基于时间序列的复杂脑网络构建与分析
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摘要
大脑是由上千亿神经元组成的有机整体，神经元网络是大脑进行信息加工和处理的信息通路，网络中拓扑或节点的改变会导致网络特性发生改变，从而导致大脑的病变。本文从复杂网络角度研究脑网络的构建及其动力学演化机制。
针对抑郁症等精神疾病无具体病灶的特点，本文首次采用了全脑域、可达大脑深部的磁刺激方案，通过脑电图分析表明该方案能有效改善抑郁状态，为了研究脑网络状态改善的内在机制，获得网络的节点动力学方程和拓扑是研究的前提和基础。对于有病灶区域的癫痫疾病，分析了病灶区切除前后脑电的不同，发现脑电信号的非线性特性存在明显区别；由于脑电信号的非线性分析并不能反映脑网络拓扑的演化特征，而传统的脑网络构建方法由于网络节点数过少难以反映网络结构的复杂性，因而必须探索新的时间序列的复杂网络构建方法。
由于神经元的动力学方程和神经元网络拓扑是未知的，本文从动力学系统角度出发，提出了仅利用含噪时间序列估计神经元动力学方程和神经元网络拓扑结构的方法。首先利用最小二乘自适应控制方法和压缩传感恢复算法实现了节点的动力学方程估计；然后利用稀疏贝叶斯学习方法辨识无标度网络和小世界网络的拓扑结构，通过仿真表明所提出的方法具有较强鲁棒性和准确性。
首次提出了混沌时间序列构建复杂网络的直接法，发现构建的Lorenz及R ssler系统的网络拓扑图与它们的混沌吸引子存在形态相似性。分析洛伦兹系统相空间重构方法构建的复杂网络，发现随着嵌入维数的增加平均路径长度逐渐增加、聚类系数逐渐减小。为克服可视图建网方法无法体现时间依赖性的缺陷，提出了局部可视图建网方法，通过分析神经元混沌簇放电时间序列，发现了网络的拓扑和统计特性能反映时间序列随时间的演化特征。
通过分析睁眼和闭眼情况下脑电信号递归图的确定性，发现了闭眼情况下确定性明显高于睁眼时，并且利用构建的复杂网络同样反映了闭眼情况下的拓扑图规则有序的确定性特征。利用提出的复杂网络构建方法研究癫痫脑电信号，发现从网络拓扑和统计特性上能明显区分癫痫发作和发作间歇期的信号；对强直性阵挛癫痫发作前、中、后的脑电信号分析，发现了滑动局部网络的聚类系数在癫痫发作时显著升高，可以用于强直性发作的预测。
本文提出的复杂网络拓扑估计方法以及时间序列的复杂网络构造方法能够刻画脑网络的动力学特性，为精神疾病治疗提供了新的思路。
The human brain as an organic whole contains nearly100billion neurons.Neuronal networks is the neural channel of information processing and treatment inthe brain. Networks characteristics will change along with networks topology or nodechange, and the change may lead to brain lesions. This paper investigate dynamicalevolution mechanism of the brain networks in complex networks terms.
Considering the fact that there is no obvious focus area for depression, a brainnetwork magnetic stimulus scheme, which can act on the whole brain domain and thedeep of cerebrum, was first adopted. This scheme can effectively be used fordepression treatment, which is confirmed by EEG analysis. In order to investigate theinternal mechanism of improvement in the brain networks, it is the premise and basisto obtain dynamical equations of node and topology of networks. For epilepsy withfocus area, we investigated the difference between the brainwave obtained from pre-and post-resection of focus area. The results show that there is significant differencein nonlinear characteristics. However, the nonlinear analysis methods cannot reflectthe brain network topological evolution properties, and there are too few networknodes to reflect the network complexity when using traditional network constructionmethods, therefore it is necessary to explore new networks construction method oftime series.
Given that neuronal dynamical equations and neuronal networks topology are notyet fully understood. This paper, viewed from dynamical system perspective,proposed a method of estimating neuronal dynamic equations and neuronal networkstopology using only noisy time series. Least squares adaptive control strategy andcompressive sensing are applied to dynamical equations estimation. Sparse Bayesianlearning is proposed to identify the topology of the scale-free network andsmall-world network, and the simulation results show that the strategies have bettereffect of identification and strong robustness to noise.
This paper first proposed direct method of complex networks construction fromchaotic time series. There are morphological resemblance between networks topologyand chaotic attractor of Lorenz and R ssler system. Lorenz system are used to analyzewhat role did embedding dimension play in networks characteristics. The results showthat average path length increase as does embedding dimension, and cluster coefficient on the contrary. According to the fact that visibility graph method cannotpresent time-dependent statistical characteristics of the complex networks, this paperproposed a local visibility graph method for constructing complex networks from timeseries. The topology and statistical characteristics of the network constructed fromneuronal chaotic bursting can reflect time-evolution of time series.
According to determinism analysis of recurrence plot for eyes-closed andeyes-open EEG signals, determinism in eyes-closed states is higher than that ofeyes-open. The methodical networks topology constructed from the eyes-closed statesalso reflect the determinism characteristic. By analyzing epileptic brainwave usingproposed complex networks construction method, we found that epileptic seizure isdifferent from seizure-free intervals in network topology and statistical characteristics.Epileptic EEG of before, during and after a tonic-clonic seizure indicate that clustercoefficients of the sliding local networks significantly increased during a seizure, sothis result provides clonic seizure prediction.
Topology estimation method of complex networks and its construction approachfrom time series can depict dynamical characteristic of brain networks. The ideologyproposed in this paper provides a new way for the treatment of neurological andpsychiatric disease.
针对抑郁症等精神疾病无具体病灶的特点，本文首次采用了全脑域、可达大脑深部的磁刺激方案，通过脑电图分析表明该方案能有效改善抑郁状态，为了研究脑网络状态改善的内在机制，获得网络的节点动力学方程和拓扑是研究的前提和基础。对于有病灶区域的癫痫疾病，分析了病灶区切除前后脑电的不同，发现脑电信号的非线性特性存在明显区别；由于脑电信号的非线性分析并不能反映脑网络拓扑的演化特征，而传统的脑网络构建方法由于网络节点数过少难以反映网络结构的复杂性，因而必须探索新的时间序列的复杂网络构建方法。
由于神经元的动力学方程和神经元网络拓扑是未知的，本文从动力学系统角度出发，提出了仅利用含噪时间序列估计神经元动力学方程和神经元网络拓扑结构的方法。首先利用最小二乘自适应控制方法和压缩传感恢复算法实现了节点的动力学方程估计；然后利用稀疏贝叶斯学习方法辨识无标度网络和小世界网络的拓扑结构，通过仿真表明所提出的方法具有较强鲁棒性和准确性。
首次提出了混沌时间序列构建复杂网络的直接法，发现构建的Lorenz及R ssler系统的网络拓扑图与它们的混沌吸引子存在形态相似性。分析洛伦兹系统相空间重构方法构建的复杂网络，发现随着嵌入维数的增加平均路径长度逐渐增加、聚类系数逐渐减小。为克服可视图建网方法无法体现时间依赖性的缺陷，提出了局部可视图建网方法，通过分析神经元混沌簇放电时间序列，发现了网络的拓扑和统计特性能反映时间序列随时间的演化特征。
通过分析睁眼和闭眼情况下脑电信号递归图的确定性，发现了闭眼情况下确定性明显高于睁眼时，并且利用构建的复杂网络同样反映了闭眼情况下的拓扑图规则有序的确定性特征。利用提出的复杂网络构建方法研究癫痫脑电信号，发现从网络拓扑和统计特性上能明显区分癫痫发作和发作间歇期的信号；对强直性阵挛癫痫发作前、中、后的脑电信号分析，发现了滑动局部网络的聚类系数在癫痫发作时显著升高，可以用于强直性发作的预测。
本文提出的复杂网络拓扑估计方法以及时间序列的复杂网络构造方法能够刻画脑网络的动力学特性，为精神疾病治疗提供了新的思路。
The human brain as an organic whole contains nearly100billion neurons.Neuronal networks is the neural channel of information processing and treatment inthe brain. Networks characteristics will change along with networks topology or nodechange, and the change may lead to brain lesions. This paper investigate dynamicalevolution mechanism of the brain networks in complex networks terms.
Considering the fact that there is no obvious focus area for depression, a brainnetwork magnetic stimulus scheme, which can act on the whole brain domain and thedeep of cerebrum, was first adopted. This scheme can effectively be used fordepression treatment, which is confirmed by EEG analysis. In order to investigate theinternal mechanism of improvement in the brain networks, it is the premise and basisto obtain dynamical equations of node and topology of networks. For epilepsy withfocus area, we investigated the difference between the brainwave obtained from pre-and post-resection of focus area. The results show that there is significant differencein nonlinear characteristics. However, the nonlinear analysis methods cannot reflectthe brain network topological evolution properties, and there are too few networknodes to reflect the network complexity when using traditional network constructionmethods, therefore it is necessary to explore new networks construction method oftime series.
Given that neuronal dynamical equations and neuronal networks topology are notyet fully understood. This paper, viewed from dynamical system perspective,proposed a method of estimating neuronal dynamic equations and neuronal networkstopology using only noisy time series. Least squares adaptive control strategy andcompressive sensing are applied to dynamical equations estimation. Sparse Bayesianlearning is proposed to identify the topology of the scale-free network andsmall-world network, and the simulation results show that the strategies have bettereffect of identification and strong robustness to noise.
This paper first proposed direct method of complex networks construction fromchaotic time series. There are morphological resemblance between networks topologyand chaotic attractor of Lorenz and R ssler system. Lorenz system are used to analyzewhat role did embedding dimension play in networks characteristics. The results showthat average path length increase as does embedding dimension, and cluster coefficient on the contrary. According to the fact that visibility graph method cannotpresent time-dependent statistical characteristics of the complex networks, this paperproposed a local visibility graph method for constructing complex networks from timeseries. The topology and statistical characteristics of the network constructed fromneuronal chaotic bursting can reflect time-evolution of time series.
According to determinism analysis of recurrence plot for eyes-closed andeyes-open EEG signals, determinism in eyes-closed states is higher than that ofeyes-open. The methodical networks topology constructed from the eyes-closed statesalso reflect the determinism characteristic. By analyzing epileptic brainwave usingproposed complex networks construction method, we found that epileptic seizure isdifferent from seizure-free intervals in network topology and statistical characteristics.Epileptic EEG of before, during and after a tonic-clonic seizure indicate that clustercoefficients of the sliding local networks significantly increased during a seizure, sothis result provides clonic seizure prediction.
Topology estimation method of complex networks and its construction approachfrom time series can depict dynamical characteristic of brain networks. The ideologyproposed in this paper provides a new way for the treatment of neurological andpsychiatric disease.
引文
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