Collaborators:
Ralph G. Andrzejak, Jochen Arnhold, Peter David, Christian E. Elger, Peter Grassberger, Alexander Kraskov, Klaus Lehnertz, Florian Mormann, Christoph Rieke, Harald Stoegbauer, Guido Widman.
Description:
This line of research dealt with the application of time series analysis to electrophysiological data, in particular to the electroencephalogram (EEG) of epilepsy patients. One important aim was the extraction of information that might be useful for diagnostic purposes. Examples include the localization of the epileptic focus and most prominently the prediction of epileptic seizures.
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. [8] and [9] below.
Publications:
[1]
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).
[2]
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).
[3]
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 (1), 57 (2003).
[4]
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).
[5]
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).
[6]
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).
[7] Kreuz T:
Measuring synchronization in model systems and electroencephalographic time
series from epilepsy patients.
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 [PDF].
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.
[8]
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.
[9]
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).
[10]
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).
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