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On the Influence of Amplitude on the Connectivity between Phases.

Daffertshofer A, van Wijk BC - Front Neuroinform (2011)

Bottom Line: For the interconnected Wilson-Cowan models we derive analytically how connectivity between phases explicitly depends on the generating oscillators' amplitudes.In consequence, the link between neurophysiological studies and computational models always requires the incorporation of the amplitude dynamics.Supplementing synchronization characteristics by amplitude patterns, as captured by, e.g., spectral power in M/EEG recordings, will certainly aid our understanding of the relation between structural and functional organizations in neural networks at large.

View Article: PubMed Central - PubMed

Affiliation: Research Institute MOVE, VU University Amsterdam Amsterdam, Netherlands.

ABSTRACT
In recent studies, functional connectivities have been reported to display characteristics of complex networks that have been suggested to concur with those of the underlying structural, i.e., anatomical, networks. Do functional networks always agree with structural ones? In all generality, this question can be answered with "no": for instance, a fully synchronized state would imply isotropic homogeneous functional connections irrespective of the "real" underlying structure. A proper inference of structure from function and vice versa requires more than a sole focus on phase synchronization. We show that functional connectivity critically depends on amplitude variations, which implies that, in general, phase patterns should be analyzed in conjunction with the corresponding amplitude. We discuss this issue by comparing the phase synchronization patterns of interconnected Wilson-Cowan models vis-à-vis Kuramoto networks of phase oscillators. For the interconnected Wilson-Cowan models we derive analytically how connectivity between phases explicitly depends on the generating oscillators' amplitudes. In consequence, the link between neurophysiological studies and computational models always requires the incorporation of the amplitude dynamics. Supplementing synchronization characteristics by amplitude patterns, as captured by, e.g., spectral power in M/EEG recordings, will certainly aid our understanding of the relation between structural and functional organizations in neural networks at large.

No MeSH data available.


Amplitude ratios [upper row; log(Rl/Rk)] and functional connectivity (lower row) of the Hagmann network using again a bimodal distribution of Pk. The left most panel is again the structural network Ckl; we here used Pk ∈ [−0.25,…,−0.20] and [0.20,…,0.25]. As in the small-world case, localized clusters of synchronized nodes emerge dependent on the overall coupling strength η. These clustered patterns apparently disagree with the underlying anatomical network (most left panel); cf. Figure 3, right column, second row, green dashed lines.
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Figure 6: Amplitude ratios [upper row; log(Rl/Rk)] and functional connectivity (lower row) of the Hagmann network using again a bimodal distribution of Pk. The left most panel is again the structural network Ckl; we here used Pk ∈ [−0.25,…,−0.20] and [0.20,…,0.25]. As in the small-world case, localized clusters of synchronized nodes emerge dependent on the overall coupling strength η. These clustered patterns apparently disagree with the underlying anatomical network (most left panel); cf. Figure 3, right column, second row, green dashed lines.

Mentions: Empirical networks are unlikely to have an organization that can be exactly described by one of the theoretical network models. To study a network that more realistically represents anatomical connections in the human brain we repeated our simulations on a network that was based on axonal pathways obtained by diffusion spectrum imaging. This dataset has been used to identify the so-called “structural core” of anatomical connections in the human cerebral cortex as described by Hagmann et al. (2008), which is accessible via http://www.connectomeviewer.org/viewer/datasets. To reduce the size of the network and, by this, accelerate simulation time, the original 998 regions were assigned to a 66-node parcellation scheme and averaged over all five subjects as was also done in the original study (Hagmann et al., 2008). The resulting weighted, undirected network was subsequently thresholded to obtain a binary network with an average degree of 10. This network served as our connectivity matrix Ckl; see Figure 2 and also Figure 6 below.


On the Influence of Amplitude on the Connectivity between Phases.

Daffertshofer A, van Wijk BC - Front Neuroinform (2011)

Amplitude ratios [upper row; log(Rl/Rk)] and functional connectivity (lower row) of the Hagmann network using again a bimodal distribution of Pk. The left most panel is again the structural network Ckl; we here used Pk ∈ [−0.25,…,−0.20] and [0.20,…,0.25]. As in the small-world case, localized clusters of synchronized nodes emerge dependent on the overall coupling strength η. These clustered patterns apparently disagree with the underlying anatomical network (most left panel); cf. Figure 3, right column, second row, green dashed lines.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3139941&req=5

Figure 6: Amplitude ratios [upper row; log(Rl/Rk)] and functional connectivity (lower row) of the Hagmann network using again a bimodal distribution of Pk. The left most panel is again the structural network Ckl; we here used Pk ∈ [−0.25,…,−0.20] and [0.20,…,0.25]. As in the small-world case, localized clusters of synchronized nodes emerge dependent on the overall coupling strength η. These clustered patterns apparently disagree with the underlying anatomical network (most left panel); cf. Figure 3, right column, second row, green dashed lines.
Mentions: Empirical networks are unlikely to have an organization that can be exactly described by one of the theoretical network models. To study a network that more realistically represents anatomical connections in the human brain we repeated our simulations on a network that was based on axonal pathways obtained by diffusion spectrum imaging. This dataset has been used to identify the so-called “structural core” of anatomical connections in the human cerebral cortex as described by Hagmann et al. (2008), which is accessible via http://www.connectomeviewer.org/viewer/datasets. To reduce the size of the network and, by this, accelerate simulation time, the original 998 regions were assigned to a 66-node parcellation scheme and averaged over all five subjects as was also done in the original study (Hagmann et al., 2008). The resulting weighted, undirected network was subsequently thresholded to obtain a binary network with an average degree of 10. This network served as our connectivity matrix Ckl; see Figure 2 and also Figure 6 below.

Bottom Line: For the interconnected Wilson-Cowan models we derive analytically how connectivity between phases explicitly depends on the generating oscillators' amplitudes.In consequence, the link between neurophysiological studies and computational models always requires the incorporation of the amplitude dynamics.Supplementing synchronization characteristics by amplitude patterns, as captured by, e.g., spectral power in M/EEG recordings, will certainly aid our understanding of the relation between structural and functional organizations in neural networks at large.

View Article: PubMed Central - PubMed

Affiliation: Research Institute MOVE, VU University Amsterdam Amsterdam, Netherlands.

ABSTRACT
In recent studies, functional connectivities have been reported to display characteristics of complex networks that have been suggested to concur with those of the underlying structural, i.e., anatomical, networks. Do functional networks always agree with structural ones? In all generality, this question can be answered with "no": for instance, a fully synchronized state would imply isotropic homogeneous functional connections irrespective of the "real" underlying structure. A proper inference of structure from function and vice versa requires more than a sole focus on phase synchronization. We show that functional connectivity critically depends on amplitude variations, which implies that, in general, phase patterns should be analyzed in conjunction with the corresponding amplitude. We discuss this issue by comparing the phase synchronization patterns of interconnected Wilson-Cowan models vis-à-vis Kuramoto networks of phase oscillators. For the interconnected Wilson-Cowan models we derive analytically how connectivity between phases explicitly depends on the generating oscillators' amplitudes. In consequence, the link between neurophysiological studies and computational models always requires the incorporation of the amplitude dynamics. Supplementing synchronization characteristics by amplitude patterns, as captured by, e.g., spectral power in M/EEG recordings, will certainly aid our understanding of the relation between structural and functional organizations in neural networks at large.

No MeSH data available.