Electroencephalographic Connectivity: A Fundamental Guide and Checklist for Optimal Study Design and Evaluation

Brain connectivity datasets comprise networks of brain regions connected by anatomical tracts or by functional associations. Complex network analysis-a new multidisciplinary approach to the study of complex systems-aims to characterize these brain networks with a small number of neurobiologically meaningful and easily computable measures. In this article, we discuss construction of brain networks from connectivity data and describe the most commonly used network measures of structural and functional connectivity. We describe measures that variously detect functional integration and segregation, quantify centrality of individual brain regions or pathways, characterize patterns of local anatomical circuitry, and test resilience of networks to insult. We discuss the issues surrounding comparison of structural and functional network connectivity, as well as comparison of networks across subjects. Finally, we describe a Matlab toolbox (http://www.brain-connectivity-toolbox.net) accompanying this article and containing a collection of complex network measures and large-scale neuroanatomical connectivity datasets. Copyright (c) 2009 Elsevier Inc. All rights reserved.

In this paper, we show how ElectroEncephaloGraphic (EEG) and MagnetoEncephaloGraphic (MEG) data can be analyzed statistically using nonparametric techniques. Nonparametric statistical tests offer complete freedom to the user with respect to the test statistic by means of which the experimental conditions are compared. This freedom provides a straightforward way to solve the multiple comparisons problem (MCP) and it allows to incorporate biophysically motivated constraints in the test statistic, which may drastically increase the sensitivity of the statistical test. The paper is written for two audiences: (1) empirical neuroscientists looking for the most appropriate data analysis method, and (2) methodologists interested in the theoretical concepts behind nonparametric statistical tests. For the empirical neuroscientist, a large part of the paper is written in a tutorial-like fashion, enabling neuroscientists to construct their own statistical test, maximizing the sensitivity to the expected effect. And for the methodologist, it is explained why the nonparametric test is formally correct. This means that we formulate a null hypothesis (identical probability distribution in the different experimental conditions) and show that the nonparametric test controls the false alarm rate under this null hypothesis.

Many complex networks have a small-world topology characterized by dense local clustering or cliquishness of connections between neighboring nodes yet a short path length between any (distant) pair of nodes due to the existence of relatively few long-range connections. This is an attractive model for the organization of brain anatomical and functional networks because a small-world topology can support both segregated/specialized and distributed/integrated information processing. Moreover, small-world networks are economical, tending to minimize wiring costs while supporting high dynamical complexity. The authors introduce some of the key mathematical concepts in graph theory required for small-world analysis and review how these methods have been applied to quantification of cortical connectivity matrices derived from anatomical tract-tracing studies in the macaque monkey and the cat. The evolution of small-world networks is discussed in terms of a selection pressure to deliver cost-effective information-processing systems. The authors illustrate how these techniques and concepts are increasingly being applied to the analysis of human brain functional networks derived from electroencephalography/magnetoencephalography and fMRI experiments. Finally, the authors consider the relevance of small-world models for understanding the emergence of complex behaviors and the resilience of brain systems to pathological attack by disease or aberrant development. They conclude that small-world models provide a powerful and versatile approach to understanding the structure and function of human brain systems.