Original Research ARTICLE

Front. Comput. Neurosci., 12 July 2011 | doi: 10.3389/fncom.2011.00034

A linear model of phase-dependent power correlations in neuronal oscillations

David Eriksson1*, Raul Vicente2 and Kerstin Schmidt1
  • 1 Research Group: Cortical function and dynamics, Max-Planck-Institute for Brain Research, Frankfurt, Germany
  • 2 Department of Neurophysiology, Max-Planck-Institute for Brain Research, Frankfurt, Germany

Recently, it has been suggested that effective interactions between two neuronal populations are supported by the phase difference between the oscillations in these two populations, a hypothesis referred to as “communication through coherence” (CTC). Experimental work quantified effective interactions by means of the power correlations between the two populations, where power was calculated on the local field potential and/or multi-unit activity. Here, we present a linear model of interacting oscillators that accounts for the phase dependency of the power correlation between the two populations and that can be used as a reference for detecting non-linearities such as gain control. In the experimental analysis, trials were sorted according to the coupled phase difference of the oscillators while the putative interaction between oscillations was taking place. Taking advantage of the modeling, we further studied the dependency of the power correlation on the uncoupled phase difference, connection strength, and topology. Since the uncoupled phase difference, i.e., the phase relation before the effective interaction, is the causal variable in the CTC hypothesis we also describe how power correlations depend on that variable. For uni-directional connectivity we observe that the width of the uncoupled phase dependency is broader than for the coupled phase. Furthermore, the analytical results show that the characteristics of the phase dependency change when a bidirectional connection is assumed. The width of the phase dependency indicates which oscillation frequencies are optimal for a given connection delay distribution. We propose that a certain width enables a stimulus-contrast dependent extent of effective long-range lateral connections.

Keywords: communication through coherence, power correlation, phase relation, axonal delays, neuronal oscillations

Citation: Eriksson D, Vicente R and Schmidt K (2011) A linear model of phase-dependent power correlations in neuronal oscillations. Front. Comput. Neurosci. 5:34. doi: 10.3389/fncom.2011.00034

Received: 16 February 2011; Accepted: 27 June 2011;
Published online: 12 July 2011.

Edited by:

Klaus R. Pawelzik, University of Bremen, Germany

Reviewed by:

Florentin Wörgötter, University Göttingen, Germany
Germán Mato, CONICET, Argentina

Copyright: © 2011 Eriksson, Vicente and Schmidt. This is an open-access article subject to a non-exclusive license between the authors and Frontiers Media SA, which permits use, distribution and reproduction in other forums, provided the original authors and source are credited and other Frontiers conditions are complied with.

*Correspondence: David Eriksson, Research Group: Cortical function and dynamics, Max-Planck-Institute for Brain Research, Deutschordenstraße 46, D-60528, Frankfurt/Main, Germany. e-mail: david.eriksson@brain.mpg.de

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