Parameters Of Quasi-attractors Research Articles

THE PROBLEM OF HOMOGENOUS SAMPLING OF CARDIOVASCULAR SYSTEM PARAMETERS AMONG MIGRANTS IN THE RUSSIAN NORTH

Adaptation of migrants to the conditions of the Russian North is largely determined by the state of the cardiovascular system. Registration of its changes due to environmental influences is associated with significant difficulties due to loss of sample homogeneity and the emergence of the Eskov-Zinchenko effect. Objective: to study the problem of loss of homogeneity in samples of RR (cardiointervals) in different age groups. Methods: samples of RR intervals of were recorded using the Eloks-01 device in three age groups of migrant women of Khanty-Mansi Autonomous Okrug (KhMAO) - Yugra. For recorded samples, matrices of paired comparisons of samples of cardiointervals and phase portraits (in 2 coordinates) were calculated. Results: calculated matrices of comparisons in pairs of samples of RR parameters steadily demonstrate a certain increase in the number of pairs (k), which have one (for this pair) common general population. The areas S of quasi-attractors, on the contrary, for cardiointervals (RR), decrease slightly with age, which can be described as a quadratic regression equation. Conclusions: All three age groups of women (alien population of KhMAO) demonstrate a steady loss of homogeneity of groups with changes in samples of cardiointervals, which confirms the validity of Eskov-Zinchenko effect. Moreover, such instability is more pronounced for individual test person than for age groups. It is proposed to calculate the parameters of quasi-attractors to assess differences in homeostasis of cardiovascular system, depending on the age of subjects. The areas S of quasi-attractors decrease with age (when normal aging), but for older-age migrants we have some increase in this area (possibly due to increase in pathological deviations in the cardiovascular system) which is not typical for indigenous population.

STATE OF ATHLETES’ CARDIOVASCULAR SYSTEM UNDER PHYSICAL LOAD IN THE RUSSIAN NORTH

Athletics in the North of the Russian Federation has significant features that are to be studied within the framework of human ecology. In this case, of particular importance are studies that are associated with controlled physical activity. The aim was to study the state of the parasympathetic and sympathetic autonomic nervous system of athletes regulating heart functioning under controlled physical activity. Methods: Data collection was performed on a group of 16 athletes according to the Helsinki Declaration. In total, 14 parameters of the cardiovascular system were recorded using the "Elox-01" and the parameters of quasi-attractors were calculated for the five-dimensional phase space. Results. Before the load (1,5 hours of playing mini-football), the indicator of parasympathetic (PAR) regulation prevailed almost 9 times (PAR = 16 c.u.) over the sympathetic (SIM) regulation (SIM = 1,75 c.u.). After the load, these indices became equal, but the volumes of quasi-attractors increased by 29 times. Conclusions. Athletes in the North of the Russian Federation can't significantly invert the state of SIM and PAR even after the load. The load only levels these indicators, but at the same time the volume of the quasi-attractor in the five-dimensional phase space of the states of diagnostic signs of the cardiovascular system of athletes increases. Such dynamic differs from the dynamics of the athletes of the Central Part of the Russian Federation, where the SIM indicator initially prevails over the PAR indicator.

Simulation of Human Limb Movement

Simulation of any processes is based on some laws that take place inside the simulated object and outside it (changing the environment in which the object is located). In the study of complex biosystems, the identification of patterns is complicated by the fact that such systems have a chaotic structure. In such systems, it is impossible to arbitrarily repeat the initial state xi, any intermediate xn and final xk. Simulation of complex biosystems should be based on random patterns. The created simulation model works based on the random number generation. There are no static values in the model. The inclusion of regulatory mechanisms of the model is based on the search of F-solutions. Chaotic dynamics of changes in the trajectory of a person's limb is established based on experimental data. In accordance with this, in the simulation model, the level of limb retention in space changes its direction by random images in real time. In the framework of the above patterns, a mathematical model of the interaction of muscle bundles was developed to solve the problem of holding the limb in space. When analyzing the performance of the simulation model, the basis of the evaluation measure was taken. The results were obtained on the basis of mathematical statistics and the calculation of the quasiattractor parameters in the framework of the theory of chaos and self-organization. As a result, the correspondence of experimental and model data was established. In the framework of mathematical statistics, when constructing matrices of paired comparisons for experimental data, the number of pairs of matches (the word "matches" refers to the possibility of assigning the compared pairs of samples to one general set) is k = 11 %. The same number of coincidence pairs in percentage terms was established when comparing model data and model with experimental data. In the framework of the theory of chaos and self-organization, the quasiattractor parameters coincide in their area and visual assessment of phase planes. As a result of the research, high accuracy of the model is established, which is ensured by some chaotic dynamics of the model with chaotic selfregulation mechanisms. There are no constants in the mathematical form of the simulation model, which ensures the reproduction of N.A. Bernstein "repetition without repetition" hypothesis, which has been proven for experimental data. For theoretical biophysics, the constructed simulation model is able to provide understanding of the neuromuscular system functioning, as well as, with some complication and expansion of the algorithm, the central nervous system.

Information-analytical system of cardiographic information functional diagnostics

The article considers the Information-analytical system of cardiographic information functional diagnostics, which allows expanding the functionality of using miniature medical devices for non-invasive diagnostics of parameters of complex dynamic biomedical systems, using the example of cardio-intervals of the cardiovascular system. The system is based on not only the methods of the deterministic-stochastic approach but also the methods of the theory of chaos-self-organization, as a new scientific approach in the natural sciences. The method is based on calculating the parameters of quasi attractors and analyzing matrices of pairwise comparisons of time series of complex biomedical systems, which allows quantitatively and qualitatively describing the chaotic dynamics of the system state vector behaviour, obtaining objective information about changes in the functional state of the system, and also warning about these changes in time (if pathologies), which creates conditions for the status of the functional systems of the human body physiological monitoring.

THE CONCEPT OF UNIFORMITY OF A GROUP IN HUMAN ECOLOGY

Over the past 100-150 years, the selection of homogeneous groups in ecology as a whole has been carried out as part of the calculation of the coefficient of variation V = о / or by the ABC method. However, the Eskov - Zinchenko effect imposes serious restrictions on all statistical methods. The aim of the study was to verify the statistical homogeneity of three groups of Khanty women of different ages. Methods: The technique of repeating measurements of the same parameters of the Khanty women's cardiovascular system (three different ages) was used, for which matrices of all (105) different pairwise comparisons of samples for each such group were constructed (these measurements were repeated). Results. It was established that the same age, gender and living conditions (ethnicity) do not guarantee the selection of physiologically (statistically) homogeneous groups of subjects. The study proves the lack of statistical homogeneity of the three age-tested groups of Khanty women. The proportion of statistical similarity is less than 20 % of all 105 comparison pairs in all three age comparison groups. It is shown that repeated measurement of the same group gives a different picture of the distribution of pairs that can be attributed to one (common) general population. Each new dimension will give other pairs of k coincidences and it will never (from the standpoint of stochastics) be able to select a homogeneous group statistically coincident in the xi samples of the homeostasis parameter. In fact, the Eskov - Zinchenko effect spreads from one subject (in the mode of n iterations of experiments) to a group of different subjects (which cannot be homogeneous). Conclusions. From the standpoint of chaos theory - self-organization, other criteria of group homogeneity are required, in which the parameters of quasi attractors and the ratio of objects of these quasi attractors are already calculated.

PRINCIPLES OF HOMEOSTATIC REGULATION OF FUNCTIONS IN HUMAN ECOLOGY

The founder of the homeostasis theory W. B. Cannon spoke about the lack of stability of homeostasis and systems of homeostatic regulation. However, to date, the postulate of the statistical stability of samples of homeostasis parameters in various functional systems has been working in human ecology. The aim of the study is to verify this fundamental postulate and to prove the lack of statistical stability of samples of the neuromuscular and cardiovascular systems. Methods: age-related dynamics of cardio intervals was studied in three groups (38 people in each group) of Khanty women and three groups of newcomers (228 people in total), tremor and tapping parameters were studied in two groups: women (18 people) and men (16 people). The Elox-01 device was used to record cardio intervals, and the patented tremograph was used to record tremorograms. Results: the absence of statistical stability of tremorograms was proved (the number of samples of k pairs that have one sampled population not more than k1 < 5 % for tremor and k2 < 12 % for tapping), for cardio intervals k3 < 17 %. The samples are not homogeneous, the probability of their statistical repeating in a row is p < 0.05 (for one subject in constant homeostasis). It is proposed to calculate the parameters of quasi attractors that really demonstrate statistical stability (in constant homeostasis). Conclusion: the samples of the parameters of neuromuscular and cardiovascular systems are not statistically homogeneous (they change chaotically). In this regard, to assess the norm (standard) of homeostasis, it is advisable to use the calculation of the parameters of quasi attractors along the first coordinate x1 (for example, the parameters of cardio intervals or tremorograms) and x2 (rate of change x1).

EFFECT OF COLD ON INVOLUNTARY MOVEMENTS IN MEN WITH DIFFERENT LEVELS OF PHYSICAL FITNESS IN THE RUSSIAN NORTH

Cold is a common environmental factor for the population of the Russian North. The aim of the study was to assess the effect of cold stress on involuntary movements (tremor) in men with different levels of physical fitness. The paper presents a new method for calculation of quasiattractor parameters for estimation of biomechanical homeostasis in two dimensions. Biomechanical analysis according to quasiattractors parameters was realized as a numerical measure of neuro-muscular functional system parameters under the stress-perturbation. We calculate the quasiattractor's squares for men with different levels of physical fitness. We obtained the following results: calculation of quasiattractors square demonstrates the difference of homeostasis between before and after local exposure to cold. After the exposure we registered a 2.7 times- and 1.8 times increase of quasiattractors square among sportsmen and sportsmen, respectively. There were also differences between the distribution of quasiattractors across levels of physical training: for sportsmen we observed a normal distribution while and for non-sportsmen the distribution was not normal. The matrix of pairwise comparison of samples demonstrate the probability p < 0,01 for two identical samples of tremorograms. Conclusions. A local cold exposure results in a nearly 3-fold increase in the number of pairs of k coincidences of the tremorogram samples for men. We also found the dynamics of increasing areas of quasi-attractors after a local cold impact, which depends on the physical training of the subject.

Classification of Uncertainties in Modeling of Complex Biological Systems

An analogue of the Heisenberg uncertainty principle (complexity) is introduced for complex biological systems in the framework of the new chaos-self-organization theory. The requirement for such an analysis is determined by the absence of stationary regimes of biosystems (dx/dt ≠ 0 is continuous for the state vector complexity x(t)), uninterrupted chaotic change of the statistical functions f (x) and other parameters. At present, this is defined as type 2 uncertainty. At the same time, type 1 uncertainty is introduced for the complexity when f (x) do not change, and the quasi-attractor parameters can change. A neuron network simulator finds the differences between the samples in the absence of statistical differences.

Automation of the Diagnosis of Age-Related Changes in Parameters of the Cardiovascular System

An algorithm for calculating the dynamics of age-related changes in parameters of the cardiovascular system of humans in the North of the Russian Federation was developed. Using one coordinate (xi, the cardiac interval) as an example, a method is presented for calculating quasi-attractor parameters in a two-dimensional phase space, where x2 = dxi /dt is the rate of change of cardiac intervals with age. Study results using the algorithm (and the whole automated system) for three age groups of Khanty women to describe age-related changes in quasi-attractor parameters during normal aging are presented.

PARAMETER EVALUATION OF CARDIOVASCULAR SYSTEM IN SCHOOLCHILDREN UNDER THE CONDITIONS OF LATITUDINAL DISPLACEMENT

In the conditions of Russian North recreation activity is usually carried out by means of latitudinal displacement from North to South and realization of health-related activity. Herein a regular question about of their effectiveness arises. Tradition statistic methods of parameter evaluation of the cardiovascular system (CVS) homeostasis of a person, in this case, show poor efficiency; often they do not show differences between the organism's state before and after the treatment. The aim of the research was to study the effect of latitudinal movements on the process of functional systems changes of children's organisms. Information on the indices state of cardiovascular system of schoolchildren was acquired by the method of pulseintervalography on the basis of the pulse oximeter "EL0KS-01". The CVS parameters of schoolchildren were analyzed in the process of latitudinal displacement (from north to south of the Russian Federation and vice versa). The result of the study showed that a two weeks' vacation in the south reduced the quasi-attractors' size of the vector state of children's organisms in the six-dimensional phase space of states (m = 6) and partially normalized the indices of their cardiorespiratory system. The volume of quasi-attractors (m = 6) after returning to Surgut decreased 2,3 times in boys and 4,7 times in girls in comparison with the state before leaving to the south. However, the reaction in girls was more expressed and persistent than in boys, who showed a partial return to their original state (before departure) after their return from the south. In fact, girls show an exponential decrease of quasi-attractors volumes, and boys - a parabolic type depending on VG from the type of stay (registration). Similar dynamics was observed in age-related changes of quasi-attractors volumes of cardiointervals of Khanty women (decrease in volumes with age) and newcomers (they had a parabola for quasi-attractors of cardiointervals). Conclusion: calculation of the parameters of CVS quasi-attractors shows a significant difference in all diagnostic parameters from the results of statistical processing of primary data.

Estimation of the Parameters for Tremograms According to the Eskov–Zinchenko Effect

The features of the chaotic dynamics of parameters of the neuromuscular system (tremors) were studied using conventional and novel biological methods based on a multidimensional phase-space representation. The dynamics of involuntary micromovements of limbs (finger tremor) both in the relaxation phase (F = 0) and under static load (F = 3N) was manifested in a change in the number of “coincidences” of randomly selected sample pairs (k) of matrices (15 × 15) in paired comparison of tremograms, which demonstrated the global statistical instability of the samples (statistical distribution functions f(x), spectral densities of signals, and autocorrelation A(t)). The samples that result from one experiment cannot be randomly repeated in the next experiment (with the same homeostasis). This represents a quantitative measure of the Eskov–Zinchenko effect in the analysis of chaotically changing statistical distribution functions of tremogram samples. In this paper, the use of quasi-attractor parameters of tremograms (their areas) is proposed to represent changes in the neuromuscular system when passing from one homeostasis to another (G1 ≠ G2).

Chaotic Dynamics of Neuromuscular System Parameters and the Problems of the Evolution of Complexity

The evolution rate v(t) varies among diverse biosystems, but a general theory can be formulated when the dynamics of the biosystem stater x = x(t) = (x1, x2, x m ) T is considered in the m-dimensional space of states. A mathematical approach is proposed for evaluating such processes and describes the processes in terms of particular chaos of the statistical distribution functions f(x). In the case of complex multicomponent systems with a high dimension number m (m ≫1) of the phase space of states, we propose using pairwise comparison matrices of samples x(t) when homeostasis is constant and calculating the parameters of quasiattractors. The Glensdorff–Prigogine thermodynamic approach to estimating evolution is inefficient in assessing the third-type systems, while it is applicable and the Prigogine theorem works at the level of molecular systems. Alterations in the state of the human neuromuscular system were found to lead to chaotic changes in the statistical functions f(x) in tremor recording samples, while quasiattractor parameters demonstrate a certain regularity.

THE ELECTROMAGNETIC FIELDS EFFECT ON CHAOTIC DYNAMICS OF CARDIOVASCULAR SYSTEM PARAMETERS OF WORKERS OF OIL AND GAS INDUSTRY

The motion of state vector of cardiovascular system in females working on Surgut condensate stabilization plant was studied in five-dimensional phase space of states. The parameters xi of cardiovascular system in four groups of women varied within the range of VG - bounding volumes of the phase space of states, which was defined as quasi-attractor. The volumes VG were measured and compared in women of different age, affected and not affected by human-made electromagnetic fields of industrial frequency, which allowed establishing the principal differences in the dynamics of VG. In particular, women, both younger and older age groups underwent stress effect of electromagnetic fields of industrial frequency. This led to breakdown in volume of quasi-attractors in phase plane of vector (x1, x2)T where x1 - duration of cardiointervals, and x2 = dx1/dt - rate of change of x1. In fact, electromagnetic fields became stress agents for human's cardiovascular system in the North of Russian. This is shown in the framework of quasi-attractors for cardio of two groups of women. Comparison of these four groups according to the parameters of quasi-attractors showed differences though statistical differences were not significant on a number of xi parameters of whole the body state vector x (f) of person's organism living in the special northern conditions.

Experimental Verification of the Bernstein Effect "Repetition without Repetition".

The necessity of studying the Bernstein effect "repetition without repetition" is dictated by the absence of quantitative description of this effect and models that could describe such unique phenomena as repeated limb movements in a person in various mental states. In 30 nominally healthy volunteers (15 men, 15 women aged 24-25 years), tappingrams and tremorograms were recorded using an eddy current sensor with an oscillatory circuit (1 MHz) and an amplifier with recording frequency 0-1000 Hz and minimum amplitude of 0.01 mm. The results were recorded as files, processed as matrices of paired comparisons of samples, the number of matching sample pairs was determined (significance level p>0.05), and phase trajectories of finger movement were plotted. The effect was observed for both tapping and tremor and it is advisable to calculate the parameters of quasi-attractors that changed upon shifts in homeostasis.

Метод многомерных фазовых пространств в оценке хаотической динамики тремора в условиях статических нагрузок

The article presents the feasibility of application of the method of multidimensional phase spaces, based on the methods of calculating the quasi-attractor parameters as a quantitative measure of the chaotic dynamics of the tremor. The measure is used in two-dimensional quasi-attractor phase space. The quasi-attractor square is used for the identification of the actual changes in the parameters of the functional state of the organism with no load and under static loads. Specifically, the static load provides the threefold increasing of the area of quasi-attractor (from 0.31 to 0.99 cu under load of 300 g). This is a quantitative measure of the body´s reaction to changes. It was proved that calculation of quasi-attractor parameters demonstrated at three phase space more statistical stable picture then two dimensional quasi-attractors.

The evolution of the chaotic dynamics of collective modes as a method for the behavioral description of living systems

Human-scaled (in complexity) systems possess a unique feature, viz., the continuous random motion of many components of the state vector x = x(t) of such living systems. Taking this property into consideration causes the rejection of any of the known types of stationary modes (e.g., dx/dt = 0) and requires revision of the concept of chaos. A new approach to the understanding of living systems (as a third paradigm of the natural sciences) and new methods for the study of living systems (as a theory of chaos and self-organization) are proposed. Common grounds of physics and theory of chaos and self-organization are revealed as a generalized uncertainty principle and a limit on the parameters of quasi-attractors.

Оценка параметров сердечно-сосудистой системы студентов сургу

It is known that the health of people living in the North is often very different from the norm.
 The research was conducted in the winter. The parameters of the autonomic nervous system and the bioelectrical
 activity of the heart are studied. To achieve results, the authors used cardiorhythmography examination and standard
 method of pulse oximetry. The parameters of the autonomic nervous system activity and the bioelectric
 activity of the heart are investigated. Synergetic analysis of parameters of quasi-attractor motion of the state vector
 of the organism students showed that the organism of young men is in a relatively unstable state to extreme
 climate and environmental conditions of the North. As a result, boys have a greater risk of developing early heart
 disease. The parameters of quasi-attractors of vector states of the body in boys (according to the indicators of the
 autonomic nervous system) are confirmed by the results of the analysis of the parameters of quasi-attractor behavior
 of another vector of states, characterizing bioelectrical activity of the heart.

Анализ параметров квазиаттракторов метеофакторов как гомеостатической системы

Climatic and ecological environmental factors constitute the objective and subjective sides of
 life quality. The influence of weather and climate for health is very important. As the complex system is considered
 a model of 3-dimensional phase space, a box, inside of this is a quasi-attractor behavior parameters of meteo
 environment. The paper deals with the comparative analysis of the dynamics of meteorological factors of
 environment in the phase space of states in the framework of the theory of chaos and stochastic laws. The authors
 used their own program on the example of two territorial zones - an average strip of Russia and the Northern
 territory (n. Nizhnesortymsky Khanty-Ugra). It is important to note that the air temperature as an essential
 feature, it is practically not manifested itself in assessing the importance of parameters for Samara in contrast to
 Nizhnesortymsk. The used method allowed to determine the parameters of the order and to their ranking and to
 identify the most important characteristics in a comparative perspective the two territorial zones. It was postulated
 the equality between weather a climate parameters and cardio-vascular system parameter. It is postulated
 that the dynamics of meteorological parameters is similar to the dynamics of the cardiovascular system.

Динамика изменения параметров биоэлектрической активности мышц в ответ на статическое усилие

This article presents the methods of analysis of the dynamics of bioelectrical activity of the
 flexor muscles of the little finger of his right hand as a reaction to the static force in compression dynamometer,
 manifested in changes of the quasi-attractors parameters. The main research methods were deterministicstochastic
 methods and methods of the chaos theory and self-organization to describe complex biological systems.
 The authors present a comparative analysis of calculating the parameters of the obtained results, in particular,
 in the framework of the chaos theory and self-organization - the calculations of the phase plane and their
 areas; in the framework of the deterministic-stochastic approach - the calculation of the Shannon entropy. Calculations
 are aimed at assessing the level of randomness of the recorded signal. Analysis of the recorded signal and
 the evaluation of the level of randomness in a signal of bioelectrical activity of muscles showed that an increase
 in the static load quasi-attractors bioelectric muscle activity increases dramatically. The degree of change was
 estimated by calculating the parameters of quasi-attractors according to the chaos theory and self-organization.
 The changes of state of the system in the direction of increasing the degree of variability in the bioelectric activity
 of the extensor muscles of the little finger are demonstrated.
 The high efficiency of application of the chaos theory and self-organization in the assessment of the neuromuscular
 human system is showed. The obtained results allow to determining the level of the ability of performing
 the specified operations under the influence of static loads.

Живые системы (complexity) с позиций теории хаоса-самоорганизации

Attempts to describe complex biological systems (complexity) in terms of modern mathematics and physics continue. However, it is now evident that complexity cannot be the object of modern science because of their continuous change in the parameters and the absence of arbitrary repetition of initial parameters x (to) of any complexity. This article presents the the arguments of lack of capacity modeling of complex biophysical systems under deterministic and stochastic approaches due to the constant chaotic change of the state vector parameters x = x(t) = (x1,x2....,xm)Tof any complex biosystem (complexity). At any point of time h, the chaotic dynamics of homeostasis in signals, such as tapping tremors, electromyograms, neurograms, cardiograms, electroencephalograms, and other biochemical recordings, can be observed. During constant and chaotic changes of x(t) (i.e., dx/dteQ), the amplitude-frequency characteristics (AFC) and the autocorrelation functions A(t) constantly change. Therefore, the mixing property fails and the Lyapunov exponents can chaotically and randomly change signs. Chaos of complex biosystems differs from chaos of physical systems primarily due to the irreproducible initial value x(to). There are two methods for studying such systems: a stochastic method for processing random samples based on a matrix of pairwise comparisons and a computing method that utilizes quasi-attractor parameters, Vg for x(t), in the phase space of states. Here, such calculations are presented for biomechanics and electrophysiology.