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The framework of the theory of nonlinear dynamics provides powerful concepts and algorithms to study complicated dynamics such as brain electrical activity (electroencephalogram, EEG). Although different influencing factors render the use of nonlinear measures in a strict sense problematic, converging evidence from various investigations now indicates that nonlinear EEG analysis provides a means to reliably characterize different states of physiological and pathophysiological brain function. We here focus on applications of nonlinear EEG analysis in epileptology. Epilepsy affects more than 50 million individuals worldwide – approximately 1% of the world's population. The disease is characterized by a recurrent and sudden malfunction of the brain that is termed seizure. Nonlinear EEG analysis techniques allow to reliably identify the seizure generating structure (epileptic focus) in different areas of the brain even during seizure-free intervals, to disentangle complex spatio-temporal interactions between the epileptic focus and other areas of the brain, and to define a specific state predictive of an impending seizure. Nonlinear EEG analysis provides supplementary information about the epileptogenic process in humans, contributes to an improvement of the presurgical evaluation of epilepsy patients, and offers a basis for the development of new therapy concepts for seizure prevention. [ABSTRACT FROM AUTHOR]

We examine a possible utilization of the recently proposed method of signal-induced excitation waves in nonlinear excitable media as a means for the noise-tolerant detection of zero-lag phase synchronization in very noisy time series. We show that in cases, where a relatively strong noise contamination aggravates the direct application of phase-based measures of synchronization, it is nevertheless possible to detect synchronization phenomena. [ABSTRACT FROM AUTHOR]

We investigate the applicability of the permutation entropy H and a synchronization index γ that is based on the changing tendency of temporal permutation entropies to analyze noisy time series from nonstationary dynamical systems with poorly understood properties. Using model systems, we first study the interdependencies of parameters involved in the calculation of both measures. Having identified appropriate parameter settings we then analyze long-lasting EEG time series recorded from an epilepsy patient. Our findings indicate that γ could be of interest for studies on the predictability of epileptic seizures. [ABSTRACT FROM AUTHOR]

We investigate the relative merit of different linear and nonlinear synchronization measures for a characterization of the spatio-temporal dynamics of the epileptic process. Analyzing long-lasting multichannel electroencephalographic recordings from more than 20 epilepsy patients we show that all measures are able to identify brain regions of pathological synchronization associated with epilepsy, even during the seizure-free interval, and are able to detect a long-lasting transitional preseizure state. These findings render synchronization measures attractive for future prospective studies on seizure prediction. [ABSTRACT FROM AUTHOR]