Simulation Research On EEG Nonlinear Time Series

The research on the human brain, which is one of the most complex nonlinear dynamics systems, has become one of the hottest areas and will be full developed in the 21st century. After the discovery of electroencephalogram (EEG) in 1929 by Hans Berger, EEG has been utilized as a non-invasive method to study the brain and plays an important role in many areas. In biomedicine, EEG is an efficient tool to diagnose and treat some brain disorders, and in cognitive science, EEG is a key to open the door of the nature of human thought, and in Brain-Computer Interface (BCI), EEG is the medium of connecting human and computer. In order to effectively apply EEG into these areas, it is necessary to find more efficient and more accurate methods to deeply understand the behavior of the underlying system described by EEGs. Traditional methods, such as frequency-spectrum and statistics, can't correctly explain the nonlinear dynamical characteristics of human brain. This thesis proposed novel methods of studying EEG from the points of nonlinear dynamics and system simulation. In the thesis, there are following five aspects discussed for simulation research on EEG nonlinear time series.(1) A method of constructing fuzzy inference system (FIS) from QSIM model of epileptic behaviors is proposed. The relationship of quantity space of QSIM and the linguistic values of FIS are viewed as the basis of the conversion rules. The efficient fuzzy rules base is built according the proposed method.(2) Reconstruction of phase space of underlying system is the basis of EEG research according to nonlinear dynamics. To reconstruct the phase space must determine the two parameters, embedding delay and embedding dimension. Two methods are proposed to improve the original ones. C-C method and Cao's algorithm are implemented in efficient ways.(3) Based on the reconstructed phase space, some nonlinear dynamical invariants are compared according their nonlinear ability and computational performance. The results show that permutation entropy (PE) and Hurst exponent (HE) are the two most practical measures to characterize and distinguish difference psycho-physiological states of human brain.(4) In the artificial phase space reconstructed from EEG nonlinear time series, the concepts of qualitative state and qualitative behavior based on nonlinear dynamical properties are presented. The algorithm of extracting qualitative states from the reconstructed phase space is proposed as well as the method of modeling the phase-space trajectory. Three methods of characterizing the qualitative behavior are also given to show different aspects of underlying system.(5) The integration methods of EEG classification and identification are presented. The nonlinear properties and the qualitative behavior are fed as the input information of the classifier. The hybrid methods can not only determine their intrinsic parameters, but also select the most respective channels, which hold the critical distinguishable information. These efforts may help improve the accuracy and performance of the classifier. In medicine diagnose, these adaptive learning methods may help automatically identify the disease foci, and in BCI, they also help to find the location of specific brain function.The methods proposed in the thesis are evaluated on several EEG data sets acquired from some common databases. These data sets have been studied by some research groups. The proposed methods may give satisfactory results on these data sets.The proposed methods are not limited in EEG time series. They can be developed and extended for other questions. The method about qualitative state and qualitative behavior in reconstructed phase space may be used in the general nonlinear times series, which recorded from underlying nonlinear dynamical systems.