Construction And Analysis Of Brain Connectivity Based On Graph Theory

Human brain is known as not only the most complex but also the most efficient system in the world. Modern science has confirmed that any function of the brain is not the result of individual neuron or single brain region but the interaction and cooperation among so many neurons^neural ensembles or brain regions. Therefore, to study the functional connectivity of the human brain on the basis of network has great value to understand the way the brain works, even explore the pathological mechanism of brain disease further.Based on resting state functional Magnetic Resonance Imaging, this paper has studied the calculation of correlation coefficient between brain regions, the construction of brain connectivity on the base of correlation matrix, and the further analysis of the character of this constructed network based on graph theory. Besides, the influence of shift on the time series has been explored in this paper. The specific work is as follows:1) The calculation and analysis of correlation between brain regions. Based on the data of the time series, three methods include pearson, spearman and partial correlation has been used for the calculation. In the three methods, partial correlation have the advantage of eliminating temperature the affects other brain regions. However, the covariance matrix of the time series should be reversible by this method. This paper proposes a matrix transformation method, have settled the problem of the calculation in the condition of the irreversible covariance matrix, which expands the sphere of application of partial correlation method.2) The generative criterion and visible analysis of the edge of brain network. Three principles have been introduced to control the range of the threshold, which ensure a reasonable threshold used to construct the functional network. Based on the result of threshold range, a proper threshold has been setted, consequently got the binary matrix,ultimately the network has been established. Besides, visualization analysis of the network has been proceed in node and anatomy model.3) The analysis and comparisons of brain networks’topology attribute. Based on graph theory, the paper analyzes the influence of different methods of correlation calculation on brain networks’topology attribute. The result show that there are significant differences in the network properties although the networks are all belong to "small-world network" from an overall perspective. 4) The calculation of time series’shift based on DTW algorithm. In order to explore the influence of interference factors and brain regions distance on time series, the correlation coefficients have been recalculated in the case of the shift of one region in relation to another.The method of calculating the partial correlation matrix and the strategy of determining threshold value proposed in the paper have been used in the process of establishing the functional brain network successfully. Based on the analysis of graph theory, our work reveal network’s rules and topological properties. These works are beneficial explorations in the field of brain function connectivity.