Shear wave elastography can assess the in-vivo nonlinear mechanical behavior of heel-pad

This study combines non-invasive mechanical testing with finite element (FE) modelling to assess for the first time the reliability of shear wave (SW) elastography for the quantitative assessment of the in-vivo nonlinear mechanical behavior of heel-pad. The heel-pads of five volunteers were compressed using a custom-made ultrasound indentation device. Tissue deformation was assessed from B-mode ultrasound and force was measured using a load cell to calculate the force – deformation graph of the indentation test. These results were used to design subject specific FE models and to inverse engineer the tissue’s hyperelastic material coefficients and its stress – strain behavior. SW speed was measured for different levels of compression (from 0% to 50% compression). SW speed for 0% compression was used to assess the initial stiffness of heel-pad (i.e. initial shear modulus, initial Young’s modulus). Changes in SW speed with increasing compressive loading were used to quantify the tissue’s nonlinear mechanical behavior based on the theory of acoustoelasticity. Statistical analysis of results showed significant correlation between SW-based and FE-based estimations of initial stiffness, but SW underestimated initial shear modulus by 64%(±16). A linear relationship was found between the SW-based and FE-based estimations of nonlinear behavior. The results of this study indicate that SW elastography is capable of reliably assessing differences in stiffness, but the absolute values of stiffness should be used with caution. Measuring changes in SW speed for different magnitudes of compression enables the quantification of the tissue’s nonlinear behavior which can significantly enhance the diagnostic value of SW elastography.     

Shear wave elastography of the supraspinatus muscle and tendon: Repeatability and preliminary findings

Shear wave elastography (SWE) is a promising tool for estimating musculoskeletal tissue properties, but few studies have rigorously assessed its repeatability and sources of error. The objectives of this study were to assess: (1) the extent to which probe positioning error and human user error influence measurement accuracy, (2) intra-user, inter-user, and day-to-day repeatability, and (3) the extent to which active and passive conditions affect shear wave speed (SWS) repeatability. Probe positioning and human usage errors were assessed by acquiring SWE images from custom ultrasound phantoms. Intra- and inter-user repeatability were assessed by two users acquiring five trials of supraspinatus muscle and tendon SWE images from ten human subjects. To assess day-to-day repeatability, five of the subjects were tested a second time, approximately 24 h later. Imaging of the phantoms indicated high inter-user repeatability, with intraclass correlation coefficient (ICC) values of 0.68–0.85, and RMS errors of no more than 4.1%. SWE imaging of the supraspinatus muscle and tendon had high repeatability, with intra- and inter-user ICC values of greater than 0.87 and 0.73, respectively. Day-to-day repeatability demonstrated ICC values greater than 0.33 for passive muscle, 0.48 for passive tendon, 0.65 for active muscle, and 0.94 for active tendon. This study indicates the technique has good to very good intra- and inter-user repeatability, and day-to-day repeatability is appreciably higher when SWE images are acquired under a low level of muscle activation. The findings from this study establish the feasibility and repeatability of SWE for acquiring data longitudinally in human subjects.     

Fourier transform electron paramagnetic resonance studies of photochemical reactions in heterogeneous media

FT-EPR has proved to be an excellent spectroscopic technique for the study of free radicals generated in photochemical reactions. The high spectral and time resolution make it possible to identify transient free radicals. Analysis of the time dependence of the spectra gives data on the kinetics of radical formation and decay. Chemically induced dynamic electron polarization (CIDEP) effects give information on reaction mechanisms and radical pair characteristics. Relaxation and linewidths data provide an insight into molecular motion. This contribution reviews instrumental aspects of the technique and CIDEP mechanisms that can affect the spectra. The utility of the method is illustrated with a discussion of applications in the study of photoinduced electron transfer reactions in homogeneous and heterogeneous media.     

A finite element model for analyzing shear wave propagation observed in magnetic resonance elastography

Magnetic resonance elastography (MRE) is a novel non-invasive approach to determine material stiffness by using a conventional magnetic resonance imaging (MRI) system incorporated with an oscillating motion-sensitizing gradient to detect nodal displacements produced by a shear excitation wave. The effects of material properties, excitation frequency, boundary conditions, and applied tension on shear wavelength measurement must be examined before MRE can become a useful diagnostic tool. We propose finite element (FE) modeling as a robust method to systematically study the effects of these parameters. An axisymmetric FE model was generated with ABAQUS to simulate agarose gel phantoms. The effects of material stiffness, density, and excitation frequency on propagating shear wavelength were examined individually. The effect of the boundary conditions on shear wavelength was also demonstrated. Results of shear wavelength from MRE measurement were compared with the results of FE model, which showed good agreement between the methods.     

Wide-range dynamic magnetic resonance elastography

Tissue mechanical parameters have been shown to be highly sensitive to disease by elastography. Magnetic resonance elastography (MRE) in the human body relies on the low-dynamic range of tissue mechanics <100 Hz. In contrast, MRE suited for investigations of mice or small tissue samples requires vibration frequencies 10–20 times higher than those used in human MRE. The dispersion of the complex shear modulus (G^?) prevents direct comparison of elastography data at different frequency bands and, consequently, frequency-independent viscoelastic models that fit to G^* over a wide dynamic range have to be employed. This study presents data of G^* of samples of agarose gel, liver, brain, and muscle measured by high-resolution MRE in a 7T-animal scanner at 200–800 Hz vibration frequency. Material constants μ and α according to the springpot model and related to shear elasticity and slope of the G^*-dispersion were determined. Both μ and α of calf brain and bovine liver were found to be similar, while a sample of fibrotic human liver (METAVIR score of 3) displayed about fifteen times higher shear elasticity, similar to μ of bovine muscle measured in muscle fiber direction. α was the highest in fibrotic liver, followed by normal brain and liver, while muscle had the lowest α-values of all biological samples investigated in this study. As expected, the least G^*-dispersion was seen in soft gel. The proposed technique of wide-range dynamic MRE can provide baseline data for both human MRE and high-dynamic MRE for better understanding tissue mechanics of different tissue structures.     

Differential effects of pre-tension on shear wave propagation in elastic media with different boundary conditions as measured by magnetic resonance elastography and finite element modeling

Magnetic resonance elastography (MRE) can non-invasively determine material stiffness based on the propagating shear wavelength. Shear wave propagation in a finite homogenous isotropic material can be affected by multiple factors. In this study we examined the effects of pre-tension and frequency on MRE shear measurements of gel phantoms with different boundary conditions, frequencies, and geometries. Results from MRE measurements were compared to wave motion theory in elastic solids and qualitatively to a finite element (FE) model. Results indicated that boundary conditions, geometry and pre-tension are important factors to be considered when performing MRE tests on a finite material, and that FE modeling can help explore how the shear wave propagation is affected under various boundary conditions and axial stresses, among other potential factors.     

Shear wave elastography: possibilities of the differential diagnosis of focal and diffuse changes in various organs and tissues

Ultrasound study (USS) using a shear wave elastography procedure was made in different groups of patients with morphologically verified focal and diffuse abnormalities of both superficial organs and structures and viscera. The qualitative and quantitative characteristics of the stiffness of normal and pathologic organs and tissues were estimated; there was a significance importance of differences in benign and malignant lesions. The magnitude of fibrous changes in the hepatic parenchyma was first estimated by a USS technique; there was evidence that there were significant differences in indicators in health and various liver abnormalities.     

Spatial coherence resonance in excitable biochemical media induced by internal noise

We show that in a spatially extended excitable medium, presently modelled with diffusively coupled FitzHugh-Nagumo neurons, internal stochasticity is able to extract a characteristic spatial frequency of waves on the spatial grid. Internal noise is introduced via a stochastic simulation method and is the only agent acting on the system. Remarkably, the spatial periodicity is best pronounced at an intermediate level of internal stochasticity. Thus, the reported phenomenon is an observation of internal noise spatial coherence resonance in excitable biochemical media.     

Validation of shear wave elastography in skeletal muscle

Skeletal muscle is a very dynamic tissue, thus accurate quantification of skeletal muscle stiffness throughout its functional range is crucial to improve the physical functioning and independence following pathology. Shear wave elastography (SWE) is an ultrasound-based technique that characterizes tissue mechanical properties based on the propagation of remotely induced shear waves. The objective of this study is to validate SWE throughout the functional range of motion of skeletal muscle for three ultrasound transducer orientations. We hypothesized that combining traditional materials testing (MTS) techniques with SWE measurements will show increased stiffness measures with increasing tensile load, and will correlate well with each other for trials in which the transducer is parallel to underlying muscle fibers. To evaluate this hypothesis, we monitored the deformation throughout tensile loading of four porcine brachialis whole-muscle tissue specimens, while simultaneously making SWE measurements of the same specimen. We used regression to examine the correlation between Young′s modulus from MTS and shear modulus from SWE for each of the transducer orientations. We applied a generalized linear model to account for repeated testing. Model parameters were estimated via generalized estimating equations. The regression coefficient was 0.1944, with a 95% confidence interval of (0.1463–0.2425) for parallel transducer trials. Shear waves did not propagate well for both the 45° and perpendicular transducer orientations. Both parallel SWE and MTS showed increased stiffness with increasing tensile load. This study provides the necessary first step for additional studies that can evaluate the distribution of stiffness throughout muscle.     

Identification process based on shear wave propagation within a phantom using finite element modelling and magnetic resonance elastography

Magnetic resonance elastography (MRE), based on shear wave propagation generated by a specific driver, is a non-invasive exam performed in clinical practice to improve the liver diagnosis. The purpose was to develop a finite element (FE) identification method for the mechanical characterisation of phantom mimicking soft tissues investigated with MRE technique. Thus, a 3D FE phantom model, composed of the realistic MRE liver boundary conditions, was developed to simulate the shear wave propagation with the software ABAQUS. The assumptions of homogeneity and elasticity were applied to the FE phantom model. Different ranges of mesh size, density and Poisson's ratio were tested in order to develop the most representative FE phantom model. The simulated wave displacement was visualised with a dynamic implicit analysis. Subsequently, an identification process was performed with a cost function and an optimisation loop provided the optimal elastic properties of the phantom. The present identification process was validated on a phantom model, and the perspective will be to apply this method on abdominal tissues for the set-up of new clinical MRE protocols that could be applied for the follow-up of the effects of treatments.     

Analyzing acoustoelastic effect of shear wave elastography data for perfused and hydrated soft tissues using a macromolecular network inspired model

Shear wave elastography (SWE) has enhanced our ability to non-invasively make in vivo measurements of tissue elastic properties of animal and human tissues. Recently, researchers have taken advantages of acoustoelasticity in SWE to extract nonlinear elastic properties from soft biological tissues. However, most investigations of the acoustoelastic effects of SWE data (AE-SWE) rely on classic hyperelastic models for rubber-like (dry) materials. In this paper, we focus solely on understanding acoustoelasticity in soft hydrated tissues using SWE data and propose a straightforward approach to modeling the constitutive behavior of soft tissue that has a direct microstructural/macromolecular interpretation. Our approach incorporates two constitutive features relevant to biological tissues into AE-SWE: static dilation of the medium associated with nonstructural components (e.g. tissue hydration and perfusion) and finite extensibility derived from an ideal network of biological filaments. We evaluated the proposed method using data from an in-house tissue-mimicking phantom experiment, and ex vivo and in vivo AE-SWE data available in the SWE literature. In conclusion, predictions made by our approach agreed well with measurements obtained from phantom, ex vivo and in vivo tissue experiments.     

Shear modulus of multifidus and longissimus muscles measured using shear wave elastography correlates with muscle activity,but depends on image quality

Shear wave elastography (SWE) estimates shear modulus in muscle. This is interpreted as an index of muscle stiffness, but depends on muscle characteristics. This study evaluated relationship between shear modulus and myoelectric activity of lumbar multifidus and longissimus muscles to assess its validity. Intramuscular electromyography (EMG) of multifidus (deep [DM], superficial [SM] fibres) at L4/5, longissimus [LG] at L2, were recorded in nine healthy participants. Participants performed isometric trunk extension in side-lying from 0 to 30% maximal voluntary contraction (MVC) with EMG amplitude feedback. Using SWE, two regions of interest (ROI) were investigated in each muscle. Generally, shear modulus was moderately correlated with root mean squared (RMS) EMG (r = 0.50–0.78). Univariate and multiple regression analyses showed ultrasound/SWE features of ‘B-mode quality’ (24.5%), ‘%Void pixels’ (17.9%) and ‘Connective tissue’ (16.2%) explained most variation in the shear modulus/EMG relationship. Regression prediction scores generated using imaging features were correlated with r-coefficients of shear modulus/EMG relationship. When analysis was restricted to high quality data (i.e., regression prediction score above an a priori defined threshold), the shear modulus/EMG relationship increased to r = 0.70–0.96. Although a linear relationship between shear modulus/EMG was confirmed, supporting validity of SWE measures in anatomically distinct back muscles, this depends on image quality.     

Viscoelastic properties of human cerebellum using magnetic resonance elastography

BackgroundThe cerebellum has never been mechanically characterised, despite its physiological importance in the control of motion and the clinical prevalence of cerebellar pathologies. The aim of this study was to measure the linear viscoelastic properties of the cerebellum in human volunteers using Magnetic Resonance Elastography (MRE).MethodsCoronal plane brain 3D MRE data was performed on eight healthy adult volunteers, at 80 Hz, to compare the properties of cerebral and cerebellar tissues. The linear viscoelastic storage (G′) and loss moduli (G″) were estimated from the MRE wave images by solving the wave equation for propagation through an isotropic linear viscoelastic solid. Contributions of the compressional wave were removed via application of the curl-operator.ResultsThe storage modulus for the cerebellum was found to be significantly lower than that for the cerebrum, for both white and grey matter. Cerebrum: white matter (mean±SD) G′=2.41±0.23 kPa, grey matter G′=2.34±0.22 kPa; cerebellum: white matter, G′=1.85±0.18 kPa, grey matter G′=1.77±0.24 kPa; cerebrum vs cerebellum, p<0.001. For the viscous behaviour, there were differences in between regions and also by tissue type, with the white matter being more viscous than grey matter and the cerebrum more viscous than the cerebellum. Cerebrum: white matter G″=1.21±0.21 kPa, grey matter G″=1.11±0.03 kPa; cerebellum: white matter G″=1.1±0.23 kPa, grey matter G″=0.94±0.17 kPa.DiscussionThese data represent the first available data on the viscoelastic properties of cerebellum, which suggest that the cerebellum is less physically stiff than the cerebrum, possibly leading to a different response to mechanical loading. These data will be useful for modelling of the cerebellum for a range of purposes.     

Nonlinear poisson equation for heterogeneous media

The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects.     

Characterization of a hyper-viscoelastic phantom mimicking biological soft tissue using an abdominal pneumatic driver with magnetic resonance elastography (MRE)

The purpose of this study was to create a polymer phantom mimicking the mechanical properties of soft tissues using experimental tests and rheological models. Multifrequency Magnetic Resonance Elastography (MMRE) tests were performed on the present phantom with a pneumatic driver to characterize the viscoelastic (μ, η) properties using Voigt, Maxwell, Zener and Springpot models. To optimize the MMRE protocol, the driver behavior was analyzed with a vibrometer. Moreover, the hyperelastic properties of the phantom were determined using compressive tests and Mooney-Rivlin model. The range of frequency to be used with the round driver was found between 60 Hz and 100 Hz as it exhibits one type of vibration mode for the membrane. MRE analysis revealed an increase in the shear modulus with frequency reflecting the viscoelastic properties of the phantom showing similar characteristic of soft tissues. Rheological results demonstrated that Springpot model better revealed the viscoelastic properties (μ=3.45 kPa, η=6.17 Pas) of the phantom and the Mooney-Rivlin coefficients were C(10)=1.09.10(-2) MPa and C(01)=-8.96.10(-3) MPa corresponding to μ=3.95 kPa. These studies suggest that the phantom, mimicking soft tissue, could be used for preliminary MRE tests to identify the optimal parameters necessary for in vivo investigations. Further developments of the phantom may allow clinicians to more accurately mimic healthy and pathological soft tissues using MRE.     

Assessment of corneal viscoelasticity using elastic wave optical coherence elastography

The corneal viscoelasticity have great clinical significance, such as the early diagnosis of keratoconus. In this work, an analysis method which utilized the elastic wave velocity, frequency and energy attenuation to assess the corneal viscoelasticity is presented. Using phase‐resolved optical coherence tomography, the spatial‐temporal displacement map is derived. The phase velocity dispersion curve and center frequency are obtained by transforming the displacement map into the wavenumber‐frequency domain through the 2D fast Fourier transform (FFT). The shear modulus is calculated through Rayleigh wave equation using the phase velocity in the high frequency. The normalized energy distribution is plotted by transforming the displacement map into the spatial‐frequency domain through the 1D FFT. The energy attenuation coefficient is derived by exponential fitting to calculate the viscous modulus. Different concentrations of tissue‐mimicking phantoms and porcine corneas are imaged to validate this method, which demonstrates that the method has the capability to assess the corneal viscoelasticity.     

Magnetic resonance elastography in nonlinear viscoelastic materials under load

Characterisation of soft tissue mechanical properties is a topic of increasing interest in translational and clinical research. Magnetic resonance elastography (MRE) has been used in this context to assess the mechanical properties of tissues in vivo noninvasively. Typically, these analyses rely on linear viscoelastic wave equations to assess material properties from measured wave dynamics. However, deformations that occur in some tissues (e.g. liver during respiration, heart during the cardiac cycle, or external compression during a breast exam) can yield loading bias, complicating the interpretation of tissue stiffness from MRE measurements. In this paper, it is shown how combined knowledge of a material’s rheology and loading state can be used to eliminate loading bias and enable interpretation of intrinsic (unloaded) stiffness properties. Equations are derived utilising perturbation theory and Cauchy’s equations of motion to demonstrate the impact of loading state on periodic steady-state wave behaviour in nonlinear viscoelastic materials. These equations demonstrate how loading bias yields apparent material stiffening, softening and anisotropy. MRE sensitivity to deformation is demonstrated in an experimental phantom, showing a loading bias of up to twofold. From an unbiased stiffness of \(4910.4 \pm 635.8\) Pa in unloaded state, the biased stiffness increases to 9767.5 \(\pm \,\)1949.9 Pa under a load of \(\approx \) 34% uniaxial compression. Integrating knowledge of phantom loading and rheology into a novel MRE reconstruction, it is shown that it is possible to characterise intrinsic material characteristics, eliminating the loading bias from MRE data. The framework introduced and demonstrated in phantoms illustrates a pathway that can be translated and applied to MRE in complex deforming tissues. This would contribute to a better assessment of material properties in soft tissues employing elastography.

     

Paediatric brain tissue properties measured with magnetic resonance elastography

Biomechanics and Modeling in Mechanobiology - The aim of this study is to characterise the stiffness of white and grey matter in paediatric subjects using magnetic resonance elastography (MRE) and...     

Viscoelastic properties of the tongue and soft palate using MR elastography

Biomechanical properties of the human tongue are needed for finite element models of the upper airway and may be important to elucidate the pathophysiology of obstructive sleep apneoa. Tongue viscoelastic properties have not been characterized previously. Magnetic resonance elastography (MRE) is an emerging imaging technique that can measure the viscoelastic properties of soft tissues in-vivo. In this study, MRE was used to measure the viscoelastic properties of the tongue and soft palate in 7 healthy volunteers during quiet breathing. Results show that the storage shear modulus of the tongue and soft palate is 2.67±0.29 and 2.53±0.31 kPa (mean ± SD), respectively. This is the first study to investigate the mechanical properties of the tongue using MRE, and it provides necessary data for future studies of patient groups with altered upper airway function.