Small-world and scale-free organization of voxel-based resting-state functional connectivity in the human brain

Rudolf Magnus Institute of Neuroscience, University Medical Center Utrecht, Department of Psychiatry, Utrecht, The Netherlands.
NeuroImage (Impact Factor: 6.36). 09/2008; 43(3):528-39. DOI: 10.1016/j.neuroimage.2008.08.010
Source: PubMed


The brain is a complex dynamic system of functionally connected regions. Graph theory has been successfully used to describe the organization of such dynamic systems. Recent resting-state fMRI studies have suggested that inter-regional functional connectivity shows a small-world topology, indicating an organization of the brain in highly clustered sub-networks, combined with a high level of global connectivity. In addition, a few studies have investigated a possible scale-free topology of the human brain, but the results of these studies have been inconclusive. These studies have mainly focused on inter-regional connectivity, representing the brain as a network of brain regions, requiring an arbitrary definition of such regions. However, using a voxel-wise approach allows for the model-free examination of both inter-regional as well as intra-regional connectivity and might reveal new information on network organization. Especially, a voxel-based study could give information about a possible scale-free organization of functional connectivity in the human brain. Resting-state 3 Tesla fMRI recordings of 28 healthy subjects were acquired and individual connectivity graphs were formed out of all cortical and sub-cortical voxels with connections reflecting inter-voxel functional connectivity. Graph characteristics from these connectivity networks were computed. The clustering-coefficient of these networks turned out to be much higher than the clustering-coefficient of comparable random graphs, together with a short average path length, indicating a small-world organization. Furthermore, the connectivity distribution of the number of inter-voxel connections followed a power-law scaling with an exponent close to 2, suggesting a scale-free network topology. Our findings suggest a combined small-world and scale-free organization of the functionally connected human brain. The results are interpreted as evidence for a highly efficient organization of the functionally connected brain, in which voxels are mostly connected with their direct neighbors forming clustered sub-networks, which are held together by a small number of highly connected hub-voxels that ensure a high level of overall connectivity.

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    • "Drawing parallels between neurological and sociotechnological networks, neuroscientists have hypothesized that in the brain we have small-world networks [1] [2] with scale-free degree distribution [3] [4]. Small-world networks are at the same time highly clustered on a local scale, yet possess some long-distance connections that link different clusters of nodes together. "
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    ABSTRACT: The structural human connectome (i.e.\ the network of fiber connections in the brain) can be analyzed at ever finer spatial resolution thanks to advances in neuroimaging. Here we analyze several large data sets for the human brain network made available by the Open Connectome Project. We apply statistical model selection to characterize the degree distributions of graphs containing up to ~10^6 nodes and ~10^8 edges. The model that in general describes the observed degrees best is a three-parameter generalized Weibull (also known as a stretched exponential) distribution. Thus the degree distribution is heavy-tailed, but not scale-free. We also calculate the topological (graph) dimension D and the small-world coefficient \sigma of these networks. While \sigma suggests a small-world topology, we found that D < 4 showing that long-distance connections provide only a small correction to the topology of the embedding three-dimensional space.
    Full-text · Article · Dec 2015
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    • "These two metrics could also be unified as one metric, called small-worldness, i.e., σ=γ/λ. A real network is considered as small-world network if it meets the criteria: C≫C rand and L≈L rand , or σ>1 [18] "
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    ABSTRACT: Training is a process to improve one's capacity or performance through the acquisition of knowledge or skills specific for the task. Although behavioral performance would be improved monotonically and reach a plateau as the learning progresses, neurophysiological process shows different pattern like an inverted U-shaped curve. One possible account for the phenomenon is that the brain first works hard to learn how to use specific task-relevant areas, followed by improvement of efficiency derived from disuse of irrelevant brain areas for good task performance. In this study, we employed the functional connectome approach to study the changes in global and local information transfer efficiency of the functional connectivity induced by training of a piloting task. Our results have demonstrated that global information transfer efficiency of the network, revealed by normalized characteristic path length in beta band, once decreased and then increased during the training sessions. We show that graph theoretical network metrics can be used as biomarkers for quantifying the degree of training progresses, in terms of efficiency, which can be differed based on cognitive proficiency of the brain.
    Full-text · Conference Paper · Jul 2015
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    • "A region-specific analysis of the lateral prefrontal cortex, part of the fronto-parietal network, found that its global connectivity predicted working memory performance and fluid intelligence (Cole et al., 2012). Two studies have reported an association between efficiency of global communication and intellectual performance, suggesting that individuals with higher intelligence have a more organized brain network overall (Van den Heuvel et al., 2008; Song et al., 2009). However, the relationships between brain functional connectivity and psychological measures such as intelligence are not fully defined. "
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    ABSTRACT: Measurements of functional connectivity support the hypothesis that the brain is composed of distinct networks with anatomically separated nodes but common functionality. A few studies have suggested that intellectual performance may be associated with greater functional connectivity in the fronto-parietal network and enhanced global efficiency. In this fMRI study, we performed an exploratory analysis of the relationship between the brain's functional connectivity and intelligence scores derived from the Portuguese language version of the Wechsler Adult Intelligence Scale (WAIS-III) in a sample of 29 people, born and raised in Brazil. We examined functional connectivity between 82 regions, including graph theoretic properties of the overall network. Some previous findings were extended to the Portuguese-speaking population, specifically the presence of small-world organization of the brain and relationships of intelligence with connectivity of frontal, pre-central, parietal, occipital, fusiform and supramarginal gyrus, and caudate nucleus. Verbal comprehension was associated with global network efficiency, a new finding.
    Full-text · Article · Feb 2015 · Frontiers in Human Neuroscience
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