International Journal of Differential Equations

Unsteady Integrodifferential Equation of Fluid-Structure Interaction in Constricted Collapsible Tube Model of Diseased Human Coronary Artery

Eric Velaski Tuema and Olusegun Ilegbusi

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Abstract

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.

Article information

Source
Int. J. Differ. Equ., Volume 2012 (2012), Article ID 376350, 21 pages.

Dates
Received: 1 July 2011
Accepted: 15 December 2011
First available in Project Euclid: 24 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1485226820

Digital Object Identifier
doi:10.1155/2012/376350

Mathematical Reviews number (MathSciNet)
MR2909473

Zentralblatt MATH identifier
06078081

Citation

Tuema, Eric Velaski; Ilegbusi, Olusegun. Unsteady Integrodifferential Equation of Fluid-Structure Interaction in Constricted Collapsible Tube Model of Diseased Human Coronary Artery. Int. J. Differ. Equ. 2012 (2012), Article ID 376350, 21 pages. doi:10.1155/2012/376350. https://projecteuclid.org/euclid.ijde/1485226820


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