Unfolding dimension and the search for functional markers in the human electroencephalogram

Abstract

A biparametric approach to dimensional analysis in terms of a so-called ''unfolding dimension'' is introduced to explore the extent to which the human EEG can be described by stable features characteristic of an individual despite the well-known problems of intraindividual variability. Our analysis comprises an EEG data set recorded from healthy individuals over a time span of 5 years. The outcome is shown to be comparable to advanced linear methods of spectral analysis with regard to intraindividual specificity and stability over time. Such linear methods have not yet proven to be specific to the EEG of different brain states. Thus we have also investigated the specificity of our biparametric approach by comparing the mental states schizophrenic psychosis and remission, i.e., illness versus full recovery. A difference between EEG in psychosis and remission became apparent within recordings taken at rest with eyes closed and no stimulated or requested mental activity. Hence our approach distinguishes these functional brain states even in the absence of an active or intentional stimulus. This sheds a different light upon theories of schizophrenia as an information-processing disturbance of the brain.

F-Ratio Test and Hypothesis Weighting: A Methodology to Optimize Feature Vector Size

“…This result is in agreement with findings from an earlier study [2] and with previous results from our sample [18, 19]. The δ power seems to be the best spectral measure because it appears in two combinations.…”

Intraindividual Specificity and Stability of Human EEG: Comparing a Linear vs a Nonlinear Approach

“…Linear analysis was carried out according to the similarity approach [1,5] and nonlinear analysis according to the unfolding dimension approach [3,4], both summarized below. Four artifact-free EEG epochs were taken into account (from up to nine 20second epochs per channel and recording day).…”

“…In this regard, we have chosen to compare and contrast the so-called si-milarity approach [1,2] with the nonlinear unfolding dimension approach proposed recently [3,4]. Some progress concerning the stable intraindividual specificity of EEG time series has already been made by advanced linear methods on healthy individuals between the ages of circa 25-35 years.…”

“…This biparametric representation of dynamical analysis applied to human EEG has been shown to: (1) successfully discriminate so-called surrogate data [7,8] from raw EEG in cases where traditional dimensional analysis lacks this capability, and (2) indicate some evidence that certain human EEG functional states are both intraindividually specific and stable over time [4]. These observations were not visible from the correlation dimension by itself.…”

“…To become acceptable for the (b0-m*) assessment, no time series yielding two successive, not well-resolved dimension estimates in the range m = 9 to 12 was accepted. Segments failing this requirement were excluded from further analysis [4]. To be in accordance with the linear treatment, the average of b0, m* and of four segments entered the statistical analysis.…”