Leonidas D. Iasemidis

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

SummaryElectrocorticograms (ECoGs) 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 systems 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 (Ls), 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 inital 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.

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.

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.

■ REVIEW : Chaos Theory and Epilepsy:

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

Dynamical resetting of the human brain at epileptic seizures: application of nonlinear dynamics and global optimization techniques

Epileptic seizures occur intermittently as a result of complex dynamical interactions among many regions of the brain. By applying signal processing techniques from the theory of nonlinear dynamics and global optimization to the analysis of long-term (3.6 to 12 days) continuous multichannel electroencephalographic recordings from four epileptic patients, we present evidence that epileptic seizures appear to serve as dynamical resetting mechanisms of the brain, that is the dynamically entrained brain areas before seizures disentrain faster and more frequently (p<0.05) at epileptic seizures than any other periods. We expect these results to shed light into the mechanisms of epileptogenesis, seizure intervention and control, as well as into investigations of intermittent spatiotemporal state transitions in other complex biological and physical systems.

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.

CONTROL OF SYNCHRONIZATION OF BRAIN DYNAMICS LEADS TO CONTROL OF EPILEPTIC SEIZURES IN RODENTS

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 closed-loop feedback control systems in epileptic seizures combining methods from seizure prediction and deep brain stimulation.

Characterizing nonlinearity in invasive EEG recordings from temporal lobe epilepsy

Abstract Invasive electroencephalographic (EEG) recordings from depth and subdural electrodes, performed in eight patients with temporal lobe epilepsy, are analyzed using a variety of nonlinear techniques. A surrogate data technique is used to find strong evidence for nonlinearities in epileptogenic regions of the brain. Most of these nonlinearities are characterized as “spiking” by a wavelet analysis. A small fraction of the nonlinearities are characterized as “recurrent” by a nonlinear prediction algorithm. Recurrent activity is found to occur in spatio-temporal patterns related to the location of the epileptogenic focus. Residual delay maps, used to characterize “lag-one nonlinearity”, are remarkably stationary for a given electrode, and exhibit striking variations among electrodes. The clinical and theoretical implications of these results are discussed.

Autoregressive modeling and feature analysis of DNA sequences

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.

Predictability analysis for an automated seizure prediction algorithm.

Epileptic seizures of mesial temporal origin are preceded by changes in signal properties detectable in the intracranial EEG. A series of computer algorithms designed to detect the changes in spatiotemporal dynamics of the EEG signals and to warn of impending seizures have been developed. In this study, we evaluated the performance of a novel adaptive threshold seizure warning algorithm (ATSWA), which detects the convergence in Short-Term Maximum Lyapunov Exponent (STLmax) values among critical intracranial EEG electrode sites, as a function of different seizure warning horizons (SWHs). The ATSWA algorithm was compared to two statistical based naïve prediction algorithms (periodic and random) that do not employ EEG information. For comparison purposes, three performance indices “area above ROC curve” (AAC), “predictability power” (PP) and “fraction of time under false warnings” (FTF) were defined and the effect of SWHs on these indices was evaluated. The results demonstrate that this EEG based seizure warning method performed significantly better (P < 0.05) than both naïve prediction schemes. Our results also show that the performance indexes are dependent on the length of the SWH. These results suggest that the EEG based analysis has the potential to be a useful tool for seizure warning.