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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.


Network of Wilson–Cowan models. At each node k a neural population containing excitatory and inhibitory units (Ek and Ik, respectively) yields self-sustained oscillations. Other nodes are connected to the excitatory unit by means of ΣCklEl. Note that this (mean-field) coupling is scaled by a scalar η – see Eq. 1 for details.
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Figure 1: Network of Wilson–Cowan models. At each node k a neural population containing excitatory and inhibitory units (Ek and Ik, respectively) yields self-sustained oscillations. Other nodes are connected to the excitatory unit by means of ΣCklEl. Note that this (mean-field) coupling is scaled by a scalar η – see Eq. 1 for details.

Mentions: To combine Wilson–Cowan models in a network, different populations are now connected via their excitatory units by virtue of the sum of all El in the dynamics of Ek (see Figure 1). The dynamics at node k then becomes


On the Influence of Amplitude on the Connectivity between Phases.

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

Network of Wilson–Cowan models. At each node k a neural population containing excitatory and inhibitory units (Ek and Ik, respectively) yields self-sustained oscillations. Other nodes are connected to the excitatory unit by means of ΣCklEl. Note that this (mean-field) coupling is scaled by a scalar η – see Eq. 1 for details.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: Network of Wilson–Cowan models. At each node k a neural population containing excitatory and inhibitory units (Ek and Ik, respectively) yields self-sustained oscillations. Other nodes are connected to the excitatory unit by means of ΣCklEl. Note that this (mean-field) coupling is scaled by a scalar η – see Eq. 1 for details.
Mentions: To combine Wilson–Cowan models in a network, different populations are now connected via their excitatory units by virtue of the sum of all El in the dynamics of Ek (see Figure 1). The dynamics at node k then becomes

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.