Using bivariate signal analysis to characterize the epileptic focus: the benefit of surrogates.

The disease epilepsy is related to hypersynchronous activity of networks of neurons. While acute epileptic seizures are the most extreme manifestation of this hypersynchronous activity, an elevated level of interdependence of neuronal dynamics is thought to persist also during the seizure-free interval. In multichannel recordings from brain areas involved in the epileptic process, this interdependence can be reflected in an increased linear cross correlation but also in signal properties of higher order. Bivariate time series analysis comprises a variety of approaches, each with different degrees of sensitivity and specificity for interdependencies reflected in lower- or higher-order properties of pairs of simultaneously recorded signals. Here we investigate which approach is best suited to detect putatively elevated interdependence levels in signals recorded from brain areas involved in the epileptic process. For this purpose, we use the linear cross correlation that is sensitive to lower-order signatures of interdependence, a nonlinear interdependence measure that integrates both lower- and higher-order properties, and a surrogate-corrected nonlinear interdependence measure that aims to specifically characterize higher-order properties. We analyze intracranial electroencephalographic recordings of the seizure-free interval from 29 patients with an epileptic focus located in the medial temporal lobe. Our results show that all three approaches detect higher levels of interdependence for signals recorded from the brain hemisphere containing the epileptic focus as compared to signals recorded from the opposite hemisphere. For the linear cross correlation, however, these differences are not significant. For the nonlinear interdependence measure, results are significant but only of moderate accuracy with regard to the discriminative power for the focal and nonfocal hemispheres. The highest significance and accuracy is obtained for the surrogate-corrected nonlinear interdependence measure.

Indications of nonlinear deterministic and finite-dimensional structures in time series of brain electrical activity: dependence on recording region and brain state.

We compare dynamical properties of brain electrical activity from different recording regions and from different physiological and pathological brain states. Using the nonlinear prediction error and an estimate of an effective correlation dimension in combination with the method of iterative amplitude adjusted surrogate data, we analyze sets of electroencephalographic (EEG) time series: surface EEG recordings from healthy volunteers with eyes closed and eyes open, and intracranial EEG recordings from epilepsy patients during the seizure free interval from within and from outside the seizure generating area as well as intracranial EEG recordings of epileptic seizures. As a preanalysis step an inclusion criterion of weak stationarity was applied. Surface EEG recordings with eyes open were compatible with the surrogates' null hypothesis of a Gaussian linear stochastic process. Strongest indications of nonlinear deterministic dynamics were found for seizure activity. Results of the other sets were found to be inbetween these two extremes.

Nonlinear EEG analysis in epilepsy: its possible use for interictal focus localization, seizure anticipation, and prevention.

Several recent studies emphasize the high value of nonlinear EEG analysis particularly for improved characterization of epileptic brain states. In this review the authors report their work to increase insight into the spatial and temporal dynamics of the epileptogenic process. Specifically, they discuss possibilities for seizure anticipation, which is one of the most challenging aspects of epileptology. Although there are numerous studies exploring basic neuronal mechanisms that are likely to be associated with seizures, to date no definite information is available regarding how, when, or why a seizure occurs. Nonlinear EEG analysis now provides strong evidence that the interictal-ictal state transition is not an abrupt phenomenon. Rather, findings indicate that it is indeed possible to detect a preseizure phase. The unequivocal definition of such a state with a sufficient length would enable investigations of basic mechanisms leading to seizure initiation in humans, and development of adequate seizure prevention strategies.

The epileptic process as nonlinear deterministic dynamics in a stochastic environment: an evaluation on mesial temporal lobe epilepsy.

The theory of deterministic chaos addresses simple deterministic dynamics in which nonlinearity gives rise to complex temporal behavior. Although biological neuronal networks such as the brain are highly complicated, a number of studies provide growing evidence that nonlinear time series analysis of brain electrical activity in patients with epilepsy is capable of providing potentially useful diagnostic information. In the present study, this analysis framework was extended by introducing a new measure xi, designed to discriminate between nonlinear deterministic and linear stochastic dynamics. For the evaluation of its discriminative power, xi was extracted from intracranial multi-channel EEGs recorded during the interictal state in 25 patients with unilateral mesial temporal lobe epilepsy. Strong indications of nonlinear determinism were found in recordings from within the epileptogenic zone, while EEG signals from other sites mainly resembled linear stochastic dynamics. In all investigated cases, this differentiation allowed to retrospectively determine the side of the epileptogenic zone in full agreement with results of the presurgical workup.