%0 Journal Article
%T Unsteady Integrodifferential Equation of Fluid-Structure Interaction in Constricted Collapsible Tube Model of Diseased Human Coronary Artery
%A Eric Velaski Tuema
%A Olusegun Ilegbusi
%J International Journal of Differential Equations
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/376350
%X Unsteady flow in a collapsible tube is analyzed to simulate a diseased human coronary artery. The novelty of the approach is that the set of equations governing the fluid-structure interaction is reduced to a single integrodifferential equation in the transient state. The equation is then solved using the finite difference method to obtain the flow characteristics and compliant wall behavior. Three control parameters are investigated, namely, Reynolds number, inlet transmural pressure, and the wall thickness. The predicted wall deflection is quite large at low Reynolds numbers, suggesting possible approach to breakdown in equilibrium. The transmural pressure increases with wall deflection and bulges appear at the ends of the membrane indicating critical stage of stability, consistent with previous studies. Increase in wall thickness reduces the wall deflection and ultimately results in its collapse which may indicate another breakdown in equilibrium. An increase in internal pressure is required to maintain membrane stability. 1. Introduction This paper describes a two-dimensional (2D) analytical study of collapsible tube simulating unsteady flow in a stenosed coronary artery. The effect is investigated of peristaltic flow in a geometrically nonlinear elastic tube, whose walls deform due to the transient transmural pressure. The arterial wall motion results in a strong fluid-structure interaction. The study is based on the hypothesis that the transient fluid-structure interaction in such a channel could be adequately represented as a single integrodifferential equation which can be solved using finite-difference numerical method. The novelty of the study is the analysis of unsteady flow and the methodology employed to solve the resulting integrodifferential equation. The problem posed by fluid flow through flexible tubes with relatively thin walls is theoretically challenging and practically significant. The theoretical challenges are due to the interaction between the fluid flow and the elastic channel walls. Thus, fluid flow and structural parameters have to be computed simultaneously. In addition, the boundary conditions cannot be completely defined in advance, due to the continuously evolving boundary. The practical significance of these problems are considerable, in particular in bioengineering and biomedical systems because of their pivotal role in describing fluid flow in living organs including cardiovascular, respiratory, and urinary systems [1]. In particular, vessels experiencing compressive transmural pressure and consequent remodeling
%U http://www.hindawi.com/journals/ijde/2012/376350/