癫痫病大脑在休息状态下的动态特征

发布时间：2018-05-27 11:46

本文选题：癫痫 + 正常大脑　；参考：《北京交通大学》2014年硕士论文

【摘要】：摘要：神经系统的基本结构单元是神经元,其放电活动涉及复杂的生物物理化过程,表现出丰富的非线性动力学行为.神经系统整体由数目众多的神经元组成,各个单元之间通过电突触和化学突触紧密联系,形成一个具有高维数、多层次、多时间尺度、多功能的复杂信息网络结构,从而导致复杂的网络动力学行为.其中同步作为是非线性研究领域的一个热门课题,事实上太多的同步往往会导致某类神经元疾病,例如癫痫病,这种同步称为病态同步.利用非线性动力学的基本理论,研究这些病态同步是非常有必要的. 本文首先基于混沌Rulkov神经元模型,根据对正常人和癫痫病患者在休息状态下的EEG数据,建立了由19个神经元在电子耦合作用下的数学模型,给出了系统的不动点以及同步流形.利用主稳定函数方法详细分析了系统的稳定性,分别给出了系统不动点稳定的条件以及出现分岔的条件. 其次比较了正常人和癫痫病患者在休息时大脑的动力学特征.根据系统雅克比矩阵特征根,指出由19个神经元组成的癫痫大脑的同步流形结构不稳定.根据光栅图和波形图的比较,指出癫痫大脑存在着异常的同步现象,放电时间也相对较长并且比较紊乱. 最后对本文的研究内容进行了总结,本文的研究成果可能会对为更全面完整地讨论癫痫病患者在不同状态(发作前、发作时和发作后)的动态特征奠定一定的基础.
[Abstract]:Abstract: the basic structural unit of the nervous system is a neuron whose discharge activities involve complex biophysical processes and exhibit rich nonlinear dynamic behaviors. The whole nervous system is composed of a large number of neurons, each unit is closely connected by electrical synapses and chemical synapses, forming a complex information network structure with high dimension, multi-level, multi-time scale and multi-function. This leads to complex network dynamics. Synchronization is a hot topic in the field of nonlinear research. In fact, too much synchronization often leads to some neuronal diseases, such as epilepsy, which is called pathological synchronization. It is necessary to study these pathological synchronization by using the basic theory of nonlinear dynamics. In this paper, based on chaotic Rulkov neuron model and EEG data of normal and epileptic patients in resting state, a mathematical model of 19 neurons under electron coupling is established, and the fixed points and synchronous manifolds of the system are given. The stability of the system is analyzed in detail by using the method of principal stability function. The conditions of the stability of the fixed point and the condition of bifurcation are given respectively. Secondly, the dynamic characteristics of brain during rest were compared between normal subjects and patients with epilepsy. According to the characteristic roots of the system Jacobian matrix, it is pointed out that the synchronous manifold structure of the epileptic brain composed of 19 neurons is unstable. According to the comparison of grating and waveform images, it is pointed out that abnormal synchronization exists in the epileptic brain, and the discharge time is relatively long and disordered. Finally, the research contents of this paper are summarized. The research results of this paper may lay a foundation for a more comprehensive and complete discussion on the dynamic characteristics of epilepsy patients in different states (before, during and after seizure).
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：R742.1

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