Anesth Analg 2006;102:966-967
© 2006 International Anesthesia Research Society
doi: 10.1213/01.ANE.0000190855.82449.E2
LETTER TO THE EDITOR
EEG During Anesthesia Is Not a Linear Random Process
Christian Jeleazcov, MD,
Jörg Fechner, MD, and
Helmut Schwilden, MD, PhD
Klinik für Anästhesiologie der Friedrich-Alexander, Universität Erlangen-Nürnberg, Erlangen, Germany, christian.jeleazcov{at}kfa.imed.uni-erlangen.de
In Response:
As Hagihira et al. mention, before calculating the bispectrum and its normalized version, bicoherence, the investigated time series must be proven to be stationary (i.e., its statistical properties must be time-invariant). Because of this important constraint in spectral and bispectral analysis, every artifact-free electroencephalogram (EEG) epoch (8 s, 210 data points) in our studies was first submitted to a commonly used test of stationary status, the so called "run-test." The estimation of the bispectrum and bicoherence was then performed only for artifact-free EEG epochs statistically proved to be stationary (1–3). In contrast, Hagihira et al. estimated the bispectrum and bicoherence from artifact-free EEG epochs (2 s, 28 data points) by averaging 360 values over time periods (i.e., 
3 min) that were assumed to be stationary because of a SEF90 of 11 ± 0.18 in 20 patients (4) and 12 ± 1.9 in 30 patients (5) during general anesthesia combined with epidural anesthesia. As this parameter of the EEG power spectrum by itself need to be computed from stationary EEG epochs, it can not serve as surrogate for stationary status in the same time series. Like the power spectrum, the bispectrum and the bicoherence are determined from EEG epochs of finite length. The missing EEG information before and after the EEG epoch translates into a statistical error of estimation of the power spectrum and all higher order spectra, such as the bispectrum. The error of estimation of a single frequency bin of the power spectrum is, for instance, approximately 100% of its value (6). As the bicoherence depends on the bispectrum and the power spectrum, its error of estimation is much larger than 100%. If one would like to determine whether a given EEG time series is a result of a linear random process, one has to test the hypothesis that the bicoherence is a constant (7). In our investigations, this hypothesis could be rejected with the Hinich test in only 6.2%, 9.1%, and 10.62% of the investigated EEG epochs during general anesthesia with isoflurane/alfentanil (3), Isoflurane/N2O (2) and propofol/alfentanil (1), respectively. In their investigations (4,5,8), Hagihira et al. made no statistical estimation of the frequency of nontrivial bicoherence as an indicator of nonlinearity in the analyzed EEG. From a practical point of view, stationary EEG data segments of at least 3 min, as they have been proposed for the accurate computation of one bicoherence value (4), may be difficult to obtain, especially during intensive electrosurgical cautery after skin incision or before skin suture. If one takes into consideration, that the transition between brain states as a result of anesthesia seems to lie within milliseconds (9), than the applicability of the bicoherence as an indicator of the consciousness (5) or analgesic state (8) of a patient during general anesthesia seems to be limited. With respect to these important methodological aspects, the remarks from Hagihira et al. do not change the conclusions from our investigations: 1) the EEG during anesthesia can be considered in more than 90% as a linear random process; and 2) the additional benefit of bispectral analysis for monitoring clinical anesthesia remains to be evaluated.
References
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