Respiratory System Model for Quasistatic Pulmonary Pressure-Volume $(P-V)$ Curve: Inflation-Deflation Loop Analyses

A respiratory system model (RSM) is developed for the deflation process of a quasistatic pressure-volume $(P-V)$ curve, following the model for the inflation process reported earlier. In the RSM of both the inflation and the deflation limb, a respiratory system consists of a large population of basic alveolar elements, each consisting of a piston-spring-cylinder subsystem. A normal distribution of the basic elements is derived from Boltzmann statistical model with the alveolar closing (opening) pressure as the distribution parameter for the deflation (inflation) process. An error minimization by the method of least squares applied to existing $P-V$ loop data from two different data sources confirms that a simultaneous inflation-deflation analysis is required for an accurate determination of RSM parameters. Commonly used terms such as lower inflection point, upper inflection point, and compliance are examined based on the $P-V$ equations, on the distribution function, as well as on the geometric and physical properties of the basic alveolar element.