COLLAPSE OF THIN-WALLED ELLIPTIC TUBES FOR HIGH VALUES OF MAJOR-TO-MINOR AXIS RATIO

The topic of this study concerns principally representative models of some elliptical thin- walled anatomic vessels and polymeric tubes unde r uniform negative transmural pressure p (internal pressure minus exte rnal pressure). The ellipse's ellipticity k(o), defined as the major-t o-minor axis ratio, varies from 1 up to 10. As p decreases from zero, at first the cross-section becomes somewhat oval, then the opposite si des touch in one point at the first-contact pressure p(c). If p is low ered beneath p(c), the curvature of the cross-section at the point of contact decreases until it becomes zero at the osculation pressure or the first line-contact pressure p(l). For p < p(l), the contact occurs along a straight-line segment, the length of which increases as p dec reases. The pressures p(c) and p(l) are determined numerically for var ious values of the wall thickness of the tubes. The nature of contact is especially described. The solution of the related nonlinear, two-bo undary-values problem is compared with previous experimental results w hich give the luminal cross-sectional area (from two tubes), and the a rea of the mid-cross-section (from a third tube).