Control of blood and gas pressure dynamics in a mathematical model of the cardiovascular-respiratory system for maintaining homeostasis during exercise in Chad

Abstract

This study develops an integrated mathematical model of the cardiovascular–respiratory system to investigate the regulation of blood and gas pressure dynamics during physical exercise in a Chadian athletic population. Heart rate and alveolar ventilation are incorporated as control inputs within an optimal control framework to explain the stabilization of systemic arterial pressure $(P_{as})$, systemic venous pressure $(P_{vs})$, and arterial partial pressures of oxygen $(P_{aO_2})$ and carbon dioxide $(P_{aCO_2})$ during moderate and intense exercise. The model is calibrated using field data collected from elite male and female football players and discretized using B-spline basis functions to compute optimal control trajectories.

Simulation results show a strong concordance between the measured physiological variables and the model predictions, as confirmed by the RMSE and MAE values reported in Tables \ref{tabRMSE} and \ref{tabMAE}. Moreover, clear sex-related ventilatory differences emerge from the simulations: under comparable exercise intensity, male and female athletes exhibit a measurable gap in alveolar ventilation, with a difference quantified as $\Delta\dot{V}_A= 1.8~\mathrm{L\cdot min^{-1}}$.

The objective of this modeling approach is primarily explanatory rather than predictive, aiming to reproduce and interpret the physiological mechanisms governing cardiorespiratory adaptation to exercise rather than to provide long-term individual predictions. The proposed framework demonstrates the capacity of optimal control–based models to capture realistic, population-specific cardiorespiratory responses and provides a foundation for future refinement and validation using larger experimental datasets.