A new model is used to analyze the fully coupled problem of pulsatile blood flow through a compliant, axisymmetric stenotic artery using the finite element method. The model uses large displacement and large strain theory for the solid, and the full Navier-Stokes equations for the fluid. The effect of increasing area reduction on fluid dynamic and structural stresses is presented. Results show that pressure drop, peak wall shear stress, and maximum principal stress in the lesion all increase dramatically as the area reduction in the stenosis is increased from 51 to 89 percent. Further reductions in stenosis cross-sectional area, however, produce relatively little additional change in these parameters due to a concomitant reduction in flow rate caused by the losses in the constriction. Inner wall hoop stretch amplitude just distal to the stenosis also increases with increasing stenosis severity, as downstream pressures are reduced to a physiological minimum. The contraction of the artery distal to the stenosis generates a significant compressive stress on the downstream shoulder of the lesion. Dynamic narrowing of the stenosis is also seen, further augmenting area constriction at times of peak flow. Pressure drop results are found to compare well to an experimentally based theoretical curve, despite the assumption of laminar flow.

1.
ADINA System User Manuals, 1997, User’s Guide (Report 97–1), Theory and Modeling Guides (Reports ARD 97–7 and 97–8), Verification Manual (Report ARD 97–9), ADINA R&D Inc.
2.
Bathe, K. J., 1996, Finite Element Procedures, Prentice Hall, NJ.
3.
Bathe, K. J., Zhang, H., and Shanhong, J., 1999, “Finite Element Analysis of Fluid Flows Fully Coupled With Structural Interactions,” Computers and Structures, in press.
4.
Bathe
K. J.
,
Zhang
H.
, and
Wang
M. H.
,
1995
, “
Finite Element Analysis of Incompressible and Compressible Fluid Flows With Free Surfaces and Structural Interactions
,”
Computers and Structures
, Vol.
56
, No.
2/3
, pp.
193
213
.
5.
Bathe
K. J.
,
Zhang
H.
, and
Zhang
X.
,
1997
, “
Some Advances in the Analysis of Fluid Flows
,”
Computers and Structures
, Vol.
64
, No.
5/6
, pp.
909
930
.
6.
Binns
R. L.
, and
Ku
D. N.
,
1989
, “
Effect of Stenosis on Wall Motion: A Possible Mechanism of Stroke and Transient Ischemic Attack
,”
Arteriosclerosis
, Vol.
9
(
6
) Nov., pp.
842
847
.
7.
Bluestein
D.
,
Niu
L.
,
Schoephoerster
R. T.
, and
Dewanjee
M. K.
,
1997
, “
Fluid Mechanics of Arterial Stenosis: Relationship to the Development of Mural Thrombus
,”
Annals of Biomedical Engineering
, Vol.
25
, pp.
344
356
.
8.
Born, G. V. R., Davies, M. J., and Richardson, P. D., 1989, “Influence of Plaque Configuration and Stress Distribution on Fissuring of Coronary Atherosclerotic Plaques,” The Lancet, Oct. 21, pp. 941–944.
9.
Caro, C. G., Pedley, R. J., Schroter, R. C., and Seed, N. A., 1978, The Mechanics of the Circulation, Oxford University Press, New York.
10.
Cheng
G. C.
,
Loree
H. M.
,
Kamm
R. D.
,
Fishbein
M. C.
, and
Lee
R. T.
,
1993
, “
Distribution of Circumferential Stress in Ruptured and Stable Atherosclerotic Lesions, A Structural Analysis With Histopathological Correlation
,”
Circulation Research
, Vol.
87
, pp.
1179
1187
.
11.
Demiray
H.
,
1988
, “
Pulse Velocities in Initially Stressed Arteries
,”
Journal of Biomechanics
, Vol.
21
, No.
1
, pp.
55
58
.
12.
Downing
J. M.
, and
Ku
D. N.
,
1997
, “
Effects of Frictional Losses and Pulsatile Flow on the Collapse of Stenotic Arteries
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
119
(
3
), pp.
317
324
.
13.
Du
W.
,
Mills
I.
,
Oluwole
B. O.
, and
Sumpio
B. E.
,
1997
, “
Gene Regulation by Mechanical Forces
,”
Endothelium
, Vol.
5
(
2
), pp.
85
93
.
14.
Fry
D. L.
,
1968
, “
Acute Vascular Endothelial Changes Associated With Increased Blood Velocity Gradients
,”
Circulation Research
, Vol.
22
, pp.
165
197
.
15.
Fung, Y. C., 1993, Biomechanics: Mechanical Properties of Living Tissues, Springer-Verlag, New York.
16.
Fung, Y. C., 1990, Biomechanics: Motion, Flow, Stress, and Growth, Edwards Brothers, Inc., Ann Arbor.
17.
Gerrity
R. G.
,
1973
, “
The Role of the Monocyte in Atherogenesis, I: Transition of Blood-Borne Monocytes Into Foam Cells in Fatty Lesions
,”
American Journal of Pathology
, Vol.
103
, pp.
181
191
.
18.
Gonzales
R. S.
, and
Wick
T. M.
,
1996
, “
Hemodynamic Modulation of Monocytecell Adherence to Vascular Endothelium
,”
Annals of Biomedical Engineering
, Vol.
24
, pp.
382
393
.
19.
Hayashi, K., and Matsumoto, T., 1996, “Response of Arterial Wall Thickening to Hypertension and Residual Stress,” Biomechanics, Functional Adaptation and Remodeling, Springer-Verlag, Tokyo.
20.
Ku
D. N.
,
Meister
J. J.
,
Moore
J. E.
,
Stergiopulos
N.
, and
Strassle
A.
,
1993
, “
Steady Flow Tests and Demonstration of Collapse on Models of Compliant Axisymmetric Stenoses
,”
Advances in Bioengineering
, ASME BED-Vol.
26
, pp.
455
458
.
21.
Lee
R. T.
,
Grodzinsky
A. J.
,
Frank
E. H.
,
Kamm
R. D.
, and
Schoen
F. J.
,
1990
, “
Structure-Dependent Dynamic Mechanical Behavior of Fibrous Caps From Human Atherosclerotic Plaques
,”
Circulation
, Vol.
83
, pp.
1764
1770
.
22.
Lee
R. T.
, and
Libby
P.
,
1997
, “
The Unstable Atheroma
,”
Arterioscler. Thromb. Vasc. Biol.
, Vol.
17
(
10
), pp.
1859
1867
.
23.
Loree
H. M.
,
Kamm
R. D.
,
Stringfellow
R. G.
, and
Lee
R. T.
,
1992
, “
Effects of Fibrous Cap Thickness on Peak Circumferential Stress in Model Atherosclerotic Vessels
,”
Circulation Research
, Vol.
71
, pp.
850
858
.
24.
Mills
I.
,
Murata
K.
, and
Sumpio
B. E.
,
1996
, “
Protein Phosphatase 2A in Stretch-Induced Endothelial Cell Proliferation
,”
Journal of Cell Biochemistry
, Vol.
63
(
3
), pp.
311
319
.
25.
Mohan
S.
,
Mohan
N.
, and
Sprague
E. A.
,
1997
, “
Differential Activation of NF-Kappa B in Human Aortic Endothelial Cells Conditioned to Specific Flow Environments
,”
American Journal of Physiology
, Vol.
273
, pp.
C572–C578
C572–C578
.
26.
Morgan, B. E., 1971, “Flow Through a Model of an Arterial Stenosis,” M.S. Thesis, Iowa State University.
27.
Munro
J. M.
,
van der Walt
J. D.
,
Munro
C. S.
,
Chalmers
J. A.
, and
Cox
E. L.
,
1987
, “
An Immunohistochemical Analysis of Human Aortic Fatty Streaks
,”
Human Pathology
, Vol.
18
, pp.
375
380
.
28.
Ogden, R. W., 1984, Nonlinear Elastic Deformations, Ellis Horwood, Chichester, U. K.
29.
Patel, D. J., and Vaishnav, R. N., 1972, “The Rheology of Large Blood Vessels,” in: Cardiovascular Fluid Dynamics, D. H. Bergel, ed., Vol. 2, pp. 1–64, London Academic Press.
30.
Pedley, T. J., 1980, The Fluid Mechanics of Large Blood Vessels, Cambridge University Press, England.
31.
Ramstack
J. M.
,
Zuckerman
L.
, and
Mockros
L. F.
,
1979
, “
Shear Induced Activation of Platelets
,”
Journal of Biomechanics
, Vol.
12
, pp.
113
125
.
32.
Rooz
E.
,
Young
D. F.
, and
Rogge
T. R.
,
1982
, “
A Finite Element Simulation of Pulsatile Flow in Flexible Obstructed Tubes
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
104
, pp.
119
124
.
33.
Santamore
W. P.
, and
Bove
A. A.
,
1985
, “
A Theoretical Model of a Compliant Arterial Stenosis
,”
American Journal of Physiology
, Vol.
248
(Heart and Circulatory Physiology, Vol. 17):
H274–H285
H274–H285
.
34.
Sato
M.
,
Hayashi
K.
,
Niimi
H.
,
Moritake
K.
,
Okumura
A.
, and
Handa
H.
,
1979
, “
Axial Mechanical Properties of Arterial Walls and Their Anisotropy
,”
Medical and Biological Engineering and Computing
, Vol.
17
, pp.
170
176
.
35.
Seeley
B. D.
, and
Young
D. F.
,
1976
, “
Effect of Geometry on Pressure Losses Across Models of Arterial Stenoses
,”
Journal of Biomechanics
, Vol.
9
, pp.
439
448
.
36.
Siebes
M.
,
Campbell
C. S.
, and
D’Argenio
D. Z.
,
1996
, “
Fluid Dynamics of a Partially Collapsible Stenosis in a Flow Model of the Coronary Circulation
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
118
, pp.
489
497
.
37.
Stergiopulos
N.
,
Young
D. F.
, and
Rooge
T. R.
,
1992
, “
Computer Simulation of Arterial Flow With Applications to Arterial and Aortic Stenoses
,”
Journal of Biomechanics
, Vol.
25
, pp.
1477
1488
.
38.
Strony
J.
,
Beaudoin
A.
,
Brands
D.
, and
Adelman
B.
,
1993
, “
Analysis of Shear Stress and Hemodynamic Factors in a Model of Coronary Artery Stenosis and Thrombosis
,”
American Journal of Physiology
, Vol.
265
, pp.
H1787–H1796
H1787–H1796
.
39.
Sumpio
B. E.
, and
Widmann
M. D.
,
1990
, “
Enhanced Production of Endothelium Derived Contracting Factor by Endothelial Cells Subjected to Pulsatile Stretch
,”
Surgery
, Vol.
108
(
2
), pp.
277
281
.
40.
Sussman
T.
, and
Bathe
K. J.
,
1987
, “
A Finite Element Formulation for Nonlinear Incompressible Elastic and Inelastic Analysis
,”
Computers and Structures
, Vol.
26
, pp.
357
409
.
41.
Tanaka, E., Yamada, H., and Murakami, S., 1996, “Inelastic constitutive modeling of arterial and ventricular walls,” in: Computational Biomechanics, K. Hayashi and H. Ishikawa, eds., pp. 137–164, Springer, Tokyo.
42.
Tandon
P. N.
, and
Rana
U. V. S.
,
1995
, “
A New Model for Blood Flow Through and Artery With Axisymmetric Stenosis
,”
International Journal of Bio-Medical Computing
, Vol.
38
, pp.
257
267
.
43.
Tsao
P. S.
,
Buitrago
R.
,
Chan
J. R.
, and
Cooke
J. P.
,
1996
, “
Fluid flow inhibits endothelial adhesiveness. Nitric oxide and transcriptional regulation of VCAM-1
,”
Circulation
, Vol.
94
, pp.
1682
1689
.
44.
Tsao
P. S.
,
Lewis
N. R.
,
Alpert
S.
, and
Cooke
J. P.
,
1995
, “
Exposure to shear stress alters endothelial adhesiveness. Role of nitric oxide
,”
Circulation
, Vol.
92
, pp.
3513
3519
.
45.
Young
D. F.
,
1979
, “
Fluid Mechanics of Arterial Stenoses
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
101
, pp.
157
175
.
46.
Young
D. F.
, and
Tsai
F. Y.
,
1973
, “
Flow Characteristics in Models of Arterial Stenoses–1. Steady Flow
,”
Journal of Biomechanics
, Vol.
6
, pp.
395
410
.
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