We describe nonlinear deterministic versus stochastic methodology, their applications to EEG research and the neurophysiological background underlying both approaches. Nonlinear methods are based on the concept of attractors in phase space. This concept on the one hand incorporates the idea of an autonomous (stationary) system, on the other hand implicates the investigation of a long time evolution. It is an unresolved problem in nonlinear EEG research that nonlinear methods per se give no feedback about the stationarity aspect. Hence, we introduce a combined strategy utilizing both stochastic and nonlinear deterministic methods. We propose, in a first step to segment the EEG time series into piecewise quasi-stationary epochs by means of nonparametric change point analysis. Subsequently, nonlinear measures can be estimated with higher confidence for the segmented epochs fulfilling the stationarity condition. Language: en

EEG analysis with nonlinear deterministic and stochastic methods: a combined strategy.

This paper presents a comparison of spectral analysis with period-amplitude analysis when applied to the quantification of narrowband electroencephalographic (EEG) activity. In particular, it examines their respective usefulness in quantifying on the average the electrographic content within the delta-frequency band of EEG epochs during human stage 4 sleep. It is shown that while the power spectrum efficiently quantifies the overall power trends in the EEG data, period-amplitude analysis seems to offer more resolution than the power spectrum in detecting electrographic details in amplitude and incidence within relatively narrow frequency bands. Examples are given of the sensitivity of spectral analysis ot both wave amplitude and incidence, and of the fact that--due to the inherent averaging process in the power spectrum generation--spectral analysis cannot differentiate between low-amplitude, high-incidence EEG activity and high-amplitude, low-incidence EEG activity, in contradistinction to period-amplitude analysis. It is also shown that although two EEG epochs may exhibit similar power spectrum plots, their corresponding period-amplitude plots may not be similar. It is emphasized that discrepancies may exist when comparing spectral to period-amplitude analysis due to differences in the definition of "frequency" in the two techniques.

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Spectral analysis vs. period-amplitude analysis of narrowband EEG activity: a comparison based on the sleep delta-frequency band.

Electroencephalograms (EEGs) were recorded during rest and during prayer in the laboratory from 6 adults aged 24 to 70 yr. belonging to the Protestant faith. The purpose was to discover whether the electrocortical rhythms during prayer are slower than they are during rest as has been reported to be the case in Transcendental Meditation. Findings did not show any evidence of EEG slowing in prayer. Indeed, the opposite result, namely, a speeding-up of the EEG, was observed in the majority of subjects. In one subject the shift from rest to prayer amounted to an average increase in frequency of 1.6 c/sec. Findings were discussed in relation to similar results which have been reported in highly experienced Yoga meditators and advanced Transcendental Meditators capable of deep meditative states. Confirmatory evidence from one subject who was a highly experienced Sufi meditator is also presented.

Brain electrical activity during prayer

EEGs were recorded in a group of 41 healthy children aged 5–17 yrs, under conditions where state of the organism was carefully controlled, For each child, durations of a sample of 760 EEG half wavelengths were measured and distributed into an interval histogram. A central-moments analysis revealed that the first four central moments of the distributions-which measure the central tendency, dispersion, skewness, and kurtosis of the interval histograms-were significantly correlated (p<.01) with age of the children. Multiple regression analysis yielded a statistically-significant multiple correlation coefficient (R) which was equal to 711. Successive recomputations of R using fewer than the four predictor predictor variable yielded an R of .704, when only the measures of dispersion, skewness. and kurtosis were employed.



The Predictive value of the multiple regression equation based on the three predictor variables was tested in an independent group of 42 children also aged 5-17 yrs. EEGs were recorded us in the previous sample, and the second, third, and fourth moments of their distributions of 760 EEG half wavelength were determined. When used in the previously-derived multiple regression equation, these moments yielded estimated ages which correlated significantly (.47) with the children's actual ages. Since the regression equation could reduce from chance the error of predicting age in the 5–17 yr old range by about 22%, it was concluded that the higher-order central moments of EEG interval histograms can be of use in charting the course of normal growth and development.

Interval histogram analysis of period of the electroencephalogram in relation to age during growth and development in normal children.

Reaction-time variability, periodicities in reaction-time distributions, and the EEG gating-signal hypothesis.

PARTH: PERIOD ANALYSIS OF THE ELECTROENCEPHALOGRAM WITH RECORDING OF INTERVAL HISTOGRAMS OF EEG HALF-WAVE DURATIONS

DEC PDP-8/I or /L (4K) [PAL-8]



Date Submitted: September 20, 1974.



Acronym: PARIH.



Machine Sensible Materials: Paper tape.



Documentation: Program description, operating manual, and annotated listing.



Authors: F. H. Sharp, G. W. Smith, W. W. Surwillo.



Submitted by: W. W. Surwillo.



Submitter's Affiliation: Department of Psychiatry and Behavioral Science, University of Louisville School of Medicine, 608 South Jackson Street, Louisville, Kentucky 40201.



PARIH determines the distribution of half-wave durations for specifiable portions of each of two simultaneously-inputed analog signals. Peaks and troughs in the signal define half-wave boundaries. Half-waves of less than a user-waves. Output is presented via a teletypewriter in the form of an interval histogram. The program operates on-line. Developed for EEG analysis, PARIH is suitable for similar analog signals.



Minimum Hardware: DEC PDP-8/I or /L with 4K core, teleypewriter, and DEC, AX08 laboratory peripheral.

Glenn W. Smith

Papers

Period analysis of the electroencephalogram with recording of interval histograms of EEG half-wave durations.