Chaos Theory in EEG Analysis

It is very important to localize the epileptogenic focus as accurately as possible for candidates undergoing epilepsy treatment through surgery. From earlier visual analysis to recent computer-assist quantitative calculation, the accuracy of the diagnosis improves with the innovation of the methods Gotman 1983; Mars 1977; Lieb et al. 1987]. In the past years, EEG signals recorded on the scalp had been known as the projection of discharges from millions of neurons to the surface of the conductive body, and power spectrum with Fast Fourier Transformation (FFT) had become the most popular method to analyze EEG signals Gersch and Goddard 1970]. Recently, non-linear dynamic theory opens a new window for understanding the behavior of EEG When a system is in chaotic state, the long-term behavior is unpredictable, although each instant state should be determined strictly by the initial state. Human EEG is neither absolutely periodic nor stochastic, and it has been assumed that EEG signals may present chaotic behavior rather than other processes. Some researchers have studied human EEG in the chaotic eld, and found that EEG presented chaotic characteristics: sensitive dependence on initial conditions, self-organization, similarity across scale and intermittence Rae-Grant and Kim 1994]. The largest Lya-punov exponent was positive Iasemidis et al 1990]; the logistic parameter was beyond the critical point of 3. A series of high-dimensional vectors can represent the system state, and the integral curves of the vectors represent the trajectories. Correlation dimension refers to the density of the points in the state space occupied by the attractors, or the minimum number of independent variables to describe the system. The correlation dimension of the human brain system is low, especially in epileptic seizures Babloyantz and Destexhe 1986; Lopes da Silva 1991]. Some authors have tried to localize epileptogenic focus with the computation of correlation dimension, and have found that it might be useful in localizing the onset of the seizure activity Pijn et al 1991]. But this should be practised on more patients and proved by other methods. Thirty-two patients with complex partial seizures were studied in our work using chaotic theory, as well as power spectral analysis, magnetic resonance imaging (MRI) and single photon emission computed topography (SPECT). Spatio-temporal mapping has been known as one of the most useful tools to understand the brain function Lehmann 1971; Ragot 1978]. In order to avoid the electrical diiusion in the physical tissue Pezard et al. 1994], EEG recorded …