O.Yu. Mayorov
V.N. Fenchenko |
CHAOS PARAMETERS FOR EEG RESEARCH - A NEW APPROACH
|
Kharkiv Medical Academy of Postgraduate Education,
Kharkiv, Ukraine
Institute of Medical Informatics and Telemedicine LTD, Kharkiv, Ukraine
Institute of Children and Adolescents Health Protection AMSci, Kharkiv,
Ukraine
Physicotechnical Institute of Low Temperatures attached to NASci of
Ukraine, Kharkiv, Ukraine; E-mail: Institute-MiT@ukr.net |
The conventional EEG spectral analysis method is not believed to possess an
adequate information value and has practically exhausted its potentialities.
We propose herein that a new approach to the EEG signal analysis should be used,
which combines the conventional methods of correlation and spectral analyses
and new techniques. Detection of cerebral formations with common organization
features. The above mentioned approach allows to detect at the first stage
cortical and subcortical brain structures temporarily involved in a particular
functional system (according to P.K. Anokhin) for the purpose to realize behavior
acts, accomplish “blockade of influences” of other brain systems,
detect and quantify at the third stage the “contribution” of separately
chosen structures in the system activity and, thus, outline the real architecture
of the functional system. Having chosen from a multitude of signals coming from
different leads the ones being most “similar” to signal y(t) with
similar organization features and real “physical” linkage, enables
us to single out cortical and subcortical structures involved in integration
with the investigated brain region. Detection of “main” system signal.
Upon defining architecture of the functional system under study, the “main”
signal of this system should be singled out. The use can be made in this case
of the known Karhunen-Loeve method. We apply the Karhunen-Loeve expansion to
signals from the leads only involved in the functional system, which is under
investigation, and, therefore, all such signals are “like”. We proceed
from the assumption that a singled out “main” signal of the functional
system being studied is described by a certain dynamic system. Selection of
delay value To be successful, the process of reconstruction has to correlate
with the correct choice of the delay value. However, the methods that are commonly
applied (autocorrelation method, method of mutual minimum information) do not
invariably produce acceptable results. That is why we have developed the new
method, basing on estimation of the “form” of the attractor to be
reconstructed. The displacement value is chosen so that the reconstructed attractor
dimensions can be as close as possible in all axes. The distinctive feature
of such method is that the displacement value depends on the embedding dimension
involved and, as shown by the results of numerous experiments, this enables
to improve materially the quality of reconstruction of EEG attractors. Determination
of neurodynamic system chaos parameters. At the next stage – executing
reconstruction of attractor structures, to estimate its dimension, to calculate
a Kolmogorov-Sinai or correlation entropy of the process, to evaluate the maximal
Lyapunov exponent, modeling dynamics of cerebral system. Conclusion. It appears
from the results obtained that our method of restoring the attractor basing
on the “main” signal of the neurodynamic system formed by a group
of cerebral structures temporarily involved in the integrative activity being
studied provides much better results than all earlier methods of restoring chaos
parameters basing on a single-lead signal. The effects of increasing the sampling
volume on account of the use of several stationary sites of EEG signal recording
promote the accuracy and reliability of the results of calculations that were
brought to analysis in our report. The model we suggest allows to identify and
quantify with a higher accuracy degree the influence exercised by external
and internal factors on the character of appropriate chaos parameters relating
to the brain neurodynamic system under study. The offered approach has been
realized in the system for computer EEG “NeuroResearcher®-Chaos’2005-2007”.
It was used for EEG analysis in the group of patients with schizophrenia and
in the control group of healthy volunteers - pilots and has shown good results.
