Measuring the Directionality of Coupling: Phase versus State Space Dynamics and Application to EEG Time Series

Measuring the directionality of coupling between dynamical systems is one of the challenging problems in nonlinear time series analysis. We investigate the relative merit of two approaches to assess directionality, one based on phase dynamics modeling and one based on state space topography. We analyze unidirectionally coupled model systems to investigate the ability of the two approaches to detect driver-responder relationships and discuss certain problems and pitfalls. In addition we apply both approaches to the intracranial electroencephalogram (EEG) recorded from one epilepsy patient during the seizure-free interval to demonstrate the general suitability of directionality measures to reflect the pathological interaction of the epileptic focus with other brain areas.

[1]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[2]  J. Martinerie,et al.  Preictal state identification by synchronization changes in long-term intracranial EEG recordings , 2005, Clinical Neurophysiology.

[3]  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.

[4]  Boualem Boashash,et al.  Time-Frequency Signal Analysis: Methods and Applications. , 1993 .

[5]  M. Rosenblum,et al.  Detecting direction of coupling in interacting oscillators. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[8]  Piotr J. Franaszczuk,et al.  Application of the Directed Transfer Function Method to Mesial and Lateral Onset Temporal Lobe Seizures , 2004, Brain Topography.

[9]  A. Kraskov,et al.  On the predictability of epileptic seizures , 2005, Clinical Neurophysiology.

[10]  R. Burke,et al.  Detecting dynamical interdependence and generalized synchrony through mutual prediction in a neural ensemble. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  P. Grassberger,et al.  A robust method for detecting interdependences: application to intracranially recorded EEG , 1999, chao-dyn/9907013.

[12]  Klaus Lehnertz,et al.  Automated detection of a preseizure state based on a decrease in synchronization in intracranial electroencephalogram recordings from epilepsy patients. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Jürgen Kurths,et al.  Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography , 1998 .

[14]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[15]  Matthäus Staniek,et al.  Measuring Synchronization in the Epileptic Brain: a Comparison of Different Approaches , 2007, Int. J. Bifurc. Chaos.

[16]  J. Bellanger,et al.  Interpretation of interdependencies in epileptic signals using a macroscopic physiological model of the EEG , 2001, Clinical Neurophysiology.

[17]  B P Bezruchko,et al.  Estimation of coupling between oscillators from short time series via phase dynamics modeling: limitations and application to EEG data. , 2005, Chaos.

[18]  M. Rosenblum,et al.  Identification of coupling direction: application to cardiorespiratory interaction. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  E. M. Hickin Modulation, Noise and Spectral Analysis , 1966 .

[20]  M. Rabinovich,et al.  Stochastic synchronization of oscillation in dissipative systems , 1986 .

[21]  D. Smirnov,et al.  Estimation of interaction strength and direction from short and noisy time series. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  J. Bellanger,et al.  Neural networks involving the medial temporal structures in temporal lobe epilepsy , 2001, Clinical Neurophysiology.

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

[24]  Dennis Gabor,et al.  Theory of communication , 1946 .

[25]  O. Rössler An equation for continuous chaos , 1976 .

[26]  P. F. Panter Modulation, noise, and spectral analysis , 1965 .

[27]  Fernando H. Lopes da Silva,et al.  Propagation of Electrical Activity: Nonlinear Associations and Time Delays between EEG Signals , 1993 .