Indications of nonlinear structures in brain electrical activity

Abstract

The dynamical properties of electroencephalogram (EEG) segments have recently been analyzed by Andrzejak and co-workers for different recording regions and for different brain states, using the nonlinear prediction error and an estimate of the correlation dimension. In this paper, we further investigate the nonlinear properties of the EEG signals using two established nonlinear analysis methods, and introduce a "delay vector variance" (DVV) method for better characterizing a time series. The proposed DVV method is shown to enable a comprehensive characterization of the time series, allowing for a much improved classification of signal modes. This way, the analysis of Andrzejak and co-workers can be extended toward classification of different brain states. The obtained results comply with those described by Andrzejak et al., and provide complementary indications of nonlinearity in the signals.

Dynamic response signatures of a scaled model platform for floating wind turbines in an ocean wave basin

“…. , N. The DVV method, for a given embedding parameter m, can be summarized [35,36,38,54], as follows:…”

“…surrogate data. The DVV method is further elaborated and tested in Gautama et al [33,35,36] and Mandic et al [37]. They show that this characterization, although not requiring any prior knowledge about the signal, is robust to the presence of noise, straightforward to interpret and visualize nonlinearity and typically exhibits improved performance over other available methods.…”

“…Also, they show that the DVV method can be used for estimating the degree of signal nonlinearity by calculating the root mean squared error (RMSE) [33]. The DVV method has been successfully applied in the past to analyse the nature of biomedical signals, such as hand tremor, electroencephalogram (EEG) signals [36], functional magnetic resonance imaging [33,38], electrocardiograms, heart rate variability [38,39], and in finance [40]. Application of the DVV method in diagnostic medicine shows that the linear or nonlinear nature of the signal conveys information concerning the health condition of the subject [38,41,42].…”

“…Andrzejak et al [43] analyse dynamical brain properties and find the strongest indication of nonlinear deterministic dynamics for epileptic seizures, and no significant indication of nonlinearity for healthy subjects. Gautama et al [36] show that DVV analysis enables a comprehensive characterization of the dynamical modes of EEG signals, allowing for accurate classification of the brain states. The method of Gautama et al [33] indicates that a difference in signal nonlinearity may also be attributed to a difference in system nonlinearity.…”

“…The DVV method detects the presence of determinism and nonlinearity in a time series and is based upon the examination of local predictability of a signal [34][35][36]; an advantage of this method lies in employing output-only signals from the system without completely knowing the system or the input. Nonlinearities of the structural responses are estimated and compared for variability of loading for different monitoring devices and the extent to which such nonlinearity estimates can be interpreted and used.…”