Control aspects of the human cardiovascular-respiratory system under a nonconstant workload

•A model of the cardiovascular-respiratory system describing its response to an imposed nonconstant workload is considered.•An optimal control for time-varying workload using Euler-Lagrange formulation of the optimal control problem is obtained.•Penalization terms are included in the cost functional depicting physiological fact and improving numerical simulations. The human cardiovascular system (CVS) and respiratory system (RS) work together in order to supply oxygen (O2) and other substrates needed for metabolism and to remove carbon dioxide (CO2). Global and local control mechanisms act on the CVS in order to adjust blood flow to the different parts of the body. This, in turn, affects the RS since the amount of O2 and CO2 transported, respectively to and away from the tissues depends on the cardiac output and blood flow in both the systemic and pulmonary circuits of the CVS. Local metabolic control is influenced by local concentrations of blood gases affecting systemic resistance, resulting to vasoconstriction/vasodilation. Thus, the exchange of blood gases demands a tight coordination between blood flow and ventilation of the lungs. In this work, a model of the cardiovascular-respiratory system (CVRS) is considered to obtain an optimal control for time-dependent ergometric workloads by using the Euler-Lagrange formulation of the optimal control problem. The essential controls in the CVRS model are variations in the heart rate and alveolar ventilation through which the central nervous system restricts the arterial partial pressure of CO2 (Pa,CO2) close to 40 mmHg. Further, penalization terms in the cost functional are included to match the metabolic need for O2 and the metabolic production of CO2 with O2- and CO2-transport by blood.