Nonlinear dynamical analysis of EEG and MEG: Review of an emerging field

Characterization of dynamical systems under noise using recurrence networks: Application to simulated and EEG data

Resume Les mathematiques non-lineaires ont vu leur champ d'application se developper de facon considerable depuis 1963. Les premieres applications a l'etude du signal EEG sont apparues en 1985. Cette revue se propose de presenter les concepts mathematiques sous-jacents a ce nouvel outil, et de rapporter les differents resultats publies. Le parametre non-lineaire le plus employe est la dimension ≪ de correlation ≫ (DC) dite egalement ≪ de complexite ≫ car elle varie en fonction de la complexite de l'information transportee par le signal EEG. Le calcul de ce parametre a permis de retrouver des notions classiques en EEG: quand l'EEG apparait plus ≪complexe≫, plus ≪desynchronise≫ ou plus ≪decorrele≫ (EEG des regions anterieures, situation yeux ouverts, tâches mentales, decharge tonique d'une crise d'epilepsie), la DC est plus elevee que lorsque l'EEG apparait plus ≪simple≫, ≪plus synchronise≫ ou plus ≪ correle ≫ (EEG des regions posterieures, situation yeux fermes, sommeil lent profond, phase clonique d'une crise d'epilepsie, etc). La dimension de complexite donne ainsi une mesure permettant de faciliter les comparaisons entre diverses situations electrophysiologiques.

Apport des mathématiques non-linéaires (théorie du chaos) à l'analyse de l'EEG

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. r 1998 Wiley-Liss, Inc.

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

Study Objectives: Sleep deprivation can affect the waking EEG that may reflect information processing of the brain. We examined the effect of total sleep deprivation (TSD) on nonlinear dynamics of the waking EEG. Design: Paired-group design Setting: A sleep disorders laboratory in a hospital. Participants: Twenty healthy male volunteers Interventions: Waking EEG data were recorded from subjects with eyes closed after (a) an 8-hour night’s sleep and (b) TSD for 24 hours. The dimensional complexity (D2), as a nonlinear measure of complexity, of the EEG after a full night sleep were compared with those of the EEG after TSD. Measurements and Results: The sleep-deprived states had lower D2 values at three channels (P4, O2, and C3) than normal states. Conclusions: TSD results in the decrease of complexity in the brain, which may imply sub-optimal information processing of the cerebral cortex. We suggest that the investigation of the relation between nonlinear dynamics of the waking EEG induced by TSD and cognitive performance may offer fruitful clues for understanding the role of sleep and the effects of sleep deprivation on brain function.

Effect of total sleep deprivation on the dimensional complexity of the waking EEG.

Studies on extended data including 37 electroencephalographic (EEG) records of ?-sleep, each 103 s long (six subjects; up to seven nights per subject, comprising normal sleep, partial deprivation and recovery), confirmed earlier conclusions that rare episodes of low-dimensional dynamic self-organization, with lifetimes between 10 and 20 s, are present in stage 4 sleep. Particular care was taken of the Theiler correction which, in some ?-sleep signals, required the deletion of trajectory points covering nearly one pseudo-period. The percentage of segments showing an episode, i.e. the attractor probability, decreased with a change in sleep conditions -- either deprivation or recovery prior to the next deprivation. Repetition of deprivation over three nights resulted in an adaptation process, manifested by an increase in attractor probability. After the sharp decrease in probability observed when recovery was established prior to the next deprivation, and on return to normal conditions of sleep at 2200 hours, the probability was immediately close to that observed in normal baseline sleep conditions free of any interference. The observation of a definite effect of sleep deprivation and recovery upon the number of stage 4 attractors observed provides a line of approach to the physiological significance of the probability of such attractors.

Low-dimensional dynamic self-organization in δ-sleep: effect of partial sleep deprivation

Attempts to demonstrate low-dimensional attractor behaviour in the analysis of electroencephalographic (EEG) signals meet with difficulties that in part stem from a departure from single-system dynamics. In order to address this problem, the α-waves can be extracted by digital filtering or by wave separation; these two techniques are compared in order to specify the conditions in which finite impulse response (FIR) bandpass filters can be used. The comparison was made using 18 EEG records of 3 min duration under resting conditions (6 subjects, 3 records per subject: prior to apomorphine administration, then 90 min and 150 min post-treatment). No presence of low-dimensional dynamic episodes in α-signals was observed without digital processing. Sixty 5 s sections showing attractor behaviour were found after filtering and twenty five 5 s sections after wave separation. The mean correlation dimension was calculated for each experimental condition and for 4 subjects, in order to observe the temporal profile of the drug. When attractors were found after wave separation, bandpass filtering then also showed attractor behaviour, with the same temporal profile. However, the reverse is not true: attractors were found after bandpass filtering that were not present after wave separation; in this case the results deserve confirmation, although the temporal profiles for all cases in which attractors were found after filtering remained comparable.

M. Toussaint

Papers

Low-dimensional dynamic self-organization in δ-sleep: effect of partial sleep deprivation

Wave separation versus bandpass filtering: a comparative non-linear analysis of brain α-EEG signals with and without psychotropic drug treatment

Automated detection of low-dimensional EEG α-episodes. An example of application to psychopharmacological data