Error in estimates of tissue material properties from shear wave dispersion ultrasound vibrometry

Exploring the Skin Brain Link: Biomarkers in the Skin with Implications for Aging Research and Alzheimer's Disease Diagnostics

Neurodegenerative diseases, including Alzheimer's disease (AD), are challenging to diagnose. Currently the field must rely on imperfect diagnostic modalities. A recent study identified differences in several key bio-mechano-physiological parameters of the skin between AD patients and healthy controls. Here, we visually align these differences with the relevant histological, aging, and embryological paradigms to raise awareness for these potential biomarkers. In a study conducted by Wu et al., a series of n = 41 patients (n = 29 with AD and n = 12 healthy controls) were evaluated, demonstrating that AD patients exhibit a less acidic skin pH, increased skin hydration, and reduced skin elasticity compared to healthy controls. We constructed a visual overview and explored the relevant paradigms. We present a visual comparison of these factors, highlighting four paradigms: (1) the findings emphasize a shared ectodermal origin of the brain and the skin; (2) functional systems such as micro-vascularization, innervation, eccrine excretory functions, and the extracellular matrix undergo distinct changes in patients with AD; (3) the human skin mirrors the alterations in brain stiffness observed in aging studies; (4) assessment of physiological features of the skin is cost-effective, accessible, and easily amenable for monitoring and integration with cognitive assessment studies. Understanding the relationship between aging skin and aging brain is an exciting frontier, holding great promise for improved diagnostics. Further prospective and larger-scale investigations are needed to solidify the brain-skin link and determine the extent to which this relationship can be leveraged for diagnostic applications.

Anisotropy in ultrasound shear wave elastography: An add-on to muscles characterization

Ultrasound shear wave elastography was developed the past decade, bringing new stiffness biomarker in clinical practice. This biomarker reveals to be of primarily importance for the diagnosis of breast cancer or liver fibrosis. In muscle this biomarker become much more complex due to the nature of the muscle itself: an anisotropic medium. In this manuscript we depict the underlying theory of propagating waves in such anisotropic medium. Then we present the available methods that can consider and quantify this parameter. Advantages and drawbacks are discussed to open the way to imagine new methods that can free this biomarker in a daily clinical practice.

Shear wave dispersion to assess liver disease progression in Fontan-associated liver disease

Aim

We aimed to analyze the dispersion slope (DS) using shear wave dispersion (SWD) in patients with Fontan-associated liver disease (FALD) and to investigate its utility as a biomarker of disease progression.

Methods

This cross-sectional study enrolled 27 adults with FALD who underwent SWD, two-dimensional shear wave elastography (2D-SWE), transthoracic echocardiography, cardiac catheterization, or abdominal computed tomography (CT) from April 2019 to April 2021. According to CT findings, patients were divided into two groups: significant fibrosis and non-significant fibrosis.

Results

The median DS in the control (n = 10), non-significant fibrosis (n = 12), and significant fibrosis (n = 15) was 9.35, 12.55, and 17.64 (m/s)/kHz, respectively. The significant fibrosis group showed a significantly higher DS than non-significant fibrosis group (P = 0.003). DS showed a significant correlation with central venous pressure (r = 0.532, P = 0.017) and liver stiffness measurements using 2D-SWE (r = 0.581, P = 0.002). The areas under the receiver operating characteristic curve for the diagnosis of significant fibrosis were 0.903 and 0.734 for SWD and 2D-SWE, respectively (P = 0.043).

Conclusions

DS measured by SWD reflects the severity of liver damage in patients with FALD. SWE may be valuable for the therapeutic management of patients with FALD.

Sources of Variability in Shear Wave Speed and Dispersion Quantification with Ultrasound Elastography: A Phantom Study

There is a growing interest in quantifying shear-wave dispersion (SWD) with ultrasound shear-wave elastography (SWE). Recent studies suggest that SWD complements shear-wave speed (SWS) in diffuse liver disease diagnosis. To accurately interpret these metrics in clinical practice, we analyzed the impact of operator-dependent acquisition parameters on SWD and SWS measurements. Considered parameters were the acquisition depth, lateral position and size of the region of interest (ROI), as well as the size of the SWE acquisition box. Measurements were performed using the Canon Aplio i800 system (Canon Medical Systems, Otawara, Tochigi, Japan) and four homogeneous elasticity phantoms with certified stiffness values ranging from 3.7 to 44 kPa. In general, SWD exhibited two to three times greater variability than SWS. The acquisition depth was the main variance-contributing factor for both SWS and SWD, which decayed significantly with depth. The lateral ROI position contributed as much as the acquisition depth to the total variance in SWD. Locations close to the initial shear-wave excitation pulse were more robust to biases because of inaccurate probe-phantom coupling. The size of the ROI and acquisition box did not introduce significant variations. These results suggest that future guidelines on multiparametric elastography should account for the depth- and lateral-dependent variability of measurements.

Shear wave imaging and classification using extended Kalman filter and decision tree algorithm

Shear wave ultrasound elastography is a quantitative imaging approach in soft tissues based on viscosity-elastic properties. Complex shear modulus (CSM) estimation is an effective solution to analyze tissues' physical properties for elasticity and viscosity based on the wavenumber and attenuation coefficient. CSM offers a way to detect and classify some types of soft tissues. However, CSM-based elastography inherits some obstacles, such as estimation precision and calculation complexity. This work proposes an approach for two-dimensional CSM estimation and soft tissue classification using the Extended Kalman Filter (EKF) and Decision Tree (DT) algorithm, named the EKF-DT approach. CSM estimation is obtained by applying EKF to exploit shear wave propagation at each spatial point. Afterward, the classification of tissues is done by a direct and efficient decision tree algorithm categorizing three types of normal, cirrhosis, and fibrosis liver tissues. Numerical simulation scenarios have been employed to illustrate the recovered quality and practicality of the proposed method's liver tissue classification. With the EKF, the estimated wave number and attenuation coefficient are close to the ideal values, especially the estimated wave number. The states of three liver tissue types were automatically classified by applying the DT coupled with two proposed thresholds of elasticity and viscosity: (2.310 kPa, 1.885 Pa.s) and (3.620 kPa 3.146 Pa.s), respectively. The proposed method shows the feasibility of CSM estimation based on the wavenumber and attenuation coefficient by applying the EKF. Moreover, the DT can automate the classification of liver tissue conditions by proposing two thresholds. The proposed EKF-DT method can be developed by 3D image reconstruction and empirical data before applying it in medical practice.

How muscle stiffness affects human body model behavior

BACKGROUND

Active human body models (AHBM) consider musculoskeletal movement and joint stiffness via active muscle truss elements in the finite element (FE) codes in dynamic application. In the latest models, such as THUMS™ Version 5, nearly all human muscle groups are modeled in form of one-dimensional truss elements connecting each joint. While a lot of work has been done to improve the active and passive behavior of this 1D muscle system in the past, the volumetric muscle system of THUMS was modeled in a much more simplified way based on Post Mortem Human Subject (PMHS) test data. The stiffness changing effect of isometric contraction was hardly considered for the volumetric muscle system of whole human body models so far. While previous works considered this aspect for single muscles, the effect of a change in stiffness due to isometric contraction of volumetric muscles on the AHBM behavior and computation time is yet unknown.

METHODS

In this study, a simplified frontal impact using the THUMS Version 5 AM50 occupant model was simulated. Key parameters to regulate muscle tissue stiffness of solid elements in THUMS were identified for the material model MAT_SIMPLIFIED_FOAM and different stiffness states were predefined for the buttock and thigh.

RESULTS

During frontal crash, changes in muscle stiffness had an effect on the overall AHBM behavior including expected injury outcome. Changes in muscle stiffness for the thigh and pelvis, as well as for the entire human body model and for strain-rate-dependent stiffness definitions based on literature data had no significant effect on the computation time.

DISCUSSION

Kinematics, peak impact force and stiffness changes were in general compliance with the literature data. However, different experimental setups had to be considered for comparison, as this topic has not been fully investigated experimentally in automotive applications in the past. Therefore, this study has limitations regarding validation of the frontal impact results.

CONCLUSION

Variations of default THUMS material model parameters allow an efficient change in stiffness of volumetric muscles for whole AHBM applications. The computation time is unaffected by altering muscle stiffness using the method suggested in this work. Due to a lack of validation data, the results of this work can only be validated with certain limitations. In future works, the default material models of THUMS could be replaced with recently published models to achieve a possibly more biofidelic muscle behavior, which would even allow a functional dependency of the 1D and 3D muscle systems. However, the effect on calculation time and model stability of these models is yet unknown and should be considered in future studies for efficient AHBM applications.

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

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

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

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

Towards a consensus on rheological models for elastography in soft tissues

A rising wave of technologies and instruments are enabling more labs and clinics to make a variety of measurements related to tissue viscoelastic properties. These instruments include elastography imaging scanners, rheological shear viscometers, and a variety of calibrated stress-strain analyzers. From these many sources of disparate data, a common step in analyzing results is to fit the measurements of tissue response to some viscoelastic model. In the best scenario, this places the measurements within a theoretical framework and enables meaningful comparisons of the parameters against other types of tissues. However, there is a large set of established rheological models, even within the class of linear, causal, viscoelastic solid models, so which of these should be chosen? Is it simply a matter of best fit to a minimum mean squared error of the model to several data points? We argue that the long history of biomechanics, including the concept of the extended relaxation spectrum, along with data collected from viscoelastic soft tissues over an extended range of times and frequencies, and the theoretical framework of multiple relaxation models which model the multi-scale nature of physical tissues, all lead to the conclusion that fractional derivative models represent the most succinct and meaningful models of soft tissue viscoelastic behavior. These arguments are presented with the goal of clarifying some distinctions between, and consequences of, some of the most commonly used models, and with the longer term goal of reaching a consensus among different sub-fields in acoustics, biomechanics, and elastography that have common interests in comparing tissue measurements.

Viscoelasticity in natural tissues and engineered scaffolds for tissue reconstruction

Viscoelasticity of living tissues plays a critical role in tissue homeostasis and regeneration, and its implication in disease development and progression is being recognized recently. In this review, we first explored the state of knowledge regarding the potential application of tissue viscoelasticity in disease diagnosis. In order to better characterize viscoelasticity with local resolution and non-invasiveness, emerging characterization methods have been developed with the potential to be supplemented to existing facilities. To understand cellular responses to matrix viscoelastic behaviors in vitro, hydrogels made of natural polymers have been developed and the relationships between their molecular structure and viscoelastic behaviors, are elucidated. Moreover, how cells perceive the viscoelastic microenvironment and cellular responses including cell attachment, spreading, proliferation, differentiation and matrix production, have been discussed. Finally, some future perspective on an integrated mechanobiological comprehension of the viscoelastic behaviors involved in tissue homeostasis, cellular responses and biomaterial design are highlighted. STATEMENT OF SIGNIFICANCE: Tissue- or organ-scale viscoelastic behavior is critical for homeostasis, and the molecular basis and cellular responses of viscoelastic materials at micro- or nano-scale are being recognized recently. We summarized the potential applications of viscoelasticity in disease diagnosis enabled by emerging non-invasive characterization technologies, and discussed the underlying mechanism of viscoelasticity of hydrogels and current understandings of cell regulatory functions of them. With a growing understanding of the molecular basis of hydrogel viscoelasticity and recognition of its regulatory functions on cell behaviors, it is important to bring the clinical insights on how these characterization technologies and engineered materials may contribute to disease diagnosis and treatment. This review explains the basics in characterizing viscoelasticity with our hope to bridge the gap between basic research and clinical applications.

In Vivo Viscoelastic Response (VisR) Ultrasound for Characterizing Mechanical Anisotropy in Lower-Limb Skeletal Muscles of Boys with and without Duchenne Muscular Dystrophy

Our group has previously found that in silico, mechanical anisotropy may be interrogated by exciting transversely isotropic materials with geometrically asymmetric acoustic radiation force excitations and then monitoring the associated induced displacements in the region of excitation. We now translate acoustic radiation force-based anisotropy assessment to human muscle in vivo and investigate its clinical relevance to monitoring muscle degeneration in Duchenne muscular dystrophy (DMD). Clinical anisotropy assessments were performed using Viscoelastic Response ultrasound, with a degree of anisotropy reflected by the ratios of Viscoelastic Response relative elasticity (RE) or relative viscosity (RV) measured with the asymmetric radiation force oriented parallel versus perpendicular to muscle fiber alignment. In vivo results from rectus femoris and gastrocnemius muscles of boys aged ∼7.9-10.4 y indicate that RE and RV anisotropy ratios in rectus femoris muscles of boys with DMD were significantly higher than those of healthy control boys (RE: DMD = 1.51 ± 0.87, control = 0.99 ± 0.69, p = 0.04, Wilcoxon rank sum test; RV: DMD = 1.04 ± 0.71, control = 0.74 ± 0.22, p = 0.02). In the gastrocnemius muscle, only the RV anisotropy ratio was significantly higher in dystrophic than control patients (DMD = 1.23 ± 0.35, control = 0.88 ± 0.31, p = 0.04). In the dystrophic rectus femoris muscle, the RE anisotropy ratio was inversely correlated (slope = -0.03/lbf, r = -0.43, p = 0.07, Pearson correlation) with quantitative muscle testing functional output measures but was not correlated with quantitative muscle testing in the dystrophic gastrocnemius. These results suggest that Viscoelastic Response RE and RV measures reflect differences in mechanical anisotropy associated with functional impairment with dystrophic degeneration that are relevant to monitoring DMD clinically.

Analysis of Transient Shear Wave in Lossy Media

The propagation of shear waves from impulsive forces is an important topic in elastography. Observations of shear wave propagation can be obtained with numerous clinical imaging systems. Parameter estimations of the shear wave speed in tissues, and more generally the viscoelastic parameters of tissues, are based on some underlying models of shear wave propagation. The models typically include specific choices of the spatial and temporal shape of the impulsive force and the elastic or viscoelastic properties of the medium. In this work, we extend the analytical treatment of 2-D shear wave propagation in a biomaterial. The approach applies integral theorems relevant to the solution of the generalized Helmholtz equation, and does not depend on a specific rheological model of the tissue's viscoelastic properties. Estimators of attenuation and shear wave speed are derived from the analytical solutions, and these are applied to an elastic phantom, a viscoelastic phantom and in vivo liver using a clinical ultrasound scanner. In these samples, estimated shear wave group velocities ranged from 1.7 m/s in the liver to 2.5 m/s in the viscoelastic phantom, and these are lower-bounded by independent measurements of phase velocity.

Mechanics of ultrasound elastography

Ultrasound elastography enables in vivo measurement of the mechanical properties of living soft tissues in a non-destructive and non-invasive manner and has attracted considerable interest for clinical use in recent years. Continuum mechanics plays an essential role in understanding and improving ultrasound-based elastography methods and is the main focus of this review. In particular, the mechanics theories involved in both static and dynamic elastography methods are surveyed. They may help understand the challenges in and opportunities for the practical applications of various ultrasound elastography methods to characterize the linear elastic, viscoelastic, anisotropic elastic and hyperelastic properties of both bulk and thin-walled soft materials, especially the in vivo characterization of biological soft tissues.

Feasibility of coded vibration in a vibro-ultrasound system for tissue elasticity measurement

The ability of various methods for elasticity measurement and imaging is hampered by the vibration amplitude on biological tissues. Based on the inference that coded excitation will improve the performance of the cross-correlation function of the tissue displacement waves, the idea of exerting encoded external vibration on tested samples for measuring its elasticity is proposed. It was implemented by integrating a programmable vibration generation function into a customized vibro-ultrasound system to generate Barker coded vibration for elasticity measurement. Experiments were conducted on silicone phantoms and porcine muscles. The results showed that coded excitation of the vibration enhanced the accuracy and robustness of the elasticity measurement especially in low signal-to-noise ratio scenarios. In the phantom study, the measured shear modulus values with coded vibration had an R(2 )= 0.993 linear correlation to that of referenced indentation, while for single-cycle pulse the R(2) decreased to 0.987. In porcine muscle study, the coded vibration also obtained a shear modulus value which is more accurate than the single-cycle pulse by 0.16 kPa and 0.33 kPa at two different depths. These results demonstrated the feasibility and potentiality of the coded vibration for enhancing the quality of elasticity measurement and imaging.

Phase Aberration and Attenuation Effects on Acoustic Radiation Force-Based Shear Wave Generation

Elasticity is measured by shear wave elasticity imaging (SWEI) methods using acoustic radiation force to create the shear waves. Phase aberration and tissue attenuation can hamper the generation of shear waves for in vivo applications. In this study, the effects of phase aberration and attenuation in ultrasound focusing for creating shear waves were explored. This includes the effects of phase shifts and amplitude attenuation on shear wave characteristics such as shear wave amplitude, shear wave speed, shear wave center frequency, and bandwidth. Two samples of swine belly tissue were used to create phase aberration and attenuation experimentally. To explore the phase aberration and attenuation effects individually, tissue experiments were complemented with ultrasound beam simulations using fast object-oriented C++ ultrasound simulator (FOCUS) and shear wave simulations using finite-element-model (FEM) analysis. The ultrasound frequency used to generate shear waves was varied from 3.0 to 4.5 MHz. Results: The measured acoustic pressure and resulting shear wave amplitude decreased approximately 40%-90% with the introduction of the tissue samples. Acoustic intensity and shear wave displacement were correlated for both tissue samples, and the resulting Pearson's correlation coefficients were 0.99 and 0.97. Analysis of shear wave generation with tissue samples (phase aberration and attenuation case), measured phase screen, (only phase aberration case), and FOCUS/FEM model (only attenuation case) showed that tissue attenuation affected the shear wave generation more than tissue aberration. Decreasing the ultrasound frequency helped maintain a focused beam for creation of shear waves in the presence of both phase aberration and attenuation.

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.

Coded excitation plane wave imaging for shear wave motion detection

Plane wave imaging has greatly advanced the field of shear wave elastography thanks to its ultrafast imaging frame rate and the large field-of-view (FOV). However, plane wave imaging also has decreased penetration due to lack of transmit focusing, which makes it challenging to use plane waves for shear wave detection in deep tissues and in obese patients. This study investigated the feasibility of implementing coded excitation in plane wave imaging for shear wave detection, with the hypothesis that coded ultrasound signals can provide superior detection penetration and shear wave SNR compared with conventional ultrasound signals. Both phase encoding (Barker code) and frequency encoding (chirp code) methods were studied. A first phantom experiment showed an approximate penetration gain of 2 to 4 cm for the coded pulses. Two subsequent phantom studies showed that all coded pulses outperformed the conventional short imaging pulse by providing superior sensitivity to small motion and robustness to weak ultrasound signals. Finally, an in vivo liver case study on an obese subject (body mass index = 40) demonstrated the feasibility of using the proposed method for in vivo applications, and showed that all coded pulses could provide higher SNR shear wave signals than the conventional short pulse. These findings indicate that by using coded excitation shear wave detection, one can benefit from the ultrafast imaging frame rate and large FOV provided by plane wave imaging while preserving good penetration and shear wave signal quality, which is essential for obtaining robust shear elasticity measurements of tissue.

Characterization of transverse isotropy in compressed tissue-mimicking phantoms

Tissues such as skeletal muscle and kidneys have well-defined structure that affects the measurements of mechanical properties. As an approach to characterize the material properties of these tissues, different groups have assumed that they are transversely isotropic (TI) and measure the shear wave velocity as it varies with angle with respect to the structural architecture of the organ. To refine measurements in these organs, it is desirable to have tissue-mimicking phantoms that exhibit similar anisotropic characteristics. Some approaches involve embedding fibers into a material matrix. However, if a homogeneous solid is under compression due to a static stress, an acoustoelastic effect can manifest that makes the measured wave velocities change with the compression stress. We propose to exploit this characteristic to demonstrate that stressed tissue mimicking phantoms can be characterized as a TI material. We tested six phantoms made with different concentrations of gelatin and agar. Stress was applied by the weight of a water container centered on top of a plate on top of the phantom. A linear array transducer and a V-1 Verasonics system were used to induce and measure shear waves in the phantoms. The shear wave motion was measured using a compound plane wave imaging technique. Autocorrelation was applied to the received in-phase/quadrature data. The shear wave velocity, c, was estimated using a Radon transform method. The transducer was mounted on a rotating stage so measurements were made every 10° over a range of 0° to 360°, where the stress is applied along 0° to 180° direction. The shear moduli were estimated. A TI model was fit to the data and the fractional anisotropy was evaluated. This approach can be used to explore many configurations of transverse isotropy with the same phantom, simply by applying stress to the tissue-mimicking phantom.

Continuous Shear Wave Elastography: A New Method to Measure Viscoelastic Properties of Tendons in Vivo

Viscoelastic mechanical properties are frequently altered after tendon injuries and during recovery. Therefore, non-invasive measurements of shear viscoelastic properties may help evaluate tendon recovery and compare the effectiveness of different therapies. The objectives of this study were to describe an elastography method for measuring localized viscoelastic properties of tendons and to discuss the initial results in healthy and injured human Achilles and semitendinosus tendons. The technique used an external actuator to generate the shear waves in the tendon at different frequencies and plane wave imaging to measure shear wave displacements. For each of the excitation frequencies, maps of direction-specific wave speeds were calculated using local frequency estimation. Maps of viscoelastic properties were obtained using a pixel-wise curve fit of wave speed and frequency. The method was validated by comparing measurements of wave speed in agarose gels with those obtained using magnetic resonance elastography. Measurements in human healthy Achilles tendons revealed a pronounced increase in wave speed as a function of frequency, which highlights the importance of tendon viscoelasticity. Additionally, the viscoelastic properties of the Achilles tendon were larger than those reported for other tissues. Measurements in a tendinopathic Achilles tendon indicated that it is feasible to quantify local viscoelastic properties. Similarly, measurement in the semitendinosus tendon revealed substantial differences in viscoelastic properties between the healthy and contralateral tendons. Consequently, this technique has the potential to evaluate localized changes in tendon viscoelastic properties caused by injury and during recovery in a clinical setting.

Characterization of transverse isotropy in compressed tissue-mimicking phantoms

Tissues such as skeletal muscle and kidneys have well-defined structure that affects the measurements of mechanical properties. As an approach to characterize the material properties of these tissues, different groups have assumed that they are transversely isotropic (TI) and measure the shear wave velocity as it varies with angle with respect to the structural architecture of the organ. To refine measurements in these organs, it is desirable to have tissue-mimicking phantoms that exhibit similar anisotropic characteristics. Some approaches involve embedding fibers into a material matrix. However, if a homogeneous solid is under compression due to a static stress, an acoustoelastic effect can manifest that makes the measured wave velocities change with the compression stress. We propose to exploit this characteristic to demonstrate that stressed tissue mimicking phantoms can be characterized as a TI material. We tested six phantoms made with different concentrations of gelatin and agar. Stress was applied by the weight of a water container centered on top of a plate on top of the phantom. A linear array transducer and a V-1 Verasonics system were used to induce and measure shear waves in the phantoms. The shear wave motion was measured using a compound plane wave imaging technique. Autocorrelation was applied to the received in-phase/quadrature data. The shear wave velocity, c, was estimated using a Radon transform method. The transducer was mounted on a rotating stage so measurements were made every 10° over a range of 0° to 360°, where the stress is applied along 0° to 180° direction. The shear moduli were estimated. A TI model was fit to the data and the fractional anisotropy was evaluated. This approach can be used to explore many configurations of transverse isotropy with the same phantom, simply by applying stress to the tissue-mimicking phantom.

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.

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.

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.

The Gaussian shear wave in a dispersive medium

In "imaging the biomechanical properties of tissues," a number of approaches analyze shear wave propagation initiated by a short radiation force push. Unfortunately, it has been experimentally observed that the displacement-versus-time curves for lossy tissues are rapidly damped and distorted in ways that can confound simple tracking approaches. This article addresses the propagation, decay and distortion of pulses in lossy and dispersive media, to derive closed-form analytic expressions for the propagating pulses. The theory identifies key terms that drive the distortion and broadening of the pulse. Furthermore, the approach taken is not dependent on any particular viscoelastic model of tissue, but instead takes a general first-order approach to dispersion. Examples with a Gaussian beam pattern and realistic dispersion parameters are given along with general guidelines for identifying the features of the distorting wave that are the most compact.

In vivo pulsed magneto-motive ultrasound imaging using high-performance magnetoactive contrast nanoagents

Previously, pulsed magneto-motive ultrasound (pMMUS) imaging has been introduced as a contrast-agent-assisted ultrasound-based imaging modality capable of visualizing biological events at the cellular and molecular level. In pMMUS imaging, a high intensity pulsed magnetic field is used to excite cells or tissue labeled with magnetic nanoparticles. Then, ultrasound (US) imaging is used to monitor the mechanical response of the tissue to an externally applied magnetic field (i.e., tissue displacement). Signal to noise ratio (SNR) in pMMUS imaging can be improved by using superparamagnetic nanoparticles with larger saturation magnetization. Metal-doped magnetic nanoparticles with enhanced tunable nanomagnetism are suitable candidates to improve the SNR and, therefore, sensitivity of pMMUS imaging, which is essential for in vivo pMMUS imaging. In this study, we demonstrate the capability of pMMUS imaging to identify the presence and distribution of zinc-doped iron oxide nanoparticles in live nude mice bearing A431 (human epithelial carcinoma) xenograft tumors.

Ultrasound vibrometry using orthogonal- frequency-based vibration pulses

New vibration pulses are developed for shear wave generation in a tissue region with preferred spectral distributions for ultrasound vibrometry applications. The primary objective of this work is to increase the frequency range of detectable harmonics of the shear wave. The secondary objective is to reduce the required peak intensity of transmitted pulses that induce the vibrations and shear waves. Unlike the periodic binary vibration pulses, the new vibration pulses have multiple pulses in one fundamental period of the vibration. The pulses are generated from an orthogonal-frequency wave composed of several sinusoidal signals, the amplitudes of which increase with frequency to compensate for higher loss at higher frequency in tissues. The new method has been evaluated by studying the shear wave propagation in in vitro chicken and swine liver. The experimental results show that the new vibration pulses significantly increase tissue vibration with a reduced peak ultrasound intensity, compared with the binary vibration pulses.

Imaging transverse isotropic properties of muscle by monitoring acoustic radiation force induced shear waves using a 2-D matrix ultrasound array

A 2-D matrix ultrasound array is used to monitor acoustic radiation force impulse (ARFI) induced shear wave propagation in 3-D in excised canine muscle. From a single acquisition, both the shear wave phase and group velocity can be calculated to estimate the shear wave speed (SWS) along and across the fibers, as well as the fiber orientation in 3-D. The true fiber orientation found using the 3-D radon transform on B-mode volumes of the muscle was used to verify the fiber direction estimated from shear wave data. For the simplified imaging case when the ARFI push can be oriented perpendicular to the fibers, the error in estimating the fiber orientation using phase and group velocity measurements was 3.5 ± 2.6° and 3.4 ± 1.4° (mean ± standard deviation), respectively, over six acquisitions in different muscle samples. For the more general case when the push is oblique to the fibers, the angle between the push and the fibers is found using the dominant orientation of the shear wave displacement magnitude. In 30 acquisitions on six different muscle samples with oblique push angles up to 40°, the error in the estimated fiber orientation using phase and group velocity measurements was 5.4 ± 2.9° and 5.3 ± 3.2°, respectively, after estimating and accounting for the additional unknown push angle. Either the phase or group velocity measurements can be used to estimate fiber orientation and SWS along and across the fibers. Although it is possible to perform these measurements when the push is not perpendicular to the fibers, highly oblique push angles induce lower shear wave amplitudes which can cause inaccurate SWS measurements.

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.

Shear wave induced resonance elastography of venous thrombi: a proof-of-concept

Shear wave induced resonance elastography (SWIRE) is proposed for deep venous thrombosis (DVT) elasticity assessment. This new imaging technique takes advantage of properly polarized shear waves to induce resonance of a confined mechanical heterogeneity. Realistic phantoms (n = 9) of DVT total and partial clot occlusions with elasticities from 406 to 3561 Pa were built for in vitro experiments. An ex vivo study was also performed to evaluate the elasticity of two fresh porcine venous thrombi in a pig model. Transient shear waves at 45-205 Hz were generated by the vibration of a rigid plate (plane wavefront) or by a needle to simulate a radiation pressure on a line segment (cylindrical wavefront). Induced propagation of shear waves was imaged with an ultrafast ultrasound scanner and a finite element method was developed to simulate tested experimental conditions. An inverse problem was then formulated considering the first resonance frequency of the DVT inclusion. Elasticity agreements between SWIRE and a reference spectroscopy instrument (RheoSpectris) were found in vitro for total clots either in plane (r(2) = 0.989) or cylindrical (r(2) = 0.986) wavefront configurations. For total and partial clots, elasticity estimation errors were 9.0 ±4.6% and 9.3 ±11.3%, respectively. Ex vivo, the blood clot elasticity was 498 ±58 Pa within the inferior vena cava and 436 ±45 Pa in the right common iliac vein (p = 0.22). To conclude, the SWIRE technique seems feasible to quantitatively assess blood clot elasticity in the context of DVT ultrasound imaging.

In vivo swine kidney viscoelasticity during acute gradual decrease in renal blood flow: pilot study

Elasticity imaging methods have been used to study kidney mechanical properties and have demonstrated that the kidney elastic modulus increases with disease state. However, studies in swine suggests that kidney elastic modulus is also affected by hemodynamic variables. A newly emerging method called Shearwave Dispersion Ultrasound Vibrometry (SDUV) offers a tool to determine renal elasticity and viscosity in vivo. The purpose of this study is directed toward evaluating the feasibility of SDUV for in vivo measurements of healthy swine kidney during acute gradual decease of renal blood flow. In this study in vivo SDUV measurements were made on a group of 5 normal swine kidneys at baseline renal blood flow (RBF) and 25, 50, 75 and 100% decrease in RBF. The shear elastic modulus at full baseline was 7.04 ± 0.92 kPa and 3.48 ± 0.20 kPa at 100% decrease in RBF. The viscosity did not change between baseline (2.23 ± 0.33 Pa·s) and 100% decrease in RBF (2.03 ± 0.32 Pa·s). The data from this study indicates that other variables such as local blood flow, pressure and volume as well as method accuracy need to be measured to illustrate the relationship between shear elasticity and viscosity associated with acute kidney processes.

The variance of quantitative estimates in shear wave imaging: theory and experiments

In this paper, we investigate the relationship between the estimated shear modulus produced in shear wave imaging and the acquisition parameters. Using the framework of estimation theory and the Cramer-Rao lower bound applied both to the estimation of the velocity field variance and to the estimation of the shear wave travel time, we can derive the analytical formulation of the shear modulus variance σ(2)(μ) using relevant physical parameters such as the shear wave frequency, bandwidth, and ultrasonic parameters. This variance corresponds to the reproducibility of shear modulus reconstruction for a deterministic, quasi-homogeneous, and purely elastic medium. We thus consider the shear wave propagation as a deterministic process which is then corrupted during its observation by electronic noise and speckle decorrelation caused by shearing. A good correlation was found between analytical, numerical, and experimental results, which indicates that this formulation is well suited to understand the parameters' influence in those cases. The analytical formula stresses the importance of high-frequency and wideband shear waves for good estimation. Stiffer media are more difficult to assess reliably with identical acquisition signal-to-noise ratios, and a tradeoff between the reconstruction resolution of the shear modulus maps and the shear modulus variance is demonstrated. We then propose to use this formulation as a physical ground for a pixel-based quality measure that could be helpful for improving the reconstruction of real-time shear modulus maps for clinical applications.

A Review of Shearwave Dispersion Ultrasound Vibrometry (SDUV) and its Applications

Measurement of tissue elasticity has emerged as an important advance in medical imaging and tissue characterization. However, soft tissue is inherently a viscoelastic material. One way to characterize the viscoelastic material properties of a material is to measure shear wave propagation velocities within the material at different frequencies and use the dispersion of the velocities, or variation with frequency, to solve for the material properties. Shearwave Dispersion Ultrasound Vibrometry (SDUV) is an ultrasound-based technique that uses this feature to characterize the viscoelastic nature of soft tissue. This method has been used to measure the shear elasticity and viscosity in various types of soft tissues including skeletal muscle, cardiac muscle, liver, kidney, prostate, and arterial vessels. This versatile technique provides measurements of viscoelastic material properties with high spatial and temporal resolution, which can be used for assessing these properties in normal and pathologic tissues. The goals of this paper are to 1) give an overview of viscoelasticity and shear wave velocity dispersion, 2) provide a history of the development of the SDUV method, and 3) survey applications for SDUV that have been previously reported.

On Lamb and Rayleigh wave convergence in viscoelastic tissues

Characterization of the viscoelastic material properties of soft tissue has become an important area of research over the last two decades. Our group has been investigating the feasibility of using a shear wave dispersion ultrasound vibrometry (SDUV) method to excite Lamb waves in organs with plate-like geometry to estimate the viscoelasticity of the medium of interest. The use of Lamb wave dispersion ultrasound vibrometry to quantify the mechanical properties of viscoelastic solids has previously been reported. Two organs, the heart wall and the spleen, can be readily modeled using plate-like geometries. The elasticity of these two organs is important because they change in pathological conditions. Diastolic dysfunction is the inability of the left ventricle (LV) of the heart to supply sufficient stroke volumes into the systemic circulation and is accompanied by the loss of compliance and stiffening of the LV myocardium. It has been shown that there is a correlation between high splenic stiffness in patients with chronic liver disease and strong correlation between spleen and liver stiffness. Here, we investigate the use of the SDUV method to quantify the viscoelasticity of the LV free-wall myocardium and spleen by exciting Rayleigh waves on the organ's surface and measuring the wave dispersion (change of wave velocity as a function of frequency) in the frequency range 40–500 Hz. An equation for Rayleigh wave dispersion due to cylindrical excitation was derived by modeling the excised myocardium and spleen with a homogenous Voigt material plate immersed in a nonviscous fluid. Boundary conditions and wave potential functions were solved for the surface wave velocity. Analytical and experimental convergence between the Lamb and Rayleigh waves is reported in a finite element model of a plate in a fluid of similar density, gelatin plate and excised porcine spleen and left-ventricular free-wall myocardium.

Shearwave dispersion ultrasound vibrometry (SDUV) on swine kidney

Shearwave dispersion ultrasound vibrometry (SDUV) is used to quantify both tissue shear elasticity and shear viscosity by evaluating dispersion of shear wave propagation speed over a certain bandwidth (50 to 500 Hz). The motivation for developing elasticity imaging techniques is the desire to diagnose disease processes. However, it is important to study the mechanical properties of healthy tissues; such data can enhance clinical knowledge and improve understanding of the mechanical properties of tissue. The purpose of this study is to evaluate the feasibility of using SDUV for in vitro measurements of renal cortex shear elasticity and shear viscosity in healthy swine kidneys. Eight excised kidneys from female pigs were used in these in vitro experiments and a battery of tests was performed to gain insight into the material proper ties of the renal cortex. In these 8 kidneys, the overall renal cortex elasticity and viscosity were 1.81 ± 0.17 kPa and 1.48 ± 0.49 Pa-s, respectively. In an analysis of the material properties over time after excision, there was not a statistically significant difference in shear elasticity over a 24-h period, but a statistically significant difference in shear viscosity was found. Homogeneity of the renal cortex was examined and it was found that shear elasticity and shear viscosity were statistically different within a kidney, suggesting global tissue inhomogeneity. In creases of more than 30% in shear elasticity and shear viscosity were observed after immersion in 10% formaldehyde. Finally, it was found that the renal cortex is rather anisotropic. Two values for shear elasticity and shear viscosity were measured depending on shear wave propagation direction. These various tests elucidated different aspects of the material properties and the structure of the ex vivo renal cortex.

AN OVERVIEW OF ELASTOGRAPHY - AN EMERGING BRANCH OF MEDICAL IMAGING

From times immemorial manual palpation served as a source of information on the state of soft tissues and allowed detection of various diseases accompanied by changes in tissue elasticity. During the last two decades, the ancient art of palpation gained new life due to numerous emerging elasticity imaging (EI) methods. Areas of applications of EI in medical diagnostics and treatment monitoring are steadily expanding. Elasticity imaging methods are emerging as commercial applications, a true testament to the progress and importance of the field.In this paper we present a brief history and theoretical basis of EI, describe various techniques of EI and, analyze their advantages and limitations, and overview main clinical applications. We present a classification of elasticity measurement and imaging techniques based on the methods used for generating a stress in the tissue (external mechanical force, internal ultrasound radiation force, or an internal endogenous force), and measurement of the tissue response. The measurement method can be performed using differing physical principles including magnetic resonance imaging (MRI), ultrasound imaging, X-ray imaging, optical and acoustic signals.Until recently, EI was largely a research method used by a few select institutions having the special equipment needed to perform the studies. Since 2005 however, increasing numbers of mainstream manufacturers have added EI to their ultrasound systems so that today the majority of manufacturers offer some sort of Elastography or tissue stiffness imaging on their clinical systems. Now it is safe to say that some sort of elasticity imaging may be performed on virtually all types of focal and diffuse disease. Most of the new applications are still in the early stages of research, but a few are becoming common applications in clinical practice.

Acoustic radiation force-based elasticity imaging methods

Conventional diagnostic ultrasound images portray differences in the acoustic properties of soft tissues, whereas ultrasound-based elasticity images portray differences in the elastic properties of soft tissues (i.e. stiffness, 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 pathological lesions. Acoustic radiation force-based elasticity imaging methods use acoustic radiation force to transiently deform soft tissues, and the dynamic displacement response of those tissues is measured ultrasonically and is used to estimate the tissue's mechanical properties. Both qualitative images and quantitative elasticity metrics can be reconstructed from these measured data, providing complimentary information to both diagnose and longitudinally monitor disease progression. Recently, acoustic radiation force-based elasticity imaging techniques have moved from the laboratory to the clinical setting, where clinicians are beginning to characterize tissue stiffness as a diagnostic metric, and commercial implementations of radiation force-based ultrasonic elasticity imaging are beginning to appear on the commercial market. This article provides an overview of acoustic radiation force-based elasticity imaging, including a review of the relevant soft tissue material properties, a review of radiation force-based methods that have been proposed for elasticity imaging, and a discussion of current research and commercial realizations of radiation force based-elasticity imaging technologies.

What challenges must be overcome before ultrasound elasticity imaging is ready for the clinic?

Ultrasound elasticity imaging has been a research interest for the past 20 years with the goal of generating novel images of soft tissues based on their material properties (i.e., stiffness and viscosity). The motivation for such an imaging modality lies in the fact that many soft tissues can share similar ultrasonic echogenicities, but may have very different mechanical properties that can be used to clearly visualize normal anatomy and delineate diseased tissues and masses. Recently, elasticity imaging techniques have moved from the laboratory to the clinical setting, where clinicians are beginning to characterize tissue stiffness as a diagnostic metric and commercial implementations of ultrasonic elasticity imaging are beginning to appear on the market. This article provides a foundation for elasticity imaging, an overview of current research and commercial realizations of elasticity imaging technology and a perspective on the current successes, limitations and potential for improvement of these imaging technologies.

Estimating material elasticity by spherical indentation load-relaxation tests on viscoelastic samples of finite thickness

A two-step viscoelastic spherical indentation method is proposed to compensate for 1) material relaxation and 2) sample thickness. In the first step, the indenter is moved at a constant speed and the reaction force is measured. In the second step, the indenter is held at a constant position and the relaxation response of the material is measured. Then the relaxation response is fit with a multi-exponential function which corresponds to a three-branch general Maxwell model. The relaxation modulus is derived by correcting the finite ramp time introduced in the first step. The proposed model takes into account the sample thickness, which is important for applications in which the sample thickness is less than ten times the indenter radius. The model is validated numerically by finite element simulations. Experiments are carried out on a 10% gelatin phantom and a chicken breast sample with the proposed method. The results for both the gelatin phantom and the chicken breast sample agree with the results obtained from a surface wave method. Both the finite element simulations and experimental results show improved elasticity estimations by incorporating the sample thickness into the model. The measured shear elasticities of the 10% gelatin sample are 6.79 and 6.93 kPa by the proposed finite indentation method at sample thickness of 40 and 20 mm, respectively. The elasticity of the same sample is estimated to be 6.53 kPa by the surface wave method. For the chicken breast sample, the shear elasticity is measured to be 4.51 and 5.17 kPa by the proposed indentation method at sample thickness of 40 and 20 mm, respectively. Its elasticity is measured by the surface wave method to be 4.14 kPa.

Shear elastic modulus estimation from indentation and SDUV on gelatin phantoms

Tissue mechanical properties such as elasticity are linked to tissue pathology state. Several groups have proposed shear wave propagation speed to quantify tissue mechanical properties. It is well known that biological tissues are viscoelastic materials; therefore, velocity dispersion resulting from material viscoelasticity is expected. A method called shearwave dispersion ultrasound vibrometry (SDUV) can be used to quantify tissue viscoelasticity by measuring dispersion of shear wave propagation speed. However, there is not a gold standard method for validation. In this study, we present an independent validation method of shear elastic modulus estimation by SDUV in three gelatin phantoms of differing stiffness. In addition, the indentation measurements are compared to estimates of elasticity derived from shear wave group velocities. The shear elastic moduli from indentation were 1.16, 3.40, and 5.6 kPa for a 7%, 10%, and 15% gelatin phantom, respectively. SDUV measurements were 1.61, 3.57, and 5.37 kPa for the gelatin phantoms, respectively. Shear elastic moduli derived from shear wave group velocities were 1.78, 5.2, and 7.18 kPa for the gelatin phantoms, respectively. The shear elastic modulus estimated from the SDUV, matched the elastic modulus measured by indentation. On the other hand, shear elastic modulus estimated by group velocity did not agree with indentation test estimations. These results suggest that shear elastic modulus estimation by group velocity will be bias when the medium being investigated is dispersive. Therefore, a rheological model should be used in order to estimate mechanical properties of viscoelastic materials.

Lamb wave dispersion ultrasound vibrometry (LDUV) method for quantifying mechanical properties of viscoelastic solids

Diastolic dysfunction is the inability of the left ventricle to supply sufficient stroke volumes under normal physiological conditions and is often accompanied by stiffening of the left-ventricular myocardium. A noninvasive technique capable of quantifying viscoelasticity of the myocardium would be beneficial in clinical settings. Our group has been investigating the use of shear wave dispersion ultrasound vibrometry (SDUV), a noninvasive ultrasound-based method for quantifying viscoelasticity of soft tissues. The primary motive of this study is the design and testing of viscoelastic materials suitable for validation of the Lamb wave dispersion ultrasound vibrometry (LDUV), an SDUV-based technique for measuring viscoelasticity of tissues with plate-like geometry. We report the results of quantifying viscoelasticity of urethane rubber and gelatin samples using LDUV and an embedded sphere method. The LDUV method was used to excite antisymmetric Lamb waves and measure the dispersion in urethane rubber and gelatin plates. An antisymmetric Lamb wave model was fitted to the wave speed dispersion data to estimate elasticity and viscosity of the materials. A finite element model of a viscoelastic plate submerged in water was used to study the appropriateness of the Lamb wave dispersion equations. An embedded sphere method was used as an independent measurement of the viscoelasticity of the urethane rubber and gelatin. The FEM dispersion data were in excellent agreement with the theoretical predictions. Viscoelasticity of the urethane rubber and gelatin obtained using the LDUV and embedded sphere methods agreed within one standard deviation. LDUV studies on excised porcine myocardium sample were performed to investigate the feasibility of the approach in preparation for open-chest in vivo studies. The results suggest that the LDUV technique can be used to quantify the mechanical properties of soft tissues with a plate-like geometry.

Shear wave dispersion ultrasonic vibrometry for measuring prostate shear stiffness and viscosity: an in vitro pilot study

This paper reports shear stiffness and viscosity "virtual biopsy" measurements of the three excised noncancerous human prostates using a new tool known as shear wave dispersion ultrasound vibrometry (SDUV) in vitro. Improved methods for prostate guided-biopsy are required to effectively guide needle biopsy to the suspected site. In addition, tissue stiffness measurement helps in identifying a suspected site to perform biopsy because stiffness has been shown to correlate with pathologies, such as cancerous tissue. More importantly, early detection of prostate cancer may guide minimally invasive therapy and eliminate insidious procedures. In this paper, "virtual biopsies" were taken in multiple locations in three excised prostates; SDUV shear elasticity and viscosity measurements were performed at the selected "suspicious" locations within the prostates. SDUV measurements of prostate elasticity and viscosity are generally in agreement with preliminary values previously reported in the literature. It is, however, important to emphasize here that the obtained viscoelastic parameters values are local, and not a mean value for the whole prostate.