| Abstract | We developed a computational model of the human respiratory control system and its chemoreflex control during sleep. Our model, which is an extension of the model of Grodins et al. (J. Appl. Physiol. 22(2):260-276, 1967), combines an accurate description of a plant with a novel controller design. The controller consists of two negative feedback loops (central and peripheral) each with its own delay and gain. The peripheral chemoreceptor (PCR) loop operates with short delay and the central chemoreceptor (CCR) loop operates with long delay. Both delays are state-dependent that is they depend on the partial pressures of oxygen and carbon dioxide in the arterial blood – state variables of the system. Periodic breathing – an oscillatory limit cycle behavior, indicative of instability in the respiratory control system, is commonly seen during sleep in premature infants, in patients with heart failure, and during exposure to high altitude. These periodicities appear to relate to the operation of, and interaction between, the two chemoreflex loops. Precisely how the gains and delays of the two loops interact to determine overall stability of the system is uncertain, however. The mathematical analysis of the control system having one negative feedback loop indicates that the oscillatory limit cycle behavior develops when feedback gain and/or delay exceed critical level. Similar analysis of the system having multiple feedback loops, each having state-dependant delay, has proven more challenging with positive results restricted to few special cases. To draw some general conclusions about stability of the respiratory control system during sleep, we employed a two dimensional plot similar in concept to the phase plane, with the chemosensitivities of the two loops serving as coordinates of each point. The plain contains a region of stability with the normal operating point for the system lying well inside its boundaries. For the normal operating point, or any other operating point from the stability region, the system exhibits stable steady state behavior. Changes to the sensitivities of either loop caused by known pathologies displace the operating point toward the border of the stability region and further into the region of bi-stability. While operating in this region, the system characterized by the same values of all parameters may exhibit either stable steady state or oscillatory limit cycle behavior. The actual behavior depends on the past history of the system. An appropriately timed transient perturbation can shift the behavior of the system from the oscillatory limit cycle to steady state or vice versa. We postulate that in many pathophysiological conditions the respiratory control system can be stabilized by means of transient intervention without changing its fundamental characteristics. |
|---|
