Revealing direction of coupling between neuronal oscillators from time series: phase dynamics modeling versus partial directed coherence.

The problem of determining directional coupling between neuronal oscillators from their time series is addressed. We compare performance of the two well-established approaches: partial directed coherence and phase dynamics modeling. They represent linear and nonlinear time series analysis techniques, respectively. In numerical experiments, we found each of them to be applicable and superior under appropriate conditions: The latter technique is superior if the observed behavior is "closer" to limit-cycle dynamics, the former is better in cases that are closer to linear stochastic processes.

Seizure prediction: the impact of long prediction horizons.

Several procedures have been proposed to be capable of predicting the occurrence of epileptic seizures. Up to now, all proposed algorithms are far from being sufficient for a clinical application. This is, however, often not obvious when results of seizure prediction performance are reported. Here, we discuss impacts of long prediction horizons with respect to clinical needs and the strain on patients by analyzing long-term continuous intracranial electroencephalography data.

Detection of directed information flow in biosignals.

Several analysis techniques have been developed for time series to detect interactions in multidimensional dynamic systems. When analyzing biosignals generated by unknown dynamic systems, awareness of the different concepts upon which these analysis techniques are based, as well as the particular aspects the methods focus on, is a basic requirement for drawing reliable conclusions. For this purpose, we compare four different techniques for linear time series analysis. In general, these techniques detect the presence of interactions, as well as the directions of information flow, in a multidimensional system. We review the different conceptual properties of partial coherence, a Granger causality index, directed transfer function, and partial directed coherence. The performance of these tools is demonstrated by application to linear dynamic systems.

Spatio-temporal patient-individual assessment of synchronization changes for epileptic seizure prediction.

OBJECTIVE: Abnormal synchronization of neurons plays a central role for the generation of epileptic seizures. Therefore, multivariate time series analysis techniques investigating relationships between the dynamics of different neural populations may offer advantages in predicting epileptic seizures. METHODS: We applied a phase and a lag synchronization measure to a selected subset of multicontact intracranial EEG recordings and assessed changes in synchronization with respect to seizure prediction. RESULTS: Patient individual results, group results, spatial aspects using focal and extra-focal electrode contacts as well as two evaluation schemes analyzing decreases and increases in synchronization were examined. Averaged sensitivity values of 60% are observed for a false prediction rate of 0.15 false predictions per hour, a seizure occurrence period of half an hour, and a prediction horizon of 10 min. For approximately half of all 21 patients, a statistically significant prediction performance is observed for at least one synchronization measure and evaluation scheme. CONCLUSIONS: The results indicate that synchronization changes in the EEG dynamics preceding seizures can be used for seizure prediction. Nevertheless, the underlying pathogenic mechanisms differ and both decreases and increases in synchronization may precede epileptic seizures depending on the structures investigated. SIGNIFICANCE: The prediction method, optimized values of intervention times, as well as preferred brain structures for the EEG recordings have to be determined for each patient individually offering the chance of a better patient-individual prediction performance.

Partial phase synchronization for multivariate synchronizing systems.

Graphical models applying partial coherence to multivariate time series are a powerful tool to distinguish direct and indirect interdependencies in multivariate linear systems. We carry over the concept of graphical models and partialization analysis to phase signals of nonlinear synchronizing systems. This procedure leads to the partial phase synchronization index which generalizes a bivariate phase synchronization index to the multivariate case and reveals the coupling structure in multivariate synchronizing systems by differentiating direct and indirect interactions. This ensures that no false positive conclusions are drawn concerning the interaction structure in multivariate synchronizing systems. By application to the paradigmatic model of a coupled chaotic Roessler system, the power of the partial phase synchronization index is demonstrated.

Testing statistical significance of multivariate time series analysis techniques for epileptic seizure prediction.

Nonlinear time series analysis techniques have been proposed to detect changes in the electroencephalography dynamics prior to epileptic seizures. Their applicability in practice to predict seizure onsets is hampered by the present lack of generally accepted standards to assess their performance. We propose an analytic approach to judge the prediction performance of multivariate seizure prediction methods. Statistical tests are introduced to assess patient individual results, taking into account that prediction methods are applied to multiple time series and several seizures. Their performance is illustrated utilizing a bivariate seizure prediction method based on synchronization theory.

Direct or indirect? Graphical models for neural oscillators.

Univariate and bivariate time series analysis techniques have enabled new insights into neural processes. However, these techniques are not feasible to distinguish direct and indirect interrelations in multivariate systems. To this aim multivariate times series techniques are presented and investigated by means of simulated as well as physiological time series. Pitfalls and limitations of these techniques are discussed.

Testing for directed influences among neural signals using partial directed coherence.

One major challenge in neuroscience is the identification of interrelations between signals reflecting neural activity. When applying multivariate time series analysis techniques to neural signals, detection of directed relationships, which can be described in terms of Granger-causality, is of particular interest. Partial directed coherence has been introduced for a frequency domain analysis of linear Granger-causality based on modeling the underlying dynamics by vector autoregressive processes. We discuss the statistical properties of estimates for partial directed coherence and propose a significance level for testing for nonzero partial directed coherence at a given frequency. The performance of this test is illustrated by means of linear and non-linear model systems and in an application to electroencephalography and electromyography data recorded from a patient suffering from essential tremor.

Do false predictions of seizures depend on the state of vigilance? A report from two seizure-prediction methods and proposed remedies.

PURPOSE: Available seizure-prediction algorithms are accompanied by high numbers of false predictions to achieve high sensitivity. Little is known about the extent to which changes in EEG dynamics contribute to false predictions. This study addresses potential causes and the circadian distribution of false predictions as well as their relation to the sleep-wake cycle. METHODS: In 21 patients, each with 24 h of interictal invasive EEG recordings, two methods, the dynamic similarity index and the mean phase coherence, were assessed with respect to time points of false predictions. Visual inspection of the invasive EEG data and additional scalp electroencephalogram data was performed at times of false predictions to identify possible correlates of changes in the EEG dynamics. RESULTS: A dependency of false predictions on the time of day is shown. Renormalized to the duration of the period patients are asleep and awake, 86% of all false predictions occurred during sleep for the dynamic similarity index and 68% for the mean phase coherence, respectively. Combining two reference intervals, one during sleep and one in an awake state, the dynamic similarity index increases its performance by reducing the number of false predictions by almost 50% without major changes in sensitivity. No obvious dependence of false predictions was noted on visible epileptic activity, such as spikes, sharp waves, or subclinical ictal patterns. CONCLUSIONS: Changes in the EEG dynamics related to the sleep-wake cycle contribute to limits of specificity of both seizure-prediction methods investigated. This may provide a clue for improving prediction methods in general. The combination of reference states yields promising results and may offer opportunities to increase further the performance of prediction methods.