Permutation entropy of the electroencephalogram: a measure of anaesthetic drug effect

It would be useful to have an open-source electroencephalographic (EEG) index of gamma-amino-butyric acid (GABA)-ergic anaesthetic drug effect that is resistant to eye-blink artifact, responds rapidly to changes in EEG pattern, and can be linked to underlying neurophysiological and neuropharmacological mechanisms that control the conscious state. The EEG waveform can be described as a sequence of ordinal patterns. The permutation entropy (PE) describes the relative occurrence of each of these patterns. It is high (approximate to 1.0) when the signal has predominantly high frequencies and low (approximate to 0.4) when the signal consists of only low frequencies. The response of the PE to various computer-generated EEG-like waveforms was assessed. A composite PE index (CPEI) was developed, which was the sum of two simple PEs and included a small measurement-noise threshold (0.5 mu V). We also applied the CPEI to two small pilot EEG data sets from patients receiving sevoflurane (n=21) or propofol (n=9) anaesthesia. With minimal pre-processing or artifact rejection, the CPEI reliably tracked the anaesthetic-related EEG changes, namely loss of high frequencies, spindle-like waves, and delta waves. Using NONMEM, it was possible to construct adequate pharmacokinetic-pharmacodynamic models from the data. The CPEI was comparable with models derived using the bispectral index [BIS R-2=0.88 (0.08) vs CPEI R-2=0.91 (0.06) for the propofol data] and M-entropy indices [M-entropy R-2=0.91 (0.06) vs CPEI R-2=0.87 (0.09) for the sevoflurane data]. PE of the EEG shows promise as a simple measure of GABAergic anaesthetic drug effect.