A comparative study of pattern synchronization detection between neural signals using different cross-entropy measures

Cross-approximate entropy (X-ApEn) and cross-sample entropy (X-SampEn) have been employed as bivariate pattern synchronization measures for characterizing interdependencies between neural signals. In this study, we proposed a new measure, cross-fuzzy entropy (X-FuzzyEn), to describe the synchronicity of patterns. The performances of three statistics were first quantitatively tested using five different coupled systems including both deterministic and stochastic models, i.e., coupled broadband noises, Lorenz–Lorenz, Rossler–Rossler, Rossler–Lorenz, and neural mass model. All the measures were compared with each other with respect to their ability to distinguish between different levels of coupling and their robustness against noise. The three measures were then applied to a real-life problem, pattern synchronization analysis of left and right hemisphere rat electroencephalographic (EEG) signals. Both simulated and real EEG data analysis results showed that the X-FuzzyEn provided an improved evaluation of bivariate series pattern synchronization and could be more conveniently and powerfully applied to different neural dynamical systems contaminated by noise.

[1]  Kenneth A. Loparo,et al.  An approach for characterizing coupling in dynamical systems , 2008 .

[2]  J. Richman,et al.  Physiological time-series analysis using approximate entropy and sample entropy. , 2000, American journal of physiology. Heart and circulatory physiology.

[3]  H. G. E. Hentschel,et al.  The infinite number of generalized dimensions of fractals and strange attractors , 1983 .

[4]  Karl J. Friston,et al.  A neural mass model for MEG/EEG: coupling and neuronal dynamics , 2003, NeuroImage.

[5]  Kantz.  Quantifying the closeness of fractal measures. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  N. Birbaumer,et al.  Spatiotemporal organization of brain dynamics and intelligence: an EEG study in adolescents. , 1999, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[7]  Steven M. Pincus.  Assessing Serial Irregularity and Its Implications for Health , 2001, Annals of the New York Academy of Sciences.

[8]  F. Mormann,et al.  Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients , 2000 .

[9]  P. Grassberger,et al.  Estimation of the Kolmogorov entropy from a chaotic signal , 1983 .

[10]  Milan Palus,et al.  Direction of coupling from phases of interacting oscillators: an information-theoretic approach. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  S M Pincus,et al.  Approximate entropy as a measure of system complexity. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[12]  W. Singer.  Consciousness and the Binding Problem , 2001, Annals of the New York Academy of Sciences.

[13]  Peter Grassberger,et al.  Generalizations of the Hausdorff dimension of fractal measures , 1985 .

[14]  Rodrigo Quian Quiroga,et al.  Nonlinear multivariate analysis of neurophysiological signals , 2005, Progress in Neurobiology.

[15]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[16]  M. Breakspear.  "Dynamic" connectivity in neural systems: theoretical and empirical considerations. , 2004, Neuroinformatics.

[17]  Chrysoula Kourtidou-Papadeli,et al.  Monitoring sleepiness with on-board electrophysiological recordings for preventing sleep-deprived traffic accidents , 2007, Clinical Neurophysiology.

[18]  C. Stam,et al.  Nonlinear dynamical analysis of EEG and MEG: Review of an emerging field , 2005, Clinical Neurophysiology.

[19]  Karl J. Friston,et al.  Evaluation of different measures of functional connectivity using a neural mass model , 2004, NeuroImage.

[20]  R. Andrzejak,et al.  Detection of weak directional coupling: phase-dynamics approach versus state-space approach. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Klaus Lehnertz,et al.  Measuring synchronization in coupled model systems: A comparison of different approaches , 2007 .

[22]  S. Aydın,et al.  Comparison of Power Spectrum Predictors in Computing Coherence Functions for Intracortical EEG Signals , 2008, Annals of Biomedical Engineering.

[23]  Honeycutt,et al.  Stochastic Runge-Kutta algorithms. I. White noise. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[24]  Wangxin Yu,et al.  Characterization of Surface EMG Signal Based on Fuzzy Entropy , 2007, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[25]  R. Quiroga,et al.  Learning driver-response relationships from synchronization patterns. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  R Quian Quiroga,et al.  Performance of different synchronization measures in real data: a case study on electroencephalographic signals. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  P. Grassberger.  Finite sample corrections to entropy and dimension estimates , 1988 .

[28]  Theiler,et al.  Spurious dimension from correlation algorithms applied to limited time-series data. , 1986, Physical review. A, General physics.

[29]  Cohen,et al.  Computing the Kolmogorov entropy from time signals of dissipative and conservative dynamical systems. , 1985, Physical review. A, General physics.

[30]  Hualou Liang,et al.  Causal influence: advances in neurosignal analysis. , 2005, Critical reviews in biomedical engineering.

[31]  Lotfi Senhadji,et al.  Quantitative evaluation of linear and nonlinear methods characterizing interdependencies between brain signals. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Zhenghui Hu,et al.  Interregional Functional Connectivity via Pattern Synchrony , 2006, 2006 9th International Conference on Control, Automation, Robotics and Vision.

[33]  Anthony G Hudetz,et al.  Effect of volatile anesthetics on interhemispheric EEG cross-approximate entropy in the rat , 2002, Brain Research.

[34]  E. Basar,et al.  Gamma, alpha, delta, and theta oscillations govern cognitive processes. , 2001, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[35]  M Palus,et al.  Synchronization as adjustment of information rates: detection from bivariate time series. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  C. Diks,et al.  Estimating invariants of noisy attractors. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[37]  Frank Schilder,et al.  Computing Arnol′d tongue scenarios , 2007, J. Comput. Phys..

[38]  H. Kantz,et al.  Nonlinear time series analysis , 1997 .

[39]  Anthony G Hudetz,et al.  Cholinergic Reversal of Isoflurane Anesthesia in Rats as Measured by Cross-approximate Entropy of the Electroencephalogram , 2003, Anesthesiology.

[40]  Tao Zhang,et al.  Cross‐sample entropy statistic as a measure of complexity and regularity of renal sympathetic nerve activity in the rat , 2007, Experimental physiology.

[41]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[42]  Steven M. Pincus.  Approximate entropy as a measure of irregularity for psychiatric serial metrics. , 2006, Bipolar disorders.