Non-linear dynamical analysis of the EEG in Alzheimer's disease with optimal embedding dimension

Abstract

We used non-linear analysis to investigate the dynamical properties underlying the EEG in patients with Alzheimer's disease. We calculated the correlation dimension D2 and the first positive Lyapunov exponent L1. We employed a new method, which was proposed by Kennel et al., to calculate the non-linear invariant measures. That method determined the proper minimum embedding dimension by looking at the behavior of nearest neighbors under a change in the embedding dimension d from d to d+1. We demonstrated that for limited noisy data, our algorithm was strikingly faster and more accurate than previous ones. Also, we found that, in almost all channels, patients with Alzheimer's disease had significantly lower D2 and L1 values than those for age-approximated healthy controls. These results suggest that brains afflicted by Alzheimer's disease show behaviors which are less chaotic than those of normal healthy brains. In this paper, we show that non-linear analysis can provide a fruitful tool for detecting relative changes, which cannot be detected by conventional linear analysis, in the complexity of brain dynamics. We propose that non-linear dynamical analyses of the EEGs from patients with Alzheimer's disease will be a diagnostic modality in the appropriate clinical setting.