Electrocorticograms (ECoG's) from 16 of 68 chronically implanted subdural electrodes, placed over the right temporal cortex in a patient with a right medial temporal focus, were analyzed using methods from nonlinear dynamics. A time series provides information about a large number of pertinent variables, which may be used to explore and characterize the system's dynamics. These variables and their evolution in time produce the phase portrait of the system. The phase spaces for each of 16 electrodes were constructed and from these the largest average Lyapunov exponents (L's), measures of chaoticity of the system (the larger the L, the more chaotic the system is), were estimated over time for every electrode before, in and after the epileptic seizure for three seizures of the same patient. The start of the seizure corresponds to a simultaneous drop in L values obtained at the electrodes nearest the focus. L values for the rest of the electrodes follow. The mean values of L for all electrodes in the postictal state are larger than the ones in the preictal state, denoting a more chaotic state postictally. The lowest values of L occur during the seizure but they are still positive denoting the presence of a chaotic attractor. Based on the procedure for the estimation of L we were able to develop a methodology for detecting prominent spikes in the ECoG. These measures (L*) calculated over a period of time (10 minutes before to 10 minutes after the seizure outburst) revealed a remarkable coherence of the abrupt 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 multielectrode analysis.

Epileptic seizures are manifestations of epilepsy, a serious brain dynamical disorder second only to strokes. Of the world's approximately 50 million people with epilepsy, fully 1/3 have seizures that are not controlled by anti-convulsant medication. The field of seizure prediction, in which engineering technologies are used to decode brain signals and search for precursors of impending epileptic seizures, holds great promise to elucidate the dynamical mechanisms underlying the disorder, as well as to enable implantable devices to intervene in time to treat epilepsy. There is currently an explosion of interest in this field in academic centers and medical industry with clinical trials underway to test potential prediction and intervention methodology and devices for Food and Drug Administration (FDA) approval. This invited paper presents an overview of the application of signal processing methodologies based upon the theory of nonlinear dynamics to the problem of seizure prediction. Broader application of these developments to a variety of systems requiring monitoring, forecasting and control is a natural outgrowth of this field.

Current epileptic seizure "prediction" algorithms are generally based on the knowledge of seizure occurring time and analyze the electroencephalogram (EEG) recordings retrospectively. It is then obvious that, although these analyses provide evidence of brain activity changes prior to epileptic seizures, they cannot be applied to develop implantable devices for diagnostic and therapeutic purposes. In this paper, we describe an adaptive procedure to prospectively analyze continuous, long-term EEG recordings when only the occurring time of the first seizure is known. The algorithm is based on the convergence and divergence of short-term maximum Lyapunov exponents (STLmax) among critical electrode sites selected adaptively. A warning of an impending seizure is then issued. Global optimization techniques are applied for selecting the critical groups of electrode sites. The adaptive seizure prediction algorithm (ASPA) was tested in continuous 0.76 to 5.84 days intracranial EEG recordings from a group of five patients with refractory temporal lobe epilepsy. A fixed parameter setting applied to all cases predicted 82% of seizures with a false prediction rate of 0.16/h. Seizure warnings occurred an average of 71.7 min before ictal onset. Similar results were produced by dividing the available EEG recordings into half training and testing portions. Optimizing the parameters for individual patients improved sensitivity (84% overall) and reduced false prediction rate (0.12/h overall). These results indicate that ASPA can be applied to implantable devices for diagnostic and therapeutic purposes.

Recently, interest has turned to the mathematical concept of chaos as an explanation for a variety of complex processes in nature. Chaotic systems, among other characteristics, can produce what appears to be random output. Another property of chaotic systems is that they may exhibit abrupt intermittent transitions between highly ordered and disordered states. Because of this property, it is hypothesized that epilepsy may be an example of chaos. In this review, some of the basic concepts of nonlinear dynamics and chaos are illustrated. Mathematical techniques developed to study the properties of nonlinear dynamical systems are outlined. Finally, the results of applying these techniques to the study of human epilepsy are discussed. The application of these powerful and novel mathematical techniques to analysis of the electroencephalogram has provided new insights into the epileptogenic process and may have considerable utility in the diagnosis and treatment of epilepsy. The Neuroscientist 2:118-126, 1996

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We have designed and implemented an automated, just-in-time stimulation, seizure control method using a seizure prediction method from nonlinear dynamics coupled with deep brain stimulation in the centromedial thalamic nuclei in epileptic rats. A comparison to periodic stimulation, with identical stimulation parameters, was also performed. The two schemes were compared in terms of their efficacy in control of seizures, as well as their effect on synchronization of brain dynamics. The automated just-in-time (JIT) stimulation showed reduction of seizure frequency and duration in 5 of the 6 rats, with significant reduction of seizure frequency (>50%) in 33% of the rats. This constituted a significant improvement over the efficacy of the periodic control scheme in the same animals. Actually, periodic stimulation showed an increase of seizure frequency in 50% of the rats, reduction of seizure frequency in 3 rats and significant reduction in 1 rat. Importantly, successful seizure control was highly correlated with desynchronization of brain dynamics. This study provides initial evidence for the use of closedloop feedback control systems in epileptic seizures combining methods from seizure prediction and deep brain stimulation.

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A parametric signal processing approach for DNA sequence analysis based on autoregressive (AR) modeling is presented. AR model residual errors and AR model parameters are used as features. The AR residual error analysis indicate a high specificity of coding DNA sequences, while AR feature-based analysis helps distinguish between coding and noncoding DNA sequences. An AR model-based string searching algorithm is also proposed. The effect of several types of numerical mapping rules in th proposed method is demonstrated.