Functional connectivity of distant cortical regions: Role of remote synchronization and symmetry in interactions
Introduction
Spontaneous fluctuations in the blood-oxygen-level-dependent (BOLD) signal of functional magnetic resonance imaging (fMRI) have been intensively investigated over the past decade to assess functional connectivity (FC) between the cortical regions of the human brain (Biswal et al., 1995, Damoiseaux et al., 2006, Vincent et al., 2007). In a typical fMRI experiment, functional connectivity is derived from regions displaying correlated activity at low-frequencies (< 0.1 Hz) even though the anatomical connections between respective regions are largely unknown. Despite important progress, the question how these highly structured and robust patterns of correlated activity arise from the underlying neural dynamics and structural connections still remains poorly understood. It has been suggested that they reflect synchronized variations in the neural activity of particular brain areas that are dynamically coupled to one another (Deco and Jirsa, 2012). These areas are usually modeled by a set of neural populations, embedded in a three-dimensional large-scale brain structure and connected through complex anatomical interactions that are derived from diffusion tensor imaging (DTI) data in humans (Cabral et al., 2011, Cabral et al., 2012, Hagmann et al., 2008) or tracing studies in monkeys (Ghosh et al., 2008a, Ghosh et al., 2008b).
Although the relationship between network topology and synchronized behavior of the network elements remains an open problem, most findings point out that the emergence of synchronized states is tightly linked to the presence of highly connected clusters. Elements of these clusters share similar dynamics indicated by high temporal correlations. This can be interpreted as organization into functional networks. However, various examples from nature suggest that functional similarities do not arise from modular interactions within the network topology alone, but can also be associated with morphological symmetries (Rodriguez et al., 1999, Rogers and Andrew, 2002, Varela et al., 2001). As a result, some units mirror their functionality; swapping their places in the network will not alter the overall functioning of the system. Thus, empirical evidence shows that synchronization of activity between brain regions plays an important role in cognitive integration and function (Rogers and Andrew, 2002, Varela et al., 2001). At the same time, recent numerical results based on generic networks have confirmed that the symmetry of interactions is crucial for remote synchronization and organization into functional modules (Arenas et al., 2006, Nicosia et al., 2013). This symmetry can be defined by the size of shared neighborhoods of the synchronized nodes.
In this paper, we aim to reproduce resting-state FC networks by modeling (neural and BOLD) the activity of interacting cortical regions on empirically derived topologies. Hence, we consider the network topology as a main ingredient of our model and derive functional interactions using both functional and anatomical connectivity between the regions in focus. In this way, important information about the presence and absence of direct neural connections between functionally connected regions is included. Controlling for direct neural links in functional networks allows us to test the hypothesis that the FC of distant cortical regions arises from the symmetry of indirect interactions. We quantify this symmetry by the size of overlapping neighborhoods of nodes that are not directly connected. This approach is close, but different from earlier works by Cabral et al., 2011, Cabral et al., 2012, whose investigations started from structural data only.
In our numerical simulations, we model the neural dynamics as self-sustained Kuramoto oscillators. Following the approach of Cabral et al., 2011, Cabral et al., 2012 we set their natural frequencies within the gamma frequency range. We explore the emergence of pairwise synchronization in the simulated networks for different coupling topologies by applying correlation thresholds to empirically derived functional connections. We show that patterns of synchrony reflect the topology of the underlying network for a narrow range of correlation thresholds. We also illustrate that the symmetry of the interactions as defined above drives remote nodes into synchronized activity and therefore plays a vital role in functional connections between distant cortical regions.
Section snippets
Empirical anatomical and functional connectivity
We consider the anatomical and functional brain connectivities that are defined on the same cortical and sub-cortical regions and that are derived from diffusion-weighted DW-MRI and fMRI data, respectively (see details in the Supplementary Material, Appendix A and also in Vuksanović and Hövel, (2014) and van Wijk et al., (2010)). In short, for the connectivity analysis, brain images are partitioned into N = 90 regions based on the Tzourio-Mazoyer brain atlas (Tzourio-Mazoyer et al., 2002) using
Empirical vs. simulated functional connectivity: comparison, agreement, and parameter selection
In order to quantify the amount of synchrony between all pairs of nodes in the network, we calculated a 90 × 90 correlation matrix for each combination of the threshold r and phase-frustration parameter α for both neural and BOLD activity. An example of these matrices is given in Fig. 2 for r = 0.56 and α = 0.9. Fig. 2 (left) and (right) shows the correlation matrix based on neural activity according to Eq. (1) and the BOLD signal, which is inferred using the Balloon–Windkessel model, respectively.
Discussion
In this study, we combined experimental and modeling approaches to investigate synchronized behavior of spatially distant cortical regions constituting large-scale resting-state functional networks. We simulated a set of resting-state networks using empirically derived topologies of the cortical functional interactions, considering only regions with direct neural links. We demonstrated that patterns of synchronized neural activity can arise from underlying complex topologies and that the
Conclusion
We have used a modeling approach in conjunction with experimental data to investigate the dynamics of functional connectivity in the human brain. We demonstrated that the functional connectivity observed between spatially distant cortical regions can be explained by remote synchronization arising from the symmetry of cortical functional interactions. This symmetry is quantified by the overlap of the neighborhoods of pairs of nodes. The level of synchrony between remote nodes strongly correlates
Acknowledgments
This work was supported by BMBF (grant no. 01Q1001B) in the framework of BCCN Berlin (Project B7). We thank John-Dylan Haynes and his group for helpful discussions concerning the fMRI data processing and Yasser Iturria-Medina for sharing the DTI data used in the study.
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2021, Physica A: Statistical Mechanics and its ApplicationsCitation Excerpt :A linear relation is also observed in this case with a smaller slope. The influence of common first neighbors on the correlation between cortical regions signals has previously been suggested in synchronization models of brain networks [34,40]. Our analysis corroborates with these results.