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81
Nonlinear Multivariate Analysis of Neurophysiological Signals
- Progress in Neurobiology
, 2005
"... 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 ..."
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Cited by 107 (5 self)
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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 interdependences 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.
A neural mass model for MEG/EEG: coupling and neuronal dynamics
- NeuroImage
, 2003
"... Although MEG/EEG signals are highly variable, systematic changes in distinct frequency bands are commonly encountered. These frequency-specific changes represent robust neural correlates of cognitive or perceptual processes (for example, alpha rhythms emerge on closing the eyes). However, their func ..."
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Cited by 81 (21 self)
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Although MEG/EEG signals are highly variable, systematic changes in distinct frequency bands are commonly encountered. These frequency-specific changes represent robust neural correlates of cognitive or perceptual processes (for example, alpha rhythms emerge on closing the eyes). However, their functional significance remains a matter of debate. Some of the mechanisms that generate these signals are known at the cellular level and rest on a balance of excitatory and inhibitory interactions within and between populations of neurons. The kinetics of the ensuing population dynamics determine the frequency of oscillations. In this work we extended the classical nonlinear lumped-parameter model of alpha rhythms, initially developed by Lopes da Silva and colleagues [Kybernetik 15 (1974) 27], to generate more complex dynamics. We show that the whole spectrum of MEG/EEG signals can be reproduced within the oscillatory regime of this model by simply changing the population kinetics. We used the model to examine the influence of coupling strength and propagation delay on the rhythms generated by coupled cortical areas. The main findings were that (1) coupling induces phase-locked activity, with a phase shift of 0 or π when the coupling is bidirectional, and (2) both coupling and propagation delay are critical determinants of the MEG/EEG spectrum. In forthcoming articles, we will use this model to (1) estimate how neuronal interactions are expressed in MEG/EEG oscillations and establish the construct validity of various indices of nonlinear coupling, and (2) generate event-related transients to derive physiologically informed basis functions for statistical modelling of average evoked responses.
A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis
- Cerebral Cortex
, 2006
"... The aim of this paper is to explain critical features of the human primary generalized epilepsies by investigating the dynamical bifur-cations of a nonlinear model of the brain’s mean field dynamics. The model treats the cortex as a medium for the propagation of waves of electrical activity, incorpo ..."
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Cited by 58 (9 self)
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The aim of this paper is to explain critical features of the human primary generalized epilepsies by investigating the dynamical bifur-cations of a nonlinear model of the brain’s mean field dynamics. The model treats the cortex as a medium for the propagation of waves of electrical activity, incorporating key physiological processes such as propagation delays, membrane physiology, and corticothalamic feedback. Previous analyses have demonstrated its descriptive validity in a wide range of healthy states and yielded specific pre-dictions with regards to seizure phenomena. We show that mapping the structure of the nonlinear bifurcation set predicts a number of crucial dynamic processes, including the onset of periodic and chaotic dynamics as well as multistability. Quantitative study of electrophysiological data supports the validity of these predictions. Hence, we argue that the core electrophysiological and cognitive differences between tonic--clonic and absence seizures are pre-dicted and interrelated by the global bifurcation diagram of the model’s dynamics. The present study is the first to present a unifying explanation of these generalized seizures using the bifurcation analysis of a dynamical model of the brain.
Causality detection based on information-theoretic approaches in time series analysis
, 2007
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Small-world properties of nonlinear brain activity in schizophrenia
- Hum. Brain Mapp
, 2009
"... Abstract: A disturbance in the interactions between distributed cortical regions may underlie the cogni-tive and perceptual dysfunction associated with schizophrenia. In this article, nonlinear measures of cortical interactions and graph-theoretical metrics of network topography are combined to inve ..."
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Cited by 37 (3 self)
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Abstract: A disturbance in the interactions between distributed cortical regions may underlie the cogni-tive and perceptual dysfunction associated with schizophrenia. In this article, nonlinear measures of cortical interactions and graph-theoretical metrics of network topography are combined to investigate this schizophrenia ‘‘disconnection hypothesis.’ ’ This is achieved by analyzing the spatiotemporal struc-ture of resting state scalp EEG data previously acquired from 40 young subjects with a recent first epi-sode of schizophrenia and 40 healthy matched controls. In each subject, a method of mapping the to-pography of nonlinear interactions between cortical regions was applied to a widely distributed array of these data. The resulting nonlinear correlation matrices were converted to weighted graphs. The path length (a measure of large-scale network integration), clustering coefficient (a measure of ‘‘cliqu-ishness’’), and hub structure of these graphs were used as metrics of the underlying brain network ac-tivity. The graphs of both groups exhibited high levels of local clustering combined with comparatively short path lengths—features consistent with a ‘‘small-world’ ’ topology—as well as the presence of strong, central hubs. The graphs in the schizophrenia group displayed lower clustering and shorter path lengths in comparison to the healthy group. Whilst still ‘‘small-world,’ ’ these effects are consistent with a subtle randomization in the underlying network architecture—likely associated with a greater
Nino-Southern Oscillation drives North Atlantic Oscillation as revealed with nonlinear techniques from climatic indices
"... [1] Based on the nonlinear techniques for estimation of coupling between oscillatory systems, we investigate the dynamics of climatic modes characterizing global and the Northern Hemisphere (NH) processes. In particular, indices of the North Atlantic Oscillation (NAO) and El Niño–Southern Oscillatio ..."
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Cited by 18 (1 self)
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[1] Based on the nonlinear techniques for estimation of coupling between oscillatory systems, we investigate the dynamics of climatic modes characterizing global and the Northern Hemisphere (NH) processes. In particular, indices of the North Atlantic Oscillation (NAO) and El Niño–Southern Oscillation (ENSO) for 1950–2004 are analyzed. The methods based on phase dynamics modeling and nonlinear ‘‘Granger causality’ ’ are used. We infer that ENSO affects NAO during the last half a century with confidence probability higher than 0.95. The influence is characterized with time delay in the range from a couple of months up to three years and increases during the last decade. Citation: Mokhov, I. I., and D. A.
Methods for quantifying the causal structure of bivariate time series
- Int. J. of Bifurcation and Chaos
, 2006
"... In the study of complex systems one of the major concerns is the detection and characterization of causal interdependencies and couplings between different subsystems. The nature of such dependencies is typically not only nonlinear but also asymmetric and thus makes the use of symmetric and linear m ..."
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Cited by 14 (1 self)
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In the study of complex systems one of the major concerns is the detection and characterization of causal interdependencies and couplings between different subsystems. The nature of such dependencies is typically not only nonlinear but also asymmetric and thus makes the use of symmetric and linear methods ineffective. Moreover, signals sampled from real world systems are noisy and short, posing additional constraints on the estimation of the underlying couplings. In this article, we compare a set of six recently introduced methods for quantifying the causal structure of bivariate time series extracted from systems with complex dynamical behavior. We discuss the usefulness of the methods for detecting asymmetric couplings and directional flow of information in the context of uni- and bidirectionally coupled deterministic chaotic systems. Key words: causal structure, nonlinear time series analysis, coupled systems, information flow
Synchronization approach to analysis of biological systems
- Fluct. Noise Lett
, 2004
"... In this article we review the application of the synchronization theory to the analysis of multivariate biological signals. We address the problem of phase estimation from data and detection and quantification of weak interaction, as well as quantification of the direction of coupling. We discuss th ..."
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Cited by 13 (0 self)
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In this article we review the application of the synchronization theory to the analysis of multivariate biological signals. We address the problem of phase estimation from data and detection and quantification of weak interaction, as well as quantification of the direction of coupling. We discuss the potentials as well as limitations and misinterpretations of the approach.
Effective Detection of Coupling in Short and Noisy Bivariate Data
- IEEE Transactions on Systems, Man and Cybernetics - Part B
, 2003
"... Abstract—In the study of complex systems, one of the primary concerns is the characterization and quantification of interdepen-dencies between different subsystems. In real-life systems, the na-ture of dependencies or coupling can be nonlinear and asymmetric, rendering the classical linear methods u ..."
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Cited by 12 (4 self)
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Abstract—In the study of complex systems, one of the primary concerns is the characterization and quantification of interdepen-dencies between different subsystems. In real-life systems, the na-ture of dependencies or coupling can be nonlinear and asymmetric, rendering the classical linear methods unsuitable for this purpose. Furthermore, experimental signals are noisy and short, which pose additional constraints for the measurement of underlying coupling. We discuss an index based on nonlinear dynamical system theory to measure the degree of coupling which can be asymmetric. The usefulness of this index has been demonstrated by several exam-ples including simulated and real-life signals. This index is found to effectively disclose the nature and the degree of interactions even when the coupling is very weak and data are noisy and of limited length; by this way, new insight into the functioning of the under-lying complex system is possible. Index Terms—Asymmetry, interdependency, noise, nonlin-earity, state space, time series.
