Nonlinear analysis of chaotic dynamics underlying the electroencephalogram(EEG) in Alzheimer's disease

Abstract

We investigated chaotic dynamics underlying the electroencephalogram (EEG) in Alzheimer``s disease by nonlinear methods in order to understand further the role of chaos in brain function. In the analysis we calculated the correlation dimensions $D_2$ and the largest Liapunov exponents $L_1$. A new method for calculating nonlinear invariant measures was introduced. The method determines an acceptable minimum embedding dimension by looking at the behaviour of nearest neighbors under changes in embedding dimension from d to d+1. We showed that it is strikingly faster and more accurate than other algorithms for limited noisy data. We found that patients with Alzheimer``s disease have significantly lower $D_2$ and $L_1$ than age-approximated non-demented controls. It is inferred from it that brains injured by Alzheimer``s disease have electrophysiological inactive elements (i. e. neurons and/or synapses) and thus show decreased chaotic behaviour. This results support the assumption that chaos plays an important role in brain function, for instance, memory and learning. And we suggest that brains can be described by deterministic models. In this paper we showed the nonlinear analysis can provide a promising tool for detecting relative changes in the complexity of brain dynamics, which cannot be detected by conventional linear analysis. And we propose the nonlinear analysis of the EEG in Alzheimer``s disease for a new method for diagnosis of it as a clinical application.