T.Yu. Pokrovskaya1, Sh.R. Yusupov2, M.K. Padenev3

1–3 Kazan National Research Technical University named after A. N. Tupolev (KNRTU-KAI) (Kazan, Russia)

1 vip89@mail.ru, 2 shamil_79@rambler.ru, 3 padenev2005@yandex.ru

The definition of heart rate depends on the individual parameters of a person. Mathematical models existing today do not take into account individual parameters, which leads to inaccurate measurement results. This is an acute problem at the current stage of the development of personalization of training programs and health monitoring systems.

The paper considers modern approaches to mathematical modeling of the effect of physical exercise on heart rate (HR). The proposed modified mathematical model describing the dynamics of heart rate in response to various modes of physical activity. The results of model verification based on experimental data using statistical analysis methods are presented. The developed model makes it possible to predict the individual response of the cardiovascular system to physical activity, which is important for the personalization of training programs and health monitoring systems.

The purpose of the work – to develop and verify a mathematical model describing the dynamics of heart rate in response to physical activity of various intensities, taking into account individual physiological parameters of a person.

The existing mathematical model is considered, in which the inaccuracy of the results of human heart rate predictions is determined due to the lack of consideration of individual parameters. A new mathematical model has been proposed, which takes into account individual human parameters, which makes it possible to more accurately determine heart rate.

The model can be used further both in medical practice and in sports to better determine human heart rate and prevent overtraining of the cardiovascular system.

Pokrovskaya T.Yu., Yusupov Sh.R., Padenev M.K. Influence of physical exercises on heart rate: mathematical modeling. Technologies of Living Systems. 2026. V. 23. № 2. Р. 73-81. DOI: https://doi.org/10.18127/j20700997-202602-07 (In Russian).

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