Characteristic Fluctuations Around Stable Attractor Dynamics Extracted from Highly Nonstationary Electroencephalographic Recordings

Abstract

Since the discovery of electrical activity of the brain, electroencephalographic (EEG) recordings constitute one of the most popular techniques of brain research. However, EEG signals are highly nonstationary and one should expect that averages of the cross-correlation coefficient, which may take positive and negative values with equal probability, (almost) vanish when estimated over long data segments. Instead, we found that the average zero-lag cross-correlation matrix estimated with a running window over the whole night of sleep EEGs, or of resting state during eyes-open and eyes-closed conditions of healthy subjects shows a characteristic correlation pattern containing pronounced nonzero values. A similar correlation structure has already been encountered in scalp EEG signals containing focal onset seizures. Therefore, we conclude that this structure is independent of the physiological state. Because of its pronounced similarity across subjects, we believe that it depicts a generic feature of the brain dynamics. Namely, we interpret this pattern as a manifestation of a dynamical ground state of the brain activity, necessary to preserve an efficient operational mode, or, expressed in terms of dynamical system theory, we interpret it as a "shadow" of the evolution on (or close to) an attractor in phase space. Nonstationary dynamical aspects of higher cerebral processes should manifest in deviations from this stable pattern. We confirm this hypothesis through a correlation analysis of EEG recordings of 10 healthy subjects during night sleep, 20 recordings of 9 epilepsy patients, and 42 recordings of 21 healthy subjects in resting state during eyes-open and eyes-closed conditions. In particular, we show that the estimation of deviations from the stationary correlation structures provides a more significant differentiation of physiological states and more homogeneous results across subjects.

Linear and nonlinear interrelations show fundamentally distinct network structure in preictal intracranial EEG of epilepsy patients

“…The nonlinear excess interrelation patterns (i.e., mutual information matrices corrected using multivariate IAAFT surrogates) on the other hand were patient specific (Figure b). Our observation for the linear interrelations is consistent with recent scalp EEG findings where a generic and very stable background pattern has been found (Müller, Rummel, Goodfellow, & Schindler, ; Olguín‐Rodríguez et al, ). We interpret this as an indication that the linear interrelations mainly reflect the mesiotemporal anatomy, which in our study was recorded in a standardized fashion.…”

Low-Dimensional Dynamics of Brain Activity Associated with Manual Acupuncture in Healthy Subjects

“…In a previous study [55], we observed fluctuations in the scaling of neural activity in a spontaneously active brain circuit. Olguin-Rodriguez et al have investigated characteristic fluctuations around stable attractor dynamics extracted from highly nonstationary EEG recordings [56]. On the other hand, researchers have demonstrated that the dynamical regime of the sensory cortex converges to stable dynamics around a single stimulus-tuned attractor [57].…”

The Influence of EEG References on the Analysis of Spatio-Temporal Interrelation Patterns

“…At each time step the median R M of all EEG-channels ( M ) is taken as a reference. Hence, for the scheme of 19 electrodes, only one scalp electrode is used as a reference point, but it may change at any instant (Müller et al, 2011, 2014; Olguín-Rodríguez et al, 2018). eqnarrayright center leftR≡RM…”