Surrogate-data testing has recently been proposed as one way to detect the presence of nonlinearity and low-dimensional chaos in experimental time series. Such testing involves estimating correlation dimension for both the original data and surrogate data from which nonlinearity has been removed. We applied such testing to the same resting, eyes-closed, and eyes-open electroencephalogram (EEG) data set that was originally analyzed using dimension estimation applied only to the original data (Pritchard & Duke, 1992). Two kinds of surrogate-data sets had higher estimated dimension and poorer saturation. This indicates that the normal resting human EEG is nonlinear and therefore not a linear-stochastic system. Because nearly complete saturation at some loci was not differently affected by the surrogate-data procedures, our results also indicate that the normal resting human EEG is high dimensional and does not represent low-dimensional chaos.
We demonstrate by using simulations that spatial embedding of single-variable time series data does not reliably reconstruct state-space dynamics. Instead, correlation dimension estimated from spatially embedded data is largely a measure of linear cross-correlation in the data set. For actual electroencephalographic (EEG) data, we demonstrate a high negative correlation between spatial correlation dimension and the average amount of lag-zero cross-correlation between "nearest-neighbor" embedding channels (the greater the cross-correlation, the lower the dimension). We also show that the essential results obtained from spatially embedding EEG data are also obtained when one spatially embeds across a set of highly cross-correlated stochastic (second-order autoregressive) processes. Although, with appropriate surrogate data, correlation dimension estimated from spatially embedded data detects nonlinearity, its use is not recommended because correlation dimension estimated from temporally embedded data both reconstructs state-space dynamics and, with appropriate surrogate data, detects nonlinearity as well.
The Gaussian surrogate-date procedure was applied to the measurement of the effect of cigarette smoking on the dimensional complexity of normal, resting EEG. Evidence of significant nonlinearity in the EEG was obtained, replicating previous results. However, unlike EEG dimensional complexity, EEG nonlinearity (difference between original and surrogate data) was not affected by smoking. This indicates that, under resting conditions, smoking/nicotine may have a modulating effect on input from the reticular activating system, with such input having a global, linearizing effect on cortical dynamics. Nonlinear dynamics resulting from intracortical processes appear not to be affected.
Electroencephalogram (EEG) and heart rate (HR) were recorded while individuals performed visual and auditory go/no-go reaction time (RT) tasks. Overnight-abstaining smokers smoked two types of cigarettes in a single morning session. The first type was smoked once and had a nicotine yield of 0.05 mg. Two cigarettes of the second type (1.1 mg) were smoked. Four recordings were made: presmoking, postsmoking 0.05 mg, and postsmoking each 1.1 mg. HR was increased only by the first 1.1-mg cigarette. Smoking both the 1.1-mg cigarettes decreased RT. Smoking the first 1.1-mg cigarette increased EEG power in the beta2 band. A flexible effect of smoking the first 1.1-mg cigarette on EEG dimensional complexity (DCx) was obtained at locus Cz. Specifically, DCx was (a) raised when the presmoking level was low, (b) not affected when the presmoking level was intermediate, and (c) lowered when the presmoking level was high. Surrogate-data testing indicated the presence of nonlinearity in the EEG data that was not affected by smoking. Decreased RT was associated with increased DCx in the visual task only.
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