Simulation and analysis of magnetic resonance elastography wave images using coupled harmonic oscillators and Gaussian local frequency estimation.

New methods for simulating and analyzing Magnetic Resonance Elastography (MRE) images are introduced. To simulate a two-dimensional shear wave pattern, the wave equation is solved for a field of coupled harmonic oscillators with spatially varying coupling and damping coefficients in the presence of an external force. The spatial distribution of the coupling and the damping constants are derived from an MR image of the investigated object. To validate the simulation as well as to derive the elasticity modules from experimental MRE images, the wave patterns are analyzed using a Local Frequency Estimation (LFE) algorithm based on Gauss filter functions with variable bandwidths. The algorithms are tested using an Agar gel phantom with spatially varying elasticity constants. Simulated wave patterns and LFE results show a high agreement with experimental data. Furthermore, brain images with estimated elasticities for gray and white matter as well as for exemplary tumor tissue are used to simulate experimental MRE data. The calculations show that already small distributions of pathologically changed brain tissue should be detectable by MRE even within the limit of relatively low shear wave excitation frequency around 0.2 kHz.     

Analysis of wave patterns in MR elastography of skeletal muscle using coupled harmonic oscillator simulations

The ability to study muscle elasticity in vivo would be of great clinical interest. Magnetic resonance elastography (MRE) has the potential to quantify noninvasively the distribution of the shear modulus in muscle tissue. Elasticity information may be derived by extracting frequencies from the wave patterns of phase-contrast MRE images. In a new approach, MRE wave patterns were reconstructed using 3D coupled harmonic oscillator calculations (CHO). To analyze in vivo MRE measurements of the biceps brachii of healthy volunteers, different anisotropic fibrous structures for the couplings between the muscle elements have to be assumed. V-shaped wave patterns as observed when excitation was applied on the tendon were reproduced by a model, where in a central band of stiff fascicles wave propagation was about twice as fast as that in surrounding tissue. Planar waves were observed for excitation near the muscle surface. They could be reconstructed by assuming a simultaneous wave excitation of all muscle fibers, where fibers along the main muscle axis were coupled more strongly than those perpendicular to the axis. The results show that CHO calculations provide a fast and reliable method for incorporating anatomical information of the investigated tissue in the reconstruction of complex wave patterns.     

Influence of composition of carbonyl iron particles on dynamic mechanical properties of magnetorheological elastomers

Magnetorheological elastomers (MRE) are known as smart materials. However, the magnetorheological (MR) effect of MRE is not high enough at present, which limits its engineering applications. Prior studies have shown that magneto-induced shear storage modulus and MR effect were mainly determined by the performance of the ferromagnetic particles. In this paper, MRE samples were prepared by carbonyl iron particles (CIP) of different compositions based on silicon rubber under external magnetic field. Their microstructures were observed using an optical digital microscope and a scanning electron microscope. The dynamic mechanical properties of MRE samples were measured using a modified dynamic mechanical analyzer under varying magnetic field strength and frequency. The results show that the carbon content of CIP have a greater impact on the dynamic mechanical properties of MRE. The magneto-induced shear storage modulus and MR effect can be increased by selecting CIP of low carbon content. In addition, the damping property is also significantly influenced by the carbon content of the CIP. This study is expected to provide guidance for fabrication of high performance MRE.     

Diffraction-biased shear wave fields generated with longitudinal magnetic resonance elastography drivers

Magnetic resonance elastography (MRE) is a technique for quantifying the acoustic response of biological tissues to propagating waves applied at low frequencies in order to evaluate mechanical properties. Application-specific MRE drivers are typically required to effectively deliver shear waves within the tissue of interest. Surface MRE drivers with transversely oriented vibrations have often been used to directly generate shear waves. These drivers may have disadvantages in certain applications, such as poor penetration depth and inflexible orientation. Therefore, surface MRE drivers with longitudinally oriented vibrations are used in some situations. The purpose of this work was to investigate and optimize a longitudinal driver system for MRE applications. A cone-like hemispherical distribution of shear waves being generated by these drivers and the wave propagation being governed by diffraction in the near field are shown. Using MRE visualization of the vector displacement field, we studied the properties of the shear wave field created by longitudinal MRE drivers of various sizes to identify optimum shear wave imaging planes. The results offer insights and improvements in both experimental design and imaging plane selection for 2-D MRE data acquisition.     

Universal elasticity and fluctuations of nematic gels

We study elasticity of spontaneously orientationally ordered amorphous solids, characterized by a vanishing transverse shear modulus, as realized by nematic elastomers and gels. We show that local heterogeneities and elastic nonlinearities conspire to lead to anomalous nonlocal universal elasticity controlled by a nontrivial infrared fixed point. Namely, such solids are characterized by universal shear and bending moduli that, respectively, vanish and diverge at long scales, are universally incompressible, and exhibit a universal negative Poisson ratio and a non-Hookean elasticity down to arbitrarily low strains. Based on expansion about five dimensions, we argue that the nematic order is stable to thermal fluctuation and local heterogeneities down to d(lc)<3.     

On the feasibility of elastic wave visualization within polymeric solids using magnetic resonance elastography

In this paper, the feasibility of extending previously described magnetic resonance elastography (MRE) dynamic displacement (and associated elasticity) measurement techniques, currently used successfully in tissue, to solid materials which have much higher shear rigidity and much lower nuclear spin densities, is considered. Based on these considerations, the MRE technique is modified in a straightforward manner and used to directly visualize shear wave displacements within two polymeric materials, one of which is relatively stiff.     

Effect of off-frequency sampling in magnetic resonance elastography

In magnetic resonance elastography (MRE), shear waves at a certain frequency are encoded through bipolar gradients that switch polarity at a controlled encoding frequency and are offset in time to capture wave propagation using a controlled sampling frequency. In brain MRE, there is a possibility that the mechanical actuation frequency is different from the vibration frequency, leading to a mismatch with encoding and sampling frequencies. This mismatch can occur in brain MRE from causes both extrinsic and intrinsic to the brain, such as scanner bed vibrations or active damping in the head. The purpose of this work was to investigate how frequency mismatch can affect MRE shear stiffness measurements. Experiments were performed on a dual-medium agarose gel phantom, and the results were compared with numerical simulations to quantify these effects. It is known that off-frequency encoding alone results in a scaling of wave amplitude, and it is shown here that off-frequency sampling can result in two main effects: (1) errors in the overall shear stiffness estimate of the material on the global scale and (2) local variations appearing as stiffer and softer structures in the material. For small differences in frequency, it was found that measured global stiffness of the brain could theoretically vary by up to 12.5% relative to actual stiffness with local variations of up to 3.7% of the mean stiffness. It was demonstrated that performing MRE experiments at a frequency other than that of tissue vibration can lead to artifacts in the MRE stiffness images, and this mismatch could explain some of the large-scale scatter of stiffness data or lack of repeatability reported in the brain MRE literature.     

Elastic strain response in the modified phase-field-crystal model

To understand and develop new nanostructure materials with specific mechanical properties, a good knowledge of the elastic strain response is mandatory. Here we investigate the linear elasticity response in the modified phase-field-crystal(MPFC) model. The results show that two different propagation modes control the elastic interaction length and time, which determine whether the density waves can propagate or not. By quantitatively calculating the strain field, we find that the strain distribution is indeed extremely uniform in case of elasticity. Further, we present a detailed theoretical analysis for the orientation dependence and temperature dependence of shear modulus. The simulation results show that the shear modulus reveals strong anisotropy and the one-mode analysis provides a good guideline for determining elastic shear constants until the system temperature falls below a certain value.     

Multiscale modeling of the effect of carbon nanotube orientation on the shear deformation properties of reinforced polymer-based composites

A combination of molecular dynamics (MD), continuum elasticity and FEM is used to predict the effect of CNT orientation on the shear modulus of SWCNT-polymer nanocomposites. We first develop a transverse-isotropic elastic model of SWCNTs based on the continuum elasticity and MD to compute the transverse-isotropic elastic constants of SWCNTs. These constants are then used in an FEM-based simulation to investigate the effect of SWCNT alignment on the shear modulus of nanocomposites. Furthermore, shear stress distributions along the nanotube axis and over its cross-sectional area are investigated to study the effect of CNT orientation on the shear load transfer.     

Using a pseudo-functionally graded interlayer in order to improve the static and dynamic behavior of wind turbine blade T-bolt root joints

The large wind turbines blades with multi-ton composite structures are mostly connected to the peach-bearings flanges using T-bolt joints which induce shear and bearing stress fields around the cross bolts. The significant differences between the modulus of elasticity of metallic bolts and composite surrounding materials cause stress concentration around interfaced zones and, also, limit the load capacity of the joints. In the present research, a pseudo functionally graded material (PFGM) as an interlayer is used around the cross bolts to examine the reduction of the stress concentration. Some radial variation of the mechanical properties would be considered for this interlayer. The finite element method is used to analyze the structures. Loadings are applied to the center of the cross bolts analogous to the real cases. Both the static and dynamic loadings are studied. For the finite element of the functionally graded material interlayer, a multilayer alternative material with constant properties in each layer is used. The results show that using an isotropic single layer with an average modulus of elasticity and specific thickness decreases the stress concentration of the composite part up to 47%. The various property models for the interlayer also show that an appropriated model can decrease the stress concentration up to 55%. Dynamic transient analyses would be implemented over the joint structure and improved considering to the practical cases. Using the PFGM interlayer decreases the constant and variable parts of the stresses up to 55% and also causes significant increasing of the joint fatigue life.     

LJ流体非牛顿现象的分子动力学模拟

使用非平衡分子动力学模拟方法研究了单原子LJ流体的非牛顿流变行为,并在系统中分别施加稳态Couette流场和振荡剪切流场.在Couette流场的模拟中,流体出现剪切变稀和法向应力差效应,不同剪切率下的径向分布函数反映了流体分子由于剪切所导致的微观结构变化,通过分析势能函数发现当剪切率增大时,分子间排斥作用增强,吸引作用减弱.在振荡剪切流场的模拟中,发现剪切应力和剪切率之间的相位差随频率增加而增加,随频率增加复数粘度的实部先增大再减小,虚部单调增加,导致虚部粘度相对实部粘度比例增大,弹性模量和粘性模量之比也随频率增加而增加.这三点现象表明LJ流体出现粘弹性行为,且在高频率下,弹性所占比重增大.     

Rigid and differential plasma crystal rotation induced by magnetic fields

Observations show that plasma crystals, suspended in the sheath of a radio-frequency discharge, rotate under the influence of a vertical magnetic field. Depending on the discharge conditions, two different cases are observed: a rigid-body rotation (all the particles move with a constant angular velocity) and sheared rotation (the angular velocity of particles has a radial distribution). When the discharge voltage is increased sufficiently, the particles may even reverse their direction of motion. A simple analytical model is used to explain qualitatively the mechanism of the observed particle motion and its dependence on the confining potential and discharge conditions. The model takes into account electrostatic, ion drag, neutral drag, and effective interparticle interaction forces. For the special case of rigid-body rotation, the confining potential is reconstructed. Using data for the radial dependence of particle rotation velocity, the shear stresses are estimated. The critical shear stress at which shear-induced melting occurs is used to roughly estimate the shear elastic modulus of the plasma crystal. The latter is also used to estimate the viscosity contribution due to elasticity in the plasma liquid. Further development is suggested in order to quantitatively implement these ideas.     

Micro-vibration suppression of equipment supported on a floor incorporating magneto-rheological elastomer core

In this study, magneto-rheological elastomers (MREs) are adopted to construct a smart sandwich beam for micro-vibration control of equipment. The micro-vibration response of a smart sandwich beam with MRE core which supports mass-concentrated equipment under stochastic support-motion excitations is investigated to evaluate the vibration suppression capability. The dynamic behavior of MREs as a smart viscoelastic material is characterized by a complex modulus dependent on vibration frequency and controllable by external magnetic fields. A frequency-domain solution method for the stochastic micro-vibration response of the smart sandwich beam supporting mass-concentrated equipment is developed based on the Galerkin method and random vibration theory. First, the displacements of the beam are expanded as series of spatial harmonic functions and the Galerkin method is applied to convert the partial differential equations of motion into ordinary differential equations. With these equations, the frequency-response function matrix of the beam–mass system and the expression of the velocity response spectrum are then obtained, with which the root-mean-square (rms) velocity response in terms of the one-third octave frequency band can be calculated. Finally, the optimization problem of the complex modulus of the MRE core is defined by minimizing the velocity response spectrum and the rms velocity response of the sandwich beam, through altering the applied magnetic fields. Numerical results are given to illustrate the influence of MRE parameters on the rms velocity response and the response reduction capacity of the smart sandwich beam. The proposed method is also applicable to response analysis of a sandwich beam with arbitrary core characterized by a complex shear modulus and subject to arbitrary stochastic excitations described by a power spectral density function, and is valid for a wide frequency range.     

Vibrational anomalies and marginal stability of glasses

The experimentally measured vibrational spectrum of glasses strongly deviates from that expected in Debye’s elasticity theory: The density of states deviates from Debye’s ω² law (“boson peak”), the sound velocity shows a negative dispersion in the boson-peak frequency regime, and there is a strong increase in the sound attenuation near the boson-peak frequency. A generalized elasticity theory is presented, based on the model assumption that the shear modulus of the disordered medium fluctuates randomly in space. The fluctuations are assumed to be uncorrelated and have a certain distribution (Gaussian or otherwise). Using field-theoretical techniques one is able to derive mean-field theories for the vibrational spectrum of a disordered system. The theory based on a Gaussian distribution uses a self-consistent Born approximation (SCBA),while the theory for non-Gaussian distributions is based on a coherent-potential approximation (CPA). Both approximate theories appear to be saddle-point approximations of effective replica field theories. The theory gives a satisfactory explanation of the vibrational anomalies in glasses. Excellent agreement of the SCBA theory with simulation data on a soft-sphere glass is reached. Since the SCBA is based on a Gaussian distribution of local shear moduli, including negative values, this theory describes a shear instability as a function of the variance of shear fluctuations. In the vicinity of this instability, a fractal frequency dependence of the density of states and the sound attenuation ∝ ω^1+a is predicted with a ? 1/2. Such a frequency dependence is indeed observed both in simulations and in experimental data. We argue that the observed frequency dependence stems from marginally stable regions in a glass and discuss these findings in terms of rigidity percolation.     

螺旋测微计在测量金属杨氏模量中的应用

本根据拉伸法测量金属杨氏模量的原理,对利用螺旋测微计测量金属杨氏模量的方法做了可行性分析,并在此基础上设计出一套完整的借助螺旋测微计测量金属杨氏模量的方法。     

基于双带宽高斯滤波器的磁共振弹性图局域频率估算算法研究与实现

本文对生物体软组织的生物力学模型进行了分析推导和简化,得到了磁共振相位图与生物组织弹性之间的力学关系,根据该关系研究了局域频率估算算法,应用Matlab对算法进行了编程实现,体模弹性图的实现验证了算法有效性,为后续开展临床肝纤维化分级研究奠定基础. 关键词： 磁共振弹性成像 弹性生物力学模型 局域频率估算     

Magnetic resonance elastography of the brain in a mouse model of Alzheimer's disease: initial results

The increasing prevalence of Alzheimer's disease (AD) has provided motivation for developing novel methods for assessing the disease and the effects of potential treatments. Magnetic resonance elastography (MRE) is an MRI-based method for quantitatively imaging the shear tissue stiffness in vivo. The objective of this research was to determine whether this new imaging biomarker has potential for characterizing neurodegenerative disease. Methods were developed and tested for applying MRE to evaluate the mouse brain, using a conventional large bore 3.0T MRI system. The technique was then applied to study APP-PS1 mice, a well-characterized model of AD. Five APP-PS1 mice and 8 age-matched wild-type mice were imaged immediately following sacrifice. Brain shear stiffness measurements in APP-PS1 mice averaged 22.5% lower than those for wild-type mice (P = .0031). The results indicate that mouse brain MRE is feasible at 3.0T, and brain shear stiffness has merit for further investigation as a potential new biomarker for Alzheimer's disease.     

A theoretical approach to local attenuation measurements of shear waves by MRE. Preliminary experimental results

An essential highlight of the presented method is the employment of Magnetic Resonance Elastography (MRE) for local measurements of the attenuation of elastic shear waves introduced into a biological sample. Such a measurement can be accomplished by combining the MRE method with those methods, in which collective displacement of spins is induced by external physical factors, such as variable electric field, strong magnetic field gradient or longitudinal elastic wave. A theoretical basis of the method involving external factors and results of preliminary experiments have been presented in this paper.     

Effect of Cyclic Deformation on Magnetorheological Elastomers

采制备了铁颗粒含量分别是60%,70%和80%的三种材料,在应变幅值为50%,75%和100%的循环加载条件下,利用改进后的动态力学分析仪测试了循环加载后材料的储能模量和损耗模量. 结果显示铁颗粒含量为70%和80%的样品,其储能模量和损耗模量都和循环加载的幅值以及循环加载的次数有关,铁颗粒含量为80%样品受加载条件的影响尤其明显. 但铁颗粒含量为60%的样品,其性能却与循环加载的幅值和次数无关. 为了更好的研究磁流变弹性体受循环加载后的性能,样品还进行了准静态拉伸测试,并用扫描电镜对测试的样品进行了原位观察.     

Cyclic stress-strain curves and internal friction of steel at ultrasonic frequencies

A new interpretation of some characteristics of material push-pull loaded at a frequency of 23 kHz can be evaluated by measuring the internal friction and elasticity modulus defect at different strain amplitudes. It is possible to obtain interesting relations describing the material's cyclic microplasticity response. The paper presents some basic relationships between the ‘plastic’ internal friction, elasticity modulus defect, hysteresis loop area, plastic strain amplitude and the cyclic deformation hardening coefficient, for low carbon steel with different grain sizes.