NIC-Serie Band 4:   Nichtlineare Analyse raum-zeitlicher Aspekte der hirnelektrischen Aktivität von Epilepsiepatienten Jochen Arnhold   ISBN 3-00-006221-1 September 2000, 120 Seiten   PDF

During the last years methods from nonlinear time series analysis have been successfully applied in many sciences, including physics, astrophysics, chemistry, and even economy. But probably the most important and interesting applications are in biology and medical sciences. The analysis of similarities and interdependences between dynamical systems has received increasing attention to describe and to understand different kinds of synchronization phenomena. In the present study cross correlation sums and derived measures were used to analyze similarities between different time sequences of modell and field data. Although these measures allow to characterize the dynamics of simple modell systems they failed to provide new information about the underlying spatio-temporal dynamics when being applied to more complex time sequences from recordings of brain electrical activity of epilepsy patients. However, in order to understand more precisely the complex mechanisms of neuronal activity underlying the epileptogenic process during physiological and pathological states a thorough analysis of spatio-temporal synchronization effects is necessary.

Therefore a new measure is presented that characterizes statistical relationships between two time sequences. In contrast to common measures like coherence and mutual information, the proposed measure is asymmetric and provides information about the direction of interdependence. It is closely related to other recently developed measures to detect generalized synchronization but without making any assumption about a strict functional relationship between the time sequences. Before this interdependence measure was applied to intracranially recorded electroencephalograms (EEGs) of epilepsy patients it was verified by means of the analysis of common modell data. The analysis of brain electrical activity of epilepsy patients demonstrated that the new interdependence measure contributes to an improvement of the clinical evaluation of these patients. Furthermore it might have impact on epileptological and neurobiological basic research.