Construction And Analysis Of Complex Brain Networks Based On Time Series

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.