EEG-Analysis and Epileptic Seizure Prediction
Ralph G. Andrzejak, Jochen Arnhold, Peter David, Christian E. Elger, Peter Grassberger, Alexander Kraskov, Klaus Lehnertz, Florian Mormann, Christoph Rieke, Harald Stoegbauer, Guido Widman.
This line of research deals with the application of time series analysis to electrophysiological data, in particular to the electroencephalogram (EEG) of epilepsy patients. One important aim is the extraction of information that might be useful for diagnostic purposes. Examples include the localization of the epileptic focus as well as the prediction of epileptic seizures and its statistical evaluation.
Typically in a study on the predictability of epileptic seizures first a characterizing measure is calculated from multi-channel EEG using a moving-window technique. The resulting measure profiles are then scanned for prominent features which can be related to the actual seizure (ictus) times. These features might be drops or peaks (e.g., quantified as threshold crossings) or any other distinct pattern in the measure profile. In a second step the measures' capability to distinguish the preictal from the interictal interval is evaluated with a test statistics quantifying the occurrence of these features relative to the seizure times and resulting in some kind of performance value. The figure below shows an example of a measure profile for a patient's quasi-continuous recording over more than five days including ten seizures (top). The difference in the distributions for the interictal and the preictal intervals (bottom, left) is then quantified by means of a ROC curve (bottom, right). For details see Refs.  and  below.
 Kreuz T, Chicharro D, Houghton C, Andrzejak RG, Mormann F:
Monitoring spike train synchrony
J Neurophysiol 109, 1457 (2013) [PDF]
Abstract: Recently, the SPIKE-distance has been proposed as a parameter-free and time-scale independent measure of spike train synchrony. This measure is time-resolved since it relies on instantaneous estimates of spike train dissimilarity. However, its original definition led to spuriously high instantaneous values for event-like firing patterns. Here we present a substantial improvement of this measure which eliminates this shortcoming. The reliability gained allows us to track changes in instantaneous clustering, i.e., time-localized patterns of (dis)similarity among multiple spike trains. Additional new features include selective and triggered temporal averaging as well as the instantaneous comparison of spike train groups. In a second step, a causal SPIKE-distance is defined such that the instantaneous values of dissimilarity rely on past information only so that time-resolved spike train synchrony can be estimated in real-time. We demonstrate that these methods are capable of extracting valuable information from field data by monitoring the synchrony between neuronal spike trains during an epileptic seizure. Finally, the applicability of both the regular and the real-time SPIKE-distance to continuous data is illustrated on model electroencephalographic (EEG) recordings.
 Andrzejak RG, Mormann F, Widman G, Kreuz T, Elger CE, Lehnertz K:
Improved spatial characterization of the epileptic brain by focusing on nonlinearity
Epilepsy Research 69, 30 (2006) [PDF]
 Mormann F, Kreuz T, Rieke C, Andrzejak RG, Kraskov A, David P, Elger CE, Lehnertz K:
On the predictability of epileptic seizures
Clin Neurophysiol 116, 569 (2005) [PDF]
 Kreuz T, Andrzejak RG, Mormann F, Kraskov A, Stoegbauer H, Elger CE, Lehnertz K, Grassberger P:
Measure profile surrogates: A method to validate the performance of epileptic seizure prediction algorithms
Phys Rev E 69, 061915 (2004) [PDF]
Abstract: In a growing number of publications it is claimed that epileptic seizures can be predicted by analyzing the electroencephalogram (EEG) with different characterizing measures. However, many of these studies suffer from a severe lack of statistical validation. Only rarely are results passed to a statistical test and verified against some null hypothesis H0 in order to quantify their significance. In this paper we propose a method to statistically validate the performance of measures used to predict epileptic seizures. From measure profiles rendered by applying a moving-window technique to the electroencephalogram we first generate an ensemble of surrogates by a constrained randomization using simulated annealing. Subsequently the seizure prediction algorithm is applied to the original measure profile and to the surrogates. If detectable changes before seizure onset exist, highest performance values should be obtained for the original measure profiles and the null hypothesis "The measure is not suited for seizure prediction" can be rejected. We demonstrate our method by applying two measures of synchronization to a quasi-continuous EEG recording and by evaluating their predictive performance using a straightforward seizure prediction statistics. We would like to stress that the proposed method is rather universal and can be applied to many other prediction and detection problems.
 Kreuz T:
Measuring synchronization in model systems and electroencephalographic time series from epilepsy patients [PDF]
Interdisciplinary PhD thesis in physics, University of Wuppertal, Research Center Juelich (2003)
Supervisors: Prof. P. Grassberger, Research Center Juelich, Germany; Dr. K. Lehnertz, University of Bonn, Germany
Abstract: The main aim of this dissertation is the comparative investigation of different measures of synchronization derived from various approaches and concepts. These include both measures for estimating the degree of dependence between two time series as well as measures which quantify the directionality of this dependence. The first group comprises the linear cross correlation, mutual information, six different indices for phase synchronization (based either on the Hilbert or on the wavelet transform) as well as symmetrized variants of two nonlinear interdependence measures and of event synchronization. The anti-symmetrized variants of the last three measures form the group of measures of directionality.
In the first part of this dissertation the symmetric measures are tested in a controlled setting by means of various model systems. Using the coupling strength as a first control parameter it is investigated to which extent the different measures are able to distinguish between different degrees of dependence. Furthermore, the robustness of the measures against external noise is estimated by varying the signal-to-noise ratio as the second control parameter.
Subsequently, all measures are employed to analyze electroencephalographic recordings from epilepsy patients. This application part consists of two single studies. First a comprehensive comparison on the predictability of epileptic seizures is carried out. Object of investigation is the capability of the different measures to reliably distinguish between the intervals preceding epileptic seizures and the intervals far away from any seizure activity. Already in this study a great deal of attention is paid to the statistical validation of seizure predictions. This issue is particularly addressed in the last part of this dissertation in which the method of measure profile surrogates is introduced as an appropriate tool to distinguish between measures and algorithms unsuited for the prediction of epileptic seizures, and more promising approaches. Two of the measures of synchronization are used to illustrate this new approach.
 Rieke C, Mormann F, Andrzejak RG, Kreuz T, David P, Elger CE, Lehnertz K:
Discerning nonstationarity from nonlinearity in seizure-free and pre-seizure EEG recordings from epilepsy patients
IEEE Trans Biomed Eng 50, 634 (2003) [PDF]
 Mormann F, Kreuz T, Andrzejak RG, David P, Lehnertz K, Elger CE:
Epileptic seizures are preceded by a decrease in synchronization
Epilepsy Res 53, 171 (2003) [PDF]
 Mormann F, Andrzejak RG, Kreuz T, Rieke C, David P, Elger CE, Lehnertz K:
Automated detection of a pre-seizure state based on a decrease in synchronization in intracranial EEG recordings from epilepsy patients
Phys Rev E 67, 021912 (2003) [PDF]
 Lehnertz K, Mormann F, Kreuz T, Andrzejak RG, Rieke C, David P, Elger CE:
Seizure prediction by nonlinear EEG analysis
IEEE Trans Biomed Eng (Special Issue: Epileptic Seizure Prediction: Models and Devices) 22, 57 (2003) [PDF]
 Andrzejak RG, Mormann F, Kreuz T, Rieke C, Kraskov A, Elger CE, Lehnertz K:
Testing the null hypothesis of the non-existence of a pre-seizure state
Phys Rev E 67, 010901 (2003) [PDF]
 Quian Quiroga R, Kreuz T, and Grassberger P
Event Synchronization: A simple and fast method to measure synchronicity and time delay patterns
Phys Rev E 66, 041904 (2002) [PDF]
 Quian Quiroga R, Kraskov A, Kreuz T, and Grassberger P
Performance of different synchronization measures in real data: A case study on electroencephalographic signals
Phys Rev E 65, 041903 (2002) [PDF]
 Lehnertz K, Andrzejak RG, Arnhold J, Kreuz T, Mormann F, Rieke C, Widman G, Elger CE:
Nonlinear EEG analysis in epilepsy: Its possible use for interictal focus localization, seizure anticipation, and prevention
J Clin Neurophysiol 18, 209-222 (2001) [PDF]