Russian Journal of Information Technology in Sports Russian Journal of Information Technology in Sports Российский журнал информационных технологий в спорте 2949-6349 103129 10.62105/2949-6349-2025-2-2-61-75 wkpmta БИОМЕХАНИКА В СПОРТЕ BIOMECHANICS IN SPORTS БИОМЕХАНИКА В СПОРТЕ Mathematical models of human breathing regulation and gas exchange during physical exercises Математические модели регуляции вентиляции легких и газообмена у человека при физических нагрузках https://orcid.org/0000-0001-9325-703X Ермолаев Евгений Сергеевич Ermolaev Evgeniy Sergeevich razzz87@mail.ru

кандидат биологических наук;

candidate of sciences in biology;

 https://orcid.org/0000-0002-5272-222X Дьяченко Александр Иванович Dyachenko Aleksandr Ivanovich alexander-dyachenko@yandex.ru

доктор технических наук;

doctor of technical sciences;

 Шулагин Юрий Алексеевич Shulagin Yurii Alekseevich shulagin-yury@yandex.ru Московский государственный технический университет имени Н. Э. Баумана Москва Россия Bauman Moscow State Technical University Moscow Russian Federation Государственный научный центр Российской Федерации - Институт медико-биологических проблем Российской академии наук Москва Россия State Scientific Center of the Russian Federation - Institute of Biomedical Problems of the Russian Academy of Sciences Moscow Russian Federation Государственный научный центр Российской Федерации - Институт медико-биологических проблем Российской академии наук Москва Россия State Scientific Center of the Russian Federation - Institute of Biomedical Problems of the Russian Academy of Sciences Moscow Russian Federation Государственный научный центр Российской Федерации - Институт медико-биологических проблем Российской академии наук Москва Россия State Scientific Center of the Russian Federation - Institute of Biomedical Problems of the Russian Academy of Sciences Moscow Russian Federation 21 08 2025 21 08 2025 2 2 61 75 11 08 2025 15 08 2025 https://rjits.ru/en/nauka/article/103129/view

Актуальность. Известно, что регуляция вентиляции легких реализуется по нескольким принципам: 1) по отклонению регулируемых параметров от их гомеостатических значений; 2) по возмущению (по нагрузке на систему), способном привести к изменению газового состава крови; 3) по прогнозированию возможных возмущений и отклонений. В основу большинства имитационных моделей регуляции вентиляции легких, представленных в статье, положен принцип регулирования по отклонению, которого оказалось достаточно, чтобы объяснить изменения дыхания, возникающие в модельных опытах, в которых специально изменяли парциальное давление углекислого газа РаСО2, кислорода РаО2 и уровень кислотности крови рН. Но принцип регулирования по отклонению не объясняет регуляцию дыхания при мышечной нагрузке. Стабильность состава альвеолярного газа в момент перехода от состояния покоя к физической нагрузке свидетельствует о высокой степени согласованности сердечно-сосудистого и дыхательного компонентов реакции. Все это требует привлечения других принципов для объяснения реакции кардиореспираторной системы на физическую нагрузку. По-видимому, на качественном уровне теория кардиодинамического гиперпное может описать реакцию кардиореспираторной системы на физическую нагрузку. Хотя конкретные физиологические механизмы, обеспечивающие очень быстрый рост кровотока и вентиляции в ответ на начало физической нагрузки, остаются неопределенными, математическое моделирование позволяет количественно проверять гипотезы о динамике реакции параметров системы на нагрузку. По сравнению с быстрой реакцией кровотока, более медленные процессы в реакции дыхания на физическую нагрузку проявляются в снижении фракционной концентрации О2 в альвеолярном пространстве и дальнейшей подстройке вентиляции, обусловленной периферическим и центральным хеморефлексами. Целью настоящего обзора являлся анализ существующих подходов в математическом моделировании реакции дыхания на изменение газового состава вдыхаемого воздуха и на физическую нагрузку.

Relevance. It is known that lung ventilation regulation works via several principles: 1) by regulated parameters deviation from their homeostatic values; 2) by disturbance (via load applying on the system), able to cause gas composition changes in the blood; 3) by forecasting possible disturbances and deviations. The majority of the presented breathing regulation simulation models are based on the deviation principle, which turned out to be sufficient to explain the breathing changes occurring in the experiments with specifically changed partial pressure of carbon dioxide PaCO2, oxygen PaO2 and blood acidity level pH. But the deviation principle does not explain the breathing regulation during physical exercises. The alveolar gas composition stability at the moment of rest to physical activity transition indicates a high degree of coordination between the cardiovascular and respiratory components of the reaction. To explain the cardiorespiratory system's response to physical exercise onset requires the involvement of other principles, than deviation principle. It's likely that, at a qualitative level, the theory of "cardiodynamic hyperpnea" describes well the cardiorespiratory system's response to physical exercise. Although physiological mechanisms that provide the very rapid increase in blood flow and ventilation in response to the physical exercise onset, remain uncertain, mathematical simulation allows us to quantitatively test hypotheses about the dynamics of the system parameters' response to simulated exercises. Compared to the rapid blood flow response to physical exercises, slower processes of respiratory response are manifested in the alveolar fractional concentration of CO2 increase, in the alveolar fractional concentration of O2 moderate decrease and in a following ventilation additional increase, expressed by the interaction of peripheral and central chemoreflexes. The aim of this literature review was to analyze existing approaches to mathematical modeling of the breathing response to changes of inhaled air's gas composition and physical exercises.

 газообмен математическое моделирование дыхание при нагрузке кардиодинамическое гиперпное вентиляция легких gasexchange simulation models breathing under load cardiodynamic hyperpnea lung ventilation Исследование выполнено за счет гранта Российского научного фонда № 25-19-00272, https://rscf.ru/project/25-19-00272/ Supported by Russian Science Fundation № 25-19-00272, https://rscf.ru/project/25-19-00272/

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