Untersuchung von Synchronisationsphänomenen in dynamischen Systemen mit Zellularen Neuronalen Netzen

Abstract

<strong>Estimating Synchronization in Dynamical Systems with Cellular Neuronal Networks</strong><br /> Over the past decade synchronization phenomena in dynamical systems have attracted much attention in various scientific fields ranging from physics to the neurosciences. Different frameworks for the mathematical description of synchronization have been developed which have led to the proposition of different concepts of synchronization. Among others, the classical concept of phase synchronization was extended from linear to nonlinear or even chaotic systems for cases where the definition of a phase variable is possi-ble for the analyzed systems. <br /> One of the most challenging dynamical systems in nature is the human brain. Constituted by a complex network of an indefinitely large number of neurons, which introduce nonlinearity to the system even on a cellular level, this system has long been a focus of (mostly univariate) linear and nonlinear time series analysis. A malfunction of the brain that is known to be par-ticularly associated with a pathological neuronal synchronization is the disease epilepsy along with its cardinal symptom, the epileptic seizure. Led by a growing interest in the possibility of seizure prediction, a number of analysis techniques - including CNN (Cellular Neuronal Networks) -based techniques have been proposed. It is only recently that bivariate analysis techniques were repeatedly shown to contribute significantly to this field. Following the approach of understanding phase synchronization in a statistical sense a straight-forward measure for phase synchronization employing the circular variance of a phase distribution has been developed. It was termed mean phase coherence R. In this approach, the phase variable is obtained from the Hilbert Transform of a signal. Recent studies show that a long-lasting (up to hours) pre-seizure state can be defined from the temporal evolution of R, which consists of a drop in synchroni-zation that deviates significantly from the values observed during the seizure-free interval. The sensitivity and specificity of this bivariate analysis techniques outperforms pre-viously used univariate analysis techniques and appears to be promising for prospective clini-cal studies. <br /> Despite its conceptual simplicity (estimation of R between two signals mainly requires a for-ward and an inverse Fast Fourier Transform), real-time applications are cur-rently limited by calculations for large number of combinations of sensors (typically up to 256 sensors in clinical or neuroscientific settings). In this thesis it is shown that CNN allow an accu-rate approximation of the degree of phase synchronization between two time series. This abil-ity along with the high computational power and the small energy and space requirements render CNN attractive for future VLSI implementations which may lead to the development of miniaturized analysis systems.