Functional Brain Networks: Random, “Small World” or Deterministic?

Katarzyna J Blinowska,Maciej Kaminski,Michal Zochowski

doi:10.1371/journal.pone.0078763

Abstract

Lately the problem of connectivity in brain networks is being approached frequently by graph theoretical analysis. In several publications based on bivariate estimators of relations between EEG channels authors reported random or “small world” structure of networks. The results of these works often have no relation to other evidence based on imaging, inverse solutions methods, physiological and anatomical data. Herein we try to find reasons for this discrepancy. We point out that EEG signals are very much interdependent, thus bivariate measures applied to them may produce many spurious connections. In fact, they may outnumber the true connections. Giving all connections equal weights, as it is usual in the framework of graph theoretical analysis, further enhances these spurious links. In effect, close to random and disorganized patterns of connections emerge. On the other hand, multivariate connectivity estimators, which are free of the artificial links, show specific, well determined patterns, which are in a very good agreement with other evidence. The modular structure of brain networks may be identified by multivariate estimators based on Granger causality and formalism of assortative mixing. In this way, the strength of coupling may be evaluated quantitatively. During working memory task, by means of multivariate Directed Transfer Function, it was demonstrated that the modules characterized by strong internal bonds exchange the information by weaker connections.

Highlights

It is more and more acknowledged that progress in understanding of information processing in the brain depends to the large degree on evaluation of temporal and spatial patterns of connections between neural populations
The methods used for estimation of connectivity include bivariate methods such as: correlation, coherence, Mutual Information (MUI), Synchronization Likelihood (SL), Transfer Entropy or multivariate methods such as Directed Transfer Function [3] and Partial Directed Coherence (PDC) [4]
The first one is connected with the fact that application of bivariate methods followed by giving all connections equal weights leads to the dense, disordered, similar to random patterns of connections, from which some ‘‘small word’’ properties may be possibly extracted with some effort

Summary

Introduction

It is more and more acknowledged that progress in understanding of information processing in the brain depends to the large degree on evaluation of temporal and spatial patterns of connections between neural populations. The methods used for estimation of connectivity include bivariate methods such as: correlation, coherence, Mutual Information (MUI), Synchronization Likelihood (SL), Transfer Entropy or multivariate methods such as Directed Transfer Function [3] and Partial Directed Coherence (PDC) [4]. Among bivariate methods: correlation (directionality can be found from the time delay of cross-correlation function), coherence (directionality can be found from the phase of coherence) and Transfer Entropy have a potential to indicate the directionality, but in many cases this information is neglected. Connectivity patterns obtained by bivariate methods are characterized by a very dense structure, without the distinct topographical features and they require further analysis

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Discussion

Conclusion