Professor, Dr.Med. V.A. Karpin
Research assistant Yu.V. Bashkatova
Professor, Dr.Med. L.V. Kovalenko
Ph.D. S.Yu. Filatova
Surgut State University, Surgut

Keywords: exercise, chaos, self-organization, quasi-attractor, cardiovascular system.

Introduction. The problem of assessment of the state of body functional systems (BFS) and their adaptive reserves for different kinds of stimulation [1-2], including physical activities, is relevant for physiology of sport, human ecology and general physiology. There is a need to introduce into the biomedical practice of modern system methods for studying the functional state of the cardiovascular system (CVS) and the autonomic nervous system (ANS) of the human body [3].

Under the new methods of the theory of chaos and self-organization, it has become possible to study the body functional reserves by means of analysis and synthesis of the parameters of BFS, detection of morphofunctional characteristics of the body under rest conditions and after loading tests [2-7]. Such information can be used to estimate the quality of human life in the North and predict its development in adulthood. Moreover, this approach enables us to objectively estimate the dynamics of reserve capacities of the body and their predictive value. It is past time to develop and use new tools based on the methods of multi-dimensional phase spaces for determination of adaptive and functional reserves of the body and early diagnostics of different pathological conditions and functional diseases, which determine the relevance of this research.

The purpose of the study was to estimate the state of the CVS in the groups of trained and untrained students with regard to stochastics and chaos theory.

Materials and methods. The 1-3-year students of SFEI HVA "Surgut State University of KhMAR-Yugra", living in the district for at least 5 years, were the object of the current study. Depending on the degree of their physical activity, the testees were divided into 2 groups 30 people each. The first group included the students of the basic health group involved in physical training under the university curriculum. The second group consisted of the SurSU students, who professionally trained in team sports (basketball and volleyball).

The students were examined using a pulse-oximeter (ELOKS-01, Samara). We registered heart rate (HR), Baevsky’s stress index and power spectrum components of HRV for 5 minutes in a sitting position using a special photo-optical sensor. Upon performing normalized dynamic exercise (30 squats) the registration was carried out for 5 more minutes.

The data were statistically processed using the software "Statistiсa 6.1". The compliance of a type of distribution of the obtained data with the normality of data distribution was assessed based on the Shapiro-Wilk test. Depending on the type of distribution, the follow-up studies were carried out using the methods of parametric and nonparametric statistics (Student's t-test, Wilcoxon test, Mann-Whitney test). When testing statistical hypotheses, the critical level of significance was deemed equal to 0.05.

Results and discussion. The consolidated quantitative characteristics of the results of the changes in the spectral indices of the cardiovascular system are presented in Table 1.

It has been established that the trained and untrained students have totally no statistically significant differences in such parameters as VLF, LF, HF, Total, LF norm, HF norm and LF/HF before and after exercise (p>0.05), which formed a 7-dimensional phase space of states of the entire human body state vector (HBSV) х = х(t). When comparing the spectral indices of regulation of the CVS on the part of the ANS in the trained and untrained students before exercise, we determined the statistically significant differences of the VLF (p= 0.0020), HF (p= 0.0333) and Total (p= 0.0110) parameters by the Kruskal-Wallis test (p<0.05).

Table 1. Spectral indices of regulation of cardiovascular system on part of autonomic nervous system

Note: n – number of testees, LF, ms² – spectrum power of low-frequency component of variability; HF, ms² – spectrum power of high-frequency component of variability; Total power, ms² – total power spectrum; VLF, % – spectrum power of very low-frequency component of variability; p – significance of differences by Wilcoxon test (p>0.05)

The students not engaged in physical training had decreased indices of LFnorm, increased HFnorm and decreased LF/HF. An opposite situation was observed with the trained testees: an increase in LF norm (from 61 to 61.7 c.u.), a decrease in Hfnorm (from 39 to 8.3 c.u.) and an increase in LF/HF (from 1.9 to 2.3 c.u.).

Basing on the methods of system analysis and synthesis, we studied the dynamics of behavior of the parameters of quasi-attractors in the 7-dimensional phase space of the spectral indices of the CVS and the ANS in the trained and untrained students before and after dynamic exercise (Table 2).

Table 2. Parameters of quasi-attractors in 7-dimensional phase space of spectral indices of cardiovascular system

As follows from Table 2, the volume of the 7-dimensional block V_G  in the untrained students, which limited QA, increased by 49 times after exercise, and in the trained students it decreased by 2.6 times. The changes in the parameters of quasi-attractors of HBSV in the 7-dimensional phase space of states were more significant than the results of statistical processing of the initial data.

The next phase of the study is dedicated to calculation of the matrices of interattractor distances Z_ij in the trained and untrained students (Table 3).

Table 3. Matrix of comparison of distances (Z_ij, c.u.) between chaotic centers of quasi-attractors of spectral indices of cardiovascular system in 7-dimensional phase space

Note: m – span of phase space of states, ∑ – total of interattractor distances (c.u.).

When comparing the interattractor distances in the trained and untrained students before and after exercise, they turned out to be 43 times higher in the latter.

The analysis of the distances Z_ij between the chaotic centers of the quasi-attractors of the spectral indices of the CVS and the ANS in the testees from both groups has revealed the following (Table 3): before dynamic exercise the distance equaled 19 089 c.u., after exercise it increased by 4.9 times and equaled 92 660 c.u.

The calculation of the matrices of interattractor distances Z_ij of quasi-attractors of the body state vector in the untrained students has revealed their decrease after exercise, which determined an insufficient level of formation of their adaptive mechanisms, and a considerable tension of the regulatory processes and a parameter mismatch of the body functional systems.

Conclusion. In the study of the influence of dynamic exercise on the parameters of the cardiovascular system using matrices of quasi-attractor distances it has been established that it causes an increase in the distance between the chaotic centers of quasi-attractors of spectral parameters of the cardiovascular system of the untrained (77,091 c.u.) and trained (1755 c.u) students. The correlation between the distances presents a quantitative level of conditioning (or deconditioning) [2-7].

It is reasonable to use the detected principles of dynamics of behavior of the body state vector in the trained and untrained students for quantitative estimation of the level of deconditioning of Yugra residents, as well as to assess the quality of the offered doses of exercise (training sessions) in athletes in terms of specialized training (with due regard to particular sports) [6, 7].

The use of patented technologies has proved that the detected principles of dynamics of behavior of the body state vector took into account variability of all possible diagnostic features in the phase space of states. Determination of the parameters of quasi-attractors of CVS reveals an individual difference, which helps objectively estimate the dynamics of reserve capacities of the body and their predictive value.

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Corresponding authors: apokin_vv@mail.ru