Abstract
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.
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References
Anokhin AP, Lutzenberger W, Birbaumer N (1999) Spatiotemporal organization of brain dynamics and intelligence: an EEG study in adolescents. Int J Psychophysiol 33: 259–273
Ansari-Asl K, Senhadji L, Bellanger J, Wendling F (2006) Quantitative evaluation of linear and nonlinear methods characterizing interdependencies between brain signals. Phys Rev E 74: 031916
Aydin S (2008) Comparison of power spectrum predictors in computing coherence functions for intracortical EEG signals. Ann Biomed Eng 37: 192–200
Basar E, Basar-Eroglu C, Karakas S, Schurmann M (2001) Gamma, alpha, delta, and theta oscillations govern cognitive processes. Int J Psychophysiol 39: 241–248
Breakspear M (2004) Dynamic connectivity in neural systems: theoretical and empirical considerations. Neuroinformatics 2: 205–226
Chen WT, Wang ZZ, Xie HB, Yu WX (2007) Characterization of surface EMG signal based on fuzzy entropy. IEEE Trans Neural Syst Rehabil Eng 15: 266–272
Cohen A, Procaccia I (1985) Computing the Kolmogorov entropy from time signals of dissipative and conservative dynamical systems. Phys Rev A 31: 1872–1882
David O, Friston KJ (2003) A neural mass model for MEG/EEG: coupling and neuronal dynamics. NeuroImage 20: 1743–1755
David O, Cosmelli D, Friston KJ (2004) Evaluation of different measures of functional connectivity using a neural mass model. NeuroImage 21: 659–673
Diks C (1996) Estimating invariants of noisy attractors. Phys Rev E 53(5): R4263–R4266
Eckmann JP, Ruelle D (1985) Ergodic theory of chaos and strange attractors. Rev Mod Phys 57: 617–656
Grassberger P (1985) Generalizations of the Hausdorff dimension of fractal measures. Phys Lett A 107: 101–105
Grassberger P (1988) Finite sample corrections to entropy and dimension estimates. Phys Lett A 128: 369–373
Grassberger P, Procaccia I (1983) Estimation of the Kolmogorov entropy froma chaotic signal. Phys Rev A 28: 2591–2593
Hentschel HGE, Procaccia I (1983) The infinite number of generalized dimensions of fractals and strange attractors. Physica D 8: 435–444
Honeycutt RL (1992) Stochastic Runge-Kutta algorithms I. White noise. Phys Rev A 45: 600–603
Hu ZH, Shi PC (2006) Interregional functional connectivity via pattern synchrony. In: 9th international conference on control, automation, robotics and vision, pp 1–6
Hudetz AG (2002) Effect of volatile anesthetics on interhemispheric EEG cross-approximate entropy in the rat. Brain Res 954: 123–131
Hudetz AG, Wood JD, Kampine JP (2003) Cholinergic reversal of isoflurane anesthesia in rats as measured by cross-approximate entropy of the electroencephalogram. Anesthesiology 99: 1125–1131
Janjarasjitt S, Loparo KA (2008) An approach for characterizing coupling in dynamical systems. Physica D 237: 2482–2486
Kaminski M, Liang H (2005) Causal influence: advances in neurosignal analysis. Crit Rev Biomed Eng 33(4): 347–430
Kantz H (1994) Quantifying the closeness of fractal measures. Phys Rev E 49(6): 5091–5097
Kantz H, Schreiber T (2004) Nonlinear time series analysis, 2nd edn. Cambridge University Press, Cambridge
Kolmogorov AN (1958) A new invariant of transitive dynamical systems. Dolk Akad Nauk SSSR 119: 861–864
Kreuz T, Mormann F, Andrzejak RG, Kraskov A, Lehnertz K, Grassberger P (2007) Measuring synchronization in coupled model systems: a comparison of different approaches. Physica D 225: 29–42
Mormann F, Lehnertz K, David P, Elger CE (2000) Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients. Physica D 144: 358–369
Palus M, Komarek V, Hrncir Z, Sterbova K (2001) Synchronization as adjustment of information rates: detection from bivariate time series. Phys Rev E 63: 046211
Palus M, Stefanovska A (2003) Direction of coupling from phases of interacting oscillators: an information-theoretic approach. Phys Rev E 67: 055201
Papadelis C, Chen Z, Kourtidou-Papadeli C, Bamidis PD, Chouvarda I, Bekiaris E, Maglaveras N (2007) Monitoring sleepiness with on-board electrophysiological recordings for preventing sleep-deprived traffic accidents. Clin Neurophysiol 118: 1906–1922
Pereda E, Quiroga RQ, Bhattacharya J (2005) Nonlinear multivariate analysis of neurophsyiological signals. Prog Neurobiol 77: 1–37
Pincus SM (1991) Approximate entropy as a measure of system complexity. Proc Natl Acad Sci 88: 2297–2301
Pincus SM (2001) Assessing serial irregularity and its implications for health. Ann NY Acad Sci 954: 245–267
Pincus SM (2006) Approximate entropy as a measure of irregularity for psychiatric serial metrics. Bipolar Disord 8: 430–440
Quiroga RQ, Arnhold J, Grassberger P (2000) Learning driver-response relationships from synchronization patterns. Phys Rev E 61: 5142–5148
Quiroga RQ, Kraskov A, Kreuz T, Grassberger P (2002) Performance of different synchronization in real data: a case study on electroencephalographyic signals. Phys Rev E 65: 041903
Richman JS, Moorman JR (2000) Physiological time-series analysis using approximate entropy and sample entropy. Am J Physiol Heart Circ Physiol 278: H2039–H2049
Schilder F, Peckham BB (2006) Computing Arnol’d tongue scenarios. J Comput Phys 220(2): 932–951
Sinai AG (1959) On the concept of entropy of a dynamical system. Dolk Akad Nauk SSSR 124: 768–771
Singer W (2001) Consciousness and the binding problem. Ann NY Acad Sci 929: 123–146
Smirnov DA, Andrzejak RG (2005) Detection of weak directional coupling: phase-dynamics approach versus state-space approach. Phys Rev E 71: 036207
Stam CJ (2005) Nonlinear dynamical analysis of EEG and MEG: review of an emerging field. Clin Neurophysiol 116: 2266–2301
Takens F (1981) Detecting strange attractors in turbulence. Lect Notes Math 898: 366–381
Takens F (1983) Invariants related to dimension and entropy. In: Atas do 13. Col. brasiliero de Matematicas, Rio de Janerio, Brasil
Theiler J (1986) Spurious dimension from correlation algorithm applied to limited time-series data. Phys Rev A 34: 2427–2432
Zhang T, Yang Z, Coote JH (2007) Cross-sample entropy statistic as a measure of complexity and regularity of renal sympathetic nerve activity in the rat. Exp Physiol 92: 659–669
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Xie, HB., Guo, JY. & Zheng, YP. A comparative study of pattern synchronization detection between neural signals using different cross-entropy measures. Biol Cybern 102, 123–135 (2010). https://doi.org/10.1007/s00422-009-0354-1
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DOI: https://doi.org/10.1007/s00422-009-0354-1