Parameters affecting the resolution and accuracy of 2-D quantitative shear wave images

Time-of-flight methods allow quantitative measurement of shear wave speed (SWS) from ultrasonically tracked displacements following impulsive acoustic radiation force excitation in tissue. In heterogeneous materials, reflections at boundaries can distort the wave shape and confound determination of the wave arrival time. The magnitude of these effects depends on the shear wavelength of the excitation, the kernel size used to calculate the SWS, and the method used to determine the wave arrival time. In this study, we perform a parametric analysis of these factors using finite element modeling of the tissue response and simulated ultrasonic tracking. Two geometries are used, a stiff vertical layer and a stiff spherical inclusion, each in a uniform background. Wave arrival times are estimated using the peak displacement, peak slope of the leading edge, and cross-correlation methods. Results are evaluated in terms of reconstruction accuracy, resolution, contrast, and contrast-to-noise ratio of reconstructed SWS images. Superior results are obtained using narrower excitation widths and arrival time estimators which identify the leading edge of the propagating wave. The optimal kernel size is determined by a tradeoff between improved accuracy for larger kernels at the expense of spatial resolution.     

Ultrasonic tracking of acoustic radiation force-induced displacements in homogeneous media

The use of ultrasonic methods to track the tissue deformation generated by acoustic radiation force is subject to jitter and displacement underestimation errors, with displacement underestimation being primarily caused by lateral and elevation shearing within the point spread function (PSF) of the ultrasonic beam. Models have been developed using finite element methods and Field II, a linear acoustic field simulation package, to study the impact of focal configuration, tracking frequency, and material properties on the accuracy of ultrasonically tracking the tissue deformation generated by acoustic radiation force excitations. These models demonstrate that lateral and elevation shearing underneath the PSF of the tracking beam leads to displacement underestimation in the focal zone. Displacement underestimation can be reduced by using tracking beams that are narrower than the spatial extent of the displacement fields. Displacement underestimation and jitter decrease with time after excitation as shear wave propagation away from the region of excitation reduces shearing in the lateral and elevation dimensions. The use of higher tracking frequencies in broadband transducers, along with 2D focusing in the elevation dimension, will reduce jitter and improve displacement tracking accuracy. Relative displacement underestimation remains constant as a function of applied force, whereas jitter increases with applied force. Underdeveloped speckle (SNR < 1.91) leads to greater levels of jitter and peak displacement underestimation. Axial shearing is minimal over the tracking kernel lengths used in acoustic radiation force impulse imaging and thus does not impact displacement tracking.     

A finite-element method model of soft tissue response to impulsive acoustic radiation force

Several groups are studying acoustic radiation force and its ability to image the mechanical properties of tissue. Acoustic radiation force impulse (ARFI) imaging is one modality using standard diagnostic ultrasound scanners to generate localized, impulsive, acoustic radiation forces in tissue. The dynamic response of tissue is measured via conventional ultrasonic speckle-tracking methods and provides information about the mechanical properties of tissue. A finite-element method (FEM) model has been developed that simulates the dynamic response of tissues, with and without spherical inclusions, to an impulsive acoustic radiation force excitation from a linear array transducer. These FEM models were validated with calibrated phantoms. Shear wave speed, and therefore elasticity, dictates tissue relaxation following ARFI excitation, but Poisson's ratio and density do not significantly alter tissue relaxation rates. Increased acoustic attenuation in tissue increases the relative amount of tissue displacement in the near field compared with the focal depth, but relaxation rates are not altered. Applications of this model include improving image quality, and distilling material and structural information from tissue's dynamic response to ARFI excitation. Future work on these models includes incorporation of viscous material properties and modeling the ultrasonic tracking of displaced scatterers.     

基于超弹性、分数导数和摩擦模型的碳黑填充橡胶隔振器动态建模

碳黑填充橡胶隔振器（以下简称＂橡胶隔振器＂）的动态特性与预载、激振频率和激振振幅相关。实验测试了一橡胶隔振器的动态特性,建立了基于超弹性、分数导数和摩擦模型的橡胶隔振器动态特性的非线性模型,其中超弹性模型用于描述橡胶隔振器的弹性,分数导数模型用于表征橡胶隔振器动态特性的激振频率相关性,摩擦模型用于表征橡胶隔振器动态特性与激振振幅相关的特性,文中论述了建模方法和参数辨识方法。有限元分析获得橡胶隔振器的静态力-位移曲线,利用测试得到的橡胶隔振器在大振幅、低频激励下的力-位移关系,拟合得到橡胶隔振器动态模型中摩擦模型的参数,利用测试得到的橡胶隔振器在小振幅、高频激励下的力-位移关系,拟合得到橡胶隔振器动态模型中分数导数模型的参数。利用建立的模型和拟合得到的参数计算分析了橡胶隔振器动态特性的振幅相关性、频率相关性和预载相关性,并与实验结果进行了对比分析。分析结果表明,建立的模型可以较好的描述橡胶隔振器的动态特性。     

非线性弹性地基上悬臂输流管的受迫振动

本文综合考虑地基的剪切效应、非线性刚度和粘滞阻尼的影响,建立了非线性Pasternak地基上输流管的运动控制方程。基于Galerkin法研究了基础激励作用下非线性弹性地基上悬臂输流管的非线性动力学行为,着重讨论了基础激励和地基剪切刚度对系统动力学特性的影响。结果表明：系统在基础激励作用下具有非常复杂的动态响应,包括多种形式的周期、概周期和混沌运动;地基的剪切刚度对系统的动态特性有重要影响,随着地基剪切刚度的增大,在基础激励参数区域内系统的概周期和混沌运动窗口逐渐减小,当地基剪切刚度足够大时,系统将始终处于周期运动状态。     

Duffing振子激励下平板声振特性研究

针对非线性振动激励下结构声辐射问题,由变分原理导出Duffing振子激励下平板声振耦合动力学方程,由模态展开法及增量谐波平衡法导出轻流体中耦合动力学方程的近似解析解,给出多频激励下平板表面平均振速及辐射声功率表达式,研究激励力频率、非线性项对系统振动及声辐射特性影响。结果表明,Duffing振子激励下平板的声振耦合问题为含离散与连续系统的复杂动力学问题;耦合运动下Duffing振子出现二次跳跃现象与新的共振特性;平板声振特性主要由三次谐波决定。研究结果可为隔振结构的声振设计提供理论依据。     

Assessment of shear modulus of tissue using ultrasound radiation force acting on a spherical acoustic inhomogeneity

An ultrasound-based method to locally assess the shear modulus of a medium is reported. The proposed approach is based on the application of an impulse acoustic radiation force to an inhomogeneity in the medium and subsequent monitoring of the spatio-temporal response. In our experimental studies, a short pulse produced by a 1.5-MHz highly focused ultrasound transducer was used to initiate the motion of a rigid sphere embedded into an elastic medium. Another 25 MHz focused ultrasound transducer operating in pulse-echo mode was used to track the displacement of the sphere. The experiments were performed in gel phantoms with varying shear modulus to demonstrate the relationship between the displacement of the sphere and shear modulus of the surrounding medium. Because the magnitude of acoustic force applied to sphere depends on the acoustic material properties and, therefore, cannot be used to assess the absolute value of shear modulus, the temporal behavior of the displacement of the sphere was analyzed. The results of this study indicate that there is a strong correlation between the shear modulus of a medium and spatio-temporal characteristics of the motion of the rigid sphere embedded in this medium.     

Dynamic effective models of two-dimensional acoustic metamaterials with cylindrical inclusions

Based on analytical solutions of elastic waves scattered by a coated cylinder in an infinite elastic matrix, we construct the localization relations for averaged displacement and stress fields in each phase. Dynamic effective mass, in-plane bulk modulus and shear modulus are defined, respectively, as the ratio between the force and acceleration, bulk stress and bulk strain, maximum shear stress and maximum shear strain. Analytic expressions for dynamic effective parameters of two-dimensional acoustic metamaterials are derived. Numerical examples are given to analyze dynamic effective properties of composites with coated inclusions. It is demonstrated that the proposed model can predict negative values of effective mass and effective bulk and shear modulus, and discover the underlying mechanisms of negative effective material parameters. The proposed model will be helpful in designing new acoustic metamaterials.     

强震下隔震连续梁桥地震响应的温度效应研究

基于某三跨隔震连续梁桥,分析了环境温度、隔震支座初始位移及铅芯热效应对其地震响应的影响。首先,分析了隔震支座产生初始位移的机理。在此基础上,选取36条近断层地震动记录,分别采用考虑与不考虑铅芯热效应的隔震支座模型,对该隔震连续梁桥进行了不同环境温度条件下的非线性动力时程分析,得到结构关键部位的动力响应。结果表明：低温环境条件下,环境温度、初始位移、铅芯热共同作用效应会使得隔震连续梁桥结构地震峰值位移明显减小,支座、墩底峰值剪力显著增大,环境温度对隔震梁桥地震峰值响应起主导作用;当环境温度超过常温（20℃）时,由于环境温度引起隔震支座力学性能显著退化,环境温度、隔震支座初始位移、铅芯热效应的共同作用使得结构地震峰值位移显著增大,此时初始位移与铅芯热对隔震支座峰值位移、剪力、墩底剪力影响更为显著。由于部分近场地震动作用下的结构峰值位移显著增大,使得其峰值剪力呈现出增大趋势。     

单级人字齿轮减速器振动噪声影响因素研究

本文以船用人字齿轮减速器为研究对象,依据人字齿轮传动结构特点,综合考虑齿轮时变啮合刚度、误差等激励以及人字齿轮轴向定位与滑动轴承支撑等因素,建立了传动系统弯-扭-轴耦合动力学模型,通过求解得到了传动系统轴承动载荷。以轴承动载荷为激励,采用FEM/BEM方法计算了齿轮箱噪声辐射,得到了齿轮箱声场声压分布云图与各场点噪声谱。系统讨论了人字齿轮基本参数(包括齿顶高系数、顶隙系数、齿宽、螺旋角及压力角)以及减速器结构特征（人字齿轮中间连接刚度、轴向定位刚度）对减速器振动噪声的影响,为减速器的减振降噪设计提供了理论基础。     

隔震曲线连续梁桥铅芯橡胶支座参数优化

为了提升铅芯橡胶支座（LRB）在隔震曲线梁桥中的减隔震效果,该文对LRB力学性能参数进行了优化分析。首先,采用ANSYS建立了某三跨隔震曲线梁桥有限元模型,考虑LRB屈服力、初始刚度及屈服后刚度等性能参数的影响,对该桥进行非线性时程分析,得到了结构关键地震响应随支座力学性能参数的变化规律,并确定了支座参数的合理取值范围。在该支座参数区间内,又以墩底剪力之和为目标函数,基于零阶优化算法,对LRB力学性能参数进行了优化。结果表明：屈服力、初始刚度及屈服后刚度对隔震连续梁桥地震响应有显著影响;隔震支座参数优化后,使得隔震支座峰值位移得到了有效控制,同时不显著增大墩底剪力,且边墩与中墩墩底剪力差值明显缩小,各墩受力更趋均衡。     

Monitored steady-state excitation and recovery (MSSER) radiation force imaging using viscoelastic models

Acoustic radiation force imaging methods distinguish tissue structure and composition by monitoring tissue responses to applied radiation force excitations. Although these responses are a complex, multidimensional function of the geometric and viscoelastic nature of tissue, simplified discrete biomechanical models offer meaningful insight to the physical phenomena that govern induced tissue motion. Applying Voigt and standard linear viscoelastic tissue models, we present a new radiation force technique - monitored steady-state excitation and recovery (MSSER) imaging - that tracks both steady-state displacement during prolonged force application and transient response following force cessation to estimate tissue mechanical properties such as elasticity and viscosity. In concert with shear wave elasticity imaging (SWEI) estimates for Young's modulus, MSSER methods are useful for estimating tissue mechanical properties independent of the applied force magnitude. We test our methods in gelatin phantoms and excised pig muscle, with confirmation through mechanical property measurement. Our results measured 10.6 kPa, 14.7 kPa, and 17.1 kPa (gelatin) and 122.4 kPa (pig muscle) with less than 10% error. This work demonstrates the feasibility of MSSER imaging and merits further efforts to incorporate relevant mechanical tissue models into the development of novel radiation force imaging techniques.     

缓冲包装设计引起的易损件移动现象的力学原理

目的研究产品在物流运输搬运过程中易损件会发生转移的行为。方法提出轻型小机电产品包装冲击动力学模型,建立基于2个易损件的产品冲击动力学方程,得到易损件的峰值加速度与刚度比的关系图,并且采用Runge-Kutta法进行数值求解,获取2个易损件在半正弦激励脉冲激励下的冲击时域响应、冲击谱和破损边界曲线。结果产品在不同的刚度比下,各个部件出现损坏的先后顺序不同,谁先坏本质上取决于哪个部件的峰值加速度响应首先达到其脆值。结论研究揭示了易损件随着冲击激励和包装材料特性发生移动的现象和本质原因。     

索端激励对斜拉索风雨致振动性能的影响

实际斜拉索的振动可能是风-雨致振动和参数振动的组合, 索端激励对斜拉索风-雨致振动性能有一定影响。将索端激励转化为作用在斜拉索上的弹性力和惯性力, 建立了斜拉索风-雨致振动和参数振动的组合分析模型, 在讨论了参数振动模型和斜拉索风-雨致振动的特性后, 探讨了索端激励对风-雨致振动振幅、水路运动以及达到最大振幅所需时间的影响。结果表明:在一定的频率范围内, 索端激励的存在会改变斜拉索风-雨致振动幅值和水路运动幅值随时间变化的特性, 并能促进斜拉索风-雨致振动的发生。     

冲击激励下含限位器的气囊-船用旋转机械系统的动力学特性分析

主要研究了冲击激励下含限位器的气囊-旋转机械系统的动力学特性。首先,考虑了轴承的非线性油膜力和转子的不平衡力等因素,建立了在冲击激励下气囊-旋转机械系统的非线性动力学模型;然后,采用数值模拟的方法分析了冲击激励下,限位器对气囊-旋转机械系统动力学特性的影响,讨论了在限位器不同刚度比、安装间隙、阻尼比等参数下气囊-旋转机械系统的动力学响应。结果表明:限位器的刚度和安装间隙对冲击激励下系统的最大相对位移和绝对加速度有较大影响,而阻尼对其影响会随着刚度比的增大而减小。     

On the effects of reflected waves in transient shear wave elastography

In recent years, novel quantitative techniques have been developed to provide noninvasive and quantitative stiffness images based on shear wave propagation. Using radiation force and ultrafast ultrasound imaging, the supersonic shear imaging technique allows one to remotely generate and follow a transient plane shear wave propagating in vivo in real time. The tissue shear modulus, i.e., its stiffness, can then be estimated from the shear wave local velocity. However, because the local shear wave velocity is estimated using a time-of- flight approach, reflected shear waves can cause artifacts in the estimated shear velocity because the incident and reflected waves propagate in opposite directions. Such effects have been reported in the literature as a potential drawback of elastography techniques based on shear wave speed, particularly in the case of high stiffness contrasts, such as in atherosclerotic plaque or stiff lesions. In this letter, we present our implementation of a simple directional filter, previously used for magnetic resonance elastography, which separates the forward- and backward-propagating waves to solve this problem. Such a directional filter could be applied to many elastography techniques based on the local estimation of shear wave speed propagation, such as acoustic radiation force imaging (ARFI), shearwave dispersion ultrasound vibrometry (SDUV), needle-based elastography, harmonic motion imaging, or crawling waves when the local propagation direction is known and high-resolution spatial and temporal data are acquired.     

The role of viscosity in the impulse diffraction field of elastic waves induced by the acoustic radiation force

Several ultrasound-based techniques for the estimation of soft tissue elasticity are currently being investigated. Most of them study the medium response to dynamic excitations. Such responses are usually modeled in a purely elastic medium using a Green's function solution of the motion equation. However, elasticity by itself is not necessarily a discriminant parameter for malignancy diagnosis. Modeling viscous properties of tissues could also be of great interest for tumor characterization. We report in this paper an explicit derivation of the Green's function in a viscous and elastic medium taking into account shear, bulk, and coupling waves. From this theoretical calculation, 3D simulations of mechanical waves in viscoelastic soft tissues are presented. The relevance of the viscoelastic Green's function is validated by comparing simulations with experimental data. The experiments were conducted using the supersonic shear imaging (SSI) technique which dynamically and remotely excites tissues using acoustic radiation force. We show that transient shear waves generated with SSI are modeled very precisely by the Green's function formalism. The combined influences of out-of-plane diffraction, beam shape, and shear viscosity on the shape of transient waves are carefully studied as they represent a major issue in ultrasound-based viscoelasticity imaging techniques.     

基于振动测试的非线性参数识别方法

研究了利用特殊的正弦扫频技术识别非线性参数的方法。该方法利用目前线性系统成熟的模态分析技术,并结合等效线性化理论,通过振动测试识别结构的非线性参数,可以建立一个更加准确的模型来反映非线性结构的动力学特性,从而提高模型的预测精度。该方法包括两部分：（1）常位移测试识别非线性刚度;（2）常速度测试识别非线性阻尼。常位移测试是在一次正弦扫频过程中,通过调整各频率下的激励力幅值使得位移响应的幅值为常数,获得一组频响函数,通过模态分析获得等效刚度;改变位移响应的幅值进行多次测试,获得多组等效刚度;对获得的一系列恒定位移响应下的等效刚度进行曲线拟合,即可获得所有线性和非线性刚度参数。常速度测试与其类似。以三自由度非线性系统为例,进行了常位移测试和     

DYNAMIC RESPONSE OF ANISOTROPIC THIN-WALLED BEAMS TO BLAST AND HARMONICALLY OSCILLATING LOADS

The dynamic response of anisotropic thin-walled beams to blast and harmonically time-dependent loads is investigated. The structural model incorporates transverse shear, and warping restraint and includes the anisotropy of the constituent materials. As a result of the beneficial implications played by the bending-twist elastic coupling, the circumferentially asymmetric stiffness configuration, inducing such a coupling is adopted and the pertinent system of governing equations is used to study the dynamic response. Efficient solution methodologies able to predict the response to arbitrary and harmonic time-dependent excitations are used and some of the implications played by the anisotropy of beam material, transverse shear and secondary warping are outlined.     

基于应变模态的连续梁动挠度识别

为了实现基于应变测量的连续梁动挠度识别,提出了一种基于应变模态的梁结构动挠度监测方法。利用应变传感器进行应变测试获得梁的动应变数据,由动应变数据的互相关函数求出应变模态振型,利用应变-位移转换关系求出位移模态振型,再由动应变数据和应变模态振型计算出位移模态坐标,最后根据计算出的位移模态坐标叠加位移模态振型得到梁结构的实时挠曲线,从而实现对动挠度的监测。为了验证方法的有效性,对连续梁在脉冲激励及地震作用下的动挠度进行了数值模拟,并进行了简支梁力锤锤击实验。数值模拟及实验的结果表明,基于应变模态监测梁结构动挠度是可行的,且具有较高的精度。