The use of fuzzy integrals and bispectral analysis of the electroencephalogram to predict movement under anesthesia

The objective of this study was to design and evaluate a methodology for estimating the depth of anesthesia in a canine model that integrates electroencephalogram (EEG)-derived autoregressive (AR) parameters, hemodynamic parameters, and the alveolar anesthetic concentration. Using a parametric approach, two separate AR models of order ten were derived for the EEG, one from the third-order cumulant sequence and the other from the autocorrelation lags of the EEG. Since the anesthetic dose versus depth of anesthesia curve is highly nonlinear, a neural network (NN) was chosen as the basic estimator and a multiple NN approach was conceived which took hemodynamic parameters, EEG derived parameters, and anesthetic concentration as input feature vectors. Since the estimation of the depth of anesthesia involves cognitive as well as statistical uncertainties, a fuzzy integral was used to integrate the individual estimates of the various networks and to arrive at the final estimate of the depth of anesthesia. Data from 11 experiments were used to train the NN's which were then tested on nine other experiments. The fuzzy integral of the individual NN estimates (when tested on 43 feature vectors from seven of the nine test experiments) classified 40 (93%) of them correctly, offering a substantial improvement over the individual NN estimates.