Detection of weak directional coupling: phase-dynamics approach versus state-space approach

Detecting directional coupling in the human epileptic brain: limitations and potential pitfalls

We study directional relationships-in the driver-responder sense-in networks of coupled nonlinear oscillators using a phase modeling approach. Specifically, we focus on the identification of drivers in clusters with varying levels of synchrony, mimicking dynamical interactions between the seizure generating region (epileptic focus) and other brain structures. We demonstrate numerically that such an identification is not always possible in a reliable manner. Using the same analysis techniques as in model systems, we study multichannel electroencephalographic recordings from two patients suffering from focal epilepsy. Our findings demonstrate that--depending on the degree of intracluster synchrony--certain subsystems can spuriously appear to be driving others, which should be taken into account when analyzing field data with unknown underlying dynamics.

Estimating nonlinear interdependences in dynamical systems using cellular nonlinear networks

We propose a method for estimating nonlinear interdependences between time series using cellular nonlinear networks. Our approach is based on the nonlinear dynamics of interacting nonlinear elements. We apply it to time series of coupled nonlinear model systems and to electroencephalographic time series from an epilepsy patient, and we show that an accurate approximation of symmetric and asymmetric realizations of a nonlinear interdependence measure can be achieved, thus allowing one to detect the strength and direction of couplings.

Estimation of the direction of the coupling by conditional probabilities of recurrence

We introduce a method to detect and quantify the asymmetry of the coupling between two interacting systems based on their recurrence properties. This method can detect the direction of the coupling in weakly as well as strongly coupled systems. It even allows detecting the asymmetry of the coupling in the more challenging case of structurally different systems and it is very robust against noise. We also address the problem of detecting the asymmetry of the coupling in passive experiments, i.e., when the strength of the coupling cannot be systematically changed, which is of great relevance for the analysis of experimental time series.

Revealing direction of coupling between neuronal oscillators from time series: phase dynamics modeling versus partial directed coherence

The problem of determining directional coupling between neuronal oscillators from their time series is addressed. We compare performance of the two well-established approaches: partial directed coherence and phase dynamics modeling. They represent linear and nonlinear time series analysis techniques, respectively. In numerical experiments, we found each of them to be applicable and superior under appropriate conditions: The latter technique is superior if the observed behavior is "closer" to limit-cycle dynamics, the former is better in cases that are closer to linear stochastic processes.

Experimental evidence for phase synchronization transitions in the human cardiorespiratory system

Transitions in the dynamics of complex systems can be characterized by changes in the synchronization behavior of their components. Taking the human cardiorespiratory system as an example and using an automated procedure for screening the synchrograms of 112 healthy subjects we study the frequency and the distribution of synchronization episodes under different physiological conditions that occur during sleep. We find that phase synchronization between heartbeat and breathing is significantly enhanced during non-rapid-eye-movement (non-REM) sleep (deep sleep and light sleep) and reduced during REM sleep. Our results suggest that the synchronization is mainly due to a weak influence of the breathing oscillator upon the heartbeat oscillator, which is disturbed in the presence of long-term correlated noise, superimposed by the activity of higher brain regions during REM sleep.

Measuring direction in the coupling of biological oscillators: a case study for electroreceptors of paddlefish

Recently developed methods for estimating directionality in the coupling between oscillators were tested on experimental time series data from electroreceptors of paddlefish, because each electroreceptor contains two distinct types of noisy oscillators. One type of oscillator is in the sensory epithelia, and another type is in the terminals of afferent neurons. Based on morphological organization and our previous work, we expected unidirectional coupling, whereby epithelial oscillations synaptically influence the spiking oscillators of afferent neurons. Using directionality analysis we confirmed unidirectional coupling of oscillators embedded in electroreceptors. We studied the performance of directionality algorithms for decreasing length of data. Also, we experimentally varied the strength of oscillator coupling, to test the effect of coupling strength on directionality algorithms.

Lag synchrony measures dynamical processes underlying progression of seizure states

We investigate the dynamics of bursting behavior in an intact hippocampal preparation using causal entropy, an adaptive measure of lag synchrony. This analysis, together with a heuristic model of coupled bursting networks, separates experimentally observed bursting dynamics into two dynamical regimes, when bursting is driven by (1) the intranetwork dynamics of a single region, or (2) internetwork feedback between spatially disjoint neural populations. Our results suggest that the abrupt transition between these two states heralds the gradual desynchronization of bursting activity. These results illustrate how superficially homogeneous behavior across loosely coupled networks may harbor hidden, but robust, dynamical processes.

Nonlinear multivariate analysis of neurophysiological signals

Multivariate time series analysis is extensively used in neurophysiology with the aim of studying the relationship between simultaneously recorded signals. Recently, advances on information theory and nonlinear dynamical systems theory have allowed the study of various types of synchronization from time series. In this work, we first describe the multivariate linear methods most commonly used in neurophysiology and show that they can be extended to assess the existence of nonlinear interdependence between signals. We then review the concepts of entropy and mutual information followed by a detailed description of nonlinear methods based on the concepts of phase synchronization, generalized synchronization and event synchronization. In all cases, we show how to apply these methods to study different kinds of neurophysiological data. Finally, we illustrate the use of multivariate surrogate data test for the assessment of the strength (strong or weak) and the type (linear or nonlinear) of interdependence between neurophysiological signals.

Estimation of coupling between oscillators from short time series via phase dynamics modeling: limitations and application to EEG data

We demonstrate in numerical experiments that estimators of strength and directionality of coupling between oscillators based on modeling of their phase dynamics [D. A. Smirnov and B. P. Bezruchko, Phys. Rev. E 68, 046209 (2003)] are widely applicable. Namely, although the expressions for the estimators and their confidence bands are derived for linear uncoupled oscillators under the influence of independent sources of Gaussian white noise, they turn out to allow reliable characterization of coupling from relatively short time series for different properties of noise, significant phase nonlinearity of the oscillators, and nonvanishing coupling between them. We apply the estimators to analyze a two-channel human intracranial epileptic electroencephalogram (EEG) recording with the purpose of epileptic focus localization.