Die präiktale Phase von epileptischen Anfällen - Untersuchung mit neuen Ansätzen der multivariaten Zeitreihenanalyse

• Applicant: Professor Dr. Christian Rummel
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2005 to 2008
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 16645421

• Final Report Year: 2008

Final Report Abstract

In the research projects many conceptual questions concerning the application of the equal-time cross-correlation matrix C and measures derived from Random Matrix Theory (RMT) to EEG recordings could be clarified. Nearest neighbor spacing distributions P (si ) and level number variances Σ2i (l) calculated from i individually unfolded eigenvalue spectra of the correlation matrix turned out as tools that can be used to distinguish random from non-random correlations and indicate the latter very sensitively. With respect to application to the EEG the influence of factors like the EEG reference, noise and artifacts was investigated quantitatively. In addition a compensation algorithm for the influence of the EEG reference was developed. The question of the appropriate test statistics for the null hypothesis of only randomly correlated multivariate data and a method for estimation of the minimal reasonable window length T (or equivalently the number of sufficiently independent data points T') were investigated. In addition summarizing measures for Total Correlation Strength (TCS), Random Correlation Strength (RCS) and genuine Cross-Correlation Strength (CCS) in the multivariate data set – all ranging between 0 for completely independent data and 1 for identical data – were introduced. In order to answer the questions how many correlation clusters are present in the data and to what extent these can be detected from the eigenvectors of the C-matrix a novel distance measure was introduced. Based on this quantity the concepts of Cluster Participation Vectors (CPV) and Cluster Participation Coefficients (CPC) were developed. Quantitative tests of the performance of the algorithms for estimation of the cluster number as well as attribution of channels to the clusters were carried out. After these rather conceptional issues extensive application was made to various types of EEG recordings (scalp and intracranial) of different types of epileptic seizures (primary generalized and focal onset). Unfiltered as well as band selective investigations were undertaken. For the low frequency bands (0 . . . 12.5Hz) of scalp recordings it turned out that during focal onset seizures random (RCS) and genuine cross-correlations (CCS) evolve in an opposite and unexpected way: CCS gradually decreases during seizure and reaches a pronounced minimum in the immediate post-ictal period. On the contrary the main effect of RCS is a highly significant post-ictal elevation. During cluster analysis of intracranial EEG data of a patient suffering from temporal lobe epilepsy a prominent involvement of the signals recorded directly from the seizure onset zone was observed interictally. Investigation of a larger set of continuous intracranial recordings is underway.

Publications

• Evolution of genuine cross-correlations during epileptic focal onset seizures. Spring School “Models in neuroscience – Turning experiments into knowledge”, April 27th – May 5th, St. Petersburg, Russia
  C. Rummel, M. Müller, G. Baier and K. Schindler
  
• Localized short-range correlations in the spectrum of the equal-time correlation matrix. Phys. Rev. E74, 041119 (2006)
  M. Müller, Y. López Jiménez, C. Rummel, G. Baier, A. Galka, H. Muhle and U. Stephani
  
• Automated detection of time-dependent cross-correlation clusters in nonstationary time series. Eur. Phys. Lett. 80, 68004 (2007)
  C. Rummel, G. Baier and M. Müller
  
• Spatio-temporal evolution of correlation clusters. “3rd International Workshop on Seizure Prediction in Epilepsy”, September 29th – October 2nd, 2007, Freiburg, Germany
  C. Rummel, M. Müller and G. Baier
  
• The influence of static correlations on multivariate correlation analysis of the EEG. J. Neurosci. Meth. 166, 138 (2007)
  C. Rummel, G. Baier and M. Müller
  
• A Multivariate Approach to Correlation Analysis Based on Random Matrix Theory. In: A. Schulze-Bonhage, J. Timmer and B. Schelter (Eds.), Seizure Prediction in Epilepsy: From Basic Mechanisms to Clinical Applications. Wiley 2008
  M. Müller, G. Baier, C. Rummel, K. Schindler and U. Stephani
  
• Quantification of Intra- and Inter-Cluster Relations in Non-Stationary and Noisy Data. Phys. Rev. E77, 016708 (2008)
  C. Rummel