Airway closure: occluding liquid bridges in strongly buckled elastic tubes

This paper is concerned with the airway closure problem and investigates the quasi-steady deformation characteristics of strongly collapsed (buckled) airways occluded by liquid bridges of high surface tension. The airway wall is modeled as a thin-walled elastic shell, which deforms in response to an external pressure and to the compression due to the surface tension of the liquid bridge. The governing equations are solved numerically using physiological parameter values. It is shown that axisymmetric configurations are statically unstable, as are buckled tubes whose opposite walls are not in contact. The quasi-steady deformation characteristics of strongly collapsed airways whose walls are in opposite wall contact show a pronounced hysteresis during the collapse/reopening cycle. Buckling is shown to occur over a short axial length with moderate circumferential wavenumbers. Finally, further implications of the results for the airway collapse/reopening problem are discussed.