神经元网络的同步、共振及控制研究
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摘要
大脑约有1000亿个神经元，它们之间相互作用构成复杂的神经网络，以实现记忆、认知、情感、行为等功能。神经网络的动力学行为与脑功能密切相关。大脑对神经信息的处理是通过不同脑区的大量神经元协同完成的，同步是神经信息处理的重要机制。而同步异常是脑功能疾病的主要体现，通过外界刺激改变神经同步状态是治疗脑疾病的有效手段。另外，噪声普遍存在于神经网络中，所引发的共振是神经元进行信息传递的重要机制。因此，本文研究神经网络的同步化机制、共振特性及同步控制等问题。
本文首次采用映射神经元模型构造离散的模块化小世界神经网络，研究其同步化机制。发现当神经元之间的耦合强度超过某个阈值时，所有神经元在簇放电时间尺度上实现同步，而在峰放电时间尺度上是不同步的，即产生混沌相同步现象。另外，发现增大随机重连概率有利于增强小世界神经网络同步放电，而提高神经元之间的耦合强度和子网络之间的连接概率都可引发模块化神经网络的同步行为发生转迁。
基于上述模型本文首次研究了模块化神经网络中的随机共振和振动共振现象。发现对于施加了弱低频信号的兴奋性神经系统，存在合适强度的外界刺激（噪声和高频信号），使得系统输出对输入信号的线性响应达到峰值。网络结构和参数对系统共振特性有重要影响。存在最优的连接结构，使得整个神经网络对弱信号的检测和传递能力最强。
鉴于大脑中神经元异常的同步化放电会导致神经生理疾病，如帕金森氏症、癫痫症等，本文采用外界周期信号刺激和延迟反馈控制两种方法有效抑制神经元的同步化放电活动，且不改变神经元本身的放电特征。特别是基于平均场的时滞反馈控制法在系统达到去同步状态后刺激信号减弱到零，不具有侵害性，适用于深度脑刺激技术。
本文所得结论有助于理解大脑中神经信息的传递和处理机制，并为治疗同步异常导致的神经系统疾病提供了新思路。
The brain has about100billion neurons each of which interacts with others toconstitute complex neural networks, so that functions of memory, cognition, emotion,and behavior are generated. The dynamical behavior of neuronal networks is closelyrelated to brain functions. Neural information processing in the brain is based on thecoordinated interactions of large numbers of neurons within different brain areas.Synchronization is an important mechanism for neural information processing. But,abnormal synchronization of individual neurons plays a key role in the emergence ofsome pathological brain functions. An effective treatment for these brain diseases iscontrolling the pathological synchronization processes of the brain by externalstimulation. Moreover, noise is widespread in neuronal networks, and resonance playsan significant role in neural information transmission. Therefore, synchronization,rensonance and synchronization control on complex neuronal networks are studied inthis work.
A discrete modular neuronal network of small-world subnetworks is pioneeringlyconstructed based on a map-based neuron model to investigate its synchronizationmechanisms. It is shown that all neurons realize the chaotic phase synchronization onthe bursting time scale when the coupling strength exceeds a threshold, while on thespiking time scale, they behave asynchronously. Furthermore, phase synchronizationon small-world neuronal networks is greatly facilitated by a large random rewiringprobability. The variations of coupling strengths and the probability of random linksbetween different subnetworks can always induce synchronization transitions inmodular neuronal networks.
Based on this model, the phenomena of stochastic resonance and vibrationalresonance on the modular neuronal networks are studied. It is found that there existsan optimal intensity of external stimulation (noise or high-frequency driving signal),by which the dynamical response of excitable neural systems to a subthresholdlow-frequency signal reaches the peak. The resonant effect of neural systems dependsextensively on the network structure and parameters. There exists an optimaltopological structure, such that the ability of neuronal networks for weak signaldetection and transmission achieves best.
Considering that abnormal synchronization of neurons may induce somepathological conditions in the brain, such as Parkinson’s disease or epilepsy, weinvestigate effective suppression of such synchronized neural activity using anexternal periodic signal and delayed feedback control, but without changing theintrinsic activities of individual neurons. In particular, the delayed feedback controlbased on mean-field activity of the neuronal network is noninvasive, since thestimulation signal tends to zero once desynchronized state is attained, which is anadvantage for practical application in deep brain stimulation.
The presented results in this work could have important implications for themechanisms of neural information transmission and processing in the brain, also thetreatment of neurological diseases induced by abnormal synchronization.
本文首次采用映射神经元模型构造离散的模块化小世界神经网络，研究其同步化机制。发现当神经元之间的耦合强度超过某个阈值时，所有神经元在簇放电时间尺度上实现同步，而在峰放电时间尺度上是不同步的，即产生混沌相同步现象。另外，发现增大随机重连概率有利于增强小世界神经网络同步放电，而提高神经元之间的耦合强度和子网络之间的连接概率都可引发模块化神经网络的同步行为发生转迁。
基于上述模型本文首次研究了模块化神经网络中的随机共振和振动共振现象。发现对于施加了弱低频信号的兴奋性神经系统，存在合适强度的外界刺激（噪声和高频信号），使得系统输出对输入信号的线性响应达到峰值。网络结构和参数对系统共振特性有重要影响。存在最优的连接结构，使得整个神经网络对弱信号的检测和传递能力最强。
鉴于大脑中神经元异常的同步化放电会导致神经生理疾病，如帕金森氏症、癫痫症等，本文采用外界周期信号刺激和延迟反馈控制两种方法有效抑制神经元的同步化放电活动，且不改变神经元本身的放电特征。特别是基于平均场的时滞反馈控制法在系统达到去同步状态后刺激信号减弱到零，不具有侵害性，适用于深度脑刺激技术。
本文所得结论有助于理解大脑中神经信息的传递和处理机制，并为治疗同步异常导致的神经系统疾病提供了新思路。
The brain has about100billion neurons each of which interacts with others toconstitute complex neural networks, so that functions of memory, cognition, emotion,and behavior are generated. The dynamical behavior of neuronal networks is closelyrelated to brain functions. Neural information processing in the brain is based on thecoordinated interactions of large numbers of neurons within different brain areas.Synchronization is an important mechanism for neural information processing. But,abnormal synchronization of individual neurons plays a key role in the emergence ofsome pathological brain functions. An effective treatment for these brain diseases iscontrolling the pathological synchronization processes of the brain by externalstimulation. Moreover, noise is widespread in neuronal networks, and resonance playsan significant role in neural information transmission. Therefore, synchronization,rensonance and synchronization control on complex neuronal networks are studied inthis work.
A discrete modular neuronal network of small-world subnetworks is pioneeringlyconstructed based on a map-based neuron model to investigate its synchronizationmechanisms. It is shown that all neurons realize the chaotic phase synchronization onthe bursting time scale when the coupling strength exceeds a threshold, while on thespiking time scale, they behave asynchronously. Furthermore, phase synchronizationon small-world neuronal networks is greatly facilitated by a large random rewiringprobability. The variations of coupling strengths and the probability of random linksbetween different subnetworks can always induce synchronization transitions inmodular neuronal networks.
Based on this model, the phenomena of stochastic resonance and vibrationalresonance on the modular neuronal networks are studied. It is found that there existsan optimal intensity of external stimulation (noise or high-frequency driving signal),by which the dynamical response of excitable neural systems to a subthresholdlow-frequency signal reaches the peak. The resonant effect of neural systems dependsextensively on the network structure and parameters. There exists an optimaltopological structure, such that the ability of neuronal networks for weak signaldetection and transmission achieves best.
Considering that abnormal synchronization of neurons may induce somepathological conditions in the brain, such as Parkinson’s disease or epilepsy, weinvestigate effective suppression of such synchronized neural activity using anexternal periodic signal and delayed feedback control, but without changing theintrinsic activities of individual neurons. In particular, the delayed feedback controlbased on mean-field activity of the neuronal network is noninvasive, since thestimulation signal tends to zero once desynchronized state is attained, which is anadvantage for practical application in deep brain stimulation.
The presented results in this work could have important implications for themechanisms of neural information transmission and processing in the brain, also thetreatment of neurological diseases induced by abnormal synchronization.
引文
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