Emerging Trends and Methods: Connectivity/Complexity Analysis

The analysis of brain connectivity is a rapidly evolving field of Neuroscience, with significant contributions from new neuroimaging techniques and methods (Bandettini, 2009). While structural and functional connectivity has been emphasized with MRI-based techniques (Johansen-Berg & Rushworth, 2009, K. Friston, 2009), the time resolution of MEG/EEG offers a unique perspective on the mechanisms of rapid neural connectivity engaging cell assemblies at multiple temporal and spatial scales.

We may summarize the research taking place in that field by mentioning two approaches that have developed somewhat distinctly in the recent years, though we might predict they will ultimately converge with forthcoming research efforts. We shall note that most of the methods summarized below are also applicable to the analysis of MEG/EEG source connectivity and are not restricted to the analysis of sensor data. We further emphasize that connectivity analysis is easily fooled by confounds in the data, such as volume conduction effects – i.e., smearing of scalp MEG/EEG data due to the distance from brain sources to sensors and the conductivity properties of head tissues, as we shall discuss below – which need to be carefully evaluated in the course of the analysis (Nunez et al.., 1997, Marzetti, Gratta, & Nolte, 2008).

Synchronized cell assemblies

The first strategy has inherited directly from the compelling intracerebral recording results demonstrating that cell synchronization is a central feature of neural communication (Gray et al.., 1989). Signal analysis techniques dedicated to the estimation of signal interdependencies in the broad sense have been largely applied to MEG/EEG sensor traces. Contrarily to what is appropriate to the analysis of fMRI’s slow hemodynamics, simple correlation measures in the time domain are thought not to be able to capture the specificity of electrophysiological signals, which components are defined over a fairly large frequency spectrum. Coherence measures are certainly amongst the techniques the most investigated in MEG/EEG, because they are designed to be sensitive to simultaneous variations of power that are specific to each frequency bin of the signal spectrum (Nunez et al.., 1997). There is however a competitive assumption that neural signals may synchronize their phases, without the necessity of simultaneous, increased power modulation (Varela et al.., 2001). Wavelet-based techniques have therefore been developed to detect episodes of phase synchronization between signals (Lachaux, Rodriguez, Martinerie, & Varela, 1999, Rodriguez et al.., 1999).


Connectivity analysis has also been recently studied through the concept of causality, whereby some neural regions would influence others in a non-symmetric, directed fashion (Gourévitch, Bouquin-Jeannès, & Faucon, 2006). The possibilities to investigate directed influence between not only pairs, but larger sets of time series (i.e. MEG/EEG sensors or brain regions) are vast and are therefore usually ruled by parametric models. These latter may either be related to the definition of the time series (i.e. through auto-regressive modeling for Granger-causality assessment (Lin et al.., 2009)), or to the very underlying structure of the connectivity between neural assemblies (i.e., through structural equation modeling (Astolfi et al.., 2005) and dynamic causal modeling (David et al.., 2006, Kiebel, Garrido, Moran, & Friston, 2008)).
The second approach to connectivity analysis pertains to the emergence of complex networks studies and associated methodology.

Complexity in brain networks

Complex networks science is a recent branch of applied mathematics that provides quantitative tools to identify and characterize patterns of organization among large inter-connected networks such as the Internet, air transportation systems, mobile telecommunication. In neuroscience, this strategy rather concerns the identification of global characteristics of connectivity within the full array of brain signals captured at the sensor or source levels. With this methodology, the concept of the brain connectome has recently emerged, and encompasses new challenges for integrative neurosciences and the technology, methodology and tools involved in neuroimaging, to better embrace spatially-distributed dynamical neural processes at multiple spatial and temporal scales (Sporns, Tononi, & Kötter, 2005, Deco, Jirsa, Robinson, Breakspear, & Friston, 2008). From the operational standpoint, brain ‘connectomics’ is contributing both to theoretical and computational models of the brain as a complex system (Honey, Kötter, Breakspear, & Sporns, 2007, Izhikevich & Edelman, 2008), and experimentally, by suggesting new indices and metrics – such as nodes, hubs, efficiency, modularity, etc. – to characterize and scale the functional organization of the healthy and diseased brain (Bassett & Bullmore, 2009). This type of approaches is very promising, and calls for large-scale validation and maturation to connect with the well-explored realm of basic electrophysiological phenomena.

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