The Use of Interattractor Distance Matrices in Assessment of Athletes’ Fitness Level

Фотографии: 

S.I. Loginov, professor, Dr.Biol.
V.V. Kozlova, Dr.Biol.
N.P. Gorlenko,
A.V. El'nikov, Dr.Sc.Phys.-Math.
Surgut state university, Surgut

Key words: human body state vector, quasi-attractor, interattractor distance, students.

Introduction. Physical culture and sport as elements of a healthy way of life are becoming increasingly important components characterizing community development in contemporary environment. The problem of practicing physical exercises in the North, as compared to the Central regions of Russian Federation, is of great importance. Training should be considered as a precondition for high physical working capacity and potential ability of a person to successfully adapt to environmental conditions, particularly to arising competitive and training loads. The persons doing sports in the conditions of high physical loads in the North, are subject to various ecological factors that increase the load on all human body functional systems [2].

The lack of information on the patterns of formation and development of athlete’s functional reserves in the Northern conditions, necessitates carrying out complex researches to estimate and control the current state and structural-functional changes in the activity of vital systems at the prenosological level under the conditions of adapting to increased physical loads in hypocomfortable environmental conditions. We propose the methods of analyzing organism parameters and subsequent development of the means for correction and disease prevention in one of the most economically important regions of Russia [3-4].

Heart rate variability (HRV) analysis is frequently applied for estimation of human body’s functional systems (HBFS). Some authors consider HRV as an integral characteristic of the functional status of cardiovascular system and the body as a whole [1, 5-8], since the autonomic nervous system is one of the most important systems of the human body.

The purpose of the study was to estimate fitness or deconditioning levels of the human body using the method of calculation of interattractor distance matrices.

Materials and methods. The students (young men) of Surgut state university and Samara state academy of social sciences and humanities, with different training levels, were the subjects of the study. The measurements were carried out before and after test physical load. The tested subjects were divided into three groups: (i) the 1st, control group comprised students engaged in physical culture (PC) twice a week according to the state program on PC; (ii) the 2nd group consisted of students regularly playing football; (iii) and the 3rd group was made of students practicing weightlifting. The students of Samara state academy of social sciences and humanities were grouped similarly.

The spectral analysis of the HRV vibration structure was fulfilled using the ELOKS-01M pulse oximeter equipped with a photo-optical sensor connected to a PC with the use of software which provide information on the processes controlling vital functions of the human body under the influence of ecological factors and physical loads [2-4]. Heart rate (HR), activity indices of the sympathetic nervous system (SNA), activity indices of parasympathetic nervous system (PNA), values of the Baevsky’s index (BI) and oxyhemoglobin saturation in the blood of subjects (SPO2) were determined.

The parameters of human body state vector (HBSV) in the phase space of states (PSS) were investigated using the method of multidimensional phase spaces, with the calculated interattractor distance matrices. When various kinds of physical load are tested on the participants that have similar functional conditions of their body (e.g. groups of persons with the same nosological parameters), with registering the functional parameters of every person before and after load, then all those parameters form sets (compartments) of diagnostic marks that are located within the limits of a single phase coordinate xi out of the whole (i=1, …, m) coordinate system for the m-dimensional phase space with similar diagnostic parameters. Each individual with his own set of parameters (components of the x(t) vector of personal body conditions, HBSV) is determined by a point in this PSS so that the group of subjects forms a “cloud” (quasi-attractor) in the phase space of conditions; and different groups, due to varying effects applied to them, form different “clouds” - quasi-attractors in the PSS. The  distances (here  and are the subject groups’ numbers) between chaotic and stochastic centers of those various quasi-attractors form  elements of the  matrix. These elements correspond to all possible distances between chaotic (or stochastic) centers of quasi-attractors that describe the condition of various groups of subjects before (vertically numbered in the  matrix) and after (horizontally numbered in the  matrix) a training impact (RF Patent No. 2010108496, Method of correction of therapeutic or sports effect on a human body in the phase space of conditions via distance matrices). The maximum differences in the Zij, distances between chaotic (or stochastic) centers of the HBSV quasi-attractors of different groups of subjects (before and after an impact) manifest a person’s detraining level or a load (training) intensity during a sport event [1, 4, 7, 8]. Reduction in the Zij values corresponds to a higher fitness level [1, 4, 7, 8].

Generally, the task solution consists in obtaining from a subject or a group of subjects the data that is represented as a set of m components (compartments) by means of repeated measurements, where m is a number of diagnostic parameters measured; then those results are plotted as points in an m-dimensional phase space of conditions, and the distances between the quasi-attractor centers are measured [2-4, 7-8].

Results and discussion. The peculiarities of the HBSV dynamics for the men of Yugra (Surgut) and the central region of Russia (Samara) under test physical loads have been determined using the method of multidirectional phase spaces. The study was carried out by comparing two regions with different ecologies, taking Surgut and Samara cities as examples. The Zij elements of three Z matrices of distances between the centers of chaotic quasi-attractors of the HBSV of trained and untrained young men from Samara and Surgut before and after dosed physical load, and a general comparative matrix before and after test load were determined.

It should be noted that the parameters for the autonomic nervous system (ANS) in Tab. 1, where the Z1 matrix is given, are the HBSV coordinates, so: x0=SNA, x1=PNA, x2=BI, x3= SPO2, x4=HR. This is a 5-dimentional space with chaotic motions of the HBSVs of all groups.

Table 1. The matrix of comparison of distances (Z1, c.u.) between the centers of chaotic quasi-attractors of the HBSVs of trained (2nd and 3rd groups) and untrained (1st group) young men from Surgut before and after dosed exercise.

Surgut

Young men before exercise

1st group (control group), c.u.

2nd group (football), c.u.

3rd group (weightlifting), c.u.

Total, c.u.

average, c.u.

Young men after exercise

1st group (control group), c.u.

z11=194.3

z12=168.49

z13=204.4

567.19

189.06

2nd group (football), c.u.

z 21=552.95

z 22=527.59

z 23=563.04

1643.58

547.86

3rd group (weightlifting), c.u.

z 31=26.46

z 32=4.11

z 33=36.33

66.9

22.3

total, c.u.

773.71

700.19

799.77

-

-

average, c.u.

257.9

233.4

266.59


Note. The xi values are: x0 = SNA, activity of the sympathetic nervous system (c.u.), x1 = PNA, activity of the parasympathetic nervous system (arb. units), x2 = BI, Baevsky’s stress index (c.u.), x3 = SPO2, oxyhemoglobin saturation in the blood (%), x4 = HR, hearth rate (bpm).

Between the positions of quasi-attractors, the HBSV values of young men (Surgut) before and after exercise showed different dynamics in the diagonal elements of the matrices of three groups. A minimum interattractor distance, z33=36.33 c.u., was observed in the group of young men who practiced weightlifting, whereas this interattractor distance was maximum in football players, z22=527.59 c.u. Trained young men differed initially by the SNA parameters, in contrast to the untrained ones who had z11=194.3 c.u. (Tab. 1).

Тable 2. The matrix of distance (Z2, a.u.) comparison between centers of chaotic quasi-attractors of the HBSVs of trained (2nd and 3rd groups) and untrained (1st group) young men from Samara before and after exercise.

Samara

Young men before exercise

1st group (control group), c.u.

2nd group (football), c.u.

3rd group (weightlifting), c.u.

Total, c.u.

average, c.u.

Young men after exercise

1st group (control group), c.u.

z11=15.78

z12=14.28

z13=30.45

60.51

20.17

2nd group (football), c.u.

z 21=186.7

z 22=160.48

z 23=142.79

489.97

163.23

3rd group (weightlifting), c.u.

z 31=136.48

z 32=110.33

z 33=91.01

337.82

112.06

total, c.u.

338.96

285.09

264.25

-

-

average, c.u.

112.9

95.03

88.08


Note. The phase space parameters are the same as in Table 1.

The analysis of diagonal elements of the matrix of interattractor distances of the HBSV of the trained (2nd and 3rd groups) and untrained (1st group) young men from Samara before and after physical load (Tab. 2) shows a trend similar to that obtained in Surgut. However, the distance values were significantly lower for all three groups: z11=15,78 c.u., z 22=160,48 c.u., and z 33=91,01 c.u.

The entire set of interattractor distances for two clusters of the test participants, the first cluster comprising the young men from Samara before exercise (3 quasi-attractors for the 1st, 2nd, and 3rd group), and the second cluster – young men from Surgut (the 1st, 2nd, and 3rd group) before exercise, is given in Tab. 3. The zij parameters are the distances (i and j are numbers of the groups) between the centers of chaotic quasi-attractors of two groups (compartments).

The HBSV between the quasi-attractor positions of young men (Samara and Surgut) has a small difference, when the diagonal elements of the matrices of the 1st and the 2nd groups of the cluster of young men is compared before exercise - the interattractor distance for those groups was z11=15,91 c.u. and z22=16,79 c.u., respectively. Unlike young men of the third group, where z33=40,59 c.u., practicing weightlifting (both in Surgut and Samara) originally had different SNA parameters.

Table 3. The matrix of distance (Z3, a.u.) comparison between centers of chaotic quasi-attractors of the HBSVs of trained (2nd and 3rd groups) and untrained (1st group) young men from Samara and Surgut before dosed exercise.

Samara

 

Surgut

Before exercise

1st group (control group), c.u.

2nd group (football), c.u.

3rd group (weightlifting), c.u.

Total, c.u.

average, c.u.

Before exercise

1st group (control group), c.u.

z11=15,91

z12=11,48

z13=30,87

52,26

19,42

2nd group (football), c.u.

z 21=41,79

z 22=16,79

z 23=4,37

62,95

20,98

3rd group (weightlifting), c.u.

z 31=5,65

z 32=21,86

z 33=40,59

61,8

22,7

total, c.u.

63.35

50.13

75.87

 

 

average, c.u.

21.12

16.71

25.28


Note. The phase space parameters are the same as in Table 1.

The comparison of the zij distances for young men from Samara and Surgut before physical load showed that the highest distance, z21=41,79 a.u., was observed among the 1st group from Samara and the 2nd one from Surgut.

The lowest interattractor distances were obtained for the 2nd group from Surgut and the 3rd group from Samara (z21=4,37 c.u.), and for the 1st group from Samara and the 3rd one from Surgut (z13=5,65 c.u.) (Tab. 3).

After exercise, the trend for the 1st and 2nd groups has not changed, interattractor distances were z11=194,87 and z22=381,35, whereas in the 3rd group the distance decreased, z33=94,99, that indicates different compensatory mechanisms of the response to physical load: physical endurance and strength were trained in the 2nd group (team sports) and the 3rd group (weightlifting), respectively (Tab. 4), that indicates the stabilizing effect from physical load on the HBFS of trained students, as well as a certain similarity of the HBFS response to load.

Table 4. The matrix of distance (Z4, a.u.) comparison between centers of chaotic quasi-attractors of the HBSVs of trained (2nd and 3rd groups) and untrained (1st group) young men from Samara and Surgut after exercise.

Samara

 

Surgut

After exercise

1st group (control group), c.u.

2nd group (football), c.u.

3rd group (weightlifting), c.u.

Total, c.u.

average, c.u.

After exercise

1st group (control group), c.u.

z11=194.87

z12=24.40

z13=74.97

294.06

98.02

2nd group (football), v

z 21=553.81

z 22=381.35

z 23=434.22

1369.38

456.46

3rd group (weightlifting), c.u.

z 31=26.79

z 32=145.76

z 33=94.99

1182.48

394.16

total. c.u.

775.47

551.51

604.18

-

-

average, c.u.

258.49

183.84

200.3


Note. The phase space parameters are the same as in Table 1.

The differentiation of physical loads in accordance with body’s adaptabilities is one of the primary problems of physical education. Computer technology is used for the differentiation of physical load in mass physical culture; however, in this case there are no criteria for the estimation of individual diagnostics of prenosological adaptive conditions.

Such differences can be used to estimate deadaptation and hypokinesis of the residents of the North of the Russian Federation, and we are already applying them for the quantitative estimation of the training effect on the HBFSs of the northern residents. Hence, an important conclusion can be drawn about the possibility to form the type of SNA regulation depending on certain ecological conditions and type of physical load.

The calculation of the matrices of interattractor distances is to be used for a quantitative estimation of the degree of deadaptation of Yugra and Central Russia residents, such loss corresponds to growth of interattractor distances zij. For example, untrained students with a pronounced hypokinesis had the highest intarattractor distances before and after physical loading, in contrast to young men that had practiced playing sports. The parameters of the matrices of interattractor distances can be applied for the quality estimation of trainings fulfilled both by athletes and untrained people as a diagnostic instrument for training loss estimation for various sports, and as indices of short- and long-term efficiency of training.

Conclusion. The determination of the matrices of interattractor distances of SNA quasi-attractors for trained young men from Surgut and Samara before exercise showed, that the control group and the group of football players differed less significantly (16 and 17 c.u.), as compared to the weightlifters group (41 c.u.). The changes of distances (zij) between the centers of chaotic quasi-attractors after exercise revealed a stabilizing effect of load for the weightlifters (approximately 95 c.u.), in contrast to untrained persons (195 c.u.) and football players (381 c.u.). The distances between the chaotic centers of quasi-attractors of students who just started doing sports increased, proving insufficient adaptation, as well as significant tension of regulatory processes and high degree of mismatch of the HBFSs.

The findings suggest, that physical load renders a significant influence on the parameters of body functional systems of untrained students, which is proved by the largest distance Zij. The method of calculation of interattractor distance matrices provides for estimating the efficiency of progressive physical load on various groups of subjects.

The findings can be applied in the assessment of the adequacy of training to an individual functional reserve. The study of the state of regulatory mechanisms, allocation of the tension level of regulatory systems is of great value for estimation of the peculiarities of human body's adaptation to physical loads. It brings us closer to the scientific forecasting of athletes' physical capabilities, which is of great importance when settling the issues of qualification for sports occupations, effective organization of the training process and monitoring of the body's functional status. Hence, it is extremely important to introduce early detection of inadequate body responses to physical loads in sports practice using the method of calculation of inter-attractor distance matrices of parameters of quasi-attractors of the human body state vector.

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Author’s contacts: apokin_vv@mail.ru