Small-world directed networks in the human brain: Multivariate Granger causality analysis of resting-state fMRI
Research Highlights
► Effective connectivity of resting-state fMRI. ► Small-world of multivariate Granger causality. ► Our finding suggest that the human brain directed influence network could have a prominent small-world topological property.
Introduction
Exploring long-range interactions between neuronal assemblies at different temporal and spatial scales is an important issue in human brain research. The human brain is a complex network, which has been characterized by spatially interconnected regions with organization in specific connectivity patterns (Bullmore and Sporns, 2009, He and Evans, 2010, Honey et al., 2009, Ioannides, 2007, Sporns et al., 2004, Stam and Reijneveld, 2007, van den Heuvel and Hulshoff Pol, 2010, Wang et al., 2010). Connectivity patterns in the brain can be described using two major approaches. One is structural connectivity that typically corresponds to white matter tracts within brain (Gong et al., 2009, Hagmann et al., 2008, Sporns et al., 2000b, Sporns et al., 2000a). The other is functional connectivity that includes temporal correlations between even remote brain regions (Biswal et al., 1995, Friston, 1994). In the last years, the definition of functional connectivity has been extended considering transfer of information such as directly causal interactions from one brain region to another: several authors refer to this extension as effective connectivity (Friston, 1994, Rubinov and Sporns, 2010). It is worth to stress that the connectivity matrix for the effective connectivity network is not symmetric; for this reason this network is also referred to as directed influence network. Small-world architectures have been widely investigated in many empirical studies of structural and functional brain networks (Bassett and Bullmore, 2006, Bullmore and Sporns, 2009, Honey et al., 2009, Honey et al., 2010, Sporns and Honey, 2006). Networks with a small-world organization have a clustering coefficient that is higher than the clustering coefficient of a randomly organized network with equivalent parameters, but still have a short path length as it is found in random networks (Watts and Strogatz, 1998). The clustering coefficient of a network describes the connectedness of direct neighbors around individual nodes, reflecting the extent of the local density of the network. Small-world topology is generally associated with global and local parallel information processing, sparse connectivity between nodes and low wiring costs (Bassett and Bullmore, 2006).
Small-world attributes have been found in brain structural networks in animal models, in which connectivity can range over multiple spatial scales, from local circuits to large-scale networks of inter-regional pathways (Sporns et al., 2000a, Sporns et al., 2004, Sporns et al., 2007, Sporns and Kotter, 2004). Moreover, recent progress has been made in mapping the structural and/or anatomical networks of the human brain (Sporns et al., 2005), which supports the view that human brain anatomical networks manifest small-world attributes, such as cerebral cortical thickness analysis (He et al., 2007), diffusion tensor imaging (DTI) (Gong et al., 2009, Iturria-Medina et al., 2007) and diffusion spectrum imaging (DSI) (Hagmann et al., 2008).
Small-world attributes have not only been observed in brain structural networks, but have been extended to studies of functional connectivity network based on fMRI blood oxygen level-dependent (BOLD) signals. Most resting-state fMRI studies, based on graph theory, have focused on inter-regional functional connectivity at both regional level (Achard et al., 2006, Achard and Bullmore, 2007, Salvador et al., 2005, Wang et al., 2009) and voxel level (Hayasaka and Laurienti, 2010, van den Heuvel et al., 2008), suggesting that the functionally connected human brain has a small-world topology. Additionally, another fMRI study engaged in simple motor and auditory tasks reported small-world attributes of functional networks derived from a set of activated regions and, furthermore, suggested a scale-free degree distribution in brain functional networks (Chialvo, 2004, Eguiluz et al., 2005). Scale-free networks are characterized by a power law distribution and by the presence of a small number of highly connected nodes that ensure a high level of global connectivity (Barabasi and Albert, 1999, Barabasi and Bonabeau, 2003).
Activity in a brain region can directly or indirectly exert influence on the activity of another brain region (see for example Friston, 1994, Friston, 2009). The network of these influences constitutes the effective connectivity in the brain. Granger causality analysis (Granger, 1969) is an operative approach that measures the causal influence and the flow of information, and can be used to extract information about the dynamics and directionality of fMRI BOLD signal in cortical circuits typically engaged in cognitive and perceptive processing (Chen et al., 2009, Gao et al., 2008, Goebel et al., 2003, Kayser et al., 2009, Liao et al., 2009, Roebroeck et al., 2005, Seth, 2005, Sridharan et al., 2008, Zhou et al., 2009). This analysis has been also applied to resting-state fMRI studies, revealing the causal influences among resting-state networks (RSNs) (Liao et al., 2010, Sridharan et al., 2008, Stevens et al., 2009, Uddin et al., 2009), and among brain regions within the default mode network (DMN) (Jiao et al., 2010), and even among cortico-limbic regions (Hamilton et al., 2010). However, it remains unknown what the architecture of the directed influence brain network might be and whether it displays small-world characteristics (Bullmore and Sporns, 2009, Ioannides, 2007, Sporns et al., 2004).
In the present study, we aimed to demonstrate that the network architecture is related to the directed influence brain network between cortical and subcortical regions in the brain. In this regard, the directed influences were estimated by calculating multivariate Granger causal analysis (GCA) (Geweke, 1984) between the time series of each pair of brain regions. The resulting Granger influence matrices were thresholded to generate a set of binary directed graphs. Topological parameters, degree of a given node, clustering coefficient, shortest path lengths, betweenness centrality, network modularity and small-world properties were evaluated for these graphs.
Section snippets
Subjects
Fifty-two (26 females, age range: 19–32 yrs, mean age: 23.1 yrs) right-handed healthy subjects participated in this study. All subjects did not have history of psychiatric disorder or neurological illness. The present study was approved by the local Medical Ethics Committee at Jinling Hospital, Nanjing University School of Medicine, and informed written consent was obtained from all subjects.
Data acquisition
Experiments were performed on a SIEMENS Trio 3 T scanner (Erlangen, German) located at Jinling Hospital,
Directed influence brain network
The mean direct influence matrix was calculated by averaging the Granger influence matrices across all the subjects (Fig. 1A) at the threshold level of Tmax. The reproducibility of the significant Granger influence of each pair of ROIs across all subjects is shown in Fig. 1B.
Degree distribution of the directed influence brain network
For each subject we computed the total degree, in-degree and out-degree from the directed influence network. The group averaged total degree, in-degree and out-degree distribution P(k) are shown in Fig. 2 at the threshold
Discussion
In the present study of resting-state fMRI, we have examined the architecture of the directed influence human brain network, combining Granger causality analysis and graph theory. Some brain regions were characterized by pivotal regions which influenced or were influenced by the other brain regions. In addition, we observed that the topological distributions for total degree, in-degree and out-degree were fitted by an exponentially truncated power law. Furthermore, we showed that the
Conclusion
In this study we focused on evaluating directed influence brain network at regional level and on understanding the underlying structure of the resulting network. We used multivariate Granger causality analysis and a well known graph theory method to gain information about the causal influences of the brain and characterize the topological properties from resting-state fMRI recordings of 52 healthy subjects. Some brain regions were characterized by pivotal regions which were influenced by or
Acknowledgments
The authors would like to thank two anonymous reviewers for their thoughtful comments. This work was supported by the Natural Science Foundation of China, Grant Nos. 30800264, 30971019, 90820006 and 61035006; and the Youth scholar grant of Nanjing Jinling Hospital, Grant No. Q2008063.
Competing interests: The authors have declared that no competing interests exist.
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Wei Liao and Jurong Ding contributed equally to this work.