Limit Cycle Stability Analysis of a Multi-Compartment Model for a Pressure-Limited Respirator and Lung Mechanics System

Acute respiratory failure due to infection, trauma, or major surgery is one of the most common problems encountered in intensive care units and mechanical ventilation is the mainstay of supportive therapy for such patients. In this paper, we develop a general mathematical model for the dynamic behavior of a multi-compartment respiratory system in response to an arbitrary applied inspiratory pressure. Specifically, we use compartmental dynamical system theory to model and analyze the dynamics of a pressure-limited respirator and lung mechanics system, and show that the periodic orbit generated by this system is globally asymptotically stable. Furthermore, we show that the individual compartmental volumes, and hence the total lung volume, converge to steady-state end-inspiratory and end-expiratory values.