Complexity Analysis Of EEG Signals

Electroencephalogram (EEG) has very fine time resolution. It's a noninvasive approach and can directly reflect brain action. It's very important for both science research and clinical application by now. Complexity measures provide objective and quantificational descriptors for the complex extent of a time series. Scientists can get new knowledge or new understanding about brain natures from analyzing EEG signals with complexity measures. From 1980's, this field becomes an important interdisciplinary subject. In this paper we will expatiate on five problems of the subject.Some conventional complexity algorithms have coarse graining procedure when applied to real time series. Researches on logistic mapping series and some real EEG signals show that in some cases, over coarse graining may distort the dynamics of series analyzed and lead to spurious results. Our lab once presented a new complexity algorithm - CO complexity(陈芳,顾凡及, 徐京华等 ,1998), which needn't over coarse graining procedure. In this paper, we improved CO complexity and analyzed EEG signals recorded from normal subjects during rest with eyes closed (REC) and rest with eyes opened (REO) with CO complexity and approximate entropy (ApEn), a wide accepted complexity algorithm which needn't over coarse graining procedure either, for compare. The CO complexity value of EEG signals shows a similar trend as approximate entropy. Its low computation cost makes it prior to approximate entropy.We extended CO complexity to two-dimensional cases. Now in the field of 2-dimensional complexity there's not so many progress as in one-dimensional series. So 2-dimensional CO complexity may be an important new method of the field. A series of images with different random degrees were constructed and their 2-dimensional CO complexity values were calculated. The 2-dimensional CO complexity value increases when random degree becoming larger, which infers that 2-dimensional CO complexity is a suitable randomness finding complexity (Rapp PE and Schmah TI (1996), Rapp PE and Schmah TI (2000)) for analysis of 2D structures. For the first time, 2-dimensional CO complexity was applied to analyzing orientation maps in the primary visual cortex of cat revealed by optical imaging method. This research shows that 2-dimensional CO complexity will be good in biological data analysis.Now there's a debate of whether totally random systems are complex. We consider that there are different levels or orders of complexity; a different order is concerned with a different aspect of complexity. Higher order complexity, a new method to consider the different levels of complexity, was presented. From the research in some quasi-stationary time series it's revealed that the first order complexity is suggested to be a measure of randomness of the original time series, while the second order complexity is a measure of its degree of nonstationarity. The different order is concerned with different aspect of complexity. For the first time, we applied higher order complexity to analyzing EEG signals. On some channels, the 2nd order ApEn values of EEG signals recorded from 8 normal subjects when doing simple and complex mental arithmetic are significantly higher than those from subjects when resting with eyes closed.We present a method to consider the influence of analysis scale. We call the approach macroscopic complexity. The affection of different observation scales on logistic mapping series...