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

Abstract

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 flow 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. Effects of stenosis severity and stiffness, pressure drop, external pressure and stiffness of the vessel wall on the flow and wall motion were evaluated. It was found that stenosis severity, pressure drop and external pressure played more dominant roles than tube wall stiffness and stenosis stiffness perturbation. Tubes with 71 and 78 per cent stenoses showed two areas of negative transmural pressure and complex contraction-expansion-contraction 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 pressure-flow 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 different pressure conditions.1998 John Wiley & Sons, Ltd.

Occlusion and Severe Stenosis Identification in Arterial System

“…In fact, severe stenoses cause considerable compressive stress in the tube wall and critical flow conditions such as high shear stress and flow separation which are related to artery compression, plaque rupture, and thrombus formation. It induces an augmentation of the reflection coefficient [12] leading to significant waves reflection [20] that may raise the risk of aortic rupture. Such diagnosis of this kind of arterial disease can help in the prevalence of peripheral arterial disease.…”

“…However, some other researchers used the impedance technique to investigate and identify occlusions and constrictions in tube-like element or branching networks [9][10][11]. Other models, which include the Navier-Stokes equations for flow in constricted elastic tubes or arterial networks, are available [12]. Many authors map the position of a reflection site by the evaluation of the time lag between incident and retrograde wave of the wave speed = .…”

“…n cl f n cl n cl   (11) (13) Where ′ = − denotes the distance between the reflecting site and the first measurement site. Combining equations (11), (12) and (13)…”

Obstruction identification in branching compliant tubes with application to airway passages

“…The developed model is applied to an airway passage in the respiratory system. Although other models are available for an occlusion or a constriction in a tube or a branched tube networks (Tang et al, 1998;Elad et al, 1988;Grotberg, 1992, 1993;Heil, 1999), approaches other than the acoustic impedance approach are also used. These include the Navier-Stokes equations for fluid flow in constricted elastic tubes, lubrication theory, etc.…”

First-order system least squares (FOSLS) for coupled fluid-elastic problems

“…A simplified version of the fully decoupled approach is frequently used in modeling blood flow with the elastic domain treated as a thin shell [3,4]. The viscous shear stress is typically ignored [5], resulting in displacement only in the radial direction.…”