A Resilient, Low-Frequency, Small-World Human Brain Functional Network with Highly Connected Association Cortical Hubs

By Sophie Achard, Raymond Salvador, Brandon Whitcher, John Suckling, E. Bullmore. Journal of Neuroscience, 2006

2,434 citations recorded by the source corpus.

Small-world properties have been demonstrated for many complex networks. Here, we applied the discrete wavelet transform to functional magnetic resonance imaging (fMRI) time series, acquired from healthy volunteers in the resting state, to estimate frequency-dependent correlation matrices characterizing functional connectivity between 90 cortical and subcortical regions. After thresholding the wavelet correlation matrices to create undirected graphs of brain functional networks, we found a small-world topology of sparse connections most salient in the low-frequency interval 0.03–0.06 Hz. Global mean path length (2.49) was approximately equivalent to a comparable random network, whereas clustering (0.53) was two times greater; similar parameters have been reported for the network of anatomical connections in the macaque cortex. The human functional network was dominated by a neocortical core of highly connected hubs and had an exponentially truncated power law degree distribution. Hubs included recently evolved regions of the heteromodal association cortex, with long-distance connections to other regions, and more cliquishly connected regions of the unimodal association and primary cortices; paralimbic and limbic regions were topologically more peripheral. The network was more resilient to targeted attack on its hubs than a comparable scale-free network, but about equally resilient to random error. We conclude that correlated, low-frequency oscillations in human fMRI data have a small-world architecture that probably reflects underlying anatomical connectivity of the cortex. Because the major hubs of this network are critical for cognition, its slow dynamics could provide a physiological substrate for segregated and distributed information processing.

Subfields: Cognitive Neuroscience, Experimental and Cognitive Psychology

View Paper: https://www.semanticscholar.org/paper/409d0886811a7c645ece8dc8e95ce1bc0edff3b0

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Citations in the corpus

Functional Magnetic Resonance Imaging Phase Synchronization as a Measure of Dynamic Functional Connectivity (2012, neutral): “However, the instantaneous characteristic of PS becomes handy when high temporal resolution is critical, such as when inspecting which aspects of a highly complex and dynamic stimulus relate to hemodynamic brain responses.”
Parcellation‐dependent small‐world brain functional networks: A resting‐state fMRI study (2009, methodology): “…from experimentally activated fMRI data at a mesoscale (voxel level) had a scale-free (i.e., power law) degree distribution, while studies from Achard et al. (2006) and Wang et al. (in press) showed that functional networks of the human brain derived from restingstate fMRI data at a…”
Decoding brain states from fMRI connectivity graphs (2011, methodology): “This methodology has brought new insights in functional connectivity at resting state, such as the small-world organisation of cortical networks at low temporal frequencies (Achard et al., 2006).”
Cognitive Neuroscience of Aging (2008, background): “Functional brain networks show evidence of “smallworld properties” (Achard et al. 2006; He et al. 2007), meaning that they are characterized by dense local connectivity with relatively few long-range connections, resulting in a short path length between any pair of regions in the network.”
Comparison of Characteristics between Region- and Voxel-Based Network Analyses in Resting-State fMRI Data (2009, positive): “…et al. 2007; Eguiluz, et al. 2005; van den Heuvel, et al. 2008) with the degree distribution following a power law distribution, but this has not been observed in region-based networks (Achard, et al. 2006; Bassett, et al. 2006; Gong, et al. 2009; He, et al. 2007; Iturria-Medina, et al. 2008).”
The resting brain: unconstrained yet reliable. (2009, methodology): “More specifically, ROIs in Sets A and B were extracted from spatially smoothed data, whereas ROIs in Set C were extracted from nonspatially smoothed data in line with previous studies (Salvador et al. 2005; Achard et al. 2006; Liu et al. 2008).”
Brain Connectivity (2011, background): “The clustering coefficient of a network is the average of the clustering coefficients over all nodes in the network, where the clustering coefficient of a node is the number of existing connections among the node’s immediate neighbors divided by all of their possible connections.”
On the relationship between emotion and cognition (2008, background): “Whereas the above discussion has emphasized the role of structural connectivity, the importance of functional connectivity (for example, signal correlations between distant regions) needs to be highlighted as wel”
The application of graph theoretical analysis to complex networks in the brain. (2007, positive): “Functional networks revealed by graph analysis of fMRI, EEG or MEG data might represent a ‘physiological substrate for segregated and distributed information processing’ (Salvador et al., 2005a,b; Achard et al., 2006; Achard and Bullmore, 2007).”
The structural-functional connectome and the default mode network of the human brain (2014, neutral): “Default mode areas also seem to play the most central role in graph-theoretical analyses of functional data acquired at rest (Achard et al., 2006; Buckner et al., 2009; Zuo et al., 2011).”
Graph theoretical analysis of complex networks in the brain (2007, methodology): “A different approach was taken by the Cambridge group who studied fMRI BOLD time series during a 'resting state' with eyes-closed and no task [95,107-109].”