Circadian variation of scalp EEG: a novel measure based on wavelet packet transform and differential entropy

We propose a novel entropy-based measure to quantify the circadian variations of scalp electroencephalogram (EEG) by analyzing waking epochs of nap opportunities under an ultradian sleep-wake cycle (USW) protocol. To compute this circadian measure for a nap opportunity, each waking epoch (~1 sec) is decomposed using wavelet packet transform and the relative energy for the desired frequency band (here, 10-12 Hz) is calculated. Then, in a bootstrapping procedure, a shape statistic (skewness or kurtosis) of the relative energy distribution, after each resampling, is computed. Finally, the probability density function of this statistic is estimated, and the corresponding differential entropy is considered as the circadian measure. This measure was evaluated using EEG recordings from 4 healthy subjects during a 72-h USW procedure. According to the results, the proposed measure showed a significant circadian variation both for individual and group data, with peak values occurring near the core body temperature minimum. The performance of the entropy-based measure was also compared with that of two other measures, namely mean energy logarithm and mean energy ratio, revealing the superiority of this measure.