Ali Yener Mutlu

A Time-Frequency-Based Approach to Phase and Phase Synchrony Estimation

Time-varying phase synchrony is an important bivariate measure that quantifies the dynamics between nonstationary signals and has been widely used in many applications including chaotic oscillators in physics and multichannel electroencephalography recordings in neuroscience. Current state-of-the-art in time-varying phase estimation uses either the Hilbert transform or the complex wavelet transform of the signals. Both of these methods have some major drawbacks such as the assumption that the signals are narrowband for the Hilbert transform and the nonuniform time-frequency resolution inherent to the wavelet analysis. In this paper, a new phase estimation method based on the Rihaczek distribution and Reduced Interference Rihaczek distribution belonging to Cohens class is proposed. These distributions offer phase estimates with uniformly high time-frequency resolution which can be used for defining time and frequency dependent phase synchrony. Properties of the phase estimator and the corresponding phase synchrony measure are evaluated both analytically and through simulations showing the effectiveness of the new measures compared to existing methods.

Multivariate empirical mode decomposition for quantifying multivariate phase synchronization

Quantifying the phase synchrony between signals is important in many different applications, including the study of the chaotic oscillators in physics and the modeling of the joint dynamics between channels of brain activity recorded by electroencephalogram (EEG). Current measures of phase synchrony rely on either the wavelet transform or the Hilbert transform of the signals and suffer from constraints such as the limit on time-frequency resolution in the wavelet analysis and the prefiltering requirement in Hilbert transform. Furthermore, the current phase synchrony measures are limited to quantifying bivariate relationships and do not reveal any information about multivariate synchronization patterns, which are important for understanding the underlying oscillatory networks. In this paper, we address these two issues by employing the recently introduced multivariate empirical mode decomposition (MEMD) for quantifying multivariate phase synchrony. First, an MEMD-based bivariate phase synchrony measure is defined for a more robust description of time-varying phase synchrony across frequencies. Second, the proposed bivariate phase synchronization index is used to quantify multivariate synchronization within a network of oscillators using measures of multiple correlation and complexity. Finally, the proposed measures are applied to both simulated networks of chaotic oscillators and real EEG data.

A Signal-Processing-Based Approach to Time-Varying Graph Analysis for Dynamic Brain Network Identification

In recent years, there has been a growing need to analyze the functional connectivity of the human brain. Previous studies have focused on extracting static or time-independent functional networks to describe the long-term behavior of brain activity. However, a static network is generally not sufficient to represent the long term communication patterns of the brain and is considered as an unreliable snapshot of functional connectivity. In this paper, we propose a dynamic network summarization approach to describe the time-varying evolution of connectivity patterns in functional brain activity. The proposed approach is based on first identifying key event intervals by quantifying the change in the connectivity patterns across time and then summarizing the activity in each event interval by extracting the most informative network using principal component decomposition. The proposed method is evaluated for characterizing time-varying network dynamics from event-related potential (ERP) data indexing the error-related negativity (ERN) component related to cognitive control. The statistically significant connectivity patterns for each interval are presented to illustrate the dynamic nature of functional connectivity.

Subspace analysis for characterizing dynamic functional brain networks

Human brain is known to be one of the most complex biological systems and understanding the functional connectivity patterns to distinguish between normal and disrupted brain behavior still remains a challenge. Previous studies focus on analyzing functional connectivity averaged over a certain time and frequency window which is generally not sufficient to address the time-varying evolution of the connectivity patterns. In this paper, we propose a framework to describe the dynamic properties of functional connectivity in the brain. The proposed approach is based on constructing time-varying connectivity graphs from multichannel electroencephalogram (EEG) data, using subspace analysis to detect network-wide changes, identifying key event intervals and then extracting representative networks that describe the connectivity in each event interval. This framework is evaluated for EEG data, containing error-related negativity (ERN) component related to cognitive control. For each time interval, the statistically significant connectivity patterns are presented to illustrate the dynamic nature of functional connectivity.

Dynamic network summarization using convex optimization

The analysis of networks has been much of interest in many fields of research ranging from neuroscience to sociology. Until recently, the major focus of network analysis has been on static networks but there is a growing need to analyze dynamic networks or graphs which evolve over time and have changing topology. One fundamental goal in analyzing dynamic networks is to infer the long term connectivity patterns that can summarize and represent the network with minimum redundancy. In this paper, we propose a signal processing framework which can both determine the transient and stationary parts of the dynamic graphs and summarize network activity with a few number of representative networks. The performance of the proposed method is illustrated for both simulated dynamic network models and real social networks.

Hyperspherical phase synchrony for quantifying multivariate phase synchronization

Time-varying phase synchrony is an important bivariate measure that quantifies both linear and nonlinear dynamics between non-stationary signals. Recently, multivariate phase synchronization has been proposed to investigate the interactions within a group of oscillators. However, current approaches are limited to either averaging all pairwise synchrony values, which causes a loss of information, or forming a matrix of bivariate synchronization indices, where the distribution of the eigenvalues is exploited to estimate the multivariate synchrony. None of these methods is a direct way to quantify the multivariate synchrony since they use bivariate synchrony values to estimate the group dynamics. Therefore, the reliability of these measures is affected by the accuracy of the bivariate synchrony estimates. In this paper, a novel and direct method of computing the multivariate phase synchrony is proposed. The performance of the new estimator is evaluated through simulations showing the effectiveness of the new measure compared to existing methods.

Inferring effective connectivity in the brain from EEG time series using dynamic bayesian networks

Effective connectivity, defined as the influence of a neuronal population on another, is known to have great significance for understanding the organization of the brain. Disruptions in the effective connectivity patterns occur in the case of neurological and psychopathological diseases. Therefore, it is important to develop models of effective brain connectivity from non-invasive neuroimaging data. In this paper, we propose to use dynamic Bayesian networks (DBN) to learn effective brain connectivity from electroencephalogram (EEG) data. DBNs use first order Markov chain to model EEG time series obtained from multiple electrodes. We explore effective brain connectivity in healthy and schizophrenic subjects using this framework. Fourier bootstrapping technique is used to identify the statistically significant pairs of interactions among electrodes.

Hyperspherical phase synchrony measure for quantifying global synchronization in the brain

Phase synchronization has been proposed as a plausible mechanism to quantify both linear and nonlinear relationships between neuronal populations and to assess functional brain connectivity. However, bivariate phase synchrony is not sufficient for complex system analysis such as the brain where the bivariate relationships do not always reflect the underlying network structure. Recently, multivariate extensions of bivariate phase synchrony has been of interest in investigating the interactions within a group of oscillators. Current extensions are based on either averaging all possible pairwise synchrony values or eigen decomposition of a matrix of bivariate synchronization indices to estimate multivariate synchrony using the entropy of the normalized eigenvalues. All of these approaches are sensitive to the accuracy of the bivariate synchrony indices, cause loss of information, computationally complex and are indirect ways to quantify the multivariate synchrony. In this paper, we propose a novel and direct measure to estimate the multivariate phase synchrony by forming direction vectors in a multidimensional hyperspherical coordinate system. The proposed method is evaluated through application to electroencephalogram (EEG) data containing error-related negativity (ERN) related to cognitive control. We compare the new measure with existing methods and show its effectiveness in quantifying multivariate synchronization of different brain regions.

Joint frequency spectral lag representation for cross-frequency modulation analysis in the brain

The concepts of modulation frequency along with modulation spectra are originally encountered in acoustics, speech and audio processing. The modulation spectrum, a function of acoustic frequency and modulation frequency, has been proposed and widely used in the speech processing community. However, modulation spectrum, much like time-frequency distribution is a representation of an individual signal and does not quantify the modulation effects between two signals. In this paper, we introduce cross frequency-spectral lag representation based on the Wigner distribution to represent the modulation relationships between two signals. The performance of the proposed distribution is illustrated for simulated signals as well as for electroencephalogram (EEG) signals.

Identifying multivariate EEG synchronization networks through multiple subject community detection

In neurophysiological studies, it is important to infer the functional networks underlying the observed physiological data. In recent years, measures of functional connectivity as well as tools from graph theory have characterized the human brain as a complex network composed of segregated modules linked by short path lengths. However, the current studies of functional connectivity focus on either solely quantifying the pairwise relationships or describing the global characteristics of the network using graph theoretic metrics. In order to understand the multivariate relationships within the network, it is important to determine the functional modules underlying the complex networks. Moreover, the study of these functional networks is confounded by the fact that most neurophysiological studies consist of data collected from multiple subjects, thus, it is important to identify functional modules representative of all subjects. We propose a hierarchical consensus spectral clustering approach based on the Fiedler vector to address these issues. Furthermore, measures based on hypothesis testing and information theory are introduced for selecting the optimal modular structure. The proposed framework is applied to EEG data collected during a study of error-related negativity (ERN) to better understand the functional networks involved in cognitive control.