Mathematical modelling of airway reopening

The theoretical and experimental investigations of the airway reopening by simulation of the progression of airflow through a fluid or liquid-filled rigid-walled tube (an initial model of pulmonary airway reopening) were performed. Positive pressure drove the "finger" of the air forward to displace the liquid and to obtain the interfacial movement. The air-liquid interface was assumed to be a simple axisymmetric meniscus. In this study the rigid tube radius was R and the "finger" of the air was (1-m)1/2R, where m was a fraction of the viscous fluid left behind on the walls of the tube. The liquid had constant surface tension and viscosity. The capillary number defined the state of the system (the air-liquid interface). This number is the dimensionless velocity that represents the ratio of the viscous to the capillary stresses. A quasi-steady state solution as a function of this parameter using the flow analysis was examined. A semi-empirical formula for the interface was generated by dimensional analysis. The results suggested that the pressures, required to reopen the collapsible airway and non-collapsible airway with the same radius, are similar in the magnitude. These studies showed that the air-liquid interface in the airway collapsible tube model could be sumulated by the meniscus of the air-liquid flow in a rigid circular tube model of the same radius.