本文選題：癲癇 + 正常大腦　； 參考：《北京交通大學》2014年碩士論文

【摘要】：摘要：神經(jīng)系統(tǒng)的基本結(jié)構(gòu)單元是神經(jīng)元,其放電活動涉及復雜的生物物理化過程,表現(xiàn)出豐富的非線性動力學行為.神經(jīng)系統(tǒng)整體由數(shù)目眾多的神經(jīng)元組成,各個單元之間通過電突觸和化學突觸緊密聯(lián)系,形成一個具有高維數(shù)、多層次、多時間尺度、多功能的復雜信息網(wǎng)絡(luò)結(jié)構(gòu),從而導致復雜的網(wǎng)絡(luò)動力學行為.其中同步作為是非線性研究領(lǐng)域的一個熱門課題,事實上太多的同步往往會導致某類神經(jīng)元疾病,例如癲癇病,這種同步稱為病態(tài)同步.利用非線性動力學的基本理論,研究這些病態(tài)同步是非常有必要的. 本文首先基于混沌Rulkov神經(jīng)元模型,根據(jù)對正常人和癲癇病患者在休息狀態(tài)下的EEG數(shù)據(jù),建立了由19個神經(jīng)元在電子耦合作用下的數(shù)學模型,給出了系統(tǒng)的不動點以及同步流形.利用主穩(wěn)定函數(shù)方法詳細分析了系統(tǒng)的穩(wěn)定性,分別給出了系統(tǒng)不動點穩(wěn)定的條件以及出現(xiàn)分岔的條件. 其次比較了正常人和癲癇病患者在休息時大腦的動力學特征.根據(jù)系統(tǒng)雅克比矩陣特征根,指出由19個神經(jīng)元組成的癲癇大腦的同步流形結(jié)構(gòu)不穩(wěn)定.根據(jù)光柵圖和波形圖的比較,指出癲癇大腦存在著異常的同步現(xiàn)象,放電時間也相對較長并且比較紊亂. 最后對本文的研究內(nèi)容進行了總結(jié),本文的研究成果可能會對為更全面完整地討論癲癇病患者在不同狀態(tài)(發(fā)作前、發(fā)作時和發(fā)作后)的動態(tài)特征奠定一定的基礎(chǔ).
[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).
【學位授予單位】：北京交通大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：R742.1

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相關(guān)期刊論文 前1條

1 趙明,汪秉宏,蔣品群,周濤;復雜網(wǎng)絡(luò)上動力系統(tǒng)同步的研究進展[J];物理學進展;2005年03期

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本文編號：1941951