Performance of a seizure warning algorithm based on the dynamics of intracranial EEG.

During the past decade, several studies have demonstrated experimental evidence that temporal lobe seizures are preceded by changes in dynamical properties (both spatial and temporal) of electroencephalograph (EEG) signals. In this study, we evaluate a method, based on chaos theory and global optimization techniques, for detecting pre-seizure states by monitoring the spatio-temporal changes in the dynamics of the EEG signal. The method employs the estimation of the short-term maximum Lyapunov exponent (STL(max)), a measure of the order (chaoticity) of a dynamical system, to quantify the EEG dynamics per electrode site. A global optimization technique is also employed to identify critical electrode sites that are involved in the seizure development. An important practical result of this study was the development of an automated seizure warning system (ASWS). The algorithm was tested in continuous, long-term EEG recordings, 3-14 days in duration, obtained from 10 patients with refractory temporal lobe epilepsy. In this analysis, for each patient, the EEG recordings were divided into training and testing datasets. We used the first portion of the data that contained half of the seizures to train the algorithm, where the algorithm achieved a sensitivity of 76.12% with an overall false prediction rate of 0.17h(-1). With the optimal parameter setting obtained from the training phase, the prediction performance of the algorithm during the testing phase achieved a sensitivity of 68.75% with an overall false prediction rate of 0.15h(-1). The results of this study confirm our previous observations from a smaller number of patients: the development of automated seizure warning devices for diagnostic and therapeutic purposes is feasible and practically useful.

Long-term prospective on-line real-time seizure prediction.

OBJECTIVE: Epilepsy, one of the most common neurological disorders, constitutes a unique opportunity to study the dynamics of spatiotemporal state transitions in real, complex, nonlinear dynamical systems. In this study, we evaluate the performance of a prospective on-line real-time seizure prediction algorithm in two patients from a common database. METHODS: We previously demonstrated that measures of chaos and angular frequency, estimated from electroencephalographic (EEG) signals recorded at critical sites in the cerebral cortex, progressively converge (i.e. become dynamically entrained) as the epileptic brain transits from the asymptomatic interictal state to the ictal state (seizure) (Iasemidis et al., 2001, 2002a, 2003a). This observation suggested the possibility of developing algorithms to predict seizures well ahead of their occurrences. One of the central points in those investigations was the application of optimization theory, specifically quadratic zero-one programming, for the selection of the critical cortical sites. This current study combines that observation with a dynamical entrainment detection method to prospectively predict epileptic seizures. The algorithm was tested in two patients with long-term (107.54h) and multi-seizure EEG data B and C (Lehnertz and Litt, 2004). RESULTS: Analysis from the 2 test patients resulted in the prediction of up to 91.3% of the impending 23 seizures, about 89+/-15min prior to seizure onset, with an average false warning rate of one every 8.27h and an allowable prediction horizon of 3h. CONCLUSIONS: The algorithm provides warning of impending seizures prospectively and in real time, that is, it constitutes an on-line and real-time seizure prediction scheme. SIGNIFICANCE: These results suggest that the proposed seizure prediction algorithm could be used in novel diagnostic and therapeutic applications in epileptic patients.

Brain dynamical disentrainment by anti-epileptic drugs in rat and human status epilepticus.

In this paper, we utilize a measure of brain dynamics, namely the short-term largest Lyapunov exponent (STLmax) to evaluate the efficacy of treatment in epileptic animals and humans with known antiepileptic drugs (AED) like diazepam and phenobarbital during status epilepticus (SE). This measure is estimated from analysis of electroencephalographic (EEG) recordings at multiple brain locations in both an SE patient and a cobalt/homocysteine thiolactone SE-induced animal. Techniques from optimization theory and statistics are applied to select optimal sets of brain sites, whose dynamics are then measured over time to study their entrainment/disentrainment. Results from such analysis indicate that the observed abnormal spatio-temporal dynamical entrainment in SE is reversed by AED administration (resetting of brain dynamics). These results may provide a potential use of nonlinear dynamical measures in the evaluation of the efficacy of AEDs and the development of new treatment strategies in epilepsy.

Measuring information flow in nonlinear systems--a modeling approach in the state space.

Directional information flow between coupled nonlinear systems is of practical interest in many areas like bioengineering, chemistry, physics and electrical engineering. Due to the high complexity and nonlinearity of the coupled chaotic systems, linear modeling approaches may fail to capture the proper dynamics and thus the proper directional information flow. This necessitates novel approaches to analyze signals derived from such systems. This paper proposes a novel approach for detecting such directional information flows between the subsystems involved. The dependability of the method is illustrated using coupled chaotic oscillators in various coupling configurations.

A new approach towards predictability of epileptic seizures: KLT dimension.

This paper proposes a measure of complexity of the epileptic electroencephalogram (EEG) based on the dimensionality of the Karhunen-Loeve Transform (KLT) in the time domain. We estimate the KLT dimensionality by assuming the same observation noise level in the EEG during the interictal period (between the seizures) as the one during an epileptic seizure (ictal period). Utilizing an optimality criterion based on the T-index [1] and the predictability time, derived from the created KLT dimensionality profiles, we show that 10 out of 15 seizures in one patient with temporal lobe epilepsy were predictable with an average predictability time of about 36 minutes.

Predictability of epileptic seizures: a comparative study using Lyapunov exponent and entropy based measures.

In this paper, a comparative study involving measures from the theory of chaos, namely the short-term largest Lyapunov exponent, Shannon and Kullback-Leibler entropies from information theory, has been carried out in terms of their predictability of temporal lobe epileptic seizures. These three measures are estimated from electroencephalographic (EEG) recordings with sub-dural and in-depth electrodes from various brain locations in patients with temporal lobe epilepsy. Techniques from optimization theory are applied to select optimal sets of electrodes whose dynamics is then followed over time. Results from analysis of multiple seizures in two epileptic patients with these measures are presented and compared in terms of their ability to identify pre-ictal dynamical entrainment well ahead of seizure onset time.

Non-linearity in invasive EEG recordings from patients with temporal lobe epilepsy.

Electrographic recordings from depth and subdural electrodes, performed in two patients with seizures of mesial temporal origin, were analyzed for the presence of non-linearities in the signal. The correlation integral, a measure sensitive to a wide variety of non-linearities, was used for detection. Statistical significance was determined by comparison of the original signal to surrogate datasets. Statistically significant non-linearities were present in signals generated by the epileptogenic hippocampus and interictal spike foci in the temporal neocortex. Less prominent non-linearities were found in EEG signals generated by more normal areas of the brain. These results indicate that techniques developed for the study of non-linear systems can be used to characterize the epileptogenic regions of the brain during the interictal period and can elucidate the dynamical mechanisms of the epileptic transition.

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.

Time-frequency representation of electrocorticograms in temporal lobe epilepsy.

Three time-frequency distributions are evaluated in terms of their efficacy in representing nonstationary electrocorticograms (ECoG's) in human temporal lobe epilepsy. The results of a new method, the exponential distribution, are compared with those of the spectrogram and the Wigner distribution. It is shown that the exponential distribution represents a considerable improvement over the spectrogram in terms of resolution and markedly reduces cross-terms present in the Wigner distribution. Exponential distribution representations of ECoG's from different stages of an epileptic record are developed as contour maps. These high-resolution representations offer a lucid display of temporal-spectral features of the rapidly varying signals that constitute ECoG's recorded in temporal lobe epilepsy.

Phase space topography and the Lyapunov exponent of electrocorticograms in partial seizures.

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.