超声弹性成像中应变滤波器的理论及其发展

弹性成像能够提供组织弹性这一基本的力学属性，具有很广阔的应用前景。应变滤波器是超声弹性成像的重要理论框架，可广泛应用于超声弹性成像效果的评估、分析和预测。本详细综述了应变滤波器的理论和发展，并对献中的一些笔误作了修正，对实现的一些细节作了说明。通过对应变滤波器的理解，可以加深对超声弹性成像效果的理解，并对采用合适的方法和参数以获得最佳的成像效果以指导。     

软组织建模中的有限元模型

用求解弹性力学问题的经典方法一有限元方法进行物理建模，并根据人体软组织的生物力学特性，对有限元模型进行修改。实验结果表明：修改后的有限元模型在形变逼真的情况下稳定性更强。     

一种超声弹性成像试验数据的快速仿真算法

基于有限元分析和FieldⅡ声场模拟的超声弹性成像试验数据的仿真需要较长时间,本研究基于超声线性系统理论和弹性力学原理,借助数字信号处理与插值技术,提出了一种快速仿真超声弹性成像试验数据的算法。实验结果显示,该算法能仿真不同组织模型在压缩过程中产生的超声回波数据集,使用标准的弹性成像程序在该仿真的数据集上运行,生成的应变图与预期目标一致;原方法仿真一帧128像素×1 039像素的回波数据需6.3 h,而新算法生成相同的一帧只需要35 s。实验结果证明了该算法的正确性和高效性,可为弹性成像研究所需要的试验数据提供有效仿真手段。     

超声弹性成像中应变滤波器的理论及其发展

弹性成像能够提供组织弹性这一基本的力学属性,具有很广阔的应用前景。应变滤波器是超声弹性成像的重要理论框架,可广泛应用于超声弹性成像效果的评估、分析和预测。本文详细综述了应变滤波器的理论和发展,并对文献中的一些笔误作了修正,对实现的一些细节作了说明。通过对应变滤波器的理解,可以加深对超声弹性成像效果的理解,并对采用合适的方法和参数以获得最佳的成像效果以指导。     

具有双特征时间参数的生物软组织黏弹性性质的理论研究

目的 探索描述生物软组织黏弹性特性的普遍行为或规律。方法 根据生物软组织的力学结构,构建由两个线性弹簧和两个黏壶的不同组合构成的四元件黏弹性结构模型;并通过弹性理论,结合不同黏弹性模型的几何构型推导其运动微分方程,利用其微分方程分析不同四元件模型的应力松弛和蠕变行为以及反映弹性和黏性相结合的应力松弛时间和蠕变推迟时间。结果 所有可能的四元件黏弹性模型都具有普遍的本构关系、应力松弛和蠕变函数形式。通过比较模型预测结果与主动脉瓣、韧带和脑动脉等生物软组织的实验数据发现,四元件黏弹性模型能够很好地描述生物软组织的力学行为。“快”和“慢”两个特征时间τ1和τ2对生物软组织的应力松弛具有显著的影响。“快”松弛时间τ1对应力达到稳定态所需时间有明显的影响,而“慢”松弛时间τ2对松弛率的影响不显著,但对应力松弛的稳定态有明显的影响。结论 生物软组织的时间依赖性行为可以通过两个特征时间尺度来表征,即“快”和“慢”时间;且具有两个特征时间的生物软组织的应力 应变关系、应力松弛和蠕变函数具有相同的数学形式,这与所选择的弹簧和黏壶的配置和排列无关,但为保证模型力学参数的合理性,针对不同的生物软组织应选取适合的模型。     

大腿残肢步态过程的非线性有限元分析

目的利用三维有限元分析方法研究大腿截肢患者在行走过程中3个不同时相下残肢的生物力学特性,为建立完整的大腿接受腔测量、设计与评估系统提供研究基础。方法首先根据CT图像三维重建大腿截肢患者的骨骼、肌肉软组织和接受腔的三维几何模型;定义软组织为超弹性和线弹性材料属性,并相应建立两个有限元仿真模型;定义残端与接受腔之间的接触关系,约束残肢近端,对模型的远端施加膝关节载荷,模拟步态周期中足跟着地时期、站立相中期、脚尖离地3个时相下大腿残肢-接受腔系统所受载荷;计算分析接触界面上的应力,并对比分析超弹性和线弹性软组织力学特性对接触界面力学行为特性的影响。结果无论线弹性还是超弹性模型,3个时相下大腿残肢-接受腔界面的最大接触压力均在残肢末端达到最大值。超弹性模型3个时相下接触压力峰值分别为55.80、47.63和50.44 kPa;而线弹性模型接触压力的最大值都增加2倍以上,其值分别为149.86、118.55和139.68 kPa。同时通过分析接触面间的径向剪切应力和轴向剪切应力发现,3个时相下接触界面间的应力在残肢末端较集中,在足跟着地到脚尖离地过程中,有部分力通过接受腔后侧缘传递转向接受腔前缘传递。结论不同时相下残肢与接受腔接触界面的压力和剪切应力分布情况不同,在设计接受腔时需要充分考虑其受力特点。     

角膜的弹性模量非均匀分布对其光学相干弹性成像的影响

目的 分析激励源位置、检测区域长度和检测深度对人眼角膜的剪切波光学相干弹性成像(optical coherence elastography, OCE)的影响。方法 结合人眼角膜的弹性模量的实际分布情况，构建角膜弹性模量非均匀分布的有限元模型。通过模拟剪切波OCE实验，对比分析有限元模拟结果和理论结果。结果 当激励源位置不同时，角膜前后基质的剪切波波速误差不同；当检测区域长度不同时，角膜前后基质的剪切波波速非线性变化；在超弹性材料模型下，当检测深度不同时，剪切波波速明显变化。结论 由于角膜弹性模量非均匀分布，在角膜前后基质不同激励源位置、不同检测区域长度和不同检测深度的有限元模拟剪切波波速的结果不同。将具有非均匀性的生物组织视作均质进行OCE实验会影响结果准确性。     

介入超声印压系统检测软组织力学特性实验研究

目的：探讨介入超声印压系统检测软组织力学属性可行性，为活体深部组织力学属性检测提供基础。方法：通过循环印压不同软组织，获得印压力和形变实验数据，以硬度计算公式获得不同软组织硬度参量值。结果：不同软组织硬度参量值不同（P〈0．05）。结论：介入超声印压系统检测软组织力学属性是可行的。可望在活体检测深部组织、器官的力学属性。     

基于MRI图像的心肌三维弹性成像

材料参数比起运动参数能够更显著地反映物体的内在属性变化,定量获得病变组织的材料参数对心脏疾病诊断具有非常重要的意义。本研究提出一种在利用MRI图像获得部分形变位移等运动信息和约束条件的情况下,依据连续力学模型,使用有限元分析结合H∞滤波估计方法实现三维弹性成像的算法。模拟数据仿真给出了与最小二乘法结果的对比,验证了方法的有效性。最后给出了对病人心脏MRI图像三维弹性成像结果。     

血管内超声弹性成像研究进展

自1997年有学者将组织力学属性测定与血管内超声成像结合以后,血管内超声弹性成像(IVUSE)技术的发展方兴未艾.IVUSE是利用血管自身的搏动产生腔内压差,通过分析压缩前后的超声图像获取血管和斑块的应变、弹性模量等弹性参数进行成像.介绍了血管内超声弹性成像技术的成像原理,并根据成像参数的不同对IVUSE分2大类介绍其计算方法和目前进展情况,最后对此技术的发展趋势进行了展望.     

超声弹性成像中的逆问题求解方法

超声弹性成像通常只能得到组织在外部压缩作用下的纵向应变分布.超声弹性成像逆问题的求解,即重建组织内部的弹性模量分布,具有重要的意义.本文提出一种利用组织的应力-应变关系和基于有限元分析的迭代计算方法,从组织的纵向应变分布重建出组织的弹性模量分布.对平面应变状态下的均匀组织内含一圆形异物的模型和弹性模量连续过渡的模型分别进行了计算机仿真.结果初步验证了该方法的可行性.     

Anatomy- and physics-based facial animation for craniofacial surgery simulations

A modelling approach for the realistic simulation of facial expressions of emotion in craniofacial surgery planning is presented. The method is different from conventional, non-physical techniques for character animation in computer graphics. A consistent physiological mechanism for facial expressions was assumed, which was the effect of contracting muscles on soft tissues. For the numerical solution of the linear elastic boundary values, the finite element method on tetrahedral grids was used. The approach was validated on a geometrical model of a human head derived from tomographic data. Using this model, individual facial expressions of emotion were estimated by the superpositioning of precomputed single muscle actions.     

Measuring the elastic modulus of ex vivo small tissue samples

Over the past decade, several methods have been proposed to image tissue elasticity based on imaging methods collectively called elastography. While progress in developing these systems has been rapid, the basic understanding of tissue properties to interpret elastography images is generally lacking. To address this limitation, we developed a system to measure the Young's modulus of small soft tissue specimens. This system was designed to accommodate biological soft tissue constraints such as sample size, geometry imperfection and heterogeneity. The measurement technique consists of indenting an unconfined small block of tissue while measuring the resulting force. We show that the measured force-displacement slope of such a geometry can be transformed to the tissue Young's modulus via a conversion factor related to the sample's geometry and boundary conditions using finite element analysis. We also demonstrate another measurement technique for tissue elasticity based on quasi-static magnetic resonance elastography in which a tissue specimen encased in a gelatine-agarose block undergoes cyclical compression with resulting displacements measured using a phase contrast MRI technique. The tissue Young's modulus is then reconstructed from the measured displacements using an inversion technique. Finally, preliminary elasticity measurement results of various breast tissues are presented and discussed.     

Coupling between elastic strain and interstitial fluid flow: ramifications for poroelastic imaging

We study the effects of interstitial fluid flow and interstitial fluid drainage on the spatio-temporal response of soft tissue strain. The motivation stems from the ability to measure in vivo strain distributions in soft tissue via elastography, and the desire to explore the possibility of using such techniques to investigate soft tissue fluid flow. Our study is based upon a mathematical model for soft tissue mechanics from the literature. It is a simple generalization of biphasic theory that includes coupling between the fluid and solid phases of the soft tissue, and crucially, fluid exchange between the interstitium and the local microvasculature. We solve the mathematical equations in two dimensions by the finite element method (FEM). The finite element implementation is validated against an exact analytical solution that is derived in the appendix. Realistic input tissue properties from the literature are used in conjunction with FEM modelling to conduct several computational experiments. The results of these lead to the following conclusions: (i) different hypothetical flow mechanisms lead to different patterns of strain relaxation with time; (ii) representative tissue properties show fluid drainage into the local microvasculature to be the dominant flow-related stress/strain relaxation mechanism; (iii) the relaxation time of strain in solid tumours due to drainage into the microvasculature is on the order of 5-10 s; (iv) under realistic applied pressure magnitudes, the magnitude of the strain relaxation can be as high as approximately 0.4% strain (4000 microstrains), which is well within the range of strains measurable by elastography.     

An inverse problem solution for measuring the elastic modulus of intact ex vivo breast tissue tumours

Soft tissue elasticity has been a subject of interest in biomedical applications as an aid to medical diagnosis since the dawn of medicine. More recently, this has led to the concept of elastography with the aim of imaging the spatial distribution of tissue elasticity. Interpreting elastography images requires reliable information pertaining to elastic properties of normal and pathological tissues. Such information is either very limited or not available in the literature. Elastic modulus measurement techniques developed for soft tissues generally require tissue excision to prepare samples for testing. While this may be done with normal tissues, tumour tissue excision is generally not permissible because tumour pathological assessment requires that the tumour be kept intact. To address this limitation, we developed a system to measure the Young's modulus of tumour specimens. The technique consists of indenting the tumour specimen while measuring indentation force and displacements. To obtain the Young's modulus from the measured force-displacement slope, we developed an iterative inversion technique that uses a finite element model of the piecewise homogeneous tissue slice in each iteration. Preliminary elasticity measurement results of various breast tumours are presented and discussed. These results indicate that the proposed method is robust and highly accurate. Furthermore, they indicate that a benign lesion and malignant tumours are roughly five times and ten times stiffer than normal breast tissues respectively.     

二维数字化超声软组织应变成像系统的研制

利用超声散射回波测量生物组织在静态压缩情况下弹性系数的超声弹性成像方法得到了很大的发展.利用国产高速数据采集卡以及商业线阵B型超声诊断仪,建立了一套二维数字化超声软组织应变成像系统.应用这一系统获得了数字化的射频组织超声散射回波信号,并对组织内的应变分布进行成像.实验结果表明,该应变成像系统在获得传统B型超声图像的同时,可以获得组织内部的应变分布图像,从而获取在B超图像上无法得到的组织弹性变化.这一系统的研制成功,不仅为超声弹性成像技术在医学临床上的应用研究打下了基础,同时也为扩宽普通商业B超的应用范围提供了途径.     

Characterization of plaque components and vulnerability with intravascular ultrasound elastography

Intravascular ultrasound elastography is a method for measuring the local elastic properties using intravascular ultrasound (IVUS). The elastic properties of the different tissues within the atherosclerotic plaque are measured through the strain. Knowledge of these elastic properties is useful for guiding interventional procedures (balloon dilatation, ablation) and detection of the vulnerable plaque. In the last decade, several groups have applied elastography intravascularly with various levels of success. In this paper, the approaches of the different research groups will be discussed. The focus will be on our approach to the application of intravascular elastography. Elastograms were acquired in vitro and in vivo using the relative local displacements between IVUS images acquired at two levels of intravascular pressure with a 30 MHz mechanical or a 20 MHz array echo catheter. These displacements were estimated from the time shift between gated radiofrequency echo signals using cross-correlation algorithms with interpolation around the peak. Experiments on gel-based phantoms mimicking atherosclerotic vessels demonstrated the capability of elastography to identify soft and hard tissues independently of the echogenicity contrast. In vitro experiments on human arteries have demonstrated the potential of intravascular elastography to identify different plaque types based on their mechanical properties. These plaques could not be identified using the IVUS image alone. In vivo experiments revealed that reproducible elastograms could be obtained near end-diastole. Partial validation using the echogram was performed. Intravascular elastography provides information that is frequently unavailable or inconclusive from the IVUS image and which may therefore assist in the diagnosis and treatment of atherosclerotic disease.     

Finite element methods for the biomechanics of soft hydrated tissues: nonlinear analysis and adaptive control of meshes.

This chapter addresses computationally demanding numerical formulations in the biomechanics of soft tissues. The theory of mixtures can be used to represent soft hydrated tissues in the human musculoskeletal system as a two-phase continuum consisting of an incompressible solid phase (collagen and proteoglycan) and an incompressible fluid phase (interstitial water). We first consider the finite deformation of soft hydrated tissues in which the solid phase is represented as hyperelastic. A finite element formulation of the governing nonlinear biphasic equations is presented based on a mixed-penalty approach and derived using the weighted residual method. Fluid and solid phase deformation, velocity, and pressure are interpolated within each element, and the pressure variables within each element are eliminated at the element level. A system of nonlinear, first-order differential equations in the fluid and solid phase deformation and velocity is obtained. In order to solve these equations, the contributions of the hyperelastic solid phase are incrementally linearized, a finite difference rule is introduced for temporal discretization, and an iterative scheme is adopted to achieve equilibrium at the end of each time increment. We demonstrate the accuracy and adequacy of the procedure using a six-node, isoparametric axisymmetric element, and we present an example problem for which independent numerical solution is available. Next, we present an automated, adaptive environment for the simulation of soft tissue continua in which the finite element analysis is coupled with automatic mesh generation, error indicators, and projection methods. Mesh generation and updating, including both refinement and coarsening, for the two-dimensional examples examined in this study are performed using the finite quadtree approach. The adaptive analysis is based on an error indicator which is the L2 norm of the difference between the finite element solution and a projected finite element solution. Total stress, calculated as the sum of the solid and fluid phase stresses, is used in the error indicator. To allow the finite difference algorithm to proceed in time using an updated mesh, solution values must be transferred to the new nodal locations. This rezoning is accomplished using a projected field for the primary variables. The accuracy and effectiveness of this adaptive finite element analysis is demonstrated using a linear, two-dimensional, axisymmetric problem corresponding to the indentation of a thin sheet of soft tissue. The method is shown to effectively capture the steep gradients and to produce solutions in good agreement with independent, converged, numerical solutions.     

A constrained reconstruction technique of hyperelasticity parameters for breast cancer assessment

In breast elastography, breast tissue usually undergoes large compression resulting in significant geometric and structural changes. This implies that breast elastography is associated with tissue nonlinear behavior. In this study, an elastography technique is presented and an inverse problem formulation is proposed to reconstruct parameters characterizing tissue hyperelasticity. Such parameters can potentially be used for tumor classification. This technique can also have other important clinical applications such as measuring normal tissue hyperelastic parameters in vivo. Such parameters are essential in planning and conducting computer-aided interventional procedures. The proposed parameter reconstruction technique uses a constrained iterative inversion; it can be viewed as an inverse problem. To solve this problem, we used a nonlinear finite element model corresponding to its forward problem. In this research, we applied Veronda-Westmann, Yeoh and polynomial models to model tissue hyperelasticity. To validate the proposed technique, we conducted studies involving numerical and tissue-mimicking phantoms. The numerical phantom consisted of a hemisphere connected to a cylinder, while we constructed the tissue-mimicking phantom from polyvinyl alcohol with freeze-thaw cycles that exhibits nonlinear mechanical behavior. Both phantoms consisted of three types of soft tissues which mimic adipose, fibroglandular tissue and a tumor. The results of the simulations and experiments show feasibility of accurate reconstruction of tumor tissue hyperelastic parameters using the proposed method. In the numerical phantom, all hyperelastic parameters corresponding to the three models were reconstructed with less than 2% error. With the tissue-mimicking phantom, we were able to reconstruct the ratio of the hyperelastic parameters reasonably accurately. Compared to the uniaxial test results, the average error of the ratios of the parameters reconstructed for inclusion to the middle and external layers were 13% and 9.6%, respectively. Given that the parameter ratios of the abnormal tissues to the normal ones range from three times to more than ten times, this accuracy is sufficient for tumor classification.     

Estimation of the viscous properties of skin and subcutaneous tissue in uniaxial stress relaxation tests

Knowledge of viscoelastic properties of soft tissues is essential for the finite element modelling of the stress/strain distributions in finger-pad during vibratory loading, which is important in exploring the mechanism of hand-arm vibration syndrome. In conventional procedures, skin and subcutaneous tissue have to be separated for testing the viscoelastic properties. In this study, a novel method has been proposed to simultaneously determine the viscoelastic properties of skin and subcutaneous tissue in uniaxial stress relaxation tests. A mathematical approach has been derived to obtain the creep and relaxation characteristics of skin and subcutaneous tissue using uniaxial stress relaxation data of skin/subcutaneous composite specimens. The micro-structures of collagen fiber networks in the soft tissue, which underline the tissue mechanical characteristics, will be intact in the proposed method. Therefore, the viscoelastic properties of soft tissues obtained using the proposed method would be more physiologically relevant than those obtained using the conventional method. The proposed approach has been utilized to measure the viscoelastic properties of soft tissues of pig. The relaxation curves of pig skin and subcutaneous tissue obtained in the current study agree well with those in literature. Using the proposed approach, reliable material properties of soft tissues can be obtained in a cost- and time-efficient manner, which simultaneously improves the physiological relevance.