Nonlinear and neuronal dynamics under
epileptic conditions: a relational approach.
Dissertation zur Erlangung des Doktorgrades der
Naturwissenschaften an der
Naturwissenschaftlichen Fakultät der Universität Wien.
Juli 2001.

Abstract

This work examines the functional role of the hippocampus under epileptic conditions by consideration of different levels.
The purpose of the theoretical level, is to outline basic properties of the hippocampus and to insert the hypotheses onto which our experimental problem relies in a broader theoretical context. These hypotheses are the interaction between single cell and ensemble activity on a biological level, the functional role assigned to the hippocampus and the pathological implications of epilepsy on a physiological level, and the equations implemented in the dynamical description of the neuronal processes on a physical level.
O´ Keefe and Nadel, conceive the hippocampus as a cognitive map: the organ is understood as constructing and storing representations which capture the spatial elements of an experienced environment. The work of Cohen and Eichenbaum proposes the hippocampus to be involved in particular memory function called declarative memories. The perspective of Jacobs, investigates the relationship between the size and the structure of the hippocampus with sexual differences, spatial memory, and spatial navigation. Freeman understands the hippocampus as the organ regulating intentional processes.

The analytical level presents the problem at hand. The dynamics of intracellular recordings obtained from epileptic activity in organotipic cultures is studied by both linear and nonlinear methods of analysis. The dynamics of intracellular recordings are compared with the dynamics of ensemble recordings from data obtained in vivo. The predictability of the time series is tested by applying the Farmer-Sidorowich forecasting algorithm to the original data and its surrogates.

The simulational level depicts a model of single neuron epileptic activity obtained by modification of the Fitzhugh-Nagumo equations. It describes the dynamics of the two principal activity patterns of the cell, pre-seizure and seizure activity, and the transition from one to the other, by means of linear causal relationships. We extend the model to ensemble activity and compare its predictions with the experimental data.

In the conclusions, problems arisen from the relational comparison between the discussed theories and our experimental work are presented. Perspectives that the adopted approach might open are outlined.