A Nonlinear Axisymmetric Model With Fluid–Wall Interactions for Steady Viscous Flow in Stenotic Elastic Tubes

[+] Author and Article Information
D. Tang

Mathematical Sciences Department, Worcester Polytechnic Institute, Worcester, MA 01609

J. Yang

Computer Science Department, University of Pittsburgh, Pittsburgh, PA 15260

C. Yang

Mathematics Department, Beijing Normal University, Beijing, China

D. N. Ku

Georgia Institute of Technology, School of Mechanical Engineering, Atlanta, GA 30332

J Biomech Eng 121(5), 494-501 (Oct 01, 1999) (8 pages) doi:10.1115/1.2835078 History: Received February 14, 1998; Revised February 18, 1999; Online January 23, 2008


Arteries with high-grade stenoses may compress under physiologic conditions due to negative transmural pressure caused by high-velocity flow passing through the stenoses. To quantify the compressive conditions near the stenosis, a nonlinear axisymmetric model with fluid–wall interactions is introduced to simulate the viscous flow in a compliant stenotic tube. The nonlinear elastic properties of the tube (tube law) are measured experimentally and used in the model. The model is solved using ADINA (Automatic Dynamic Incremental Nonlinear Analysis), which is a finite element package capable of solving problems with fluid–structure interactions. Our results indicate that severe stenoses cause critical flow conditions such as negative pressure and high and low shear stresses, which may be related to artery compression, plaque cap rupture, platelet activation, and thrombus formation. The pressure field near a stenosis has a complex pattern not seen in one-dimensional models. Negative transmural pressure as low as −24 mmHg for a 78 percent stenosis by diameter is observed at the throat of the stenosis for a downstream pressure of 30 mmHg. Maximum shear stress as high as 1860 dyn/cm2 occurs at the throat of the stenoses, while low shear stress with reversed direction is observed right distal to the stenosis. Compressive stresses are observed inside the tube wall. The maximal principal stress and hoop stress in the 78 percent stenosis are 80 percent higher than that from the 50 percent stenosis used in our simulation. Flow rates under different pressure drop conditions are calculated and compared with experimental measurements and reasonable agreement is found for the prebuckling stage.

Copyright © 1999 by The American Society of Mechanical Engineers
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