Population Analysis of Kalman-Filtered Permutation Entropy of the Electroencephalogram
Department of Anesthesiology, Leiden University Medical Center, Leiden, The Netherlands
Objectives: General anesthetics produce dose-dependent effects on the electroencephalogram (EEG). A novel EEG parameter is the permutation entropy (PE). An important advantage is its robustness under eye blinks. EEG data fits often show correlated residuals, which might lead to false statistical conclusions. The main objective was to construct a pharmacokinetic-pharmacodynamic (PK-PD) model with a Kalman filter. Another objective was to assess whether covariate sex is a significant one.
Methods: Fourteen EEG data sets (7 male and 7 females) were analyzed, using a population PK-PD model. Two versions of the Kalman filter were constructed. Version A assumes that colored noise is present at the PD model output; version B assumes that noise is present at the level of anesthetic concentration. The best model was used to generate artificial data, which were analyzed by the same model, and the model without Kalman filter.
Results: Analysis of the PE data with Kalman filter A displayed a large value of the steepness parameter of the PD model. In contrast, analysis with Kalman filter B showed a relatively low value, so that the model output responds smoothly to changes in concentration. Gender was no statistically significant covariate. Estimated parameter values from simulated data were similar if the Kalman filter was present or absent, except for the inter-individual variabilities. Without the Kalman filter, these were overestimated with a factor of 10-30.
Conclusions: While the PE is insensitive to eye blinks, it is sensitive to high frequency components present in the EEG just before loss of consciousness. Analysis of EEG data with a Kalman filter accentuated or filtered out this phenomenon, depending on the postulated location of process noise. The model parameter values were not dependent on the gender of the patients. The simulation study showed that, if Kalman filtering is not applied, inter-individual variability may be overestimated; variability that is actually intra-individual process noise.
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