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      Improved measures of phase-coupling between spikes and the Local Field Potential

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          Abstract

          An important tool to study rhythmic neuronal synchronization is provided by relating spiking activity to the Local Field Potential (LFP). Two types of interdependent spike-LFP measures exist. The first approach is to directly quantify the consistency of single spike-LFP phases across spikes, referred to here as point-field phase synchronization measures. We show that conventional point-field phase synchronization measures are sensitive not only to the consistency of spike-LFP phases, but are also affected by statistical dependencies between spike-LFP phases, caused by e.g. non-Poissonian history-effects within spike trains such as bursting and refractoriness. To solve this problem, we develop a new pairwise measure that is not biased by the number of spikes and not affected by statistical dependencies between spike-LFP phases. The second approach is to quantify, similar to EEG-EEG coherence, the consistency of the relative phase between spike train and LFP signals across trials instead of across spikes, referred to here as spike train to field phase synchronization measures. We demonstrate an analytical relationship between point-field and spike train to field phase synchronization measures. Based on this relationship, we prove that the spike train to field pairwise phase consistency (PPC), a quantity closely related to the squared spike-field coherence, is a monotonically increasing function of the number of spikes per trial. This derived relationship is exact and analytic, and takes a linear form for weak phase-coupling. To solve this problem, we introduce a corrected version of the spike train to field PPC that is independent of the number of spikes per trial. Finally, we address the problem that dependencies between spike-LFP phase and the number of spikes per trial can cause spike-LFP phase synchronization measures to be biased by the number of trials. We show how to modify the developed point-field and spike train to field phase synchronization measures in order to make them unbiased by the number of trials.

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          Neuronal synchrony: a versatile code for the definition of relations?

          W. Singer (1999)
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            Phase lag index: assessment of functional connectivity from multi channel EEG and MEG with diminished bias from common sources.

            To address the problem of volume conduction and active reference electrodes in the assessment of functional connectivity, we propose a novel measure to quantify phase synchronization, the phase lag index (PLI), and compare its performance to the well-known phase coherence (PC), and to the imaginary component of coherency (IC). The PLI is a measure of the asymmetry of the distribution of phase differences between two signals. The performance of PLI, PC, and IC was examined in (i) a model of 64 globally coupled oscillators, (ii) an EEG with an absence seizure, (iii) an EEG data set of 15 Alzheimer patients and 13 control subjects, and (iv) two MEG data sets. PLI and PC were more sensitive than IC to increasing levels of true synchronization in the model. PC and IC were influenced stronger than PLI by spurious correlations because of common sources. All measures detected changes in synchronization during the absence seizure. In contrast to PC, PLI and IC were barely changed by the choice of different montages. PLI and IC were superior to PC in detecting changes in beta band connectivity in AD patients. Finally, PLI and IC revealed a different spatial pattern of functional connectivity in MEG data than PC. The PLI performed at least as well as the PC in detecting true changes in synchronization in model and real data but, at the same token and like-wise the IC, it was much less affected by the influence of common sources and active reference electrodes. Copyright 2007 Wiley-Liss, Inc.
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              Identifying true brain interaction from EEG data using the imaginary part of coherency.

              The main obstacle in interpreting EEG/MEG data in terms of brain connectivity is the fact that because of volume conduction, the activity of a single brain source can be observed in many channels. Here, we present an approach which is insensitive to false connectivity arising from volume conduction. We show that the (complex) coherency of non-interacting sources is necessarily real and, hence, the imaginary part of coherency provides an excellent candidate to study brain interactions. Although the usual magnitude and phase of coherency contain the same information as the real and imaginary parts, we argue that the Cartesian representation is far superior for studying brain interactions. The method is demonstrated for EEG measurements of voluntary finger movement. We found: (a) from 5 s before to movement onset a relatively weak interaction around 20 Hz between left and right motor areas where the contralateral side leads the ipsilateral side; and (b) approximately 2-4 s after movement, a stronger interaction also at 20 Hz in the opposite direction. It is possible to reliably detect brain interaction during movement from EEG data. The method allows unambiguous detection of brain interaction from rhythmic EEG/MEG data.
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                Author and article information

                Contributors
                martinvinck@gmail.com
                Journal
                J Comput Neurosci
                J Comput Neurosci
                Journal of Computational Neuroscience
                Springer US (Boston )
                0929-5313
                1573-6873
                21 December 2011
                21 December 2011
                August 2012
                : 33
                : 1
                : 53-75
                Affiliations
                [1 ]Cognitive and Systems Neuroscience Group, Center for Neuroscience, University of Amsterdam, Amsterdam, The Netherlands
                [2 ]Centre for Vision Research, Department of Biology, York University, Toronto, ON Canada
                Author notes

                Action Editor: Alain Destexhe

                Article
                374
                10.1007/s10827-011-0374-4
                3394239
                22187161
                4d0952b3-d78e-4517-b88e-2fa6e72d8692
                © The Author(s) 2011
                Categories
                Article
                Custom metadata
                © Springer Science+Business Media, LLC 2012

                Neurosciences
                spike-triggered average,phase-synchronization,spike-field locking,phase locking,spike-lfp,spike-field coherence

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