Manchester Applied Mathematics and Numerical Analysis Seminars Spring 1999

May 5, 1999, 4.00 pm

Airway Closure: Liquid Bridges in Non-Axisymmetrically Buckled Tubes

Dr. Matthias Heil, Dept. of Mathematics, Univ. of Manchester

Airway closure is caused by the formation of occluding liquid bridges in the airways of the lung. Surface tension creates a pressure jump over the two air-liquid interfaces which enclose the liquid bridge. Consequently, the parts of the airway wall which are wetted by the liquid bridge are subject to a compressive load. This surface tension-induced compression can be so strong that the occluded airway collapses (buckles) non-axisymmetrically.

We model the airway as a thin walled elastic tube which contains a liquid bridge of given volume and study the airway's quasi-steady deformation characteristics in response to variations in the external pressure which represents the variations in pleural pressure throughout the breathing cycle.

The governing equations are solved by finite element methods. Parameter studies show that for physiological values of the relevant parameters (the surface tension and the wall's geometric and elastic properties), the axisymmetric configuration is indeed strongly unstable. Non-axisymmetric buckling is predicted to occur with a moderate number of circumferential waves and over a short axial length. Following the loss of axisymmetric stability, the airway is predicted to (dynamically) jump into a new strongly collapsed equilibrium position in which large parts of the opposite walls are in contact. The deformation characteristics of strongly collapsed airways with opposite wall contact show a pronounced hysteresis in the collapse/reopening cycle. The implications of these predictions for the airway collapse/reopening problem will be discussed.

For further info contact either Matthias Heil (mheil@ma.man.ac.uk), Mark Muldoon (M.Muldoon@umist.ac.uk)or the seminar secretary (Tel. 0161 275 5800).