Cross-sectional shape of collapsible tubes

Abstract

In order to quantify the collapse phenomenon in veins, this paper presents a mathematical analysis of the cross-sectional shape of a flexible tube as its internal pressure varies. Quantitative results are presented in terms of the physical parameters of the tube, such as wall thickness and Young's modulus. It is assumed that the tube is thin walled, that no stretching occurs, that the cross-sectional shape is elliptical when the transmural pressure is zero, and that the longitudinal prestress is zero. The equations were solved on a digital computer which displayed the cross-sectional shapes on an oscilloscope, which were then photographed. A selection of these photographs is presented. Curves are shown which give the cross-sectional area and compliance as functions of transmural pressure. Other curves are shown which are useful for interpolation, and for use in the experimental determination of the physical parameters which may otherwise be difficult or impossible to measure accurately.