Limitations of the open loop gain concept in studies of respiratory control

A steady state mathematical model was used to study the limitations of applying the open loop gain concept to the ventilatory control system. Open loop gain is a term used in the study of linear control systems and is an indicator of how well the controlled variable is regulated. The model contained descriptions of the O2 and CO2 control systems as well as their interactions. Disturbances to the system were modelled as occurring via inspired air, metabolic rate and ventilation. The ventilatory response to hypoxia was simulated for (a) hypocapnic hypoxia, (b) normocapnic hypoxia (PaCO2 = 40 torr) and (c) hypercapnic hypoxia (PaCO2 = 45 torr). The open loop gains of the O2 and CO2 loops were calculated at each operating point. In addition, the sensitivity of the controlled variable to disturbances to the loop were also compared. It was observed that open loop gain did not completely describe the characteristics of the ventilatory control system. This was due to the fact that the ventilatory system is nonlinear and the regulatory ability of the ventilatory system depends on the route of the disturbance, and (2) open loop gain ignores the interactions of the CO2 and O2 loops, which can be substantial.