWE stiffness maps. SWE was then performed in vivo in three sheep (N = 3). First, the stiffness of normal atrial tissues was assessed quantitatively as well as its variation during the cardiac cycle. SWE was then performed in atrial tissue after RFCA.

RESULTS

A large increase in stiffness was observed in ablated ex vivo regions (average shear modulus across samples in normal tissue: 22 ± 5 kPa, average shear-wave speed (ct): 4.5 ± 0.4 m s(-1) and in determined ablated zones: 99 ± 17 kPa, average ct: 9.0 ± 0.5 m s(-1) for a mean shear modulus increase ratio of 4.5 ± 0.9). In vivo, a threefold increase of the shear modulus was measured in the ablated regions, and the lesion extension was clearly visible on the stiffness maps.

CONCLUSIONS

By its quantitative and real-time capabilities, Intracardiac SWE is a promising intraoperative imaging technique for the evaluation of thermal ablation during RFCA.

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

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

What do we know about shear wave dispersion in normal and steatotic livers?

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

WFUMB guidelines and recommendations for clinical use of ultrasound elastography: Part 1: basic principles and terminology

Conventional diagnostic ultrasound images of the anatomy (as opposed to blood flow) reveal differences in the acoustic properties of soft tissues (mainly echogenicity but also, to some extent, attenuation), whereas ultrasound-based elasticity images are able to reveal the differences in the elastic properties of soft tissues (e.g., elasticity and viscosity). The benefit of elasticity imaging lies in the fact that many soft tissues can share similar ultrasonic echogenicities but may have different mechanical properties that can be used to clearly visualize normal anatomy and delineate pathologic lesions. Typically, all elasticity measurement and imaging methods introduce a mechanical excitation and monitor the resulting tissue response. Some of the most widely available commercial elasticity imaging methods are 'quasi-static' and use external tissue compression to generate images of the resulting tissue strain (or deformation). In addition, many manufacturers now provide shear wave imaging and measurement methods, which deliver stiffness images based upon the shear wave propagation speed. The goal of this review is to describe the fundamental physics and the associated terminology underlying these technologies. We have included a questions and answers section, an extensive appendix, and a glossary of terms in this manuscript. We have also endeavored to ensure that the terminology and descriptions, although not identical, are broadly compatible across the WFUMB and EFSUMB sets of guidelines on elastography (Bamber et al. 2013; Cosgrove et al. 2013).

Ultrasound Elastography and MR Elastography for Assessing Liver Fibrosis: Part 2, Diagnostic Performance, Confounders, and Future Directions

OBJECTIVE

The purpose of the article is to review the diagnostic performance of ultra-sound and MR elastography techniques for detection and staging of liver fibrosis, the main current clinical applications of elastography in the abdomen.

CONCLUSION

Technical and instrument-related factors and biologic and patient-related factors may constitute potential confounders of stiffness measurements for assessment of liver fibrosis. Future developments may expand the scope of elastography for monitoring liver fibrosis and predict complications of chronic liver disease.

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

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

Could linear hysteresis contribute to shear wave losses in tissues?

For nearly 100 y in the study of cyclical motion in materials, a particular phenomenon called "linear hysteresis" or "ideal hysteretic damping" has been widely observed. More recently in the field of shear wave elastography, the basic mechanisms underlying shear wave losses in soft tissues are in question. Could linear hysteresis play a role? An underlying theoretical question must be answered: Is there a real and causal physical model that is capable of producing linear hysteresis over a band of shear wave frequencies used in diagnostic imaging schemes? One model that can approximately produce classic linear hysteresis behavior, by examining a generalized Maxwell model with a specific power law relaxation spectrum, is described here. This provides a theoretical plausibility for the phenomenon as a candidate for models of tissue behavior.

Non-contact, ultrasound-based indentation method for measuring elastic properties of biological tissues using harmonic motion imaging (HMI)

Noninvasive measurement of mechanical properties of biological tissues in vivo could play a significant role in improving the current understanding of tissue biomechanics. In this study, we propose a method for measuring elastic properties non-invasively by using internal indentation as generated by harmonic motion imaging (HMI). In HMI, an oscillating acoustic radiation force is produced by a focused ultrasound transducer at the focal region, and the resulting displacements are estimated by tracking radiofrequency signals acquired by an imaging transducer. In this study, the focal spot region was modeled as a rigid cylindrical piston that exerts an oscillatory, uniform internal force to the underlying tissue. The HMI elastic modulus EHMI was defined as the ratio of the applied force to the axial strain measured by 1D ultrasound imaging. The accuracy and the precision of the EHMI estimate were assessed both numerically and experimentally in polyacrylamide tissue-mimicking phantoms. Initial feasibility of this method in soft tissues was also shown in canine liver specimens in vitro. Very good correlation and agreement was found between the measured Young's modulus and the HMI modulus in the numerical study (r(2) > 0.99, relative error <10%) and on polyacrylamide gels (r(2) = 0.95, relative error <24%). The average HMI modulus on five liver samples was found to EHMI = 2.62  ±  0.41 kPa, compared to EMechTesting = 4.2  ±  2.58 kPa measured by rheometry. This study has demonstrated for the first time the initial feasibility of a non-invasive, model-independent method to estimate local elastic properties of biological tissues at a submillimeter scale using an internal indentation-like approach. Ongoing studies include in vitro experiments in a larger number of samples and feasibility testing in in vivo models as well as pathological human specimens.

A versatile and experimentally validated finite element model to assess the accuracy of shear wave elastography in a bounded viscoelastic medium

The feasibility of shear wave elastography (SWE) in arteries for cardiovascular risk assessment remains to be investigated as the artery's thin wall and intricate material properties induce complex shear wave (SW) propagation phenomena. To better understand the SW physics in bounded media, we proposed an in vitro validated finite element model capable of simulating SW propagation, with full flexibility at the level of the tissue's geometry, material properties, and acoustic radiation force. This computer model was presented in a relatively basic set-up, a homogeneous slab of gelatin-agar material (4.35 mm thick), allowing validation of the numerical settings according to actual SWE measurements. The resulting tissue velocity waveforms and SW propagation speed matched well with the measurement: 4.46 m/s (simulation) versus 4.63 ± 0.07 m/s (experiment). Further, we identified the impact of geometrical and material parameters on the SW propagation characteristics. As expected, phantom thickness was a determining factor of dispersion. Adding viscoelasticity to the model augmented the estimated wave speed to 4.58 m/s, an even better match with the experimental determined value. This study demonstrated that finite element modeling can be a powerful tool to gain insight into SWE mechanics and will in future work be advanced to more clinically relevant settings.

Investigating liver stiffness and viscosity for fibrosis, steatosis and activity staging using shear wave elastography

BACKGROUND & AIMS

Quantitative shear wave elastography was shown to be an effective tool for the non-invasive diagnosis and staging of chronic liver diseases. The liver shear modulus, estimated from the propagation velocity of shear waves, is correlated to the degree of fibrosis and can therefore be used for the non-invasive staging of fibrosis.

METHODS

We performed a clinical prospective study in a total of 120 patients with various chronic liver diseases to compare the accuracy of supersonic shear imaging (SSI), a technique based on acoustic radiation and ultrafast ultrasound imaging, to 1D transient elastography (FibroScan) for the staging and grading of fibrosis as assessed by liver biopsy. Since shear wave propagation spectroscopy can also provide additional mechanical information on soft tissues, such as viscosity, we also investigated those new mechanical parameters as possible predictors of fibrosis, steatosis, and disease activity.

RESULTS

SSI was successfully performed in 98.3% of patients and it was shown to be as accurate as FibroScan for the staging of fibrosis both for the whole population (N=120) and for the subgroup with viral hepatitis (n=70) (AUC=0.85 [0.77-0.96] and 0.89 [0.81-0.97] for significant fibrosis, AUC=0.90 [0.83-0.97] and 0.87 [0.75-0.98] for cirrhosis, with respect to SSI [n=68/70] and FibroScan [n=66/68]). Viscosity could also be used to stage the degree of fibrosis (AUC=0.76 [0.64-0.87] for significant fibrosis and AUC=0.87 [0.74-0.99] for cirrhosis), for the subgroup of patients with viral hepatitis (n=67/70) but was a poor predictor of disease activity and steatosis levels.

CONCLUSIONS

Supersonic shear imaging is a robust technique for the staging of liver fibrosis. Liver viscosity was found to be correlated with fibrosis but not to steatosis or disease activity.

Imaging strategies for tissue engineering applications

Tissue engineering has evolved with multifaceted research being conducted using advanced technologies, and it is progressing toward clinical applications. As tissue engineering technology significantly advances, it proceeds toward increasing sophistication, including nanoscale strategies for material construction and synergetic methods for combining with cells, growth factors, or other macromolecules. Therefore, to assess advanced tissue-engineered constructs, tissue engineers need versatile imaging methods capable of monitoring not only morphological but also functional and molecular information. However, there is no single imaging modality that is suitable for all tissue-engineered constructs. Each imaging method has its own range of applications and provides information based on the specific properties of the imaging technique. Therefore, according to the requirements of the tissue engineering studies, the most appropriate tool should be selected among a variety of imaging modalities. The goal of this review article is to describe available biomedical imaging methods to assess tissue engineering applications and to provide tissue engineers with criteria and insights for determining the best imaging strategies. Commonly used biomedical imaging modalities, including X-ray and computed tomography, positron emission tomography and single photon emission computed tomography, magnetic resonance imaging, ultrasound imaging, optical imaging, and emerging techniques and multimodal imaging, will be discussed, focusing on the latest trends of their applications in recent tissue engineering studies.

Modeling transversely isotropic, viscoelastic, incompressible tissue-like materials with application in ultrasound shear wave elastography

In this paper, we propose a method to model the shear wave propagation in transversely isotropic, viscoelastic and incompressible media. The targeted application is ultrasound-based shear wave elastography for viscoelasticity measurements in anisotropic tissues such as the kidney and skeletal muscles. The proposed model predicts that if the viscoelastic parameters both across and along fiber directions can be characterized as a Voigt material, then the spatial phase velocity at any angle is also governed by a Voigt material model. Further, with the aid of Taylor expansions, it is shown that the spatial group velocity at any angle is close to a Voigt type for weakly attenuative materials within a certain bandwidth. The model is implemented in a finite element code by a time domain explicit integration scheme and shear wave simulations are conducted. The results of the simulations are analyzed to extract the shear wave elasticity and viscosity for both the spatial phase and group velocities. The estimated values match well with theoretical predictions. The proposed theory is further verified by an ex vivo tissue experiment measured in a porcine skeletal muscle by an ultrasound shear wave elastography method. The applicability of the Taylor expansion to analyze the spatial velocities is also discussed. We demonstrate that the approximations from the Taylor expansions are subject to errors when the viscosities across or along the fiber directions are large or the maximum frequency considered is beyond the bandwidth defined by radii of convergence of the Taylor expansions.

Derivation and analysis of viscoelastic properties in human liver: impact of frequency on fibrosis and steatosis staging

Commercially-available shear wave imaging systems measure group shear wave speed (SWS) and often report stiffness parameters applying purely elastic material models. Soft tissues, however, are viscoelastic, and higher-order material models are necessary to characterize the dispersion associated with broadband shear waves. In this paper, we describe a robust, model-based algorithm and use a linear dispersion model to perform shear wave dispersion analysis in traditionally difficult-to-image subjects. In a cohort of 135 non-alcoholic fatty liver disease patients, we compare the performance of group SWS with dispersion analysis-derived phase velocity c(200 Hz) and dispersion slope dc/df parameters to stage hepatic fibrosis and steatosis. Area under the ROC curve (AUROC) analysis demonstrates correlation between all parameters [group SWS, c(200 Hz), and, to a lesser extent dc/df ] and fibrosis stage, whereas no correlation was observed between steatosis stage and any of the material parameters. Interestingly, optimal AUROC threshold SWS values separating advanced liver fibrosis (≥F3) from mild-to-moderate fibrosis (≤F2) were shown to be frequency-dependent, and to increase from 1.8 to 3.3 m/s over the 0 to 400 Hz shear wave frequency range.

Dynamic ultrasound imaging applications to quantify musculoskeletal function

Advances in imaging methods have led to new capability to study muscle and tendon motion in vivo. Direct measurements of muscle and tendon kinematics using imaging may lead to improved understanding of musculoskeletal function. This review presents quantitative ultrasound methods for muscle dynamics that can be used to assess in vivo musculoskeletal function when integrated with other conventional biomechanical measurements.

Assessment of fibrosis during the development of fatty liver in rabbits using real-time shear-wave elastography

Nonalcoholic and alcoholic rabbit models of fatty liver were established by feeding on high-fat diet and alcohol, respectively, and fatty liver stiffness at different pathological stages was assessed with real-time shear-wave elastography (SWE), so as to investigate the fibrosis process during the development of fatty liver. The fatty liver stiffness of rabbit in nonalcoholic and alcoholic groups was higher than that in the control group, and that in alcohol group was higher than that in the nonalcoholic group (P<0.01). The elasticity modulus of liver in fatty liver rabbits of nonalcoholic and alcoholic groups showed a positive correlation with progression of liver fibrosis (P<0.01). Real-time SWE, as a noninvasive diagnostic method, can objectively reflect the liver stiffness change and progression of liver fibrosis during the development of fatty liver.

Imaging of shear waves induced by Lorentz force in soft tissues

This study presents the first observation of elastic shear waves generated in soft solids using a dynamic electromagnetic field. The first and second experiments of this study showed that Lorentz force can induce a displacement in a soft phantom and that this displacement was detectable by an ultrasound scanner using speckle-tracking algorithms. For a 100 mT magnetic field and a 10 ms, 100 mA peak-to-peak electrical burst, the displacement reached a magnitude of 1 μm. In the third experiment, we showed that Lorentz force can induce shear waves in a phantom. A physical model using electromagnetic and elasticity equations was proposed. Computer simulations were in good agreement with experimental results. The shear waves induced by Lorentz force were used in the last experiment to estimate the elasticity of a swine liver sample.

Shear modulus estimation on vastus intermedius of elderly and young females over the entire range of isometric contraction

Elderly people often suffer from sarcopenia in their lower extremities, which gives rise to the increased susceptibility of fall. Comparing the mechanical properties of the knee extensor/flexors on elderly and young subjects is helpful in understanding the underlying mechanisms of the muscle aging process. However, although the stiffness of skeletal muscle has been proved to be positively correlated to its non-fatiguing contraction intensity by some existing methods, this conclusion has not been verified above 50% maximum voluntary contraction (MVC) due to the limitation of their measurement range. In this study, a vibro-ultrasound system was set up to achieve a considerably larger measurement range on muscle stiffness estimation. Its feasibility was verified on self-made silicone phantoms by comparing with the mechanical indentation method. The system was then used to assess the stiffness of vastus intermedius (VI), one of the knee extensors, on 10 healthy elderly female subjects (56.7±4.9 yr) and 10 healthy young female subjects (27.6±5.0 yr). The VI stiffness in its action direction was confirmed to be positively correlated to the % MVC level (R² = 0.999) over the entire range of isometric contraction, i.e. from 0% MVC (relaxed state) to 100% MVC. Furthermore, it was shown that there was no significant difference between the mean VI shear modulus of the elderly and young subjects in a relaxed state (p>0.1). However, when performing step isometric contraction, the VI stiffness of young female subjects was found to be larger than that of elderly participants (p<0.001), especially at the relatively higher contraction levels. The results expanded our knowledge on the mechanical property of the elderly’s skeletal muscle and its relationship with intensity of active contraction. Furthermore, the vibro-ultrasound system has a potential to become a powerful tool for investigating the elderly’s muscle diseases.

Magnetomotive optical coherence elastography using magnetic particles to induce mechanical waves

Magnetic particles are versatile imaging agents that have found wide spread applicability in diagnostic, therapeutic, and rheology applications. In this study, we demonstrate that mechanical waves generated by a localized inclusion of magnetic nanoparticles can be used for assessment of the tissue viscoelastic properties using magnetomotive optical coherence elastography. We show these capabilities in tissue mimicking elastic and viscoelastic phantoms and in biological tissues by measuring the shear wave speed under magnetomotive excitation. Furthermore, we demonstrate the extraction of the complex shear modulus by measuring the shear wave speed at different frequencies and fitting to a Kelvin-Voigt model.

In vivo monitoring of structural and mechanical changes of tissue scaffolds by multi-modality imaging

Degradable tissue scaffolds are implanted to serve a mechanical role while healing processes occur and putatively assume the physiological load as the scaffold degrades. Mechanical failure during this period can be unpredictable as monitoring of structural degradation and mechanical strength changes at the implant site is not readily achieved in vivo, and non-invasively. To address this need, a multi-modality approach using ultrasound shear wave imaging (USWI) and photoacoustic imaging (PAI) for both mechanical and structural assessment in vivo was demonstrated with degradable poly(ester urethane)urea (PEUU) and polydioxanone (PDO) scaffolds. The fibrous scaffolds were fabricated with wet electrospinning, dyed with indocyanine green (ICG) for optical contrast in PAI, and implanted in the abdominal wall of 36 rats. The scaffolds were monitored monthly using USWI and PAI and were extracted at 0, 4, 8 and 12 wk for mechanical and histological assessment. The change in shear modulus of the constructs in vivo obtained by USWI correlated with the change in average Young's modulus of the constructs ex vivo obtained by compression measurements. The PEUU and PDO scaffolds exhibited distinctly different degradation rates and average PAI signal intensity. The distribution of PAI signal intensity also corresponded well to the remaining scaffolds as seen in explant histology. This evidence using a small animal abdominal wall repair model demonstrates that multi-modality imaging of USWI and PAI may allow tissue engineers to noninvasively evaluate concurrent mechanical stiffness and structural changes of tissue constructs in vivo for a variety of applications.

Rheology over five orders of magnitude in model hydrogels: agreement between strain-controlled rheometry, transient elastography, and supersonic shear wave imaging

Shear wave elastography helps physicians to characterize pathologies by assessing biomechanical properties of soft tissues. Compared with classical rheology, these techniques allow the quantification of the mechanical properties of tissues in the frequency range of hundreds of hertz. In this paper, ultrasound elastographic measurements and classical rheology are compared over a frequency range spanning five orders of magnitude [0.01 to 1200 Hz] to characterize model gels at multiple scales. Hybrid hydrogels were specially synthesized to get a fine tuning of the material dissipative response. Strain-controlled rheology (SCR) experiments were performed to get the elastic moduli G" and loss moduli G" from 0.01 Hz to 10 Hz and were confirmed by tensile tests. Transient elastography (TE from 50 to 400 Hz) and supersonic shear imaging (SSI from 200 to 1200 Hz) were used to characterize polymers at high frequency. Two different hydrogels were tested in the ultrasound setup with different concentration of scatterers. From low-frequency measurements, elastic moduli were extrapolated at high frequency and a very good correlation was obtained between SCR and TE and between SCR and SSI (r = 0.92 and r = 0.95, respectively). This paper demonstrates the capability of shear wave elastography to accurately image rheological properties of soft tissues, to differentiate soft elastic domains from viscous ones. It also gives new insights into soft material science because it provides a rheological tool in a high-frequency domain complementary to conventional rheometry.

Model validation for a noninvasive arterial stenosis detection problem

A current thrust in medical research is the development of a non-invasive method for detection, localization, and characterization of an arterial stenosis (a blockage or partial blockage in an artery). A method has been proposed to detect shear waves in the chest cavity which have been generated by disturbances in the blood flow resulting from a stenosis. In order to develop this methodology further, we use one-dimensional shear wave experimental data from novel acoustic phantoms to validate a corresponding viscoelastic mathematical model. We estimate model parameters which give a good fit (in a sense to be precisely defined) to the experimental data, and use asymptotic error theory to provide confidence intervals for parameter estimates. Finally, since a robust error model is necessary for accurate parameter estimates and confidence analysis, we include a comparison of absolute and relative models for measurement error.

Evaluation of fatty liver fibrosis in rabbits using real-time shear wave elastography

The aim of the present study was to detect the elastic modulus (stiffness) of the livers of rabbits with non-alcoholic and alcoholic fatty liver disease using real-time shear wave elastography (SWE), and to investigate the fibrosis development process in the formation of fatty liver. The stiffness of the fatty livers in rabbit models prepared via feeding with alcohol or a high-fat diet were measured using a real-time SWE ultrasound system and a 4-15-MHz linear array probe, and the liver stiffness was compared with the pathological staging of the disease. The stiffness of the liver was positively correlated with the degree of pathological change in fatty liver disease (P<0.01). The stiffness of the liver in the alcoholic fatty liver group was higher compared with that in the non-alcoholic fatty liver and control groups, and the stiffness in the non-alcoholic fatty liver group was higher than that in the control group (P<0.01). Real-time SWE objectively identified the trend in the changing stiffness of the liver and noninvasively detected the development of fibrosis in the progression of non-alcoholic and alcoholic fatty liver disease.

Quantitative analysis of liver fibrosis in rats with shearwave dispersion ultrasound vibrometry: comparison with dynamic mechanical analysis

Ultrasonic elastography, a non-invasive technique for assessing the elasticity properties of tissues, has shown promising results for disease diagnosis. However, biological soft tissues are viscoelastic in nature. Shearwave dispersion ultrasound vibrometry (SDUV) can simultaneously measure the elasticity and viscosity of tissue using shear wave propagation speeds at different frequencies. In this paper, the viscoelasticity of rat livers was measured quantitatively by SDUV for normal (stage F0) and fibrotic livers (stage F2). Meanwhile, an independent validation study was presented in which SDUV results were compared with those derived from dynamic mechanical analysis (DMA), which is the only mechanical test that simultaneously assesses the viscoelastic properties of tissue. Shear wave speeds were measured at frequencies of 100, 200, 300 and 400 Hz with SDUV and the storage moduli and loss moduli were measured at the frequency range of 1-40 Hz with DMA. The Voigt viscoelastic model was used in the two methods. The mean elasticity and viscosity obtained by SDUV ranged from 0.84±0.13 kPa (F0) to 1.85±0.30 kPa (F2) and from 1.12±0.11 Pa s (F0) to 1.70±0.31 Pa s (F2), respectively. The mean elasticity and viscosity derived from DMA ranged from 0.62±0.09 kPa (F0) to 1.70±0.84 kPa (F2) and from 3.38±0.32 Pa s (F0) to 4.63±1.30 Pa s (F2), respectively. Both SDUV and DMA demonstrated that the elasticity of rat livers increased from stage F0 to F2, a finding which was consistent with previous literature. However, the elasticity measurements obtained by SDUV had smaller differences than those obtained by DMA, whereas the viscosities obtained by the two methods were obviously different. We suggest that the difference could be related to factors such as tissue microstructure, the frequency range, sample size and the rheological model employed. For future work we propose some improvements in the comparative tests between SDUV and DMA, such as enlarging the harmonic frequency range of the shear wave to highlight the role of viscosity, finding an appropriate rheological model to improve the accuracy of tissue viscoelasticity estimations.

Spatial variations in Achilles tendon shear wave speed

Supersonic shear imaging (SSI) is an ultrasound imaging modality that can provide insight into tissue mechanics by measuring shear wave propagation speed, a property that depends on tissue elasticity. SSI has previously been used to characterize the increase in Achilles tendon shear wave speed that occurs with loading, an effect attributable to the strain-stiffening behavior of the tissue. However, little is known about how shear wave speed varies spatially, which is important, given the anatomical variation that occurs between the calcaneus insertion and the gastrocnemius musculotendon junction. The purpose of this study was to investigate spatial variations in shear wave speed along medial and lateral paths of the Achilles tendon for three different ankle postures: resting ankle angle (R, i.e. neutral), plantarflexed (P; R - 15°), and dorsiflexed (D; R+15°). We observed significant spatial and posture variations in tendon shear wave speed in ten healthy young adults. Shear wave speeds in the Achilles free tendon averaged 12 ± 1.2m/s in a resting position, but decreased to 7.2 ± 1.8m/s with passive plantarflexion. Distal tendon shear wave speeds often reached the maximum tracking limit (16.3m/s) of the system when the ankle was in the passively dorsiflexed posture (+15° from R). At a fixed posture, shear wave speeds decreased significantly from the free tendon to the gastrocnemius musculotendon junction, with slightly higher speeds measured on the medial side than on the lateral side. Shear wave speeds were only weakly correlated with the thickness and depth of the tendon, suggesting that the distal-to-proximal variations may reflect greater compliance in the aponeurosis relative to the free tendon. The results highlight the importance of considering both limb posture and transducer positioning when using SSI for biomechanical and clinical assessments of the Achilles tendon.

Muscle as a molecular machine for protecting joints and bones by absorbing mechanical impacts

We hypothesize that dissipation of mechanical energy of external impact to absorb mechanical shock is a fundamental function of skeletal muscle in addition to its primary function to convert chemical energy into mechanical energy. In physical systems, the common mechanism for absorbing mechanical shock is achieved with the use of both elastic and viscous elements and we hypothesize that the viscosity of the skeletal muscle is a variable parameter which can be voluntarily controlled by changing the tension of the contracting muscle. We further hypothesize that an ability of muscle to absorb shock has been an important factor in biological evolution, allowing the life to move from the ocean to land, from hydrodynamic to aerodynamic environment with dramatically different loading conditions for musculoskeletal system. The ability of muscle to redistribute the energy of mechanical shock in time and space and unload skeletal joints is of key importance in physical activities. We developed a mathematical model explaining the absorption of mechanical shock energy due to the increased viscosity of contracting skeletal muscles. The developed model, based on the classical theory of sliding filaments, demonstrates that the increased muscle viscosity is a result of the time delay (or phase shift) between the mechanical impact and the attachment/detachment of myosin heads to binding sites on the actin filaments. The increase in the contracted muscle's viscosity is time dependent. Since the forward and backward rate constants for binding the myosin heads to the actin filaments are on the order of 100s(-1), the viscosity of the contracted muscle starts to significantly increase with an impact time greater than 0.01s. The impact time is one of the key parameters in generating destructive stress in the colliding objects. In order to successfully dampen a short high power impact, muscles must first slow it down to engage the molecular mechanism of muscle viscosity. Muscle carries out two functions, acting first as a nonlinear spring to slow down impact and second as a viscous damper to absorb the impact. Exploring the ability of muscle to absorb mechanical shock may shed light to many problems of medical biomechanics and sports medicine. Currently there are no clinical devices for real-time quantitative assessment of viscoelastic properties of contracting muscles in vivo. Such assessment may be important for diagnosis and monitoring of treatment of various muscle disorders such as muscle dystrophy, motor neuron diseases, inflammatory and metabolic myopathies and many more.

Corneal biomechanical properties in different ocular conditions and new measurement techniques

Several refractive and therapeutic treatments as well as several ocular or systemic diseases might induce changes in the mechanical resistance of the cornea. Furthermore, intraocular pressure measurement, one of the most used clinical tools, is also highly dependent on this characteristic. Corneal biomechanical properties can be measured now in the clinical setting with different instruments. In the present work, we review the potential role of the biomechanical properties of the cornea in different fields of ophthalmology and visual science in light of the definitions of the fundamental properties of matter and the results obtained from the different instruments available. The body of literature published so far provides an insight into how the corneal mechanical properties change in different sight-threatening ocular conditions and after different surgical procedures. The future in this field is very promising with several new technologies being applied to the analysis of the corneal biomechanical properties.

An efficient block matching and spectral shift estimation algorithm with applications to ultrasound elastography

An efficient block matching and spectral shift estimation algorithm for freehand quasi-static ultrasound elastography is described in this paper. The proposed method provides a balance between computational speed and robustness against displacement estimation error and bias; a fundamental aspect of elastography. The new algorithm was tested on an extensive set of simulated 1-D RF ultrasound signals, replicating various strain profiles. Additionally, real 2-D scans were conducted on an ultrasound phantom with prescribed elastic properties; the algorithm output was further validated with a comparison to a finite element model (FEM) of the phantom. Clinical data from a breast cancer study and histology slides were used to demonstrate the in vivo use of the new elastography technique. The algorithm showed a significant computational savings (at least 60 times faster) over existing spectral shift analysis methods. Accurate strain images were produced in as little as 2 s with the scope for further speed enhancements through parallel processing; making real-time implementation a future possibility. Moreover, it demonstrated a robustness toward displacement estimation error when compared with conventional gradient-based techniques, and was able to perform at high strain values (>5%) while showing relative insensitivity to various parameters settings, such as sample rate and block window size; a desirable performance for a practical clinical tool.

Rheological assessment of a polymeric spherical structure using a three-dimensional shear wave scattering model in dynamic spectroscopy elastography

With the purpose of assessing localized rheological behavior of pathological tissues using ultrasound dynamic elastography, an analytical shear wave scattering model was used in an inverse problem framework. The proposed method was adopted to estimate the complex shear modulus of viscoelastic spheres from 200 to 450 Hz. The inverse problem was formulated and solved in the frequency domain, allowing assessment of the complex viscoelastic shear modulus at discrete frequencies. A representative rheological model of the spherical obstacle was determined by comparing storage and loss modulus behaviors with Kelvin-Voigt, Maxwell, Zener, and Jeffrey models. The proposed inversion method was validated by using an external vibrating source and acoustic radiation force. The estimation of viscoelastic properties of three-dimensional spheres made softer or harder than surrounding tissues did not require a priori rheological assumptions. The proposed method is intended to be applied in the context of breast cancer imaging.

Reconstructing 3-D maps of the local viscoelastic properties using a finite-amplitude modulated radiation force

A modulated acoustic radiation force, produced by two confocal tone-burst ultrasound beams of slightly different frequencies (i.e. 2.0 MHz ± Δf/2, where Δf is the difference frequency), can be used to remotely generate modulated low-frequency (Δf ≤ 500 Hz) shear waves in attenuating media. By appropriately selecting the duration of the two beams, the energy of the generated shear waves can be concentrated around the difference frequency (i.e., Δf ± Δf/2). In this manner, neither their amplitude nor their phase information is distorted by frequency-dependent effects, thereby, enabling a more accurate reconstruction of the viscoelastic properties. Assuming a Voigt viscoelastic model, this paper describes the use of a finite-element-method model to simulate three-dimensional (3-D) shear-wave propagation in viscoelastic media containing a spherical inclusion. Nonlinear propagation is assumed for the two ultrasound beams, so that higher harmonics are developed in the force and shear spectrum. Finally, an inverse reconstruction algorithm is used to extract 3-D maps of the local shear modulus and viscosity from the simulated shear-displacement fields based on the fundamental and second-harmonic component. The quality of the reconstructed maps is evaluated using the contrast between the inclusion and the background and the contrast-to-noise ratio (CNR). It is shown that the shear modulus can be accurately reconstructed based on the fundamental component, such that the observed contrast deviates from the true contrast by a root-mean-square-error (RMSE) of only 0.38 and the CNR is greater than 30 dB. If the second-harmonic component is used, the RMSE becomes 1.54 and the corresponding CNR decreases by approximately 10-15 dB. The reconstructed shear viscosity maps based on the second harmonic are shown to be of higher quality than those based on the fundamental. The effects of noise are also investigated and a fusion operation between the two spectral components is applied to enhance the reconstruction quality. Finally, a modified shear-wave spectroscopy technique, shown to be more robust to noise, is described for the estimation of the viscoelastic properties inside and outside the spherical inclusion under conditions of increased noise.

In vivo evaluation of the elastic anisotropy of the human Achilles tendon using shear wave dispersion analysis

Non-invasive evaluation of the Achilles tendon elastic properties may enhance diagnosis of tendon injury and the assessment of recovery treatments. Shear wave elastography has shown to be a powerful tool to estimate tissue mechanical properties. However, its applicability to quantitatively evaluate tendon stiffness is limited by the understanding of the physics on the shear wave propagation in such a complex medium. First, tendon tissue is transverse isotropic. Second, tendons are characterized by a marked stiffness in the 400 to 1300 kPa range (i.e. fast shear waves). Hence, the shear wavelengths are greater than the tendon thickness leading to guided wave propagation. Thus, to better understand shear wave propagation in tendons and consequently to properly estimate its mechanical properties, a dispersion analysis is required. In this study, shear wave velocity dispersion was measured in vivo in ten Achilles tendons parallel and perpendicular to the tendon fibre orientation. By modelling the tendon as a transverse isotropic viscoelastic plate immersed in fluid it was possible to fully describe the experimental data (deviation<1.4%). We show that parallel to fibres the shear wave velocity dispersion is not influenced by viscosity, while it is perpendicularly to fibres. Elasticity (found to be in the range from 473 to 1537 kPa) and viscosity (found to be in the range from 1.7 to 4 Pa.s) values were retrieved from the model in good agreement with reported results.

Shear wave pulse compression for dynamic elastography using phase-sensitive optical coherence tomography

Assessing the biomechanical properties of soft tissue provides clinically valuable information to supplement conventional structural imaging. In the previous studies, we introduced a dynamic elastography technique based on phase-sensitive optical coherence tomography (PhS-OCT) to characterize submillimetric structures such as skin layers or ocular tissues. Here, we propose to implement a pulse compression technique for shear wave elastography. We performed shear wave pulse compression in tissue-mimicking phantoms. Using a mechanical actuator to generate broadband frequency-modulated vibrations (1 to 5 kHz), induced displacements were detected at an equivalent frame rate of 47 kHz using a PhS-OCT. The recorded signal was digitally compressed to a broadband pulse. Stiffness maps were then reconstructed from spatially localized estimates of the local shear wave speed. We demonstrate that a simple pulse compression scheme can increase shear wave detection signal-to-noise ratio (>12  dB gain) and reduce artifacts in reconstructing stiffness maps of heterogeneous media.