Capillary-Elastic Instabilities with an Oscillatory Forcing Function

Abstract

The lung is comprised of a network of bifurcating airway tubes which are coated with a thin viscous film. Often times, especially in the case of disease, the liquid film can form a meniscus which blocks the tube, thus obstructing airflow. The formation of the liquid meniscus is due to capillary driven instabilities which can arise in the lining, causing the lining to close up. In addition, airflow can also be obstructed if the airway tube collapses in on itself. This occurs when the elastic forces of the tube are not large enough to sustain the negative fluid pressures caused by the surface-tension of the airliquid interface. Premature babies, whose lungs haven’t developed sufficient surfactant to maintain the surface tension of the lung at a sufficiently low level for healthy functioning, are especially predisposed to problems caused by airway closure. In such cases, the patients are sometimes put on high frequency ventilation machines to improve gas exchange (Heldt et al. 1992, Patel 1995, Paulson it el al. 1996). The frequency of the breathing cycle, as well as the tidal volume, are two control parameters at the disposal of the clinician. Little is known, however, of the effect that these two parameters can have on the occurrence of airway closure. Indeed, if airways can be kept open by using some given machine frequency, then this would be of vital importance in the treatment of such patients. The present work examines and quantifies these particular issues.