# Use Electroencephalogram Entropy as an Indicator to Detect Stress-Induced Sleep Alteration
## 1 Introduction  
Electroencephalography (EEG) corresponds to several vigilance states of the brain. These states, such as wakefulness and sleep, are demonstrated by distinct brain waves [1, 2]. Nevertheless, stress influences brain rhythms in both sleep and wakefulness in humans and rodents [3, 4, 5, 6]. For instance, theta waves are predominant during an anxious condition in rodents [7, 8, 9, 10, 11]. Moreover, the literature, also, demonstrates that theta waves are dominant during learning and navigation in rodents [1, 10, 12]. In comparison to wakefulness, the function of electrical activities during sleep is much less known. There are two distinct states of sleep, rapid eye movement (REM) sleep and non-rapid-eye movement (NREM) sleep, and each sleep state has a unique EEG pattern. The delta powers of EEGs during NREM sleep are positively correlated with the level of sleep depth, implying the sleep quality. Stages 3 and 4 of NREM sleep generate large slow waves within the delta frequency band (0.5-4 Hz). Theta waves can be observed during REM sleep in rodents [1, 2, 10, 13]. Diagnostic criteria for acute stress disorder (ASD) or post-traumatic stress disorder (PTSD) include hyperarousal conditions, such as insomnia or hypervigilance [14]. Stress is frequently associated with sleep disturbance (approximate 78%) in insomnia patients [15]. The studies for measuring stress-related sleep problem mainly count on the parametersof polysomnography, e.g., the duration and transitions between different states [5] and the powers of different frequency spectra [4,16,17]. EEG is a composition of distinct brain waves, which contain certain basic features, including amplitude, frequency, and oscillation phases. Some researchers link these features to potential physiological meanings. These features might be correlated and associated with physiological functions. For example, the amplitudes extracted from frequencies between 0.5 and 4 Hz are greater during NREM sleep, during which the amplitudes are positively correlated with sleep intensity [18,19]. The coupling of oscillation phases and frequencies in the hippocampus are elevated when rodents learn a new behavioral task [20,21]. These EEG features can also, solely, correlate with a physiological meaning. For example, instantaneous running speed is positively correlated with the frequencies of theta [11,22] and gamma waves in rats [23,24]. Therefore, the aim of the present study is investigating the features of EEGs during sleep after exposure to an acute stressor and revealing the stressor's potential effects on EEG features. Measuring the spectrum of a period of EEGs, or counting densities of a unique waveform, is a regular method to study the alterations of EEGs [4,5,16,17]. However, EEG has a unique property: EEG amplitude decreases as the frequency increases. The inverse relationship between amplitude and frequency is due to the slower oscillation of EEGs, which involves larger numbers of neurons and generates stronger brain waves [1]. In other words, the distributions between the amplitude and frequency of EEG are non-linear [1]. Moreover, the features of EEGs, e.g., amplitude, frequency, and phase, are, also, non-linear or circular. For instance, the amplitude of EEGs as a function of time can be regard as a sine wave but not a straight line. Therefore, it is important to develop a method to describe these non-linear changes of EEGs, when animals come across a certain stimulation. In the present study, we focus on stress-induced EEG alterations. The Shannon entropy (information theory) can measure the uncertainty, by calculating the probability of a variable appearing [25]. It has the potential to detect non-linear changes of EEGs, since the Shannon entropy is related to probabilities and distributions but is not affected by the distribution of data. If the uncertainty level is high, which means the probability of appearance is even, the entropy would be high.