Box 1 Brain connectivity and networks
The term “functional connectivity” (FC) (Fig. 3a) reflects the notion that similarity between patterns of activity of different brain regions (in terms of statistical dependency) may arise from interactions between those regions. At the spatial and temporal resolutions afforded by noninvasive neuroimaging techniques in humans, neural activity is most frequently estimated in terms of electrophysiology (using EEG or magnetoencephalography) or from the blood-oxygen-level-dependent signal measured by fMRI. Activity is simultaneously measured for each sensor (for EEG/magnetoencephalography) or each voxel (for fMRI) over a period of time.
On the basis of these measurements of brain activity, the most common ways to quantify FC are measures of linear association between pairs of regional time series (primarily, Pearson correlation, but also methods based on phase coherence or spectral properties of the signals), which are therefore agnostic to interactions between more than two elements and ignore the direction of information flow between the two regions. However, more sophisticated measures also exist, capable of addressing various shortcomings of traditional FC (although often at the expense of computational feasibility) [21–26].
Distinct sets of brain regions, termed “resting-state networks,” spontaneously organize into consistently cofluctuating assemblies during both tasks and also at rest. Prominent among these resting-state networks are the frontoparietal control network and the default mode network: these networks typically exhibit inversely correlated time courses at rest [27, 28], but their interactions are consistently perturbed in unconscious individuals [29, 30].
Measures of effective connectivity have also been introduced to identify directed information flow (from region A to region B and not vice versa). Some effective connectivity approaches rely on probabilistic accounts to infer the direction of interactions from statistical relationships in the data (e.g., transfer entropy, Granger causality [31–33]). Another approach to characterize the directionality and strength of interactions, albeit limited to a small number of brain areas, is dynamic causal modeling (DCM), which has also been applied to patients with DOC [34]. The DCM framework is used to infer the direction of connectivity between regions by comparing possible models of how regional signals were generated. First, alternative models are constructed on the basis of possible coupling between regions, viewed as nodes in a directed network. In a second step, the models are compared through Bayesian model selection to identify the model that best explains the empirically observed data [35]. Finally, effective connectivity can be assessed by a perturb-and-measure approach, in which causal interactions are measured by directly stimulating a subset of neurons and by measuring the responses of the rest of the system. In addition to functional and effective connectivity, structural connectivity can also be measured in vivo in humans from diffusion magnetic resonance imaging data (Fig. 3b), for instance, through diffusion tensor imaging (DTI), which can measure the relative diffusion of water molecules along white matter fibers connecting different regions (although without providing information about directionality) [36]. Thus, structural connectivity and FC can be related in the same individual [24, 25, 37, 38].
Whether functional or structural, the interactions between brain regions can be conceived as a network (Fig. 3c), and the mathematical study of networks, known as graph theory, can be used to obtain insights about such networks at multiple levels of resolution [39, 40]: from properties of individual nodes (e.g., degree, measuring how well connected they are [41, 42]) to network modules [26] to macroscale properties such as small-world organization [24, 25, 30, 43–45].