The flicker-noise spectroscopy (FNS) approach is used to determine the dynamic characteristics of neuromagnetic responses by analyzing the magnetoencephalographic (MEG) signals recorded as the response of a group of control human subjects and a patient with photosensitive epilepsy (PSE) to equiluminant flickering stimuli of different color combinations. Parameters characterizing the analyzed stochastic biomedical signals for different frequency bands are identified. It is shown that the classification of the parameters of analyzed MEG responses with respect to different frequency bands makes it possible to separate the contribution of the chaotic component from the overall complex dynamics of the signals. It is demonstrated that the chaotic component can be adequately described by the anomalous diffusion approximation in the case of control subjects. On the other hand, the chaotic component for the patient is characterized by a large number of high-frequency resonances. This implies that healthy organisms can suppress the perturbations brought about by the flickering stimuli and reorganize themselves. The organisms affected by photosensitive epilepsy no longer have this ability. This result also gives a way to simulate the separate stages of the brain cortex activity in vivo. The examples illustrating the use of the "FNS device" for identifying even the slightest individual differences in the activity of human brains using their responses to external standard stimuli show a unique possibility to develop the "individual medicine" of the future.
Many studies into the dynamics of living organisms and their subsystems, including the analysis of electroencephalograms, electrocardiograms, and tremor velocities of Parkinsonian patients [1][2][3][4][5][6][7][8][9], demonstrate that the real time series V(t), where t is the time, for measured dynamic variables, which characterize the current condition of a living system, on some specific time intervals T usually contain chaotic components with a "long memory". In other words, there are correlation links on large intervals Т tot of the time series. The links are commonly determined by analyzing the power spectrum S P (f), where f is the frequency, when S P (f) is described by the flicker-noise function f -n with exponent n ~ 1 [6,7]. In some cases, special "memory functions" characterizing the long-range correlations are introduced [8,9]. The long-range links virtually indicate that the living organism, which is an open nonstationary system operating under variable external conditions, can quickly and efficiently reorganize itself, thus manifesting its property of biological adaptability [8]. Specifically, the analysis of heartbeat interval series shows that the mechanisms of neurohormonal cardiac regulation are brought into effect as dynamical rearrangements in the visual chaos of the studied time series. The decrease in chaoticity and the loss of long-range correlations in the measured biomedical signals may sometimes be associated with unfavorable changes in the organism, deviation of its functioning state from the normal state, and pathological changes in the organs [2][3][4][5].
As the real signals generated by living systems contain both chaotic and regular components [1,8,9], the above conceptual conclusions may not be directly used for evaluating the state of a specific organism and the effect of various factors such as medications and stimulation on its operation. In this case, it is necessary to separate the contribution of each component from the informative medical characteristics of the system before making any conclusions about the degree of loss in the correlation links. For example, stochastic quantifiers of a statistical memory were used to describe the phenomenological regularity accounting for the fundamental role of chaoticity and robustness in the functioning of living systems [8]. Based on the fundamental laws and concepts of memory functions formalism and FNS phenomenology, an original algorithm in which the effects of dynamic intermittency, nonstationarity, and characteristic frequencies in the original time series of a pathological tremor are separated out was proposed to evaluate the effectiveness and quality of different methods of treating Parkinson’s disease [9]. This separation procedure can be used to advance in solving the general problems of medical diagnosis by providing the basis for the standards of medical signals through relating the values of specific signal characteristics to the particular state of the organism [10]. It is obvious that the general analysis of such problems is complicated by the presence of individual features in each organism and the specificity of its response to various treatment techniques.
The individual features of a living organism manifest themselves primarily in the lowfrequency components of its biomedical signals, which account for the collection of characteristic and stimulus-initiated frequencies particular to each organism, as well as in the interferential contributions of these resonances. In this case, the low-frequency “envelopes” are always accompanied by high-frequency chaotic (“noise”) components the series of which is used to identify the informative correlation links individual to each organism. The state of the living organism exposed to external, including therapeutic, stimuli and the dynamics of its subsystems can be adequately evaluated only by sequential separation of the contributions of these components in the physiological time series for different frequency bands and introduction of the corresponding parameterization.
The phenomenological scheme for representing the information stored in various complex signals developed by Nicholis [11] provided a conceptual foundation for making some progress in the practical extraction of both chaotic and resonant components from medical time series. This scheme assumes that there is an infinite number of levels in the evolution hierarchy of the system under study and that there are some recurrent rules that generate information on a specific hierarchy level and compress it on a higher level. The general ideas of Nicholis’ scheme were used to develop flicker-noise spectroscopy (FNS) [12,13], the phenomenological framework in which the concept of the information contained in the signals generated by open dissipative systems is generalized. According to the basic idea of FNS, the correlation links existing in the sequences of different irregularities such as spikes and “jumps” in or
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