The control of ventilation: a theoretical analysis of the response to transient disturbances.

Serial measurements of respiration in infants from birth to 7 months have revealed a changing pattern of response with age to spontaneous transient disturbances (e.g. deep sighs). These responses may be interpreted in terms of changing stability of the respiratory control system. The simplest possible model of respiratory control is analysed here. The control system is described by a feedback loop comprising a lung compartment, central and peripheral CO2 detectors and a circulatory delay. The differential equations representing this model are analysed in terms of the phase portrait. First we define the bounds of the solutions in the phase space and the equilibrium points. Next we discuss the local stability and damping of the system under small displacements from these equilibrium points. This local stability can be described in terms of the solution of a linear approximation about the equilibrium points. The trajectories of the solution vector under larger displacements from the equilibrium points are discussed in terms of Taylor expansions. It is shown by this analyses that this simple model can account qualitatively for the observed patterns of respiration following a deep sigh and the changes in that response from birth to 7 months.