Dr.Med., Professor N.N. Zakharyeva¹
PhD, Professor E.N. Yashkina¹
Master's student I. Konyaev^{1                                                                 
1}Russian State University of Physical Education, Sport, Youth and Tourism (GTSOLIFK), Moscow

Keywords: rhythmic gymnasts, mathematical model, autonomous nervous regulation of heart rates, SBP, DBP, functional state, functionality rates, correlation analysis, “strong” and “tight” correlations of functionality rates.

Background. In rhythmic gymnastics a high priority has always been given to new data and analyses for the training and competitive process management in view of the extreme loads on and tension of the body functionality required for competitive success; and this is the reason why the potential competitive success rating and forecasting criteria may help develop a highly efficient training system. One of the most promising methods of the athletic functional state rating is the modern functionality rating mathematical models designed to rate physical fitness and qualities for competitive performance forecasting purposes [7, 6, 8, 1 et al.]. The method implies, among other things, remote control and biological functionality management tools that may contribute to competitive success and help select the most promising gymnasts for the top-ranking competitions.

Objective of the study was to develop and offer a potential competitive success forecasting mathematical model applicable to elite rhythmic gymnasts competing in top-ranking events, based on their test rates indicative of the bodily adaptation processes.

Methods and structure of the study. The study was designed to apply the following methods:

• Questionnaire survey to obtain age, experience in rhythmic gymnastics, training load volume and sport qualification data of each subject;
• Body somatotyping by M.V. Chernorutskiy's method to group the subjects with asthenic, normosthenic, hypersthenic and mixed types;
• Physiological test method to obtain heart rate variability, systolic and diastolic blood pressure (SBP and DBP) and respiratory rates by spectral analysis using a spiro-arterio-cardiorhythmograph SACR system (simultaneous tests in sitting position taking 5min). The tests generated ТP indices in the HR variability spectrum; АBPV - arterial blood pressure variability indices; and LF/HF – vegetative balance indices. 
• URA test for mental (psycho-physiological) capacity rating (3 tests by V.V. Sonkin, V.D. Sonkin and V.P. Zaitsev, 2009).
• Physical working capacity rating method including the cycle ergometer version of the РWС₁₇₀ probe, plus anthropometrical measurements including body length (cm), weight (kg) and chest circumference (cm).
• Physical qualities were rated by the relevant flexibility, dexterity, strength (wrist dynamometry) tests.
• Coordination qualities were rated by the stabilometric Target Test to rate the standing balancing abilities.
• Cardiovascular system functionality was rated by the HR, SBP and DBP rates generated by the Korotkov’s method; and the external respiration was rated by the electronic spirometer SpiroS-100 made by Altonika Ltd., Moscow.

For the forecasting mathematical model design purposes, we applied a set of collinear (with correlation rate of r>0.8) key factors falling in causal correlation with the resultant indicators. Quality of the regression models was rated by the coefficient of determination R taking into consideration that its value 0.8 is indicative of the close correlation of the factors. Significance of the model was rated by the Fisher’s F-factor with an equation being rated valid at F<0.05.

For the model design purposes, we selected the parameters indicative of the systemic autonomous HR regulation, SBP and DBP [2009-11]: LF/HF>.u.n, LF/HFS>n.u , LF/HFD >n.u similar to the R.M. Bayevskiy’s tension index (2000, 1996); taking into account that LF/HF>n.u parameter grows with the competitive stress tolerance forming the so called “tough rhythm”.

The study was performed at Russian State University of Physical Education, Sport, Youth and Tourism (GTSOLIFK) at its Sport Research Institute Laboratory. Subject to the study were 40 highly-skilled rhythmic gymnasts aged 17-24 years with 10-20-year records in the sport including: 5 Masters of Sports of International Level (MSIL, 7.5%), 29 Masters of Sport (MS, 77.5%) and 6 Candidate Masters of Sport (CMS, 15%). The subjects were healthy, free of bad habits and joining the tests on a voluntary basis. The tests were performed in the hours of physiological sympathicotonia (before 1 a.m.).

Study results and discussion. The study data and analysis showed the MSIL respiratory system functionality rates being in strong intra-systemic (r= 0.7-0.9) and strong inter-systemic correlations with the HR regulation parameters (LF/HF>n.u and LF > n.u), HR, end diastolic volume (EDV), end systolic volume (ESV), stroke volume (SV), physical qualities (wrist strength, knee range of motion, pivot left foot plantography parameters), working capacity and coordination rates.

The MS were tested with lower correlation rates of the functionality parameters (with the correlation “tightness” and “strength” sagging, r<0.7); with the strong correlations found only for the 1^st external respiration function parameter i.e. maximum breathing capacity (MBC) rate with the HR variability, HR and flexibility rates.

The CMS were ranked by the tests in between the above groups by the functionality rates correlation “tightness” and “strength”; with the strongest correlations found between the vital capacity (VC), reserve inspiratory reserve volume (IRV), SBP, DBP, and left-foot standing balance indices.

Therefore, the functionality rates of the high-ranking rhythmic gymnasts were found correlating with the autonomous nervous control (ANC) of HR, SBP, DBP, respiratory rhythms and physical qualities. The MSIL most successful in the top-ranking events were tested with the highest “tightness” and “strength” of the correlations of the inter-systemic functionality rates.

Knowing that the physiological parameters related to the autonomous nervous control (ANC) of HR and SBP are the most significant for the body functional state rating [9-11], we selected the relevant mathematical parameters for the forecasting mathematical model design: LF/YF>n.u, LF/HFS>n.u,  LF/HFD>n.u, similar to the R.M. Bayevskiy’s tension indices (2000, 1996, 1979), plus the test rates indicative of the system-level activity of the autonomous nervous control (ANC) of HR, SBP and DBP (LF/HF>n.u,  LF/HFSD>n.u, LF/HFD>n.u) and the relevant rates in the low- and high-frequency ranges of the HR spectrum, SBP and DBP (LFn.u; HFn> n.u;  HFS> n.u; HFDn>n.u).

We also took into account the fact that LF/HF>n.u (vegetative balance rate in the HR spectrum) is indicative of the degree of the HR centralisation i.e. domination of sympathetic or parasympathetic departments of the autonomous nervous system is pivotal for competitive stress tolerance; and in some pathological conditions it may provoke the so-called “tough rhythm” (growing in the above conditions). 

The mathematical model for the MSIL may be described as follows: direct correlation of the fast-growing LF/HF>n.u and LFS/HFS> n.u rates with the low-frequency range of the HR spectrum and SBP (LFn.u and LFS>n.u); high regression index; high sensitivity of LF/HF>n.u rate to variations of LF>n.u and LFSn.u; with LFD/HFD>n.u showing a variation trend; plus the reverse correlation of the rate with HFD rates in the high-frequency range of the HR spectrum and DBP.

The mathematical model for the MS and CMS showed LF/HF>n.u and LFS/HFS>n.u being much the same, slowly growing and directly independent of the low-frequency range of the HR spectrum and SBP (LF n.u, LFS> n.u).

Therefore, the study data and analysis found differences in the functionality rates and their correlations in the differently skilled rhythmic gymnasts, with the MSIL tested with high “tightness” and “strength” of the inter-systemic functionality rate correlations that form a basis for the high mobilisation of the bodily regulatory and functionality systems and, as a result, for the highest competitive accomplishments.

Based on the correlation regression analysis, we selected the most informative factors to design the potential competitive success forecasting mathematical model including the HR nervous control parameters, SBP, DBP, and the low-and high-frequency range of the HR spectrum.

Conclusion. The competitive success forecasting model is recommended to be based on the test rates indicative of the activity of the system-level nervous heart-rate regulation processes, systolic and diastolic blood pressure, and the extreme values in the heart rate variation range.

References

1. Arolova N.I., Mastykash Y.I., Ostavchuk Y.N. Prognozirovanie sostoyaniya bortsa v protsesse poedinka na osnove matematicheskoy modeli funktsionalnoy sistemy dykhaniya [Forecasting wrestler's condition during bout based on mathematical model of respiratory functional system]. Kompyuternaya matematika, 2005, no. 2, pp. 69-70.
2. muscular work in junior and senior athletes (case study of rhythmic gymnastics). PhD diss. abstract]. Moscow, 1987, 23 p.
3. Makarova G.A., Baranovskaya I.B., Bushtseva T.V. Fiziologicheskie kriterii v sisteme prognozirovaniya uspeshnosti sorevnovatelnoy deyatelnosti sportsmenov v izbrannom godichnom trenirovochnom tsikle [Physiological criteria in athletes' competitive success forecasting system in selected annual training cycle]. Fizicheskaya kultura, sport – nauka i praktika, 2013, no. 3, pp. 36-40.
4. Markhasin V.S., Katsselson L.B., Moskvin A.S., Solovyeva E.B. Matematicheskoe modelirovanie v fiziologii [Mathematical simulation in physiology]. Fiziologiya. Zhurnal im. I.M. Sechenova, 1996, no. 9, pp. 234-245.
5. Pertsov S., Mezentseva L. Matematicheskoe modelirovanie v biomeditsine [Mathematical simulation in biomedicine]. Vestnik novykh meditsinskikh tekhnologiy, 2013, vol. 20, no. 1, pp. 4.
6. Proshin A.P., Solodovnikova J.V. Matematicheskoe modelirovanie i identifikatsiya sistemy krovoobrascheniya. Razvitie teorii i praktiki [Mathematical simulation and identification of circulatory system. Development of theory and practice]. Mater. Vseros. soveschaniya po problemam upravleniya. [Proc. All-Rus. management meeting]. Ves PU (Accessed 11.01.17)
7. Aubert A.E., Seht B., Beckers F. Heart Rate Variability in Athletes. Laboratory of Experimental Cardiology, School of Medicine, K.U. Lenven, Belgium. Sports Med., 2003, vol. 33.
8. Blasquez I.C.C., Font G.R., Ortis L.C. Heart-rate variability and precompetitive anxiety in swimmers. Psicothema, 2009, vol. 21, no. 4, pp. 531-536.
9. Britton W.B. Sport psychology: Handbook of sports medicine and science. UR. Wilee – Blackwell, 2009, 139 p.

Corresponding author: zakharyeva.natalia@mail.ru

Abstract

Objective of the study was to develop and offer a potential competitive success forecasting mathematical model applicable to elite rhythmic gymnasts competing in top-ranking events, based on their test rates indicative of the bodily adaptation processes. The study found some differences in the elite rhythmic gymnasts’ competitive success rating mathematical model data for different skill levels (Masters of Sports of International Level, Masters of Sports and Candidate Masters of Sports – MSIL, MS and CMS) giving the means to forecast individual competitive performance and qualify gymnasts for top-ranking events. The elite rhythmic gymnasts’ potential competitive success rating model prioritizes the following test rates pivotal for the performance forecasts: systolic and diastolic blood pressure (SBP and DBP) and heart rate variability; correlations of the rate variation speeds with the extreme values in the heart rate variation range; SBP and DBP. The competitive success forecast model is recommended to be based on the test rates indicative of the activity of the system-level nervous heart-rate regulation processes, systolic and diastolic blood pressure, and the extreme values in the heart rate variation range.