The Use of Method of Multidimensional Phase Spaces to Estimate the Effect from Physical Loadings on Functional State of Athletes' Skin

Фотографии: 

S.A. Borisevich, associate professor, Ph.D.
State agrarian university of Northern Urals, Tyumen
S.I. Loginov, professor, Dr.Biol.
Surgut state university KhMAR-Yugra, Surgut

Key words: physical loads, kinds of sport, microvasculature, transcutaneous partial pressure of oxygen, girls and boys aged 16-22, method of multidimensional state phase spaces.

Introduction. Microcirculatory disorders are among the most frequent phenomena, accompanying any skin inflammatory reaction [1, 2]. The study of microcirculation in those engaged in sport represents a relevant part of physiology of muscular work, as it enables revealing the subtle mechanisms laying the basis of adaptive responses of the body to physical loads, performed in different conditions of external environment [3]. Microcirculatory disorder at physical overloads is related to action of products of metabolism and biologically active substances, being released from the destroyed cell structures and due to exhaustion of energy sources for muscle work [4].

The purpose of the study was to examine the peculiarities of the influence of multi-purpose physical loads on skin microcirculation and transcutaneous partial pressure of oxygen in athletes using the method of multidimensional state phase spaces.

Materials and methods. Representatives of such sports as artistic gymnastics (10 girls and 10 boys), rowing (10 girls and 10 boys), team sports (volleyball, handball, table tennis) (10 girls and 10 boys) and the control group (10 girls and 10 boys), engaged in the academic program on physical culture, were involved in the work. All research subjects (40 girls and 40 boys aged 16-22 years) were randomly selected. Skin microcirculation indices (ml/min) on the forehead, abdomen, back and the magnitude of transcutaneous partial pressure of oxygen (mmHg) on the forehead and abdomen were recorded in athletes in the state of relative physiological rest. The skin microcirculation indices were registered using laser Doppler flowmeter BLF-21 by Perimed (Sweden), transcutaneous partial pressure of oxygen - using the monitor TSM-400 by Radiometer (Denmark).

The obtained data were processed using the method of multidimensional state phase spaces (SPS) [5]. The peculiarities of describing the response of the human biological dynamic system in view of chaos theory and self-organization based on the system approach [5-8]. According to this approach, if the state of skin is studied in groups of athletes from different sports, who are in practically same conditions regarding the body’s functional state (eg, a group of people in similar ecological and climatic conditions) and parameters of body functions of each person from the group are recorded, then these parameters form sets (compartments) of studied features within a single phase coordinate xi – of a set of all coordinates of the m-dimensional SPS with the same diagnostic patterns. In addition, each person with his own set of features (components of human body state vector - HBSV) at a given instant of time is given by the point in this space so that the group of patients constitutes some kind of "cloud" (quasi-attractor) in SPS, and different groups (due to different effects on them) form different "clouds" (quasi-attractors) in SPS. Generally, the problems of choosing the most important parameters of order in this approach are solved by the fact that the data obtained from a group of athletes or a single athlete by means of repeated measurements as a set of m data units (compartments), where m - number of measured diagnostic patterns, are transferred as points in the m-dimensional SPS and the parameters of obtained quasi-attractors are measured [5, 6].

We used this method for group comparisons of different groups of people engaged in different sports. In the case of multiple data clusters available (one cluster for each group of athletes or for each examination method), these clusters can be described by individual body state vector of man, belonging to the examined  group in the form , where  - the number of diagnostic pattern (parameter of subject’ body), and - the cluster number (number of a group of athletes or number of a specific impact - exercise, where). At the same time each vector  in the same  dimensional SPS has the same sets of components (diagnostic patterns) , which in turn have sets (total number, where - the number of athletes in a group, and - athlete’s number in a group) of specific ranges, they form a quasi-attractor in SPS of values ​​of diagnostic patterns themselves for each of the coordinates . The volumes of quasi-attractors and coordinates of their centers are integrative measures of evaluation of effectiveness of the training impact [5, 6].

Results and discussion. According to the studies, the biggest volume of 5-dimensional state phase spaces is in rowing and gymnastics both among boys and girls. Herewith, the ones engaged in these sports have substantially higher indices of asymmetry compared to the ones from team sports and the control group among boys but not girls (Tab. 1).

Table 1. The volume of 5-dimensional parallelepiped with a quasi-attractor of behavior of athletes’ body state vector and indicators of asymmetry at multi-purpose physical loads within it

Sports

General V value

General asymmetry value

Boys

Girls

Boys

Girls

Gymnastics

24,3·103

10,6·103

7.3598

3.6777

Rowing

70,1·103

19,5·103

4.1449

5.3696

Team sports

2,8·103

5,5·103

0.7107

12.6222

Control group

10,0·103

4,2·103

4.8481

4.2322


Note. Here in Tables 2-7: 5-dimensional state phase space includes the following parameters: X1 - skin microcirculation (forehead), X2 - skin microcirculation (abdomen), X3 - skin microcirculation (back), X4 - transcutaneous partial pressure of oxygen in microvasculature (forehead), X5 - transcutaneous partial pressure of oxygen in microvasculature (back).

Using the method of exclusion of individual features the effect of the Xi feature (in our case, these are parameters of skin microcirculation, transcutaneous partial pressure of oxygen) on the Z value (the distance between centers of quasi-attractors) was determined with the gradual exclusion from the calculation of the individual components of the girls' body state vector. The distance between the centers of two quasi-attractors of movement of the body state vector (Tab. 2) of girls engaged in gymnastics and the control group were determined, where Z0 = 14,95.

Table 2. Results of the analysis of exclusion of certain features of parameters of quasi-attractors of body state vector of girls engaged in gymnastics and the control group, n = 10

Volume of first attractor

Volume of second attractor

Difference between volumes of attractors

Relative error, %

Z-index

Vy0 = 4,2·103

Vx0 = 10,6·103

dif=6,4·103

R0= 60,52

Z0=14,95

Vy1 = 0,9·103

Vx1 = 1,6·103

dif=0,7·103

R1= 45,08

Z1=14,75

Vy2 = 4,6·103

Vx2 = 9,6·103

dif=5,0·103

R2= 51,75

Z2=14,94

Vy3 = 3,2·103

Vx3 = 9,6·103

dif=6,4·103

R3= 66,60

Z3=14,94

Vy4 = 0,1·103

Vx4 =0,4·103

dif=0,3·103

R4=74,39

Z4=3,21

Vy5 = 0,2·103

Vx5 =0,19·103

dif=0,01·103

R5=7,14

Z5=14,81


The feature Z4 = 3,21 (transcutaneous partial pressure of oxygen in microvasculature, forehead) was shown to be more significant and when excluded promotes the distance decrease by almost 5 times (at Z4 = 3,21) from the initial one (Z0 = 14,95).

When determining the distance between the centers of two quasi-attractors of movement of the body state vector of boys engaged in gymnastics and the control group (Table 3), the feature Z5 = 1,82 (transcutaneous partial pressure of oxygen in microvasculature, back) was found to be more significant and when excluded promoted the distance decrease by almost 11 times (at Z5 = 1,82) from the initial one (Z0 = 19,48).

Table 3. Results of the analysis of exclusion of certain features of parameters of quasi-attractors of the body state vector of boys engaged in gymnastics and the control group, n = 10

Volume of first attractor

Volume of second attractor

Difference between volumes of attractors

Relative error, %

Z- index

Vy0 = 10,0·103

Vx0 = 24,3·103

dif=14,3·103

R0= 58,87

Z0=19,48

Vy1 = 2,22·103

Vx1 = 2,19·103

dif=0,03·103

R1= 1,45

Z1=19,48

Vy2 = 11,1·103

Vx2 = 27,0·103

dif=15,9·103

R2= 58,87

Z2=19,46

Vy3 = 10,0·103

Vx3 = 17,3·103

dif=7,3·103

R3= 42,42

Z3=19,48

Vy4 = 0,26·103

Vx4 =0,66·103

dif=0,4·103

R4=59,95

Z4=19,43

Vy5 = 0,15·103

Vx5 =0,52·103

dif=0,37·103

R5=70,25

Z5=1,82

 

Based on the measurement of the distances between the centers of two quasi-attractors of movement of the body state vector of girls engaged in rowing and the control group (Table 4), the feature Z5 = 2,04 (transcutaneous partial pressure of oxygen in microvasculature (back)) was more significant and when excluded facilitated the decrease of the distance by 3.5 times (Z5 = 2,04) from the initial one (Z0 = 7,19).

Table 4. Results of exclusion of certain features of parameters of quasi-attractors of the body state vector of girls engaged in rowing and the control group, n = 10

Volume of first attractor

Volume of second attractor

Difference between volumes of attractors

Relative error, %

Z- index

Vy0 = 4,2·103

Vx0 = 19,5·103

dif=15,3·103

R0= 78,59

Z0=7,19

Vy1 = 0,9·103

Vx1 = 4,9·103

dif=4,0·103

R1= 81,38

Z1=7,13

Vy2 = 4,6·103

Vx2 = 13,9·103

dif=9,3·103

R2= 66,70

Z2=7,19

Vy3 = 3,2·103

Vx3 = 10,3·103

dif=7,1·103

R3= 68,71

Z3=7,19

Vy4 = 0,11·103

Vx4 =0,57·103

dif=0,46·103

R4=80,32

Z4=6,97

Vy5 = 0,2·103

Vx5 =0,36·103

dif=0,16·103

R5=44,95

Z5=2,04


When determining the distance between the centers of two quasi-attractors of movement of the body state vector of boys engaged in rowing and the control group (Table 5), the feature Z5=4,54 (transcutaneous partial pressure of oxygen in microvasculature, back) was proved to be more significant and when excluded caused a decrease of the distance by 3 times (Z5=4,54) from the initial one (Z0 = 15,1).

As for the distance between the centers of two quasi-attractors of movement of the body state vector of girls engaged in team sports and the control group (Table 6), the feature Z5=2,74 (transcutaneous partial pressure of oxygen in microvasculature, back) was proved to be more significant and when excluded provoked a decrease of the distance by 2 times (Z5=2,74) from the initial one (Z0 = 5,35).

Table 5. Results of exclusion of certain features of parameters of quasi-attractors of the body state vector of boys engaged in rowing and the control group, n=10

Volume of first attractor

Volume of second attractor

Difference between volumes of attractors

Relative error, %

Z-index

Vy0 = 10,0·103

Vx0 = 70,1·103

dif=60,1·103

R0= 85,74

Z0=15,1

Vy1 = 2,2·103

Vx1 = 6,2·103

dif=4,0·103

R1= 64,51

Z1=15,1

Vy2 = 11,1·103

Vx2 = 58,5·103

dif=47,4·103

R2= 80,99

Z2=15,07

Vy3 = 10,0·103

Vx3 = 46,7·103

dif=36,7·103

R3= 78,61

Z3=15,1

Vy4 = 0,25·103

Vx4 =1,2·103

dif=0,95·103

R4=78,24

Z4=14,4

Vy5 = 0,15·103

Vx5 =1,17·103

dif=1,02·103

R5=86,84

Z5=4,54


Note. Legend is the same as for Fig. 1.

Table 6. Results of exclusion of certain features of parameters of quasi-attractors of the body state vector of girls engaged in team sports and the control group, n=10

Volume of first attractor

Volume of second attractor

Difference between volumes of attractors

Relative error, %

Z – index

Vy0 = 4,2·103

Vx0 = 5,5·103

dif=1,3·103

R0= 23,65

Z0=5,35

Vy1 = 0,9·103

Vx1 = 2,6·103

dif=1,7·103

R1= 65,15

Z1=4,71

Vy2 = 4,64·103

Vx2 = 4,56·103

dif=0,08·103

R2= 1,79

Z2=5,35

Vy3 = 3,2·103

Vx3 = 4,2·103

dif=1,0·103

R3= 23,65

Z3=5,35

Vy4 = 0,11·103

Vx4 =0,06·103

dif=0,05·103

R4=81,58

Z4=5,26

Vy5 = 0,20·103

Vx5 =0,28·103

dif=0,08·103

R5=30,92

Z5=2,74


When estimating the distance between the centers of two quasi-attractors of movement of the body state vector of boys engaged in team sports and the control group (Table 7), the feature Z5=2,11 (transcutaneous partial pressure of oxygen in microvasculature, back) was proved to be more significant and when excluded caused a decrease of the distance by almost 3 times (Z5=2,11) from the initial one (Z0 = 6,13).

Table 7. Results of exclusion of certain features of parameters of quasi-attractors of the body state vector of boys engaged in team sports and the control group, n=10

Volume of first attractor

Volume of second attractor

Difference between volumes of attractors

Relative error, %

Z- index

Vy0 = 2,8·103

Vx0 = 10,0·103

dif=7,2·103

R0= 71,39%

Z0=6,13

Vy1 = 0,84·103

Vx1 = 2,22·103

dif=1,38·103

R1= 62,10 %

Z1=5,84

Vy2 = 2,4·103

Vx2 = 11,1·103

dif=8,7·103

R2= 78,52%

Z2=6,11

Vy3 = 2,2·103

Vx3 = 10,0·103

dif=7,8·103

R3= 77,98 %

Z3=6,12

Vy4 = 0,14·103

Vx4 =0,26·103

dif=0,12·103

R4=45,60 %

Z4=6,08

Vy5 = 0,10·103

Vx5 =0,15·103

dif=0,05·103

R5=31,07 %

Z5=2,11


Note. Legend is the same as for Fig. 1.

Conclusion. Hence, transcutaneous partial pressure of oxygen (back and forehead) in boys and girls was proved to be the most significant parameter that is to be used in diagnostics of skin functional state during sports classes.

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Corresponding author: apokin_vv@mail.ru