Critical Behavior And Dynamics Of Brain In Resting State

In the early days of statistical physics,physicists mainly focused on systems composed of a large number of non-interacting individuals.With the development of statistical physics,the research object gradually transferred from simple systems such as ideal gas to more complicated systems with complex interaction between individuals.The brain,as a typical complex system composed of huge number of neurons and with complex synaptic connections,has attracted much attention from statistical physicists in the past two decades.With the development of non-invasive measurement techniques,such as MRI,EEG and MEG,people have obtained the observation data of the working state of the brain from macro to micro scales.Based on fMRI(functional Magnetic Resonance Imaging)data,this thesis studies the spatial correlation and temporal correlation of brain from the voxel level,and reveals the internal statistical law of brain activity in resting state.The first part of this paper is the analysis of BOLD(Blood Oxygen Level Dependent)time series in voxel level,and discusses the spatial correlation of voxel activation.By adjusting the threshold of the activation degree,the time when the first monotonous rise of voxel bold time series exceeds a given threshold is defined as the time of voxel activation.In this paper,we defined a group of voxels which are activated at the same time and have spatial nearest neighbor relationship to be one cluster.When we made statistics on the cluster size,we found that the distribution of cluster size obeys the power-law distribution,and the critical exponent does not change with the change of threshold.Through the correlation analysis of different voxel activation states in the brain area,we found that the correlation of voxel level was power law,which implied that the correlation length in the brain area is the same as that in the brain area.These findings support the idea that the brain is in a critical state in resting state.The second part of this paper is about the statistics of the number of activated voxels at each time in the brain area,and discusses the time correlation of activationin the brain area.In this paper,we defined the "extreme events" in the brain area,and made statistics of their time intervals between two neighboring extreme event.It was found that the most probable event interval does not change with the activation threshold or other parameters,which indicates an intrinsic characteristic scale in the process of brain activity.In this paper,it is defined as the characteristic time of brain activation.Further study also found that different brain area have their own characteristic time,and in the comparison with the probability of brain area co-activation,the closer the characteristic time is,the more likely the brain area are to co-activate.The findings reveal the close internal relationship between the time-domain characteristics of brain activity and the functional connections of brain regions,increase the understanding of the mechanism of the coupling relationship between brain functional networks,and provide a new reference for clinical diagnosis of brain dysfunction.