On Lamb and Rayleigh wave convergence in viscoelastic tissues

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.

Adjacent tissues modulate shear wave propagation in axially loaded tendons

Shear wave tensiometry is a noninvasive approach for gauging tendon loads based on shear wave speed. Transient shear waves are induced and tracked via sensors secured to the skin overlying a superficial tendon. Wave speeds measured in vivo via tensiometry modulate with tendon load but are lower than that predicted by a tensioned beam model of an isolated tendon, which may be due to the added inertia of adjacent tissues. The objective of this study was to investigate the effects of adjacent fat tissue on shear wave propagation measurements in axially loaded tendons. We created a layered, dynamic finite element model of an elliptical tendon surrounded by subcutaneous fat. Transient shear waves were generated via an impulsive excitation delivered across the tendon or through the subcutaneous fat. The layered models demonstrated dispersive behavior with phase velocity increasing with frequency. Group shear wave speed could be ascertained via dispersion analysis or time-to-peak measures at sequential spatial locations. Simulated wave speeds in the tendon and adjacent fat were similar and modulated with tendon loading. However, wave speed magnitudes were consistently lower in the layered models than in an isolated tendon. For all models, the wave speed-stress relationship was well described by a tensioned beam model after accounting for the added inertia of the adjacent tissues. These results support the premise that externally excited shear waves are measurable in subcutaneous fat and modulate with axial loading in the underlying tendon. The model suggests that adjacent tissues add inertia to the system, which in turn lowers shear wave speeds. This information must be considered when using tensiometry as a clinical or research tool to infer absolute tendon loading.

The lens capsule significantly affects the viscoelastic properties of the lens as quantified by optical coherence elastography

The crystalline lens is a transparent, biconvex structure that has its curvature and refractive power modulated to focus light onto the retina. This intrinsic morphological adjustment of the lens to fulfill changing visual demands is achieved by the coordinated interaction between the lens and its suspension system, which includes the lens capsule. Thus, characterizing the influence of the lens capsule on the whole lens’s biomechanical properties is important for understanding the physiological process of accommodation and early diagnosis and treatment of lenticular diseases. In this study, we assessed the viscoelastic properties of the lens using phase-sensitive optical coherence elastography (PhS-OCE) coupled with acoustic radiation force (ARF) excitation. The elastic wave propagation induced by ARF excitation, which was focused on the surface of the lens, was tracked with phase-sensitive optical coherence tomography. Experiments were conducted on eight freshly excised porcine lenses before and after the capsular bag was dissected away. Results showed that the group velocity of the surface elastic wave, V, in the lens with the capsule intact (V=2.55±0.23 m/s) was significantly higher (p < 0.001) than after the capsule was removed (V=1.19±0.25 m/s). Similarly, the viscoelastic assessment using a model that utilizes the dispersion of a surface wave showed that both Young’s modulus, E, and shear viscosity coefficient, η, of the encapsulated lens (E=8.14±1.10 kPa,η=0.89±0.093 Pa∙s) were significantly higher than that of the decapsulated lens (E=3.10±0.43 kPa,η=0.28±0.021 Pa∙s). These findings, together with the geometrical change upon removal of the capsule, indicate that the capsule plays a critical role in determining the viscoelastic properties of the crystalline lens.

In Vivo Evaluation of the Effects of SMILE with Different Amounts of Stromal Ablation on Corneal Biomechanics by Optical Coherence Elastography

This work aims to depth-resolved quantitatively analyze the effect of different stromal ablation amounts on the corneal biomechanical properties during small incision lenticule extraction (SMILE) using optical coherence elastography (OCE). A 4.5-MHz ultrasonic transducer was used to excite elastic waves in the corneal tissue. The OCE system combined with the antisymmetric Lamb wave model was employed to achieve a high-resolution, high-sensitivity, and depth-resolved quantitative detection of the corneal Young's modulus. Eighteen rabbits were randomly divided into three groups; each group had six rabbits. The first and second groups underwent -3D and -6D SMILE surgeries, and the third group was the control group, respectively. Young's modulus of the corneal cap and residual stromal bed (RSB) were both increased after SMILE, which shared the stress under intraocular pressure (IOP). Furthermore, the Young's modulus of both the corneal cap and RSB after 3D SMILE group were significantly lower than that in the -6D group, which indicated that the increases in the post-operative corneal Young's modulus were positively correlated with the amount of stromal ablation. The OCE system for quantitative spatial characterization of corneal biomechanical properties can provide useful information on the extent of safe ablation for SMILE procedures.

Viscoelasticity assessment of tumoral skin with the use of a novel contact-free palpation methodology based upon surface waves

The ensuing pilot investigation sheds new light on characterizing tumoral and non-tumoral human skin mechanical properties that will not only assist the dermatologist's diagnosis but also could constitute the creation of an Artificial Intelligence database for upcoming research. A modern, non-invasive, and contact-free methodology-UNDERSKIN-was developed, and hinges upon Fourier transform computations that permit the analysis of surface wave dispersion with a specific skin inversion model and viscoelastic model. It yields a detailed look at how particle movements of the medium propagate throughout its near sub-surface, hence a novel knowledge of the mechanical responses of skin tumors. The research results display the tumors' viscoelastic responses alongside their respective healthy skin outcomes for each skin layer as well as the dermatologist's touch analysis. Although dermatologists are capable of sensing and having a fair overall assessment of what they are palpating, they are unable heretofore to quantify it and inform where the firmness or softness derives from, which it is necessary to be acquainted with so as to perform an accurate diagnosis, prognosis, treatment, future surgery, and teledermatology.

Longitudinal assessment of the effect of alkali burns on corneal biomechanical properties using optical coherence elastography

Eye injury due to alkali burn is a severe ocular trauma that can profoundly affect corneal structure and function, including its biomechanical properties. Here, we assess the changes in the mechanical behavior of mouse corneas in response to alkali-induced injury by conducting longitudinal measurements using optical coherence elastography (OCE). A non-contact air-coupled ultrasound transducer was used to induce elastic waves in control and alkali-injured mouse corneas in vivo, which were imaged with phase-sensitive optical coherence tomography. Corneal mechanical properties were estimated using a modified Rayleigh-Lamb wave model, and results show that Young's modulus of alkali-burned corneas were significantly greater than that of their healthy counterparts on days 7 (p = 0.029) and 14 (p = 0.026) after injury. These findings, together with the changes in the shear viscosity coefficient postburn, indicate that the mechanical properties of the alkali-burned cornea are significantly modulated during the wound healing process.

High-Frequency Ultrasound Elastography for Assessing Elastic Properties of Skin and Scars

Scars are a type of fibrous tissue that typically forms during the wound healing process to replace damaged skin. Because studies have indicated a high correlation between scar stiffness and clinical symptoms, assessing the mechanical properties of scar is crucial for determining an appropriate treatment strategy and evaluating the treatment's efficacy. Shear wave elastography (SWE) is a common technique for measuring tissue elasticity. Because scars are typically a few millimeters thick, they are thin-layer tissues, and therefore, the dispersion effect must be considered to accurately estimate their elasticity. In this study, high-frequency ultrasound (HFUS) elastography was proposed for estimating the elastic properties of scars by using the Lamb wave model (LWM). An external vibrator was used to generate elastic waves in scar tissue and skin, and the propagation of the elastic waves was tracked through 40-MHz ultrafast ultrasound imaging. The elasticity was estimated through shear wave models (SWMs) and LWMs. The effectiveness of using HFUS elastography was verified through phantom and human studies. The phantom experiments involved bulk phantoms with gelatin concentrations of 7% and 15% and 2-4-mm-thick thin-layer 15% gelatin phantoms. The studies of three patients with eight cases of scarring were also conducted. The phantom experimental results demonstrated that the elasticity estimation biases for the thin-layer mediums were approximately -36% to -50% and 3% to -9% in the SWMs and LWMs, respectively, and the estimated shear moduli were 12.8 ± 5.4 kPa and 74.8 ± 26.8 kPa for healthy skin and scar tissue, respectively. All the results demonstrated that the proposed HFUS elastography has a great potential for improving the accuracy of elasticity estimations in clinical dermatological diagnoses.

Soft elastomers: A playground for guided waves

Mechanical waves propagating in soft materials play an important role in physiology. They can be natural, such as the cochlear wave in the inner ear of mammalians, or controlled, such as in elastography in the context of medical imaging. In a recent study, Lanoy, Lemoult, Eddi, and Prada [Proc. Natl. Acad. Sci. U.S.A. 117(48), 30186-30190 (2020)] implemented an experimental tabletop platform that allows direct observation of in-plane guided waves in a soft strip. Here, a detailed description of the setup and signal processing steps is presented as well as the theoretical framework supporting them. One motivation is to propose a tutorial experiment for visualizing the propagation of guided elastic waves. Last, the versatility of the experimental platform is exploited to illustrate experimentally original features of wave physics, such as backward modes, stationary modes, and Dirac cones.

Wave-based optical coherence elastography: The 10-year perspective

After 10 years of progress and innovation, optical coherence elastography (OCE) based on the propagation of mechanical waves has become one of the major and the most studied OCE branches, producing a fundamental impact in the quantitative and nondestructive biomechanical characterization of tissues. Preceding previous progress made in ultrasound and magnetic resonance elastography; wave-based OCE has pushed to the limit the advance of three major pillars: (1) implementation of novel wave excitation methods in tissues, (2) understanding new types of mechanical waves in complex boundary conditions by proposing advance analytical and numerical models, and (3) the development of novel estimators capable of retrieving quantitative 2D/3D biomechanical information of tissues. This remarkable progress promoted a major advance in answering basic science questions and the improvement of medical disease diagnosis and treatment monitoring in several types of tissues leading, ultimately, to the first attempts of clinical trials and translational research aiming to have wave-based OCE working in clinical environments. This paper summarizes the fundamental up-to-date principles and categories of wave-based OCE, revises the timeline and the state-of-the-art techniques and applications lying in those categories, and concludes with a discussion on the current challenges and future directions, including clinical translation research.

Quantitative ultrasound imaging of soft biological tissues: a primer for radiologists and medical physicists

Quantitative ultrasound (QUS) aims at quantifying interactions between ultrasound and biological tissues. QUS techniques extract fundamental physical properties of tissues based on interactions between ultrasound waves and tissue microstructure. These techniques provide quantitative information on sub-resolution properties that are not visible on grayscale (B-mode) imaging. Quantitative data may be represented either as a global measurement or as parametric maps overlaid on B-mode images. Recently, major ultrasound manufacturers have released speed of sound, attenuation, and backscatter packages for tissue characterization and imaging. Established and emerging clinical applications are currently limited and include liver fibrosis staging, liver steatosis grading, and breast cancer characterization. On the other hand, most biological tissues have been studied using experimental QUS methods, and quantitative datasets are available in the literature. This educational review addresses the general topic of biological soft tissue characterization using QUS, with a focus on disseminating technical concepts for clinicians and specialized QUS materials for medical physicists. Advanced but simplified technical descriptions are also provided in separate subsections identified as such. To understand QUS methods, this article reviews types of ultrasound waves, basic concepts of ultrasound wave propagation, ultrasound image formation, point spread function, constructive and destructive wave interferences, radiofrequency data processing, and a summary of different imaging modes. For each major QUS technique, topics include: concept, illustrations, clinical examples, pitfalls, and future directions.

High Frequency Ultrasound Elastography for Estimating the Viscoelastic Properties of the Cornea Using Lamb Wave Model

OBJECTIVE

Estimating the elasticity distribution in the cornea is important because corneal elasticity is usually influenced by corneal pathologies and surgical treatments, especially for early corneal sclerosis. Because the thickness of the cornea is typically less than 1 mm, high-resolution ultrasound elastography as well as the Lamb wave model is required for viscoelastic property estimation. In the present study, an array high-frequency ultrasound (HFUS) elastography method based on ultrafast ultrasound imaging was proposed for estimating the viscoelastic properties of porcine cornea.

METHODS

The elastic wave was generated by an external vibrator, after which the wave propagation image was obtained using a 40-MHz array transducer. Viscoelasticity estimation was performed by fitting the phase velocity curve using the Lamb wave model. The performance of the proposed HFUS elastography system was verified using 2-mm-thick thin-layer gelatin phantoms with gelatin concentrations of 7% and 12%. Ex vivo experiments were carried out using fresh porcine cornea with artificial sclerosing.

RESULTS

Experimental results showed that the estimated elasticity was close to the standard value obtained in the phantom study when the Lamb wave model was used for elasticity measurement. However, the error between the standard elasticity values and the elasticity values estimated using group shear wave velocity was large. In the ex vivo eyeball experiments, the estimated elasticities and viscosities were respectively 9.1 ± 1.3 kPa and 0.5 ± 0.10 Pa·s for a healthy cornea and respectively 15.9 ± 2.1 kPa and 1.1 ± 0.12 Pa·s for a cornea with artificial sclerosis. A 3D HFUS elastography was also obtained for distinguishing the region of sclerosis in the cornea.

CONCLUSION

The experimental results demonstrated that the proposed HFUS elastography method has high potential for the clinical diagnosis of corneal diseases compared with other HFUS single-element transducer elastography systems.

Parasternal Versus Apical View in Cardiac Natural Mechanical Wave Speed Measurements

Shear wave speed measurements can potentially be used to noninvasively measure myocardial stiffness to assess the myocardial function. Several studies showed the feasibility of tracking natural mechanical waves induced by aortic valve closure in the interventricular septum, but different echocardiographic views have been used. This article systematically studied the wave propagation speeds measured in a parasternal long-axis and in an apical four-chamber view in ten healthy volunteers. The apical and parasternal views are predominantly sensitive to longitudinal or transversal tissue motion, respectively, and could, therefore, theoretically measure the speed of different wave modes. We found higher propagation speeds in apical than in the parasternal view (median of 5.1 m/s versus 3.8 m/s, , n = 9 ). The results in the different views were not correlated ( r = 0.26 , p = 0.49 ) and an unexpectedly large variability among healthy volunteers was found in apical view compared with the parasternal view (3.5-8.7 versus 3.2-4.3 m/s, respectively). Complementary finite element simulations of Lamb waves in an elastic plate showed that different propagation speeds can be measured for different particle motion components when different wave modes are induced simultaneously. The in vivo results cannot be fully explained with the theory of Lamb wave modes. Nonetheless, the results suggest that the parasternal long-axis view is a more suitable candidate for clinical diagnosis due to the lower variability in wave speeds.

Multimodal quantitative optical elastography of the crystalline lens with optical coherence elastography and Brillouin microscopy

Assessing the biomechanical properties of the crystalline lens can provide crucial information for diagnosing disease and guiding precision therapeutic interventions. Existing noninvasive methods have been limited to global measurements. Here, we demonstrate the quantitative assessment of the elasticity of crystalline lens with a multimodal optical elastography technique, which combines dynamic wave-based optical coherence elastography (OCE) and Brillouin microscopy to overcome the drawbacks of individual modalities. OCE can provide direct measurements of tissue elasticity rapidly and quantitatively, but it is a challenge to image transparent samples such as the lens because this technique relies on backscattered light. On the other hand, Brillouin microscopy can map the longitudinal modulus with micro-scale resolution in transparent samples. However, the relationship between Brillouin-deduced modulus and Young's modulus is not straightforward and sample dependent. By combining these two techniques, we can calibrate Brillouin measurements with OCE, based on the same sample, allowing us to completely map the Young's modulus of the crystalline lens. The combined system was first validated with tissue-mimicking gelatin phantoms of varying elasticities (N = 9). The OCE data was used to calibrate the Brillouin shift measurements and subsequently map the Young's modulus of the phantoms. After validation, OCE and Brillouin measurements were performed on ex-vivo porcine lenses (N = 6), and the Young's modulus of the lenses was spatially mapped. The results show a strong correlation between Young's moduli measured by OCE and longitudinal moduli measured by Brillouin microscopy. The correlation coefficient R was 0.98 for the phantoms and 0.94 for the lenses, respectively. The mean Young's modulus of the anterior and posterior lens was 1.98 ± 0.74 kPa and 2.93 ± 1.13 kPa, respectively, and the Young's modulus of the lens nucleus was 11.90 ± 2.94 kPa. The results presented in this manuscript open a new way for truly quantitative biomechanical mapping of optically transparent (or low scattering) tissues in 3D.

Reverberant 3D optical coherence elastography maps the elasticity of individual corneal layers

The elasticity mapping of individual layers in the cornea using non-destructive elastography techniques advances diagnosis and monitoring of ocular diseases and treatments in ophthalmology. However, transient Lamb waves, currently used in most dynamic optical coherence and ultrasound elastography techniques, diminish the translation of wave speed into shear/Young’s modulus. Here, we present reverberant 3D optical coherence elastography (Rev3D-OCE), a novel approach leveraging the physical properties of diffuse fields in detecting elasticity gradients not only in the lateral direction, but also along the depth axis of the cornea. A Monte Carlo analysis, finite element simulations, and experiments in layered phantoms are conducted to validate the technique and to characterize the axial elastography resolution. Experiments in ex vivo porcine cornea at different intraocular pressures reveal that Rev3D-OCE enables the elastic characterization of single layers that matches the anatomical description of corneal layers with unprecedented contrast in the dynamic OCE field.

Elastic mapping of individual layers of the cornea with elastography uses Lamb waves, which are dependent on the thickness of each layer and the direction of propagation. Here the authors present Reverberant 3D Optical Coherence Elastography to measure elasticity of single layers using waves propagating in all directions.

Two Point Method For Robust Shear Wave Phase Velocity Dispersion Estimation of Viscoelastic Materials

Ultrasound shear wave elastography (SWE) is an imaging modality used for noninvasive, quantitative evaluation of tissue mechanical properties. SWE uses an acoustic radiation force to produce laterally propagating shear waves that can be tracked in spatial and temporal domains in order to obtain the wave velocity. One of the ways to study the viscoelasticity is through examining the shear wave velocity dispersion curves. In this paper, we present an alternative method to two-dimensional Fourier transform (2D-FT). Our unique approach (2P-CWT) considers shear wave propagation measured in two lateral locations only and uses wavelet transformation analysis. We used the complex Morlet wavelet function as the mother wavelet to filter two shear waves at different locations. We examined how the first signal position and the distance between the two locations affect the shear wave velocity dispersion estimation in 2P-CWT. We tested this new method on a digital phantom data created using the local interaction simulation approach (LISA) in viscoelastic media with and without added white Gaussian noise to the wave motion. Moreover, we tested data acquired from custom made tissue mimicking viscoelastic phantom experiments and ex vivo porcine liver measurements. We compared results from 2P-CWT with the 2D-FT technique. 2P-CWT provided dispersion curves estimation with lower errors over a wider frequency band in comparison to 2D-FT. Tests conducted showed that the two-point technique gives results with better accuracy in simulation results and can be used to measure phase velocity of viscoelastic materials.

Natural Shear Wave Imaging in the Human Heart: Normal Values, Feasibility, and Reproducibility

Left ventricular myocardial stiffness could offer superior quantification of cardiac systolic and diastolic function when compared to the current diagnostic tools. Shear wave elastography in combination with acoustic radiation force has been widely proposed to noninvasively assess tissue stiffness. Interestingly, shear waves can also result from intrinsic cardiac mechanical events (e.g., closure of valves) without the need for external excitation. However, it remains unknown whether these natural shear waves always occur, how reproducible they can be detected and what the normal range of shear wave propagation speed is. The present study, therefore, aimed at establishing the feasibility of detecting shear waves created after mitral valve closure (MVC) and aortic valve closure (AVC), the variability of the measurements, and at reporting the normal values of propagation velocity. Hereto, a group of 30 healthy volunteers was scanned with high-frame rate imaging (>1000 Hz) using an experimental ultrasound system transmitting a diverging wave sequence. Tissue Doppler velocity and acceleration were used to create septal color M-modes, on which the shear waves were tracked and their velocities measured. Overall, the methodology was capable of detecting the transient vibrations that spread throughout the intraventricular septum in response to the closure of the cardiac valves in 92% of the recordings. Reference velocities of 3.2±0.6 m/s at MVC and 3.5±0.6 m/s at AVC were obtained. Moreover, in order to show the diagnostic potential of this approach, two patients (one with cardiac amyloidosis and one undergoing a dobutamine stress echocardiography) were scanned with the same protocol and showed markedly higher propagation speeds: the former presented velocities of 6.6 and 5.6 m/s; the latter revealed normal propagation velocities at baseline, and largely increased during the dobutamine infusion (>15 m/s). Both cases showed values consistent with the expected changes in stiffness and cardiac loading conditions.

Feasibility study of using the dispersion of surface acoustic wave impulse for viscoelasticity characterization in tissue mimicking phantoms

The aim of this study was to investigate the feasibility of utilizing the phase velocity dispersion of impulse surface acoustic wave (SAW) for viscoelasticity characterization of soft materials. The focused ultrasound transducer and the phase-sensitive optical coherence tomography were applied as the impulse SAW inducer and tracker, respectively. Three types of liquid-paraffin-based cream-in-agar phantoms were tested. Phase velocity dispersion curve was extracted using a Fourier transform-based phase velocity analysis algorithm. Viscoelastic parameters were obtained by fitting the dispersion curve of SAW into Rayleigh wave dispersion equation. The estimated viscoelasticity was compared with that from spherical indenter, ramp-hold relaxation testing for validation. Both results show an increasing trend in the elasticity and decreasing trend in the viscosity with the concentration of liquid-paraffin-based cream increasing in the samples. The proposed method has the capability of evaluating the viscoelastic properties of homogeneous soft tissue. By combining viscoelastic parameters estimated from the proposed method, the dispersive SAW-impulse-based viscosity-compensated elastography could be further developed.

High-Resolution Shear Wave Imaging of the Human Cornea Using a Dual-Element Transducer

Estimating the corneal elasticity can provide valuable information for corneal pathologies and treatments. Ophthalmologic pathologies will invariably cause changes to the elasticity of the cornea. For example, keratoconus and the phototoxic effects of ultraviolet radiation usually increase the corneal elasticity. This makes a quantitative estimation of the elasticity of the human cornea important for ophthalmic diagnoses. The present study investigated the use of a proposed high-resolution shear wave imaging (HR-SWI) method based on a dual-element transducer (comprising an 8-MHz element for pushing and a 32-MHz element for imaging) for measuring the group shear wave velocity (GSWV) of the human cornea. An empirical Young’s modulus formula was used to accurately convert the GSWV to Young’s modulus. Four quantitative parameters, bias, resolution, contrast, and contrast-to-noise ratio (CNR), were measured in gelatin phantoms with two different concentrations (3% and 7%) to evaluate the performance of HR-SWI. The biases of gelatin phantoms (3% and 7%) were 5.88% and 0.78%, respectively. The contrast and CNR were 0.76, 1.31 and 3.22, 2.43 for the two-side and two-layer phantoms, respectively. The measured image resolutions of HR-SWI in the lateral and axial directions were 72 and 140 μm, respectively. The calculated phase SWV (PSWV) and their corresponding Young’s modulus from six human donors were 2.45 ± 0.48 m/s (1600 Hz) and 11.52 ± 7.81 kPa, respectively. All the experimental results validated the concept of HR-SWI and its ability for measuring the human corneal elasticity.

In Vivo Open- and Closed-chest Measurements of Left-Ventricular Myocardial Viscoelasticity using Lamb wave Dispersion Ultrasound Vibrometry (LDUV): A Feasibility Study

Diastolic dysfunction causes close to half of congestive heart failures and is associated with increased stiffness in left-ventricular myocardium. A clinical tool capable of measuring viscoelasticity of the myocardium could be beneficial in clinical settings. We used Lamb wave Dispersion Ultrasound Vibrometry (LDUV) for assessing the feasibility of making in vivo non-invasive measurements of myocardial elasticity and viscosity in pigs. In vivo open-chest measurements of myocardial elasticity and viscosity obtained using a Fourier space based analysis of Lamb wave dispersion are reported. The approach was used to perform ECG-gated transthoracic in vivo measurements of group velocity, elasticity and viscosity throughout a single heart cycle. Group velocity, elasticity and viscosity in the frequency range 50-500 Hz increased from diastole to systole, consistent with contraction and relaxation of the myocardium. Systolic group velocity, elasticity and viscosity were 5.0 m/s, 19.1 kPa, 6.8 Pa·s, respectively. In diastole, the measured group velocity, elasticity and viscosity were 1.5 m/s, 5.1 kPa and 3.2 Pa·s, respectively.

Quantitative Assessment of Thin-Layer Tissue Viscoelastic Properties Using Ultrasonic Micro-Elastography With Lamb Wave Model

Characterizing the viscoelastic properties of thin-layer tissues with micro-level thickness has long remained challenging. Recently, several micro-elastography techniques have been developed to improve the spatial resolution. However, most of these techniques have not considered the medium boundary conditions when evaluating the viscoelastic properties of thin-layer tissues such as arteries and corneas; this might lead to estimation bias or errors. This paper aims to integrate the Lamb wave model with our previously developed ultrasonic micro-elastography imaging system for obtaining accurate viscoelastic properties in thin-layer tissues. A 4.5-MHz ring transducer was used to generate an acoustic radiation force for inducing tissue displacements to produce guided wave, and the wave propagation was detected using a confocally aligned 40-MHz needle transducer. The phase velocity and attenuation were obtained from k-space by both the impulse and the harmonic methods. The measured phase velocity was fit using the Lamb wave model with the Kelvin-Voigt model. Phantom experiments were conducted using 7% and 12% gelatin and 1.5% agar phantoms with different thicknesses (2, 3, and 4 mm). Biological experiments were performed on porcine cornea and rabbit carotid artery ex vivo. Thin-layer phantoms with different thicknesses were confirmed to have the same elasticity; this was consistent with the estimates of bulk phantoms from mechanical tests and the shear wave rheological model. The trend of the measured attenuations was also confirmed with the viscosity results obtained using the Lamb wave model. Through the impulse and harmonic methods, the shear viscoelasticity values were estimated to be 8.2 kPa for $0.9~\text {Pa}{\cdot} \text {s}$ and 9.6 kPa for $0.8~\text {Pa}{\cdot} \text {s}$ in the cornea and 27.9 kPa for $0.1~\text {Pa}\cdot \text {s}$ and 26.5 kPa for $0.1~\text {Pa}\cdot \text {s}$ in the artery.

Ultrasonic Microelastography to Assess Biomechanical Properties of the Cornea

OBJECTIVE

To both qualitatively and quantitatively investigate corneal biomechanical properties through an ultrasonic microelastography imaging system, which is potentially useful in the diagnosis of diseases, such as keratoconus, postrefractive keratectasia, and tracking treatment such as cross-linking surgery.

METHODS

Our imaging system has a dual-frequency configuration, including a 4.5 MHz ring transducer to push the tissue and a confocally aligned 40 MHz needle transducer to track micron-level displacement. Two-dimensional/three-dimensional acoustic radiation force impulse (ARFI) imaging and Young's modulus in the region of interest were performed on ex vivo porcine corneas that were either cross-linked using formalin solution or preloaded with intraocular pressure (IOPs) from 5 to 30 mmHg.

RESULTS

The increase of corneal stiffness and the change in cross-linked volume following formalin crosslinking could be precisely observed in the ARFI images and reflected by the reconstructed Young's modulus while the B-mode structural images remained almost unchanged. In addition, the relationship between the stiffness of the cornea and IOPs was investigated among 12 porcine corneas. The corneal stiffness is significantly different at various IOPs and has a tendency to become stiffer with increasing IOP.

CONCLUSION

Our results demonstrate the principle of using ultrasonic microelastography techniques to image the biomechanical properties of the cornea. Integrating high-resolution ARFI imaging labeled with reconstructed Young's modulus and structural imaging of the cornea can potentially lead to a routinely performed imaging modality in the field of ophthalmology.

A 2D finite element model for shear wave propagation in biological soft tissues: Application to magnetic resonance elastography

Dynamic elastography is a virtual palpation tool that aims at investigating the mechanical response of biological soft tissues in vivo. The objective of this study is to develop a finite element model (FEM) with low computational cost for reproducing realistically wave propagation for magnetic resonance elastography in heterogeneous soft tissues. Based on the first-order shear deformation theory for moderately thick structures, this model is developed and validated through comparison with analytical formulations of wave propagating in heterogeneous, viscoelastic infinite medium. This 2D-FEM is then compared to experimental data and a 3D-FEM using a commercial software. Our FEM is a powerful promising tool for investigations of magnetic resonance elastography.

Nanobomb optical coherence elastography

Wave-based optical elastography is rapidly emerging as a powerful technique for quantifying tissue biomechanical properties due to its noninvasive nature and high displacement sensitivity. However, current approaches are limited in their ability to produce high-frequency waves and highly localized mechanical stress. In this Letter, we demonstrate that the rapid liquid-to-gas phase transition of dye-loaded perfluorocarbon nanodroplets ("nanobombs") initiated by a pulsed laser can produce highly localized, high-frequency, and broadband elastic waves. The waves were detected by an ultra-fast line-field low-coherence holography system. For comparison, we also excited waves using a focused micro-air-pulse. Results from tissue-mimicking phantoms showed that the nanobombs produced elastic waves with frequencies up to ∼9  kHz, which was much greater than the ∼2  kHz waves excited by the air-pulse. Consequently, the nanobombs enabled more accurate quantification of sample viscoelasticity. Combined with their potential for functionalization, the nanobombs show promise for accurate and highly specific noncontact all-optical elastography.

ELASTICITY MEASUREMENTS BY SHEAR WAVE ELASTOGRAPHY: COMPARISON AND SELECTION OF SHEAR WAVE, RAYLEIGH WAVE AND LAMB WAVE THEORY

Shear wave elastography (SWE) is a powerful method for the diagnosis of tissue disorders or degeneration based on tissue elasticity. In SWE application, it was recognized that the wave speed depends not only on the tissue elasticity but also on the structural shape, leading to different theoretical models. For liver, skin and myocardium, the appropriate theoretical model is known to be shear wave, Rayleigh wave and Lamb wave theory, respectively. Therefore, appropriate theoretical model should be adopted for the proper application of SWE. In this study, we verify these theoretical models in gelatin samples of different thicknesses, using experimental and numerical SWE tests. The results indicate that the wave speed was influenced by the ratio of the wavelength and sample thickness and the measurement region. Based on these results, the selection of theoretical model could be divided into three cases, and the appropriate theoretical model can be selected accordingly.

Near field effect on elasticity measurement for cartilage-bone structure using Lamb wave method

Background

Cartilage elasticity changes with cartilage degeneration. Hence, cartilage elasticity detection might be an alternative to traditional imaging methods for the early diagnosis of osteoarthritis. Based on the wave propagation measurement, Shear wave elastography (SWE) become an emerging non-invasive elasticity detection method. The wave propagation model, which is affected by tissue shapes, is crucial for elasticity estimating in SWE. However, wave propagation model for cartilage was unclear.

Methods

This study aimed to establish a wave propagation model for the cartilage-bone structure. We fabricated a cartilage-bone structure, and studied the elasticity measurement and wave propagation by experimental and numerical Lamb wave method (LWM).

Results

Results indicated the wave propagation model satisfied the lamb wave theory for two-layered structure. Moreover, a near field region, which affects wave speed measurements and whose occurrence can be prevented if the wave frequency is larger than one critical frequency, was observed.

Conclusion

Our findings would provide a theoretical foundation for further application of LWM in elasticity measurement of cartilage in vivo. It can help the application of LWM to the diagnosis of osteoarthritis.

Cardiac Shear Wave Velocity Detection in the Porcine Heart

Cardiac muscle stiffness can potentially be estimated non-invasively with shear wave elastography. Shear waves are present on the septal wall after mitral and aortic valve closure, thus providing an opportunity to assess stiffness in early systole and early diastole. We report on the shear wave recordings of 22 minipigs with high-frame-rate echocardiography. The waves were captured with 4000 frames/s using a programmable commercial ultrasound machine. The wave pattern was extracted from the data through a local tissue velocity estimator based on one-lag autocorrelation. The wave propagation velocity was determined with a normalized Radon transform, resulting in median wave propagation velocities of 2.2 m/s after mitral valve closure and 4.2 m/s after aortic valve closure. Overall the velocities ranged between 0.8 and 6.3 m/s in a 95% confidence interval. By dispersion analysis we found that the propagation velocity only mildly increased with shear wave frequency.

Optical coherence elastography - OCT at work in tissue biomechanics [Invited]

Optical coherence elastography (OCE), as the use of OCT to perform elastography has come to be known, began in 1998, around ten years after the rest of the field of elastography - the use of imaging to deduce mechanical properties of tissues. After a slow start, the maturation of OCT technology in the early to mid 2000s has underpinned a recent acceleration in the field. With more than 20 papers published in 2015, and more than 25 in 2016, OCE is growing fast, but still small compared to the companion fields of cell mechanics research methods, and medical elastography. In this review, we describe the early developments in OCE, and the factors that led to the current acceleration. Much of our attention is on the key recent advances, with a strong emphasis on future prospects, which are exceptionally bright.

Optical coherence elastography assessment of corneal viscoelasticity with a modified Rayleigh-Lamb wave model

The biomechanical properties of the cornea play a critical role in forming vision. Diseases such as keratoconus can structurally degenerate the cornea causing a pathological loss in visual acuity. UV-A/riboflavin corneal collagen crosslinking (CXL) is a clinically available treatment to stiffen the cornea and restore its healthy shape and function. However, current CXL techniques do not account for pre-existing biomechanical properties of the cornea nor the effects of the CXL treatment itself. In addition to the inherent corneal structure, the intraocular pressure (IOP) can also dramatically affect the measured biomechanical properties of the cornea. In this work, we present the details and development of a modified Rayleigh-Lamb frequency equation model for quantifying corneal biomechanical properties. After comparison with finite element modeling, the model was utilized to quantify the viscoelasticity of in situ porcine corneas in the whole eye-globe configuration before and after CXL based on noncontact optical coherence elastography measurements. Moreover, the viscoelasticity of the untreated and CXL-treated eyes was quantified at various IOPs. The results showed that the stiffness of the cornea increased after CXL and that corneal stiffness is close to linear as a function of IOP. These results show that the modified Rayleigh-Lamb wave model can provide an accurate assessment of corneal viscoelasticity, which could be used for customized CXL therapies.

Moving-source elastic wave reconstruction for high-resolution optical coherence elastography

Optical coherence tomography (OCT)-based elasticity imaging can map soft tissue elasticity based on speckle-tracking of elastic wave propagation using highly sensitive phase measurements of OCT signals. Using a fixed elastic wave source and moving detection, current imaging sequences have difficulty in reconstructing tissue elasticity within speckle-free regions, for example, within the crystalline lens of the eye. We present a moving acoustic radiation force imaging sequence to reconstruct elastic properties within a speckle-free region by tracking elastic wave propagation from multiple laterally moving sources across the field of view. We demonstrate the proposed strategy using heterogeneous and partial speckle-free tissue-mimicking phantoms. Harder inclusions within the speckle-free region can be detected, and the contrast-to-noise ratio slightly enhanced compared to current OCE imaging sequences. The results suggest that a moving source approach may be appropriate for OCE studies within the large speckle-free regions of the crystalline lens.

Quantifying tissue viscoelasticity using optical coherence elastography and the Rayleigh wave model

This study demonstrates the feasibility of using the Rayleigh wave model (RWM) in combination with optical coherence elastography (OCE) technique to assess the viscoelasticity of soft tissues. Dispersion curves calculated from the spectral decomposition of OCE-measured air-pulse induced elastic waves were used to quantify the viscoelasticity of samples using the RWM. Validation studies were first conducted on 10% gelatin phantoms with different concentrations of oil. The results showed that the oil increased the viscosity of the gelatin phantom samples. This method was then used to quantify the viscoelasticity of chicken liver. The Young’s modulus of the chicken liver tissues was estimated as E=2.04±0.88??kPa with a shear viscosity ?=1.20±0.13??Pa?s. The analytical solution of the RWM correlated very well with the OCE-measured phased velocities (R2=0.96±0.04). The results show that the combination of the RWM and OCE is a promising method for noninvasively quantifying the biomechanical properties of soft tissues and may be a useful tool for detecting disease.

Indentation Measurements to Validate Dynamic Elasticity Imaging Methods

We describe macro-indentation techniques for estimating the elastic modulus of soft hydrogels. Our study describes (a) conditions under which quasi-static indentation can validate dynamic shear-wave imaging estimates and (b) how each of these techniques uniquely biases modulus estimates as they couple to the sample geometry. Harmonic shear waves between 25 and 400 Hz were imaged using ultrasonic Doppler and optical coherence tomography methods to estimate shear dispersion. From the shear-wave speed of sound, average elastic moduli of homogeneous samples were estimated. These results are compared directly with macroscopic indentation measurements measured two ways. One set of measurements applied Hertzian theory to the loading phase of the force-displacement curves using samples treated to minimize surface adhesion forces. A second set of measurements applied Johnson-Kendall-Roberts theory to the unloading phase of the force-displacement curve when surface adhesions were significant. All measurements were made using gelatin hydrogel samples of different sizes and concentrations. Agreement within 5% among elastic modulus estimates was achieved for a range of experimental conditions. Consequently, a simple quasi-static indentation measurement using a common gel can provide elastic modulus measurements that help validate dynamic shear-wave imaging estimates.

Investigation of the effects of myocardial anisotropy for shear wave elastography using impulsive force and harmonic vibration

The myocardium is known to be an anisotropic medium where the muscle fiber orientation changes through the thickness of the wall. Shear wave elastography methods use propagating waves which are measured by ultrasound or magnetic resonance imaging (MRI) techniques to characterize the mechanical properties of various tissues. Ultrasound- or MR-based methods have been used and the excitation frequency ranges for these various methods cover a large range from 24-500 Hz. Some of the ultrasound-based methods have been shown to be able to estimate the fiber direction. We constructed a model with layers of elastic, transversely isotropic materials that were oriented at different angles to simulate the heart wall in systole and diastole. We investigated the effect of frequency on the wave propagation and the estimation of fiber direction and wave speeds in the different layers of the assembled models. We found that waves propagating at low frequencies such as 30 or 50 Hz showed low sensitivity to the fiber direction but also had substantial bias in estimating the wave speeds in the layers. Using waves with higher frequency content (>200 Hz) allowed for more accurate fiber direction and wave speed estimation. These results have particular relevance for MR- and ultrasound-based elastography applications in the heart.

Characterization of material properties of soft solid thin layers with acoustic radiation force and wave propagation

Evaluation of tissue engineering constructs is performed by a series of different tests. In many cases it is important to match the mechanical properties of these constructs to those of native tissues. However, many mechanical testing methods are destructive in nature which increases cost for evaluation because of the need for additional samples reserved for these assessments. A wave propagation method is proposed for characterizing the shear elasticity of thin layers bounded by a rigid substrate and fluid-loading, similar to the configuration for many tissue engineering applications. An analytic wave propagation model was derived for this configuration and compared against finite element model simulations and numerical solutions from the software package Disperse. The results from the different models found very good agreement. Experiments were performed in tissue-mimicking gelatin phantoms with thicknesses of 1 and 4 mm and found that the wave propagation method could resolve the shear modulus with very good accuracy, no more than 4.10% error. This method could be used in tissue engineering applications to monitor tissue engineering construct maturation with a nondestructive wave propagation method to evaluate the shear modulus of a material.

In vivo patient measurements of bladder elasticity using Ultrasound Bladder Vibrometry (UBV)

A healthy compliant bladder is capable of storing increasing volumes of urine at low pressures. The loss of bladder compliance is associated with various diseases. The urodynamic studies (UDS), the current clinical gold standard for measuring bladder compliance, requires catheterization and measuring intra-bladder pressure as a function of filling volumes. Ultrasound Bladder Vibrometry (UBV) is a noninvasive technique that uses focused ultrasound radiation force to excite Lamb waves in the bladder wall and pulse-echo techniques to track the wave motion in tissue. Cross-spectral analysis is used to calculate the wave velocity, which is directly related to the elastic properties of the bladder wall. In this study, we compare the measurements of changes in bladder elasticity as a function of bladder pressure and volume obtained using UBV and the pressure-volume measurements obtained using UDS. UBV and UDS of an excised porcine bladder are presented. Comparative studies in neurogenic and healthy patient bladders are also summarized.

Analysis of the effects of curvature and thickness on elastic wave velocity in cornea-like structures by finite element modeling and optical coherence elastography

Wave models that have been used to extract the biomechanical properties of the cornea from the propagation of an elastic wave are based on an assumption of thin-plate geometry. However, this assumption does not account for the effects of corneal curvature and thickness. This study conducts finite element (FE) simulations on four types of cornea-like structures as well as optical coherence elastography (OCE) experiments on contact lenses and tissue-mimicking phantoms to investigate the effects of curvature and thickness on the group velocity of an elastic wave. The elastic wave velocity as determined by FE simulations and OCE of a spherical shell section decreased from ∼2.8 m/s to ∼2.2 m/s as the radius of curvature increased from 19.1 mm to 47.7 mm and increased from ∼3.0 m/s to ∼4.1 m/s as the thickness of the agar phantom increased from 1.9 mm to 5.6 mm. Both the FE simulation and OCE results confirm that the group velocity of the elastic wave decreases with radius of curvature but increases with thickness. These results demonstrate that the effects of the curvature and thickness must be considered in the further development of accurate wave models for reconstructing biomechanical properties of the cornea.

Quantitative methods for reconstructing tissue biomechanical properties in optical coherence elastography: a comparison study

We present a systematic analysis of the accuracy of five different methods for extracting the biomechanical properties of soft samples using optical coherence elastography (OCE). OCE is an emerging noninvasive technique, which allows assessment of biomechanical properties of tissues with micrometer spatial resolution. However, in order to accurately extract biomechanical properties from OCE measurements, application of a proper mechanical model is required. In this study, we utilize tissue-mimicking phantoms with controlled elastic properties and investigate the feasibilities of four available methods for reconstructing elasticity (Young's modulus) based on OCE measurements of an air-pulse induced elastic wave. The approaches are based on the shear wave equation (SWE), the surface wave equation (SuWE), Rayleigh-Lamb frequency equation (RLFE), and finite element method (FEM), Elasticity values were compared with uniaxial mechanical testing. The results show that the RLFE and the FEM are more robust in quantitatively assessing elasticity than the other simplified models. This study provides a foundation and reference for reconstructing the biomechanical properties of tissues from OCE data, which is important for the further development of noninvasive elastography methods.

Viscoelasticity of hyaluronic acid-gelatin hydrogels for vocal fold tissue engineering

Crosslinked injectable hyaluronic acid (HA)-gelatin (Ge) hydrogels have remarkable viscoelastic and biological properties for vocal fold tissue engineering. Patient-specific tuning of the viscoelastic properties of this injectable biomaterial could improve tissue regeneration. The frequency-dependent viscoelasticity of crosslinked HA-Ge hydrogels was measured as a function of the concentration of HA, Ge, and crosslinker. Synthetic extracellular matrix hydrogels were fabricated using thiol-modified HA and Ge, and crosslinked by poly(ethylene glycol) diacrylate. A recently developed characterization method based on Rayleigh wave propagation was used to quantify the frequency-dependent viscoelastic properties of these hydrogels, including shear storage and loss moduli, over a broad frequency range; that is, from 40 to 4000 Hz. The viscoelastic properties of the hydrogels increased with frequency. The storage and loss moduli values and the rate of increase with frequency varied with the concentrations of the constituents. The range of the viscoelastic properties of the hydrogels was within that of human vocal fold tissue obtained from in vivo and ex vivo measurements. Frequency-dependent parametric relations were obtained using a linear least-squares regression. The results are useful to better fine-tune the storage and loss moduli of HA-Ge hydrogels by varying the concentrations of the constituents for use in patient-specific treatments.

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.

Acoustic waves in medical imaging and diagnostics

Up until about two decades ago acoustic imaging and ultrasound imaging were synonymous. The term ultrasonography, or its abbreviated version sonography, meant an imaging modality based on the use of ultrasonic compressional bulk waves. Beginning in the 1990s, there started to emerge numerous acoustic imaging modalities based on the use of a different mode of acoustic wave: shear waves. Imaging with these waves was shown to provide very useful and very different information about the biological tissue being examined. We discuss the physical basis for the differences between these two basic modes of acoustic waves used in medical imaging and analyze the advantages associated with shear acoustic imaging. A comprehensive analysis of the range of acoustic wavelengths, velocities and frequencies that have been used in different imaging applications is presented. We discuss the potential for future shear wave imaging applications.

Rayleigh wave propagation method for the characterization of a thin layer of biomaterials

An experimental method based on Rayleigh wave propagation was developed for quantifying the frequency-dependent viscoelastic properties of a small volume of expensive biomaterials over a broad frequency range. Synthetic silicone rubber and gelatin materials were fabricated and tested to evaluate the proposed method. Planar harmonic Rayleigh waves at different frequencies, from 80 to 4000 Hz, were launched on the surface of a sample composed of a substrate with known material properties coated with a thin layer of the soft material to be characterized. A transfer function method was used to obtain the complex Rayleigh wavenumber. An inverse wave propagation problem was solved and a complex nonlinear dispersion equation was obtained. The complex shear and elastic moduli of the sample materials were then calculated through the numerical solution of the obtained dispersion equation using the measured wavenumbers. The results were in good agreement with those of a previous independent study. The proposed method was found to be reliable and cost effective for the measurement of viscoelastic properties of a thin layer of expensive biomaterials, such as phonosurgical biomaterials, over a wide frequency range.

Experimental methods for the characterization of the frequency-dependent viscoelastic properties of soft materials

A characterization method based on Rayleigh wave propagation was developed for the quantification of the frequency-dependent viscoelastic properties of soft materials at high frequencies; i.e., up to 4 kHz. Planar harmonic surface waves were produced on the surface of silicone rubber samples. The phase and amplitude of the propagating waves were measured at different locations along the propagation direction, which allowed the calculation of the complex Rayleigh wavenumbers at each excitation frequency using a transfer function method. An inverse wave propagation problem was then solved to obtain the complex shear/elastic moduli from the measured wavenumbers. In a separate, related investigation, dynamic indentation tests using atomic force microscopy (AFM) were performed at frequencies up to 300 Hz. No systematic verification study is available for the AFM-based method, which can be used when the dimensions of the test samples are too small for other existing testing methods. The results obtained from the Rayleigh wave propagation and AFM-based indentation methods were compared with those from a well-established method, which involves the generation of standing longitudinal compression waves in rod-shaped test specimens. The results were cross validated and qualitatively confirmed theoretical expectations presented in the literature for the frequency-dependence of polymers.

Ultrasound bladder vibrometry method for measuring viscoelasticity of the bladder wall

Increase in bladder stiffness could be associated with various pathophysiologic conditions. Measuring bladder viscoelasticity could be an important step towards understanding various disease processes and improving patient care. Here, we introduce ultrasound bladder vibrometry (UBV), a novel method for rapid and noninvasive measurement of bladder wall viscoelasticity. UBV uses acoustic radiation force to excite mechanical waves in the bladder wall and track the motion using ultrasound pulse-echo techniques. Fourier domain analysis of the tissue motion versus time is used to calculate the phase velocity dispersion (change of phase velocity as a function of frequency). The measured phase velocity dispersion is fit with the antisymmetric Lamb wave model to estimate tissue elasticity and viscosity. We used finite element analysis of viscoelastic plate deformation to investigate the effect of curvature on Lamb wave dispersion and showed that the effects of curvature are negligible. The feasibility of the UBV technique was demonstrated in ex vivo and in vivo settings. Elasticity and viscosity of excised pig at various filling volumes (V) and pressures (p) were found to be µ1 = 9.6 kPa and µ2 = 0.2 Pa s (V = 187 ml and p = 8.6 mmHg), µ1 = 48.7 kPa and µ2 = 3.5 Pa s (V = 267 ml and p = 17.6 mmHg), and µ1 = 106.9 kPa and µ2 = 1.5 Pa s (V = 327 ml and p = 27.6 mmHg) respectively. Transabdominal measurements in an anesthetized pig found values of bladder elasticity µ1 = 26.1 kPa and viscosity µ2 = 0.9 Pa s and demonstrate the ability of UBV to perform in vivo measurements. The results presented in this paper introduce a novel technique for measuring mechanical properties of the bladder and lay the foundation for further investigation of the effects of pathology on bladder viscoelasticity.

Measurement of viscoelastic properties of in vivo swine myocardium using lamb wave dispersion ultrasound vibrometry (LDUV)

Viscoelastic properties of the myocardium are important for normal cardiac function and may be altered by disease. Thus, quantification of these properties may aid with evaluation of the health of the heart. Lamb wave dispersion ultrasound vibrometry (LDUV) is a shear wave-based method that uses wave velocity dispersion to measure the underlying viscoelastic material properties of soft tissue with plate-like geometries. We tested this method in eight pigs in an open-chest preparation. A mechanical actuator was used to create harmonic, propagating mechanical waves in the myocardial wall. The motion was tracked using a high frame rate acquisition sequence, typically 2500 Hz. The velocities of wave propagation were measured over the 50-400 Hz frequency range in 50 Hz increments. Data were acquired over several cardiac cycles. Dispersion curves were fit with a viscoelastic, anti-symmetric Lamb wave model to obtain estimates of the shear elasticity, μ(1), and viscosity, μ(2) as defined by the Kelvin-Voigt rheological model. The sensitivity of the Lamb wave model was also studied using simulated data. We demonstrated that wave velocity measurements and Lamb wave theory allow one to estimate the variation of viscoelastic moduli of the myocardial walls in vivo throughout the course of the cardiac cycle.