Non-linear analysis of EEG signals at various sleep stages

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Summary

Application of non-linear dynamics methods to the physiological sciences demonstrated that non-linear models are useful for understanding complex physiological phenomena such as abrupt transitions and chaotic behavior. Sleep stages and sustained fluctuations of autonomic functions such as temperature, blood pressure, electroencephalogram (EEG), etc., can be described as a chaotic process. The EEG signals are highly subjective and the information about the various states may appear at random in the time scale. Therefore, EEG signal parameters, extracted and analyzed using computers, are highly useful in diagnostics. The sleep data analysis is carried out using non-linear parameters: correlation dimension, fractal dimension, largest Lyapunov entropy, approximate entropy, Hurst exponent, phase space plot and recurrence plots. These non-linear parameters quantify the cortical function at different sleep stages and the results are tabulated.

Introduction

Non-linear dynamical analysis has emerged as a novel method for the study of complex systems in the past few decades. The non-linear analysis method is effectively applied to electroencephalogram (EEG) to study the dynamics of the complex underlying behavior [1]. The growth of this method as a tool for mental health evaluation mainly rests on the non-invasive nature of EEG. The approach is based on the principles of non-linear dynamics and deterministic chaos that involves the characterization of the system attractors with its invariant parameters. This method is far more superior to the traditional linear methods such as the Fourier transforms and power spectral analysis [2]. Yet, since the EEG signal is non-stationary and noisy, all such studies should be carried out with care and caution [3]. Analysis of sleep EEGs is a very important research branch of medicine, because of its clinical applications (such as diagnosis of schizophrenia) and in brain dynamics research.

Sleep is not a uniform state, but is characterized by a cyclic alternating pattern of non-rapid eye movement (REM) and REM sleep [4], [5], [6], [7], [8], [9]. Non-REM sleep encompasses the deeper stages of sleep (sleep stages 1 and 2, and slow wave sleep with sleep stages 3 and 4), whereas REM sleep is a highly activated state of the brain accompanied by dreaming. Sleep patterns in humans undergo a marked change from birth to old age.

In sleep 0 (awake) stage, the patient's eyes are open and the EEG is rapidly varying. The voltage is low and the “beta waves” are prominent. Eyes move very slowly, the EEG frequency will be 6–8 Hz and alpha waves are more predominant in the sleep 1 (drowsiness) stage. Sleep 2 stage is the light sleep state, where the eye movements stop and our brain waves become slower. Special waves ‘K-complexes’ and sleep spindles begin to appear. In this state, EEG amplitude is medium and EEG frequency is 4–7 Hz. In stage 3 (deep sleep), extremely slow brain waves called delta waves begin to appear, interspersed with smaller, faster waves. EEG signal will have the frequency 1–3 Hz and amplitude will be high. By stage 4 (deep sleep, slow wave sleep), the brain produces delta waves. It is very difficult to wake someone during stages 3 and 4, which together are called deep sleep. In stage 4, the amplitude of EEG will be high, but the frequency will be less than 2 Hz. The subject's eyes move rapidly along with the occasional muscular twitches in sleep 5 (REM) stage. Theta wave is more predominant in this sleep stage.

The importance of the biological time-series analysis, which exhibits typically complex dynamics, has long been recognized in the area of non-linear analysis. Several features of these approaches have been proposed to detect the hidden important dynamical properties of the physiological phenomenon. The analysis of these biological signals is complicated due to its highly irregular and non-stationary property. The non-linear dynamical techniques are based on the concept of chaos and it has been applied to many areas including the areas of medicine and biology. The theory of chaos has been used to detect some cardiac arrhythmia such as ventricular fibrillation [10]. Efforts have been made in determining non-linear parameters like correlation dimension for pathological signals and it has been shown that they are useful indicators of pathologies. Non-linear dynamics theory opens new window for understanding behavior of EEG. EEG models were proposed by Freeman [11] for neocortical dynamics. The technique has been extended here to identify the abnormalities of different types. In analysis of EEG data, different chaotic measures such as correlation dimension, Lyapunov exponent and entropy are used in recent literature [12], [13], [14], [15], [16], [17].

Baumgaurt-Schmitt et al. have used neural network to classify the various sleep stages by extracting the features from the genetic algorithms [18]. Recently, the polysomnography of a healthy male subject was analyzed by evaluating the correlation dimensions. The correlation dimensions decreased from the ‘awake’ stage to sleep stages 1–3 and increased during rapid eye movement sleep. In each sleep cycle, the correlation dimensions decrease for slow wave sleep, and increase for REM sleep [19], [20]. Fell et al. have calculated the first Lyapunov exponents (L1) for different sleep EEG signal in 15 healthy subjects corresponding to the sleep stages 1–4 and REM. And they found statistically significant differences between the values of L1 for different sleep stages [21]. Fell et al. have studied the sleep stages using the spectral analysis and non-linear techniques [22], [23]. They concluded that non-linear measures yield additional information, which improves the ability to discriminate sleep stages. Recently, Dingli et al. have shown the spectral analysis technique for the detection of cortical activity changes in sleep apnoea subjects. The most consistent significant change is the decrease in theta power, during NREM sleep is either associated with an increase in high frequencies (alpha and sigma) or delta increase [24]. In this work, we study the six different types of sleep signals using the non-linear parameters, namely correlation dimension (CD), Hurst exponent (H), approximate entropy (ApEn), largest Lyapunov entropy (LLE), fractal dimension (FD), phase space plot and recurrence plots (RP).

Section snippets

Subjects

The EEG data for analysis were obtained from the Sleep-EDF Database available from the PhysioBank, a data resource. The recordings were obtained from Caucasian males and females (21–35 years old) without any medication. The recordings were taken for 24 h from eight subjects. Sleep EEG for 80 h is extracted from the recordings and sampled at 100 Hz. The sleep stages are coded according to Rechtschaffen and Kales based on Fpz-Cz/Pz-Oz EEG [25]. In this work, the maximum available samples for

Results

The ApEn, CD, LLE, FD and H have higher value for the sleep 0 (awake) state due to the highly active cortex and desynchronized EEG signals. In this state, the EEG signal becomes highly random. In sleep 1–4 states, this value falls gradually due to the reduction in the variability of EEG signals and the cortex becomes more inactive. In sleep 4 state, the ApEn will be lowest due to the very low variation in the EEG signals. The sleep 5 state is the REM state. In this state, the variation is

Discussion

The cortex becomes more inactive as the person goes through from one sleep stage to the next stage, until sleep 4 state. Hence, less number of neurons will be available for processing the information and as a result the entropy, CD, LLE and H fall. But in sleep 5 (REM) state, the brain is very active in this state, almost to the level at which it is when a person is awake. Blood flow to the brain is also increased during this stage of sleep. As a result, the cortex becomes more active and more

Conclusion

In this work, we have analyzed the cortical functioning at different sleep stages using the non-linear parameters: FD, CD, λmax, ApEn and Hurst exponent. These values decrease indicating the reduction in the disorder from sleep states 0 to 4, due to the lesser number of available neurons in each state for processing. But in sleep 5 state, these values increase due to the highly active cortex. The spread of the phase space plot and the recurrence plot are unique for each sleep state. In this

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