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.
Ermolaev et al. (Tue,) studied this question.