Inferring Asymmetric Relations between Interacting Neuronal Oscillators

Abstract

We apply a quantitative method for the identification of asymmetric relations between weakly interacting self-sustained oscillators to the study of rhythmic neural electrical activity. We begin by testing the method on biophysically motivated neural oscillator models considering first two diffusively coupled Hindmarsh-Rose oscillators, and then two ensembles of globally coupled neurons interacting through their mean fields. Next, we consider the more complex case of interactions among several oscillatory units. The method is further applied to the analysis of the control of externally vs internally paced movements in humans. A pilot study in one healthy subject reveals that asymmetry of interactions between different brain areas may strongly change with the transition from external to internal pacing, while the degree of synchronization hardly changes. Furthermore, our preliminary results highlight the important role of the secondary auditory cortex in internal rhythm generation. at University of Washington Libraries on March 15, 2015 http://ptps.oxfordjournals.org/ Downloaded from

Synchronization phenomena in human epileptic brain networks

“…Recently, correction schemes have been proposed in order to recover some assumed properties of the phase variables (Kralemann et al, 2007(Kralemann et al, , 2008Revzen and Guckenheimer, 2008). Measures for the strength of interactions can then be derived by exploiting phase differences either statistically (Lachaux et al, 1999;Mormann et al, 2000;Kalitzin et al, 2002;Canolty et al, 2006;Chavez et al, 2006a;Schelter et al, 2006Schelter et al, , 2007Stam et al, 2007b) or via information-theoretical approaches (Tass et al, 1998), and the direction of interactions can be quantified with a phase modeling approach Smirnov and Bezruchko, 2003;Cimponeriu et al, 2003;Paluš and Stefanovska, 2003;Smirnov and Andrzejak, 2005;Bahraminasab et al, 2008;Smirnov and Bezruchko, 2009).…”

Evaluation of Cortical Connectivity During Real and Imagined Rhythmic Finger Tapping

“…Developed within the framework of weakly coupled nonlinear oscillator systems [36,37], phase synchronization analysis can detect a weak form of nonlinear interaction between oscillator systems, which may be not revealed by cross-correlation or coherence. In a previous work [38], we have demonstrated the performance of phase synchronization analysis in identifying connectivity patterns between brain areas engaged in a paced finger-tapping task. Here we use the instantaneous phase of the EEG signals obtained by the complex wavelet decomposition to quantify the inter-channel synchronization and evaluate the patterns coupling in the beta frequency range.…”

Synchronization Approach to Analysis of Biological Systems

“…Stochastic phase synchronization in sensory systems and its role in mediating sensory responses was studied in a series of papers of the St.Louis group, in experiments with electrosensitive afferent neurons of the paddlefish and with light-sensitive and mechanosensitive neurons of the crayfish, as well as theoretically [15-17, 23, 40]. The algorithm for estimation of the directionality in coupling was exploited for understanding of the functional connectivity in the brain during a prescribed motor task [32,41].…”

“…For examples of application to the cardiorespiratory and brain data see [30,32]. Statistical properties of the directionality estimation are considered in [33].…”