【作者】 刘长征；

【导师】 孙尧；

【作者基本信息】 哈尔滨工程大学 ， 导航、制导与控制， 2003， 博士

【摘要】 心血管疾病是威胁人类健康的一大顽症，尤其是晚期心脏病患者更是难以救治。现在的有效治疗手段除了心脏移植就是安装人工心脏。心脏移植受到诸多因素的限制，远不能满足需要，直到现在也没能开发出象自然心脏一样完美的人工心脏。有工艺、材料方面的原因，另外一个重要的原因是没有创建自然心脏搏动的真实模型。因此，对自然心脏搏动性质的研究一直是学者们所关注的课题。本文从心脏搏动的内部机理研究出发，结合心脏电生理、血流动力学与突变理论，构造了一种反映心脏搏动的基于B-R方程的突变形式，从根本上揭示了心脏运动的性质和规律。又利用非线性动力学、小波变换技术、超声影像学和自动控制原理，研究了心律失常的产生原因、检测和控制手段，为心脏病定量诊断、治疗提供了新的方法。本文还将心脏搏动性质应用于虚拟心脏和人工心脏的研究中，提出了基于心脏搏动特性的虚拟心脏和人工心脏的设计思想。论文主要完成的工作有： 本文针对心脏搏动，引入时变系统，给出相应的一些定义和定理。正常情况下的心脏搏动处在一个相对稳定平衡轨道上；当受到外界刺激或发生病变时，系统将从平衡轨道跳到另外一个引力轨道。而疾病则使心脏搏动较多停留在某一平衡轨道。轨道的改变揭示了心率变异的动态过程。在趋向于一条引力轨道的过程中，心脏的运动轨迹将越过斥力轨道而直接跃迁到另一条引力轨道，发生突变。 通过对心肌细胞电生理活动分析，基于B-R方程提出用势函数模型来描述自然心脏周期性搏动的研究方法。心脏运动的势函数模型是以收缩末和舒张末为节点的尖点突变的形式来表示的。通过尖点突变流形表征与心脏搏动有关参数，确定其稳定与不稳边界。本文所提出的突变势函数以及分析方法，与传统的电模拟相比，更接近真实心脏的搏动过程。根据血流动力学改变建立了层流、紊流势函数方程，并分析了孤波的影响。基于流体力学理论，给出了方程解法。将突变方法用于心脏变异性分析中，得以揭示无论是健康人还是心脏病人，心率变异中均存在不稳定平衡轨道分级，说明了健康人心脏节律的动力学特性中包含着显著的突变行为。其突变行为能力越强，心脏就越健康。 心电图是心肌电生理的外部测量结果。本文选择小波变换对微分心电信号进行分析，找到突变点并确定突变点在心电图上的位置。利用突变势函数方程，进行了双参数突变分析，找到了突变发生的原因。并在动力学参数平哈尔滨工程大学博士学位论文面上划分出五个动力学性质不同的区域:当选择合适的参数，心肌纤维会产生自发节律;还有一个小的区域，振荡态与静息态共存，揭示了临床上房性停搏与室颤的内在机理以及冠心病人突变点普遍增多的原因。 对突变的控制，本文提出状态反馈方法。当利用线性状态反馈控制时，突变幅值得到控制，从而改变了临界状态，消除了多态，阻止了心肌细胞在扰动情况下发生突变，抑制了心律失常;当为非线性状态反馈时，可以测到歧点位置的改变，但并没有去掉突变，没有消除潜在的异位起搏、恢复振动的机制。本文所设计的控制器，也可应用于智能起搏器。 由于现在临床上使用的人工心脏不能完全达到人体要求，所以本文利用突变模型对其重新进行了设计。首先利用心室内外膜边缘检测技术，在超声心动图上对心脏短轴和四腔截面进行处理，勾画出心脏室壁轮廓，并将室壁进行固定参考轴节段划分，获得各节段指标的定量计算结果，为整体运动分解为节段运动奠定了基础。将速度场的低阶动力学模型和基本光流约束方程相结合，形成虚拟心脏运动矢量的估值数学模型。该模型克服了传统的数字粒子成像测速相关算法费时、产生虚假相关峰值的缺点。通过解方程组就能直接获得速度场的运动矢量估值结果。设置节段参数，得到虚拟心脏仿真结果。最后引入各种人工心脏专用传感器以及获取控制信息的方法，把整个人工心脏的搏动转化为节段的振动求解。根据不同节段对不同参量的敏感程度，采用不同参量描述各节段搏动。通过改进节段间兴奋传播算法，获得了接近人体生理特点的特异性人工心脏。 总之，通过对心脏突变振动系统势函数模型的研究，不但为心脏病诊断、治疗提供新方法，而且使神经系统影响下的自然心脏固有搏动节律及运动特性在虚拟心脏和人工心脏中得到真实体现。更多还原

【Abstract】 Cardiopathy is a chronic and stubborn disease threatening mankind health, particularly difficult to save the terminal heart disease suffers. Now the validity treatment is to install the artificial heart besides the heart transplantation. The heart transplantation is restrict by many factors, and is far from meeting the demands, until now no artificial heart develop to perfect as the nature heart. I think the most important is that there is no the reality model of nature heart beating other then craft and material. Therefore, the study of nature heart beating is a task for scholars paying attention. This thesis starts from internal mechanism of heart beating, combines heart electrobiology, blood stream dynamical and catastrophe theory. A catastrophe form was constructed based on B-R equation. It reveals characters and rules of the heart beating radically. Making use of nonlinear dynamics, wavelet transformation technique, supersonic imaging and automatic control theory, a study on the causation, examine and control means of arrhythmia, provides a new method for cardiopathy ration diagnosis and treatment. This dissertation applies the heart beating characters to the thought of virtual and artificial heart design. The main work and achievement are as following:In allusion to the heart beating, the time changing system is introduced, and some of definitions and theorems are given. A nature heart appearances in a comparative stable equilibrium orbit commonly. When suffering the outsider incitement or the pathological changes, the system will jump from the equilibrium orbit to a attractive orbit. But the disease makes the heart beating stay at an equilibrium orbit. The orbit’s changes announce the dynamic process of heart rate variability. In the process toward the attractive orbit, the track of heart beating transits to another attractive orbit directly over the repulsion orbit, catastrophe occurrence.By the analysis of myocardial cell electrobiology, the potential model is put forward to describe nature heart periodic beating based on B- R equation. The heart beating model is described as cusp catastrophe with end node of systole and diastole. The boundary of steady and unsteady is confirmed by two parameters ofcatastrophe flow form token the beating. The catastrophe model and its analysis method are more approaching to the real heart compared to tradition electric virtual method. The potential functions of laminar flow and turbulence flow are established according to the blood flow dynamics, and the influence of the isolated wave is analyzed. According to the fluid mechanics theory, the solution of equation is given. By the application of catastrophe theory to the analysis of heart rate variability, unsteady equilibrium orbits grades are opened out to health person or cardiopathy suffers. It proves that dynamics character comprises marked catastrophe action of the health rhythm. More strong the catastrophe ability is, more health the heart is.The electrocardiogram is the external measure result of myocardial electrobiology. As wavelet transformation analysis the differential electrocardiogram, catastrophe points were discovered in electrocardiogram. Make use of the potential model to analyze the double parameters, the reason of catastrophe generation is found. Five dynamics regions of different characters are marked off. When the two parameters chosen right parameters, myocardial muscle can produce the self-moving rhythms. In a little region, oscillation state and quiescence state coexist. It discovered the internal mechanism of atria halt and ventricular fibrillation, and the reason of manifold catastrophe points of coronary heart disease suffers.The method of state feedback is put forward to control the catastrophe. With the linear control, the range of catastrophe is controlled, and the critical state is changed, multistate is dissolved, so the catastrophe occurrence of cardiac muscle cell is prevented under disturbance, pathological heart rhythms is restrained. With the nonlinear control, the更多还原