abstract: Interictal spikes, together with seizures, have been recognized as the two hallmarks of epilepsy, a brain disorder that 1% of the world's population suffers from. Even though the presence of spikes in brain's electromagnetic activity has diagnostic value, their dynamics are still elusive. It was an objective of this dissertation to formulate a mathematical framework within which the dynamics of interictal spikes could be thoroughly investigated. A new epileptic spike detection algorithm was developed by employing data adaptive morphological filters. The performance of the spike detection algorithm was favorably compared with others in the literature. A novel spike spatial synchronization measure was developed and tested on coupled spiking neuron models. Application of this measure to individual epileptic spikes in EEG from patients with temporal lobe epilepsy revealed long-term trends of increase in synchronization between pairs of brain sites before seizures and desynchronization after seizures, in the same patient as well as across patients, thus supporting the hypothesis that seizures may occur to break (reset) the abnormal spike synchronization in the brain network. Furthermore, based on these results, a separate spatial analysis of spike rates was conducted that shed light onto conflicting results in the literature about variability of spike rate before and after seizure. The ability to automatically classify seizures into clinical and subclinical was a result of the above findings. A novel method for epileptogenic focus localization from interictal periods based on spike occurrences was also devised, combining concepts from graph theory, like eigenvector centrality, and the developed spike synchronization measure, and tested very favorably against the utilized gold rule in clinical practice for focus localization from seizures onset. Finally, in another application of resetting of brain dynamics at seizures, it was shown that it is possible to differentiate with a high accuracy between patients with epileptic seizures (ES) and patients with psychogenic nonepileptic seizures (PNES). The above studies of spike dynamics have elucidated many unknown aspects of ictogenesis and it is expected to significantly contribute to further understanding of the basic mechanisms that lead to seizures, the diagnosis and treatment of epilepsy. / Dissertation/Thesis / Ph.D. Electrical Engineering 2012