In this study, the entrainment of brain dynamics in epilepsy was investigated in a thorough, systematic way. In the first part of the study, diagnosis of epilepsy, elements from the theory of chaos were used to measure the brain dynamics over time from EEGs (electroencephalograms) recorded in humans with either epileptic or non-epileptic seizures. In the second part of the study, treatment of epilepsy, data from rats undergoing VNS (vagus nerve stimulation) treatment were analyzed in the same way. The results suggest that a) the differential diagnosis in humans with epileptic and non-epileptic seizures can be significantly improved by analysis of brain dynamics, and b) the Vagus Nerve Stimulation may be working by controlling the entrainment level of brain dynamics.

Development of post-traumatic epilepsy (PTE) after traumatic brain injury (TBI) is a major health concern (5% - 50% of TBI cases). A significant problem in TBI management is the inability to predict which patients will develop PTE. Such prediction, followed by timely treatment, could be highly beneficial to TBI patients. Six male Sprague-Dawley rats were subjected to a controlled cortical impact (CCI). A 6mm piston was pneumatically driven 3mm into the right parietal cortex with velocity of 5.5m/s. The rats were subsequently implanted with 6 intracranial electroencephalographic (EEG) electrodes. Long-term (14-week) continuous EEG recordings were conducted. Using linear (coherence) and non-linear (Lyapunov exponents) measures of EEG dynamics in conjunction with measures of network connectivity, we studied the evolution over time of the functional connectivity between brain sites in order to identify early precursors of development of epilepsy. Four of the six TBI rats developed PTE 6 to 10 weeks after the initial insult to the brain. Analysis of the continuous EEG from these rats showed a gradual increase of the connectivity between critical brain sites in terms of their EEG dynamics, starting at least 2 weeks prior to their first spontaneous seizure. In contrast, for the rats that did not develop epilepsy, connectivity levels did not change, or decreased during the whole course of the experiment across pairs of brain sites. Consistent behavior of functional connectivity changes between brain sites and the "focus" (site of impact) over time was demonstrated for coherence in three out of the four epileptic and in both non-epileptic rats, while for STLmax in all four epileptic and in both non-epileptic rats. This study provided us with the opportunity to quantitatively investigate several aspects of epileptogenesis following traumatic brain injury. Our results strongly support a network pathology that worsens with time. It is conceivable that the observed changes in spatiotemporal dynamics after an initial brain insult, and long before the development of epilepsy, could constitute a basis for predictors of epileptogenesis in TBI patients.

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.

Virtual environments are used for many physical rehabilitation and therapy purposes with varying degrees of success. An important feature for a therapy environment is the real-time monitoring of a participants' movement performance. Such monitoring can be used to evaluate the environment in addition to the participant's learning. Methods for monitoring and evaluation include tracking kinematic performance as well as monitoring muscle and brain activities through EMG and EEG technology. This study aims to observe trends in individual participants' motor learning based on changes in kinematic parameters and use those parameters to characterize different types of learners. This information can then guide EEG/EMG data analysis in the future. The evaluation of motor learning using kinematic parameters of performance typically compares averages of pre- and post-data to identify patterns of changes of various parameters. A key issue with using pre- and post-data is that individual participants perform differently and have different time-courses of learning. Furthermore, different parameters can evolve at independent rates. Finally, there is great variability in the movements at early stages of learning a task. To address these issues, a combined approach is proposed using robust regression, piece-wise regression and correlation to categorize different participant's motor learning. Using the mixed reality rehabilitation system developed at Arizona State University, it was possible to engage participants in motor learning, as revealed by improvements in kinematic parameters. A combination of robust regression, piecewise regression and correlation were used to reveal trends and characterize participants based on motor learning of three kinematic parameters: trajectory error, supination error and the number of phases in the velocity profile.