Zwanzig–Mori’s projection technique
S.A. Demin, O.Yu. Panischev, A.V. Yatsenko, R.M. Yulmetyev
Here we develop the pseudoparticle method for the description of complex systems on the basis of Zwanzig-Mori's projective formalism for discrete time correlation memory functions. The analysis of neuromagnetic responses of human cerebral cortex generated from a group of healthy people, and from a patient with photosensitive epilepsy is performed.
We assume the dynamics of the registered physiological parameter as a coordinate of the pseudoparticle with the unit mass, moving in one-dimensional space. A set of values characterizing a pseudoparticle motion, such as its velocity, acceleration, kinetic energy, energetic current is introduced by the finite differences. By Zwanzig-Mori's projection technique, we derive the set of correlation functions and information measures of statistical memory, kinetic and relaxation parameters which are directly defined by the experimental time series of live systems.
In recent authors' papers it is shown that the greatest differences in reaction to the flickering stimuli between the group of healthy people and the patient with photosensitive epilepsy are observed in the neighborhood of the 10th sensor, located in the frontal region (the MEG registration is done by 61 sensors). For that matter we analyze the neuromagnetic responses, registered from this sensor.
The results, received for a dynamics of values, describe a pseudoparticle motion. They reflect the essential differences in cerebral cortex signals of the healthy people and the patient, such as the significant stratification of phase portraits, the critical changes in statistical memory effects and in velocity of relaxation processes. The abnormal behavior of brain rhythms (spontaneous brain electric activity) is revealed in patient's MEG signals.
We have discovered the original protective mechanism which blocks the abnormal neural collective activity. This activity observed at photosensitive epilepsy is a response to external visual stimuli. At this disease the influence of this mechanism is depressed, that is reflected by occurrence of a high-frequency component in dynamics of the brain signals.
The opportunity to derive an adequate estimation for the organism conditions by analyzing the biomedical signals is a serious problem existing in a modern medical physics. The pseudoparticle description of neuromagnetic responses caused by influence of flickering light stimuli, allows to demonstrate the differences in dynamics of brain signals from the patient and healthy people, and also to quantitatively diagnose the manifestations of photosensitive epilepsy.
Thus the findings demonstrate the principal opportunities for reflection of even small individual differences in the live systems signals at the external influences and allow to characterize the pseudoparticle description as one of tools of the future «individual medicine».