Indications of nonlinear deterministic and finite-dimensional structures in time series of brain electrical activity: Dependence on recording region and brain state

Abstract

We compare dynamical properties of brain electrical activity from different recording regions and from different physiological and pathological brain states. Using the nonlinear prediction error and an estimate of an effective correlation dimension in combination with the method of iterative amplitude adjusted surrogate data, we analyze sets of electroencephalographic (EEG) time series: surface EEG recordings from healthy volunteers with eyes closed and eyes open, and intracranial EEG recordings from epilepsy patients during the seizure free interval from within and from outside the seizure generating area as well as intracranial EEG recordings of epileptic seizures. As a preanalysis step an inclusion criterion of weak stationarity was applied. Surface EEG recordings with eyes open were compatible with the surrogates' null hypothesis of a Gaussian linear stochastic process. Strongest indications of nonlinear deterministic dynamics were found for seizure activity. Results of the other sets were found to be inbetween these two extremes.

Approximate entropy and auto mutual information analysis of the electroencephalogram in Alzheimer’s disease patients

“…Non-linearity in the brain is introduced even at the neuronal level [5], since the dynamical behaviour of individual neurons is governed by threshold and saturation phenomena. Given the highly non-linear nature of the neuronal interactions at multiple levels of temporal and spatial scales, the EEG appears to be an appropriate area for non-linear time series analysis [26].…”

Analysis of regularity in the EEG background activity of Alzheimer's disease patients with Approximate Entropy

“…the brain (Andrzejak et al, 2001). Many studies are known in which non-linear time series analysis techniques were applied to different kinds of EEGs from humans, such as recordings from healthy volunteers at rest , sleep (Babloyantz et al, 1985), during periods of cognitive activity (Theiler and Rapp, 1996), or from patients with acute ischemic stroke (Hwa and Ferree, 2002) or with diseases like Alzheimer's (Stam et al, 1995;Jelles et al, 1999), Parkinson's (Pezard et al, 2001), Creutzfeldt-Jakob (Babloyantz and Destexhe, 1988), epilepsy (Hornero et al, 1999), depression (Nandrino et al, 1994) and schizophrenia (Fell et al, 1995) in comparison with control subjects.…”

Interpretation of the auto-mutual information rate of decrease in the context of biomedical signal analysis. Application to electroencephalogram recordings

“…Several physiological signals, including cardiovascular and brain activity recordings, exhibit a partially non-linear behaviour (Andrzejak et al 2001, Hoyer et al 2002, Palacios et al 2007. Additionally, some authors have suggested that healthy systems have non-linear complex relationships that fail with ageing and disease (Costa et al 2005, Goldberger et al 2002.…”