Time dependencies in the occurrences of epileptic seizures

A new method of analysis, developed within the framework of nonlinear dynamics, is applied to patient recorded time series of the occurrence of epileptic seizures. These data exhibit broad band spectra and generally have no obvious structure. The goal is to detect hidden internal dependencies in the data without making any restrictive assumptions, such as linearity, about the structure of the underlying system. The basis of our approach is a conditional probabilistic analysis in a phase space reconstructed from the original data. The data, recorded from patients with intractable epilepsy over a period of 1-3 years, consist of the times of occurrences of hundreds of partial complex seizures. Although the epileptic events appear to occur independently, we show that the epileptic process is not consistent with the rules of a homogeneous Poisson process or generally with a random (IID) process. More specifically, our analysis reveals dependencies of the occurrence of seizures on the occurrence of preceding seizures. These dependencies can be detected in the interseizure interval data sets as well as in the rate of seizures per time period. We modeled patient's inaccuracy in recording seizure events by the addition of uniform white noise and found that the detected dependencies are persistent after addition of noise with standard deviation as great as 1/3 of the standard deviation of the original data set. A linear autoregressive analysis fails to capture these dependencies or produces spurious ones in most of the cases.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31879/1/0000830.pd

On the dynamics of the human brain in temporal lobe epilepsy.

Epileptic seizures reflect a pathological state of brain electrical activity, which may occur spontaneously as a result of functional neuronal disturbances in the cerebral cortex. Investigation of the epileptic human brain as a nonlinear system, that undergoes a phase transition (seizure), is the topic of this study. The existence of limit cycles during the ictal state (seizure), characteristic of nonlinear systems, was shown by modeling data recorded by subdural chronically implanted electrodes (ECoG). Theoretical measures of complexity ($\nu$) and chaoticity (L) of a steady state and their relation to the Shannon entropy rate were derived. Methods for the estimation of the aforementioned measures were developed and applied to simulation examples from the literature and experimental data from various seizures of epileptic patients. The required phase space of the system, for the estimation of $\nu$ and L, was reconstructed by the method of delays. The estimated values of the phase correlation dimension $\nu$ indicate that the epileptic brain possesses fewer degrees of freedom ictally (2 $\sim$ 3) than preictally or postictally (5 $\sim$ 10). This trend is in agreement with the fitting of the data with linear and nonlinear autoregressive models. The estimated mean values of the largest Lyapunov exponent L over time indicate a more chaotic state postictally than ictally or preictally. The start of a seizure corresponds to a simultaneous drop in the values of L at the focal electrode sites. The slow cyclic variations, that are observed in the temporal Lyapunov profiles, imply attempts of the system to undergo a phase transition minutes before the seizure's onset. The analysis of the rate of entropy production over space revealed, preictally, an initial phase difference of minutes for the sites overlying the seizure focus, which progressed to phase locking, with a slow entrainment of the rest of the cortical sites shortly before the onset of the seizure. The above results suggest that localization and prediction of an impending seizure may be possible up to 10 minutes before the actual event. Also, this study suggests a model for the generation of a focal epileptic seizure.Ph.D.Applied SciencesBiological SciencesBiomedical engineeringNeurosciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/128688/2/9124026.pd

Interactive rehabilitation and dynamical analysis of scalp EEG

Electroencephalography (EEG) has been used for decades to measure the brain\u27s electrical activity. Planning and performing a complex movement (e.g., reaching and grasping) requires the coordination of muscles by electrical activity that can be recorded with scalp EEG from relevant regions of the cortex. Prior studies, utilizing motion capture and kinematic measures, have shown that an augmented reality feedback system for rehabilitation of stroke patients can help patients develop new motor plans and perform reaching tasks more accurately. Historically, traditional signal analysis techniques have been utilized to quantify changes in EEG when subjects perform common, simple movements. These techniques have included measures of event-related potentials in the time and frequency domains (e.g., energy and coherence measures). In this study, a more advanced, nonlinear, analysis technique, mutual information (MI), is applied to the EEG to capture the dynamics of functional connections between brain sites. In particular, the cortical activity that results from the planning and execution of novel reach trajectories by normal subjects in an augmented reality system was quantified by using statistically significant MI interactions between brain sites over time. The results show that, during the preparation for as well as the execution of a reach, the functional connectivity of the brain changes in a consistent manner over time, in terms of both the number and strength of cortical connections. A similar analysis of EEG from stroke patients may provide new insights into the functional deficiencies developed in the brain after stroke, and contribute to evaluation, and possibly the design, of novel therapeutic schemes within the framework of rehabilitation and BMI (brain machine interface)

Phase Space Topography and the Lyapunov Exponent of Electrocorticograms in Partial Seizures

over a period of time (10 minutes before to 10 minutes after the seizure outburst) revealed a remarkable coherence of theabrupt transient drops of L* for the electrodes that showed the initial ictal onset. The L* values for the electrodes away from the focus exhibited less abrupt transient drops. These results indicate that the largest average Lyapunov exponent L can be useful in seizure detection as well as a discriminatory factor for focus localization in multielectrocle analysis. Key words: phase space; chaos; Lyapunov exponents; ECoG; partial epileptic seizures; epileptogenic focus localization. Introduction Long-term recordings of brain electrical activity recorded from scalp and sphenoidal electrodes, depth electrodes or subdural electrodes are employed in our clinical laboratories to localize the origin of seizure discharges in patients with partial (focal) seizures who are candidates for surgical removal of the seizure focus. Currently, in clinical practice, t

Modelling of ECoG in Temporal Lobe Epilepsy

Subdural recordings of the electrical activity of the human brain give electrocorticograms (ECoG) almost free of artifacts and distortions by the skull and other intervening material. This paper discusses the modelling of the ECoG during the pre-ictal, ictal and post-ictal phases of an epileptic seizure. Optimum order linear autoregressive (AR) models are formed and the movement of the poles of the models are traced with time. Nonlinear extension to the AR models (NAR) is formulated based on the assumption of existenceof nonlinear oscillations in the data. The optimum order of this model is determined and its performance is compared with that of the linear AR models. The analysis of the data with NAR resulted in the satisfaction of sufficient conditions for limit cycles in the ictal phase. KEY WORDS: Electrocorticography; focal epilepsy; nonlinear modelling; limit cycles. I. INTRODUCTION In this paper we are concerned with the building of models for discrete time domain ECoG data. Ou..