Analyzing Functional Connectivity Networks in the Brain and the Relationshipof Node-Level Characteristics

Abstract

It might be difficult to comprehend how the brain functions and how its structureand function interact because it is the body�s most complicated organ. Recentadvances in the non-invasive measurement techniques of brain signals andlarge-scale computing originating from advances in complex systems have enabledhigh-resolution temporal and spatial data analysis, thereby providing newinsights into the functional connectivity of the different brain regions.High-resolution temporal data, such as those obtained from EEG, can providesignificant insights into the dynamics of the brain at very short time scales. Thesesignals, however, are non-stationary and complex. This has resulted in applicationsof methods outside those of conventional statistics.During the previous two decades, developments in the field of complex networkshave provided a range of methods to analyze EEG data and thereby constructa picture of the brain�s functional network. Complex networks providea simple representation of the connectivity between the different EEG channelsregarding nodes and edges. The connectivity is obtained by looking at the amplitudeor phase relationship between the signals from different channels. Differentnetwork measures are then used to study the problem at the level of individualchannels or nodes, groups of nodes, and all the nodes. This provides an understandingof how the brain organizes itself as it performs different tasks and theinterrelationship between these different levels of description.Deep learning techniques have also provided new opportunities and directionsin studies of brain signals. It involves training a neural network to discoverpatterns in massive datasets. Statistical methods and deep learning techniquesare usually used together. Statistical methods are typically used to pre-processthe data, identify essential features, and identify the data set�s dimensionality. Atthe same time, deep learning techniques allow studying the intricate relationshipsbetween the brain signals.Despite the plethora of different techniques, our understanding of the brainis still in its nascent stage. Apart from the complexity originating from the brainas an organ, the methods used have limitations. For example, the properties ofthe network are sensitive to the methods used to construct the network itself. Forinstance, Pearson correlation based network construction is a linear correlation,and hence the network properties would be the ones that are best captured bysuch linear correlations. While the deep learning methods are certainly promisingsince they consider any nonlinear correlations, the advantages they providecompared to the other methods still need to be discovered.Given the complexity of brain dynamics and the limitations of the differentmethods, we explore how well the various ways correlate in this thesis. Specifically,we have looked at the relationship between the fluctuations in the signalsat a channel, the channel represented as a node in the brain�s functional network,and the observations from deep learning techniques. Based on sliding windowanalysis, our main observation is that for resting state data, the mean and varianceof the raw signal at a channel show a positive correlation to the fluctuationsin the weighted degree of the node in the corresponding network. And a scatterplot of correlation values between different channels using simple statisticalmethods and deep learning-based methods gives information about the associationand similarity between the two approaches in capturing the patterns of functionalconnectivity in the brain.