Steady viscous flow in constricted elastic tubes subjected to a uniform external pressure

Cardiovascular illness is most commonly caused by a constriction, called a stenosis. A non-linear mathematical model with a free moving boundary was introduced to study viscous ßow in tapered elastic tubes with axisymmetric constrictions subject to a prescribed pressure drop and a uniform external pressure. An iterative numerical scheme using a boundary iteration method was developed to solve the model. E¤ects of stenosis severity and sti¤ness, pressure drop, external pressure and sti¤ness of the vessel wall on the ßow and wall motion were evaluated. It was found that stenosis severity, pressure drop and external pressure played more dominant roles than tube wall sti¤ness and stenosis sti¤ness perturbation. Tubes with 71 and 78 per cent stenoses showed two areas of negative transmural pressure and complex contractionÐexpansion Ðcontraction wall motion patterns. Two types of tube diameter contraction and negative transmural pressure were observed, one was just distal to the stenosis and the other was near the outlet of the tube. Experiments using stenotic silicone tubes were conducted to quantify the tube law and verify the predicted pressureÐßow relationship. The agreement between the numerical results and experimental measurements is better than that from a previous model which assumed periodicity of the tube and imposed di¤erent pressure conditions