Kinematic and Dynamic Characteristics of Pulsatile Flows in Stenotic Vessels
Publication: Journal of Engineering Mechanics
Volume 123, Issue 3
Abstract
Nonlinear pulsatile blood flows in distensible vessels were calculated using an implicit finite-difference scheme. The time-dependent wavy lumen was mapped to a fixed rectangular domain. The transient geometric, kinematic, and dynamic boundary conditions were grouped as dimensionless parameters in the Navier-Stokes equations. The flow was controlled by a time-dependent von Karman number and the dilatation and contraction of the wall. Local acceleration components along the wall, the inlet, and the outlet were employed in the determination of the Neumann boundary condition for the pressure field. The momentum flux associated with wall motion had a significant effect on the flow rate and the resistance coefficient. The interaction of the main flow and flow separation was dominated by flow acceleration and deceleration.
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References
1.
Bertram, C. D., and Pedley, T. J.(1983). “Steady and unsteady separation in an approximately two-dimensional indented channel.”J. Fluid Mech., 130, 315–346.
2.
Brown, T. D., and Hung, T. K.(1977). “A numerical method for solving the Navier-Stokes equations in orthogonal curvilinear coordinates.”J. Computational Phys., 23, 343–363.
3.
Cheng, L. C., Clark, M. E., and Robertson, J. M.(1972). “Numerical analysis of oscillating flow in the vicinity of square wall obstacles in plane conduits.”J. Biomechanics, 5, 467–484.
4.
Cheng, L. C., Clark, M. E., and Robertson, J. M.(1973). “Numerical calculations of plane oscillatory non-uniform flow. II: parametric study of pressure gradient and frequency with square wall obstacles.”J. Biomechanics, 6, 521–538.
5.
Daly, B. J.(1976). “A numerical study of pulsatile flow through stenosed canine femoral arteries.”J. Biomechanics, 22, 465–475.
6.
Deshpande, M. D., Giddens, D. P., and Mabon, R. F.(1976). “Steady laminar flow through modelled vascular stenoses.”J. Biomechanics, 9, 165–174.
7.
Fry, D. L.(1968). “Acute vascular endothelial changes associated with increased blood velocity gradients.”Circulation Res., 2, 165–197.
8.
Harlow, F. H., and Welch, J. E.(1965). “Numerical calculation of viscous incompressible flow of fluid with free surface.”Phys. of Fluids, 8, 2182–2189.
9.
Hung, T. K. (1967). “A computational investigation of impulsively-generated eddies.”Proc., 12th Congr. Int. Assoc. Hydraulic Res., 2, 315–322.
10.
Hung, T. K.(1970). “Vortices in pulsatile flows.”Proc., 5th Int. Congr. Rheology, 2, 115–127.
11.
Hung, T. K.(1973). “Spiral flows in finite rotating annular tubes.”J. Engrg. Mech. Div., ASCE, 99, 13–19.
12.
Hung, T. K.(1981). “Forcing functions in Navier-Stokes equations.”J. Engrg. Mech. Div., ASCE, 107, 643–648.
13.
Hung, T. K., and Tsai, Tommy(1996). “Pulsatile blood flows in stenotic artery.”J. Engrg. Mech., ASCE, 122, 890–896.
14.
Lee, J. S., and Fung, Y. C. (1970). “Flow in locally constricted tubes at low Reynolds number.”J. Appl. Mech., E37(1), 9–16.
15.
Ling, S. C., and Atabek, H. B.(1972). “A nonlinear analysis of pulsatile flow in arteries.”J. Fluid Mech., 55, 493–511.
16.
Macagno, E. O., and Hung, T. K.(1967). “Computational and experimental study of a captive annular eddy.”J. Fluid Mech., 28, 43–64.
17.
Pedley, T. J., and Stephanoff, K. D.(1985). “Flow around a channel with a time-dependent indentation in one wall: the generation of vorticity waves.”J. Fluid Mech., 160, 337–368.
18.
Perktold, K.(1987). “On the paths of fluid particle in an axisymmetrical aneurysm.”J. Biomechanics, 20, 311–317.
19.
Savvudes, C. N., and Gerrard, J. H.(1984). “Numerical analysis of flow through a corrugated tube with application to arterial prostheses.”J. Fluid Mech., 138, 129–160.
20.
Shapiro, A. H., Jaffrin, M. Y., and Weinberg, S. L.(1969). “Peristaltic pumping with long wave-lengths at low Reynolds number.”J. Fluid Mech., 37, 799–825.
21.
Siouffi, M., Pelissierr, R., Farahifar, D., and Rieu, R.(1984). “The effect of unsteadiness on the flow through stenoses and bifurcations.”J. Biomechanics, 17, 299–315.
22.
Sobey, I. J.(1980). “On flow through furrowed channel, part 1. Calculated flow patterns.”J. Fluid Mech., 96, 1–26.
23.
Sobey, I. J.(1985). “Observation of waves during oscillatory channel flow.”J. Fluid Mech., 151, 395–426.
24.
Tsai, T. M.-C. (1984). “A computational analysis of pulsating flow in rigid and deformable tubes,” PhD thesis, Univ. of Pittsburgh, Pittsburgh, Pa.
25.
Tu, C., Deville, M., Dheur, L., and Vanderschuren, L.(1992). “Finite element simulation of pulsatile flow through arterial stenosis.”J. Biomechanics, 25, 1141–1152.
26.
Womersley, J. R.(1955). “Oscillatory motion of a viscous liquid in a thin-walled elastic tube-1: The linear approximation for long waves.”Philos. Mag., 46, 199–221.
27.
Young, D. F., and Tsai, F. Y.(1973a). “Flow characteristics in models of arterial stenosis-I. Steady flow.”J. Biomechanics, 6, 395–410.
28.
Young, D. F., and Tsai, F. Y.(1973b). “Flow characteristics in models of arterial stenosis-II. Unsteady flow.”J. Biomechanics, 6, 547–559.
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Copyright © 1997 American Society of Civil Engineers.
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Published online: Mar 1, 1997
Published in print: Mar 1997
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