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

Abstract

Background: 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.

Methods: 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 ( approximately 1.0) when the signal has predominantly high frequencies and low ( approximately 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 microV). We also applied the CPEI to two small pilot EEG data sets from patients receiving sevoflurane (n=21) or propofol (n=9) anaesthesia.

Results: 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].

Conclusions: PE of the EEG shows promise as a simple measure of GABAergic anaesthetic drug effect.