Does the EEG during isoflurane/alfentanil anesthesia differ from linear random data?

Bispectral analysis of the electroencephalogram (EEG) has been used to monitor depth of anesthesia. In the majority of publications this has been done using the so called Bispectral (BIS) Index. The exact relation of this index to bispectral quantities like the bispectrum and its normalized version the bicoherence has not yet been published. In case the EEG is a linear random process the bicoherence is trivial. It is a mere constant independent of the EEG frequency. If the signal is a linear Gaussian random process this constant is zero. In this case both the bispectrum and bicoherence are zero. The aim of this study was to determine the proportion of EEG epochs with non-trivial bicoherence during anesthesia with isoflurane/nitrous oxide.

We reanalyzed 26.4 hr of EEG signal recorded in 8 patients during anesthesia for general abdominal surgery which were stored in digitized form on CD-Rom. The test developed by Hinich for Gaussianity and linearity was applied to these data. The test was validated with various kinds of surrogate data; especially the phase randomized (pr) EEG, synthetic Gaussian random data and the z-component of the Lorenz attractor and its pr version.

The proportion of epochs for which a non-trivial bicoherence was detected by the test was as follows: Lorenz data 95%, pr Lorenz data 5%, synthetic Gaussian data 13.8%, pr EEG 5.4%, original EEG 6.2%.

As expected the test procedure correctly identified for the Lorenz data for 95% of all epochs a non-trivial bicoherence. For the original EEG data we could not find a significant greater percentage of epochs with non-trivial bicoherence than for the pr data and the synthetic Gaussian data. We conclude that the EEG during anesthesia with isoflurane/alfentanil appears to be largely a linear random process.