Some basic properties of autoregressive (AR) modeling and bispectral analysis are reviewed, and examples of their application in electroencephalography (EEG) research are provided. A second-order AR model was used to score cortical EEGs in order. In tests performed on five adult rats to distinguish between different vigilance states such a quiet-waking (QW), rapid-eye-movement (REM), and slow-wave sleep (SWS), SWS activity was correctly identified over 96% of the time, and a 95% agreement rate was achieved in recognizing the REM sleep stage. In a bispectral analysis of the rat EEG, third-order cumulant (TOC) sequences of 32 epochs belonging to the same vigilance state were estimated and then averaged. Preliminary results have shown that bispectra of hippocampal EEGs during REM Sleep exhibit significant quadratic phase couplings between frequencies in the 6-8-Hz range, associated with the theta rhythm.
Bispectra were computed to detect phase coupling in the cortical and hippocampal EEG of the rat during various vigilance states. For EEG's recorded from the hippocampus, significant phase coupling was obtained during REM sleep between the frequency components (6-8 Hz) associated with theta rhythm.
The paper discusses the use of nonlinear bispectral analysis in examining the hippocampal EEG collected at subfields of CA1 and the dentate gyrus during the vigilance state of REM sleep. The cross-bispectrum and its unique capabilities of detecting and quantifying quadratic nonlinear interactions occurring between these two hippocampal subfields are explained and demonstrated with simulation examples and EEG data. It was found in this study that quadratic nonlinear interactions exist between CA1 and the dentate gyrus in the 6-8 frequency band which dominates the theta (theta) rhythm observed in the hippocampal EEG during REM sleep. As a result, energy components around the frequency band of the second-order harmonics of theta rhythm are not totally spontaneous, but generated largely due to quadratic nonlinear interactions.
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