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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.


The synchronization ρ as a function of overall coupling strength η for the network of Wilson–Cowan oscillators [Eq. 4; three upper rows] and for the Kuramoto network [Eq. 5; bottom row]. For the upper row, Pk values were drawn from the interval [−0.25,…,0.25], for the second and third row from the indicated intervals (see right-hand side).
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Figure 3: The synchronization ρ as a function of overall coupling strength η for the network of Wilson–Cowan oscillators [Eq. 4; three upper rows] and for the Kuramoto network [Eq. 5; bottom row]. For the upper row, Pk values were drawn from the interval [−0.25,…,0.25], for the second and third row from the indicated intervals (see right-hand side).

Mentions: The changes in synchronization ρ as a function of overall coupling strength η are summarized in Figure 3. First thing to notice is that, for a critical η, the Wilson–Cowan model shows a brisk increase in ρ after which maximal synchronization is reached. Increasing η again after a critical value breaks down the synchronization as the individual Wilson–Cowan oscillators leave the stable limit cycle regime when their inputs exceed a certain value (Schuster and Wagner, 1990a). That means, the neural masses at the different nodes stop oscillating altogether if coupling is too strong. Of course, this does not apply for the Kuramoto model since, by construction, the phases keep oscillating. In consequence, ρ keeps increasing with η and reaches asymptotically maximum synchronization (see bottom row's panels in Figure 3).


On the Influence of Amplitude on the Connectivity between Phases.

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

The synchronization ρ as a function of overall coupling strength η for the network of Wilson–Cowan oscillators [Eq. 4; three upper rows] and for the Kuramoto network [Eq. 5; bottom row]. For the upper row, Pk values were drawn from the interval [−0.25,…,0.25], for the second and third row from the indicated intervals (see right-hand side).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 3: The synchronization ρ as a function of overall coupling strength η for the network of Wilson–Cowan oscillators [Eq. 4; three upper rows] and for the Kuramoto network [Eq. 5; bottom row]. For the upper row, Pk values were drawn from the interval [−0.25,…,0.25], for the second and third row from the indicated intervals (see right-hand side).
Mentions: The changes in synchronization ρ as a function of overall coupling strength η are summarized in Figure 3. First thing to notice is that, for a critical η, the Wilson–Cowan model shows a brisk increase in ρ after which maximal synchronization is reached. Increasing η again after a critical value breaks down the synchronization as the individual Wilson–Cowan oscillators leave the stable limit cycle regime when their inputs exceed a certain value (Schuster and Wagner, 1990a). That means, the neural masses at the different nodes stop oscillating altogether if coupling is too strong. Of course, this does not apply for the Kuramoto model since, by construction, the phases keep oscillating. In consequence, ρ keeps increasing with η and reaches asymptotically maximum synchronization (see bottom row's panels in Figure 3).

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.