Professor, Dr.Med. S.N. Simonov¹
Associate Professor, PhD A.A. Chastikhin²
Professor, Dr.Med. A.V. Gulin¹
Associate Professor, PhD V.V. Apokin^3
1Tambov State University n.a. G.R. Derzhavin, Tambov
²Military Training and Research Center of the Air Force "Air Force Academy n.a. Professor N.E. Zhukovsky and Yu.A. Gagarin", Ministry of Defence of the Russian Federation, Voronezh
³Surgut State University, Surgut

Keywords: multidivariate modeling, age-specific variations of motor qualities, children's and adolescents’ growth and development process, pupils' physical health monitoring.

Introduction. As a rule, motor skills of school children are attributable to the relation between the biological, economic, climatic, ecological and other living conditions, which determines their dependence on the region of residence [3]. Therefore, it becomes reasonably relevant to develop the regional standards for physical training of pupils and adolescents aimed to make physical education of the rising generation more effective [2].

In the furtherance of this goal it is necessary to develop a methodology of modeling of the age-specific motor skill variations in pupils with due regard to the specific features of the region of their residence, which would enable a probabilistic forecast of the average motor test results at any school age, as well as in the border age intervals relating to the preschool age and adolescence, respectively.

Mathematical modeling of the age-specific motor skill variations in children and adolescents during their biological development is made possible with the current rapid progress in the development of the nonlinear dynamics methods and their employment in chronobiology and other natural sciences, in particular, the presence of the well-developed logistic models describing different growth processes.

Childhood and adolescence fall within the period of man’s intensive growth, so it is natural to compare the results of testing of the basic motor skills of school children, first, with the "universal" analytic growth functions, available in the literature, and second, with the trend curves of the length of the body and its different parts and tissues. The first is needed to study the possibility to forecast an increase in average test results, and the age of the maximal statistically average result, and the second - to study the role of different body parts and/or its subsystems in the formation of the average result of testing of the given motor skill in pupils.

Research objective was to find the optimal mathematical models to describe the age-specific variations of physical fitness and typical rhythms of motor qualities of pupils.

Methods and structure of the research. As a primary data source we used the electronic database that contained the results of testing of motor skills of the 7-17-year-old pupils of Tambov, a total of 1874 people [8-10].

The approximation of the averaged trend in the test results of pupils by means of the analytic functions was carried out using the software package "Origin" ("Origin Nonlinear fitting"), which involves the least square method. The original family functions were the Pearl-Verhulst and Weibull-Kolmogorov logistic functions [1], matching well with various growth processes. For the purpose of the correlation analysis of the test data with the age-related changes in separate body parameters, such as body length, foot size, etc., we calculated the correlation coefficient k with the help of the «Mathcad» software package. The irregular age-specific variations in the test results were studied by means of spectral analysis. The age-specific variations are, generally speaking, a broadband "signal", which can be expanded in the Fourier series [4, 5].

During the present study we used the Blackman’s computer program, which realized a fast Fourier transform of discrete time series. This program was drawn from a pool of similar programs based on the calibration test results that involved harmonic signals, signals in the form of a rectangle, as well as complex time series with the power spectra known form the literature [5, 6].

Results and discussion. The growth curves of various body tissues, showing four main types of growth, are well known [5, 6]. It should be noted that these curves bear little resemblance to the age chart of the results of testing of various motor qualities of school children. For example, the brain endocasts are 95% formed by the age of 10, and their age-related growth - from 10 to 17 years old does not exceed 5%. The development of lymph nodes, reproductive system and body in general has a pronounced pubertal shift during puberty. Among the qualitative results of the present study is the identified absence of the test data shift within the age interval corresponding to the growth spurt during adolescence (11-12 years old for girls, 14-15 years old for boys). Therefore, the correlation between the age-specific variations in the test results should be associated with the age-related changes in separate body parts that do not show any significant pubertal shifts. It is first and foremost hand and foot, and taking into consideration the effects of the gradient growth, the adjacent limb segments: forearm, shoulder and lower leg, thigh - respectively, as well as the age-related increase in the red blood cell count, which, firstly, does not have a pronounced puberty shift and, secondly, is associated with the increase in the energy capacities of the body.

We compared the main results of the age-specific motor skill variations in pupils of Tambov with the literature data on the age-related changes in these segments, body length and red blood cell count [6, 9, 10].

Strength abilities ("Modified pull-up on high bar" test for boys and "Pull-up in hang on low bar" test for girls). The correlation analysis of the curves reveals that the highest correlation between the pull-up test results is observed during hand, arm and forearm development, as well as during an increase in the red blood cell count (all k>0.964), and the lowest one – during the increase in the total body length (k=0.925). Similar correlations are observed among the girls. The coefficients of correlation between the age-specific variations in pull-ups and increasing red blood cell count in boys are even higher – k = 0.953. The comparison of the pull-up test results demonstrated by the boys and girls with the age-related changes in the red blood cell count and handgrip force indicates the differentiation of these relationships by sex: based on the handgrip force - after 14 years, based on the blood cell count - after 12 years, and based on the pull-up test results - after 8-9 years.

Between 7 and 17 years old, the average body length of boys increases by about 1.5 times (from 115 to 178 cm), and their average body weight - almost threefold (from 20 to 60 kg). At the same time, the average number of pull-ups increases almost sixfold (from 2 to 12). Let us compare the work done by the pupils aged 7 and 17 years while pulling up:

,

where – adolescent’s body weight,  – number of pull-ups,  – body lift height when pulling up, =9,8 m/s² – gravitational acceleration. To make an assessment, let us assume , where l - shoulder length. The dependence of shoulder length on children’s age is calculated according to the following formula [5]: cm. At the age of 7 l₇≈24, m₇≈20 kg, and at 17 l₇≈40, m₇≈60 kg [7]. According to the above given formula: (J) and  (J).

If we assume that each pull-up takes on the average 1 sec, the mean movement power required for one pull-up  at the age of 17 nearly fivefold exceeds the corresponding values of the movement power at the age of 7 (≈175 W, ≈36 W), and the total energy cost is more than 40 times greater: ≈40. That is why, pull-ups are a measure of the body "efficiency coefficient" (e.c.). In turn, it depends on the operating effect of each cell (i.e. "cell efficiency"), which is largely determined by its oxygen supply, that is, the red blood cell count and other factors (development of chest, circulatory system, etc.). Apparently, these circumstances explain the high correlation between the pull-up test results of pupils of both sexes and the age-related development of the red blood cell count in addition to the upper limbs.

Speed-strength abilities ("Standing long jump" test) and strength abilities ("30m run" test). The age-related dependences of the standing long jump test results l and the length L of the foot, lower leg and thigh, demonstrating a very high correlation k>0.999, which decreases slightly in the sequence as follows: jump-foot (=0.9997), jump-lower leg (=0.9996), jump-thigh (=0.9993). Almost the same ratio of the correlation coefficients is observed during the 30m run test. At the same time, the general endurance test "6 minute run" shows that the difference between the correlation coefficients is reduced: , , . This means that at long distances all the lower limb segments are nearly equally "responsible" for the test results. When covering short distances, and when performing a standing long jump, the foot plays a slightly more important role than the lower leg and thigh. It is obvious that the result of the standing jump test depends on the instep of the foot, which, in case of the normal development of a pupil, grows in proportion to the size of the foot. Hence, it appears that the role of the foot during the jump and sprint tests is somewhat more prominent.

The observed correlation decreases sharply when testing coordination skills - "3x10 m shuttle run". The correlation coefficient of the age-specific variations in the shuttle run results and changes in foot size is k₁₂=0.751, and in case of 30m run – k₁₂=0.9996. Obviously, the contribution of a single factor (foot) to the final result of the more complex test ("Shuttle run") is smaller than during the simple test of speed abilities ("30m run"). The absence of the pubertal shift during the testing of speed abilities is probably due to the fact that the increase in the body length during adolescence is realized mainly by means of the trunk, and the puberty shift of the lower limbs is less pronounced, especially in the foot.

Conclusions:

• We detected a high level of correlation between the age-specific variations of pull-ups and age-related changes in the length of the arm segment (hands, forearms, and shoulders), and the red blood cell count; and in the motor tests - "Standing long jump", "30m run from standing start" and "6 min run" – with age-related changes in the length of the lower limb segments (foot, lower leg, and thigh).
• It was found that the age-related trends in boys and girls during the "3x10 m shuttle run" test are less correlated with the changes in the length of the lower limbs () as compared to the ''30m run" test ().
• The spectral analysis of the irregular age-specific variations in the test results of pupils against the chaotic component revealed three characteristic rhythms: 264 months, months and about 2.6 months. Presumably, the rhythm with a period of months is associated with the peak of physical activity of children after the school holidays, and the rest of the rhythms develop from the interaction of the endogenous year with the winter and summer vacation seasons.

References

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A.A. Chastikhin, A.V. Gulin, V.V. Apokin // Teoriya i praktika fizicheskoy kultury. – 2016. – № 1. – P. 29–31.

Corresponding author: apokin_vv@mail.ru

Abstract. The Tambov provincial government has established a physical progress and physical fitness multilevel monitoring system applied to school children. An electronic personal account database gives the means to efficiently rate the physical health/ progress of the pupils under monitoring and, when necessary, take timely corrective actions. It is the multidimensional nonparametric analysis as a basis for complex models potentially capable of forecasting the children’s and adolescents’ growth and development processes that needs to be applied to find correlations of the anthropometric rates and motor qualities in the subjects. This method, among other things, makes it possible to implement the school physical education process differentiation and individualization initiatives.