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Time-Delayed Mutual Information of the Phase as a Measure of Functional Connectivity

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  • Andreas Wilmer
  • Marc de Lussanet
  • Markus Lappe

Abstract

We propose a time-delayed mutual information of the phase for detecting nonlinear synchronization in electrophysiological data such as MEG. Palus already introduced the mutual information as a measure of synchronization [1]. To obtain estimates on small data-sets as reliably as possible, we adopt the numerical implementation as proposed by Kraskov and colleagues [2]. An embedding with a parametric time-delay allows a reconstruction of arbitrary nonstationary connective structures – so-called connectivity patterns – in a wide class of systems such as coupled oscillatory or even purely stochastic driven processes [3]. By using this method we do not need to make any assumptions about coupling directions, delay times, temporal dynamics, nonlinearities or underlying mechanisms. For verifying and refining the methods we generate synthetic data-sets by a mutual amplitude coupled network of Rössler oscillators with an a-priori known connective structure. This network is modified in such a way, that the power-spectrum forms a power law, which is also observed in electrophysiological recordings. The functional connectivity measure is tested on robustness to additive uncorrelated noise and in discrimination of linear mixed input data. For the latter issue a suitable de-correlation technique is applied. Furthermore, the compatibility to inverse methods for a source reconstruction in MEG such as beamforming techniques is controlled by dedicated dipole simulations. Finally, the method is applied on an experimental MEG recording.

Suggested Citation

  • Andreas Wilmer & Marc de Lussanet & Markus Lappe, 2012. "Time-Delayed Mutual Information of the Phase as a Measure of Functional Connectivity," PLOS ONE, Public Library of Science, vol. 7(9), pages 1-22, September.
  • Handle: RePEc:plo:pone00:0044633
    DOI: 10.1371/journal.pone.0044633
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    References listed on IDEAS

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    1. Gustavo Deco & Viktor K Jirsa & Peter A Robinson & Michael Breakspear & Karl Friston, 2008. "The Dynamic Brain: From Spiking Neurons to Neural Masses and Cortical Fields," PLOS Computational Biology, Public Library of Science, vol. 4(8), pages 1-35, August.
    2. Wolf Singer, 1999. "Striving for coherence," Nature, Nature, vol. 397(6718), pages 391-393, February.
    3. Pieter R. Roelfsema & Andreas K. Engel & Peter König & Wolf Singer, 1997. "Visuomotor integration is associated with zero time-lag synchronization among cortical areas," Nature, Nature, vol. 385(6612), pages 157-161, January.
    4. Eugenio Rodriguez & Nathalie George & Jean-Philippe Lachaux & Jacques Martinerie & Bernard Renault & Francisco J. Varela, 1999. "Perception's shadow: long-distance synchronization of human brain activity," Nature, Nature, vol. 397(6718), pages 430-433, February.
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