Modelling and Analysis of Respiratory System with Congestive Heart Failure

Respiratory system (RS) is one of the most important systems inside the human body. It works with cardiovascular system and neural system. The primary function of the respiratory system is to exchange and distribute gases inside the body. The system maintains homeostasis condition of those gases inside the body by a feedback mechanism. Literature suggests major research on respiratory system is directed towards the analysis of the regulatory function of this system and it is identified that transport delay is one of the most crucial parameter for stability of the system. Literature also suggests that for stability purpose, the minimal model is sufficient. In this work, a nonlinear state-space model with two states are considered. Those are partial pressure of oxygen and carbon dioxide in an alveolar compartment and are considered as state variables. The delay occurs in the feedback control loop, as blood takes finite time to reach from alveolar compartment to the sensory location. This system is analyzed for delay-dependent stability and maximum delay tolerable by the system is calculated Physiologically. Congestive heart failure (CHF) condition is one of such condition, when delay caused by the cardiovascular system is higher than the maximum tolerable limit and it makes the system oscillatory. Such kind of oscillation is manifested by Periodic Breathing (PB) waveform. The delay-dependent stability analysis on the linearized model is done using the Pseudo-delay method (PDM).