Christian Uhl

Synergetic Analysis of Human Electroencephalograms: Petit-Mal Epilepsy

The clinical diagnosis of epileptic seizures is usually based on an inspection of the electroencephalogram (EEG). The present paper is devoted to a description of a more refined analysis of EEG patterns of petit-mal epilepsy. The treatment is based on the synergetic approach to macroscopic patterns in complex systems which has been inaugurated by H. Haken. This approach aims at an understanding of both spatial as well as dynamical aspects of macroscopic EEG patterns.

Reconstruction of spatio-temporal signals of complex systems

We propose a novel method to analyze spatiotemporal signals emerging from synergetic systems. By this approach we are able to reconstruct the spatial modes, as well as their dynamic interaction close to instabilities. Our method is an extension of the principal component analysis to the case of nonlinear self-organizing systems. We demonstrate our method by an example of a codimension one instability, apply the algorithm to a simulated Bénard instability and present a generalization to bifurcations with several order parameters.

A new concept for EEG/MEG signal analysis : Detection of interacting spatial modes

We propose a new concept for analyzing EEG/MEG data. The concept is based on a projection of the spatiotemporal signal into the relevant phase space and the interpretation of the brain dynamics in terms of dynamical systems theory. The projection is obtained by a simultaneous determination of spatial modes and coefficients of differential equations. The resulting spatiotemporal model can be characterized by stationary points and corresponding potential field maps. Brain information processing can be interpreted by attraction and repulsion of spatial field distributions given by these stationary points. This allows an objective and quantitative characterization of the brain dynamics. We outline this concept and the underlying algorithm. Results of the application of this method to an event related potential (ERP) study of auditory memory processes are discussed. Hum. Brain Mapping 6:137–149, 1998.

Experiments with an extended adaptive SVD enhancement scheme for speech recognition in noise

An extension to adaptive signal subspace methods is presented, based on singular value decomposition (SVD) with an online estimation of the noise variance. With this approach aiming at automatic speech recognition (ASR) in adverse environmental conditions no speech detection has to be performed. A comparison of different SVD approaches and nonlinear spectral subtraction within ASR experiments of different applications is conducted for weakly correlated noise scenarios. Better performance in the case of signal subspace speech enhancement with respect to both accuracy as well as robustness of parameter tuning are reported.

Improvement of Source Localization by Dynamical Systems Based Modeling (DSBM)

Recently, we have proposed a new concept for analyzing EEG/MEG data (Uhl et al. 1998), which leads to a dynamical systems based modeling (DSBM) of neurophysiological data. We report the application of this approach to four different classes of simulated noisy data sets, to investigate the impact of DSBM-filtering on source localization. An improvement is demonstrated of up to above 50% of the distance between simulated and estimated dipole positions compared to principal component filtered and unfiltered data. On a noise level on which two underlying dipoles cannot be resolved from the unfiltered data, DSBM allows for an extraction of the two sources.

Spatio-Temporal Modeling Based on Dynamical Systems Theory

In the preceding contributions of Part II “Methods & Applications” different approaches of analyzing neurophysiological data have been presented.

Analyzing Spatio-Temporal Patterns of Complex Systems

Rapid progress in the field of noninvasive imaging methods in medicine will provide huge amounts of data sets in the nearest future. Especially imaging methods with high time resolutions like multivariate measurements of the electroencephalogram (EEG) or the magnetoencephalogram (MEG) will allow for a detailed documentation of spatio-temporal processes in biological systems. Therefore, it is of extreme importance to develop methods which allow for a characterization and classification of spatio-temporal processes with special emphasis on medical applications.

Spatiotemporal signal analysis: recognition of interacting modes

We present a new algorithm to analyse spatiotemporal signals emerging from nonlinear systems which are close to instability. The algorithm aims at a recognition of spatial modes, both order parameters and enslaved modes, and equations describing the dynamics of the amplitudes by order parameter equations and center manifolds. We demonstrate the method by a simulated example from the field of hydrodynamics (Benard instability) and discuss results of the method applied to spatiotemporal EEG-data of epileptic seizures.