Analyzing Epileptic EEG By Nonlinear Methods

Since in 1924, Dr. Hans Berger, who was a Germany psychiatrist, collected the electrical activity of human brain from a whole scalp, the research of electroencephalogram (EEG) has had a history of 80 years. With the development of electrophysiological technology, the EEG has developed from the early period that the EEG experts made analysis based on the multi-channel EEG recorded on the paper up to the present day that an integrated qualitative and quantitative analysis of EEG can be made by using the clinical evoked electric potential and computer based automated detection. Meanwhile, as the EEG examination is to make the self-discharge activity of the brain cells recorded on paper or displayed on screen through amplification, and can reflect the state of the brain function objectively, whereas its operation does no wound to the patient, hence it has been widely applied in the diagnosis of encephalic disease.At present, the EEG has been one of the indispensable clinical examination techniques, and it has a considerably high value for the diagnosis of brain disease. However, the limitation of the available techniques makes the analysis of EEG not up to a nice effect, especially it is not satisfactory in the aspect of the diagnosis of brain disease and quantitative analysis, and up to now the EEG can not be used as a sufficient proof for the diagnosis. Therefore, it is greatly important to explore the application of new techniques in the EEG and develop new analysis methods of the EEG. Approximately 1 % of the people in the world are suffering from the epilepsy, which is a kind of chronic brain disease. The prediction and diagnosis of epilepsy is significant for the therapy of epilepsy. The EEG signal is an important tool for the diagnosis of epilepsy. With the development of computer, nonlinear dynamic based methods begin to be used for the analysis of EEG signals; researches showed that during the several minutes before the seizure, some features of EEG signals change. In this paper, we conducted the research below about the nonlinear dynamic characteristics of EEG signals and the detection of epileptic seizure:A typical feature of chaotic oscillators is to be sensitive to the initial conditions and immune to white noise, and Duffing oscillator is a typical chaotic oscillator. Based on these characteristics of Duffing oscillator, several methods have been proposed for the detection of weak signals or recovery of the parameters of a signal (the parameters include the amplitude, frequency and phase), and the SNR (signal to noise ratio) of the detection or recovery of signals buried in the background of strong noise was improved considerably. Some scholars even made use of the characteristics of the driven Duffing oscillator to process the practical seismic data, and obtained good results. However, the common point of these researches is that the signals they processed were all periodic, whereas in practice, a great deal of signals, for example, biomedical signals such as the electrocardiograph (ECG), EEG and hand tremor, are aperiodic, even chaotic, which greatly limits the application of Duffing oscillator. To fill up this gap, we studied the nonlinear response of the driven Duffing oscillator to chaotic time series, and found that the driven Duffing oscillator can show regular nonlinear response to chaotic time series, i.e., the higher the degree of chaocity of the input time series is, the higher the degree of chaocity of the driven Duffing oscillator is. Two kinds of artificial chaotic time series and real-world EEG signals were employed to verify the new characteristic of the driven Duffing oscillator, and the Lyapunov exponent, phase plane and Poincarésection were applied for the analysis of the results of the numerical experiments. Moreover, as EEG signals are chaotic series time, and the degree of chaocity of EEG signals decrease significantly during seizure, a method based on the new characteristic of the driven Duffing oscillator was proposed for the detection of epileptic seizure. The proposed method has several advantages such as low computation burden, simple algorithm and visualization.Currently, it has been widely proved that the EEG signals are chaotic time series, and phase space reconstruction is an important tool for the analysis of chaotic system, as an important parameter for the phase space reconstruction of a time series, the embedding dimension can indicate the change of the nature of a chaotic system to some extent. To study the change of the nonlinear dynamic system of EEG signals during epileptic seizure, we computed the embedding dimension of normal and epileptic EEG signals by Cao's method and differential entropy method respectively. The rule reflected by the results of two methods were consistent, namely that the embedding dimension of EEG signals during seizure were larger than that of normal signals, and the embedding dimension of epileptic EEG signals fluctuated more fiercely, and had a wider fluctuation interval, further, the results of two methods indicated that the embedding dimension of EEG signals can be a supplementary parameter for the diagnosis of epilepsy. As the embedding dimension shows the upper limit of the degree of freedom of a system, the results of embedding dimension also indicated that normal and epileptic EEG signals corresponded to different chaotic time series generating systems, and different dynamic systems were needed for the mathematical modeling of normal and epileptic EEG signals, and the status of the nonlinear dynamic system of brain was very unstable. In addition, based on the results of Cao's method, it was found that normal EEG signals were of some degree of randomness, whereas epileptic EEG signals were of high determinism, which reflects that epileptic EEG signals can be predicted to some extent.As a patient will lose consciousness during seizure and the epileptic seizure is unexpected and iterative, it is very meaningful to predict the seizure. If drugs or other methods can be carried out to avoid the onset of seizure, the suffering of a patient can be released greatly, and accidents can also be avoided. We made use of degree of nonlinearity as a nonlinear characteristic quantity to distinguish normal and epileptic EEG signals, and succeeded in showing the seizure moment, the results of numerical experiments showed that the degree of nonlinearity of EEG signals increased clearly during seizure. The degree of nonlinearity of EEG signals was compared to that of artificial time series, and the results showed that the degree of nonlinearity of EEG signals was between that of linear and nonlinear time series. Moreover, when compared with the degree of nonlinearity of linear time series, it was found that at some time normal EEG signals were linear, which was not consistent with the impression that EEG signals were low-dimensional chaotic time series and needs further research. The method based on the degree of nonlinearity for the detection of epileptic seizure had a lower computation burden than that based on Lyapunov exponent.The EEG recordings used for the detection of epileptic seizure usually last for a long time, even for a week. Whereas for the time being, the visual observation method, which was proposed by the International League Against Epilepsy (ILAE) is still mainly adopted for the clinical diagnosis of epilepsy, i.e., the medical experts diagnose the epileptic seizure by observing the epileptic characteristic waves, this kind of method is time-consuming and boring, and confines the efficiency of medical experts considerably. Therefore, it is a research focus to realize the automated detection of epileptic seizure. As the nonlinear dynamic characteristic of EEG signals changes during seizure, we proposed a method for the automated detection of epileptic seizure based on the embedding parameters (including embedding dimension and delay time) and artificial neural network. The results showed that this scheme was of high accuracy, needed a small amount of data, and could effectively reduce the amount of work of medical experts to analyze the EEG data clinically. As the embedding dimension and delay time are the parameters for the phase space reconstruction, the nonlinear characteristics they reflect are consistent; however, as the computation burden of delay time is much lower than that of embedding dimension, and it is easier for the delay time to reach the real-time requirements, thus in the condition that the accuracies of the methods based on the two parameters were the same, we recommend to adopt the delay time to combined with the artificial neural network for the automated detection of epileptic seizure.