Delay dependent analysis of respiratory system: Application to obstructive sleep apnea

The respiratory system maintains homeostasis of oxygen and carbon dioxide partial pressures inside blood using feedback mechanism. Mathematical modeling of this system helps in understanding the system's properties and performance under different diseased conditions. One such situation addressed here is obstructive sleep apnea. In this condition, periodic breathing pattern is observed. It is characterized by waxing and waning of nasal airflow, which in turn makes minute ventilation oscillatory, and it is quite detrimental to the survival of a human being. In the literature, several reasons have been reported for the oscillations (gain, delay, altitude, etc.). This work is focused on Ventilatory control. Ventilation becomes oscillatory when delay posed by blood flow becomes greater than the tolerable limit. There are two chemoreceptor sites, and delay for these two locations along with their implication are different. Hence, analysis of the system for two different delays are introduced. Using LK functional method, here it is shown by analysis, that the system will become oscillatory when the delay limit crosses the specified limit during sleep. Also, it is seen that the peripheral chemoreceptors are much more susceptible to oscillation in the system.