In this study, newly developed two-equation turbulence models and transitional variants are employed for the prediction of blood flow patterns in a diseased carotid artery where the growth, progression, and structure of the plaque at rupture are closely linked to low and oscillating wall shear stresses. Moreover, the laminar-turbulent transition in the poststenotic zone can alter the separation zone length, wall shear stress, and pressure distribution over the plaque, with potential implications for stresses within the plaque. Following the validation with well established experimental measurements and numerical studies, a magnetic-resonance (MR) image-based model of the carotid bifurcation with 70% stenosis was reconstructed and simulated using realistic patient-specific conditions. Laminar flow, a correlation-based transitional version of Menter’s hybrid kϵkω shear stress transport (SST) model and its “scale adaptive simulation” (SAS) variant were implemented in pulsatile simulations from which analyses of velocity profiles, wall shear stress, and turbulence intensity were conducted. In general, the transitional version of SST and its SAS variant are shown to give a better overall agreement than their standard counterparts with experimental data for pulsatile flow in an axisymmetric stenosed tube. For the patient-specific case reported, the wall shear stress analysis showed discernable differences between the laminar flow and SST transitional models but virtually no difference between the SST transitional model and its SAS variant.

1.
Lopez
,
A. D.
,
Mathers
,
C. D.
,
Ezzati
,
M.
,
Jamison
,
D. T.
, and
Murray
,
C. J. L.
, 2006, “
Global and Regional Burden of Disease and Risk Factors, 2001: Systematic Analysis of Population Health Data
,”
Lancet
0140-6736,
367
(
9524
), pp.
1747
1757
.
2.
Topol
,
E. J.
, and
Yadav
,
J. S.
, 2000, “
Recognition of the Importance of Embolization in Atherosclerotic Vascular Disease
,”
Circulation
0009-7322,
101
(
5
), pp.
570
580
.
3.
Ku
,
D. N.
, 1997, “
Blood Flow in Arteries
,”
Annu. Rev. Fluid Mech.
0066-4189,
29
(
1
), pp.
399
434
.
4.
Giddens
,
D. P.
,
Mabon
,
R. F.
, and
Cassanova
,
R. A.
, 1976, “
Measurements of Disordered Flows Distal to Subtotal Vascular Stenoses in the Thoracic Aortas of Dogs
,”
Circ. Res.
0009-7330,
39
(
1
), pp.
112
119
.
5.
Slager
,
C. J.
,
Wentzel
,
J. J.
,
Gijsen
,
F. J. H.
,
Schuurbiers
,
J. C. H.
,
van der Wal
,
A.
,
van der Steen
,
A.
, and
Serruys
,
P. W.
, 2005, “
The Role of Shear Stress in the Generation of Rupture-Prone Vulnerable Plaques
,”
Nat. Clin. Pract. Cardiovasc. Med.
,
2
, pp.
401
407
.
6.
Slager
,
C. J.
,
Wentzel
,
J. J.
,
Gijsen
,
F. J. H.
,
Thury
,
A.
,
van der Wal
,
A.
,
Schaar
,
J. A.
, and
Serruys
,
P. W.
, 2005, “
The Role of Shear Stress in the Destabilization of Vulnerable Plaques and Related Therapeutic Implications
,”
Nat. Clin. Pract. Cardiovasc. Med.
,
2
, pp.
456
464
.
7.
Lehoux
,
S.
,
Castier
,
Y.
, and
Tedgui
,
A.
, 2006, “
Molecular Mechanisms of the Vascular Responses to Haemodynamic Forces
,”
J. Intern Med.
0954-6820,
259
, pp.
381
392
.
8.
Li
,
Y. J.
,
Haga
,
J. H.
, and
Chien
,
S.
, 2005, “
Molecular Basis of the Effects of Shear Stress on Vascular Endothelial Cells
,”
J. Biomech.
0021-9290,
38
, pp.
1949
1971
.
9.
Malek
,
A. M.
,
Alper
,
S. L.
, and
Izumo
,
S.
, 1999, “
Hemodynamic Shear Stress and Its Role in Atherosclerosis
,”
JAMA, J. Am. Med. Assoc.
0098-7484,
282
(
21
), pp.
2035
2042
.
10.
Karino
,
T.
, and
Goldsmith
,
H. L.
, 1979, “
Adhesion of Human Platelets to Collagen on the Walls Distal to a Tubular Expansion
,”
Microvasc. Res.
0026-2862,
17
(
3
), pp.
238
262
.
11.
Pritchard
,
W. F.
,
Davies
,
P. F.
,
Derafshi
,
Z.
,
Polacek
,
D. C.
,
Tsao
,
R.
,
Dull
,
R. O.
,
Jones
,
S. A.
, and
Giddens
,
D. P.
, 1995, “
Effects of Wall Shear Stress and Fluid Recirculation on the Localization of Circulating Monocytes in a Three-Dimensional Flow Model
,”
J. Biomech.
0021-9290,
28
(
12
), pp.
1459
1469
.
12.
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
0009-7322,
87
(
4
), pp.
1179
1187
.
13.
Lee
,
R. T.
,
Schoen
,
F. J.
,
Loree
,
H. M.
,
Lark
,
M. W.
, and
Libby
,
P.
, 1996, “
Circumferential Stress and Matrix Metalloproteinase 1 in Human Coronary Atherosclerosis: Implications for Plaque Rupture
,”
Arterioscler., Thromb., Vasc. Biol.
1079-5642,
16
(
8
), pp.
1070
1073
.
14.
Ojha
,
M.
,
Cobbold
,
R. S. C.
,
Johnston
,
K. W.
, and
Hummel
,
R. L.
, 1989, “
Pulsatile Flow Through Constricted Tubes: An Experimental Investigation Using Photochromic Tracer Methods
,”
J. Fluid Mech.
0022-1120,
203
, pp.
173
197
.
15.
Ahmed
,
S. A.
, and
Giddens
,
D. P.
, 1984, “
Pulsatile Poststenotic Flow Studies with Laser Doppler Anemometry
,”
J. Biomech.
0021-9290,
17
(
9
), pp.
695
705
.
16.
Lieber
,
B. B.
, and
Giddens
,
D. P.
, 1990, “
Post-Stenotic Core Flow Behavior in Pulsatile Flow and Its Effects on Wall Shear Stress
,”
J. Biomech.
0021-9290,
23
(
6
), pp.
597
605
.
17.
Ghalichi
,
F.
,
Deng
,
X.
,
Champlain
,
A. D.
,
Douville
,
Y.
,
King
,
M.
, and
Guidoin
,
R.
, 1998, “
Low Reynolds Number Turbulence Modeling of Blood Flow in Arterial Stenoses
,”
Biorheology
0006-355X,
35
(
4–5
), pp.
281
294
.
18.
Bluestein
,
D.
,
Gutierrez
,
C.
,
Londono
,
M.
, and
Schoephoerster
,
R. T.
, 1999, “
Vortex Shedding in Steady Flow Through a Model of an Arterial Stenosis and Its Relevance to Mural Platelet Deposition
,”
Ann. Biomed. Eng.
0090-6964,
27
(
6
), pp.
763
773
.
19.
Varghese
,
S. S.
, and
Frankel
,
S. H.
, 2003, “
Numerical Modeling of Pulsatile Turbulent Flow in Stenotic Vessels
,”
ASME J. Biomech. Eng.
0148-0731,
125
(
4
), pp.
445
460
.
20.
Ryval
,
J.
,
Straatman
,
A. G.
, and
Steinman
,
D. A.
, 2004, “
Two-Equation Turbulence Modeling of Pulsatile Flow in a Stenosed Tube
,”
ASME J. Biomech. Eng.
0148-0731,
126
(
5
), pp.
625
635
.
21.
Banks
,
J.
, and
Bressloff
,
N. W.
, 2007, “
Turbulence Modeling in Three-Dimensional Stenosed Arterial Bifurcations
,”
ASME J. Biomech. Eng.
0148-0731,
129
(
1
), pp.
40
50
.
22.
Stroud
,
J. S.
,
Berger
,
S. A.
, and
Saloner
,
D.
, 2002, “
Numerical Analysis of Flow Through a Severely Stenotic Carotid Artery Bifurcation
,”
ASME J. Biomech. Eng.
0148-0731,
124
(
1
), pp.
9
20
.
23.
Ahmed
,
S. A.
, and
Giddens
,
D. P.
, 1983, “
Velocity Measurements in Steady Flow Through Axisymmetric Stenoses at Moderate Reynolds Numbers
,”
J. Biomech.
0021-9290,
16
(
7
), pp.
505
516
.
24.
Ahmed
,
S. A.
, and
Giddens
,
D. P.
, 1983, “
Flow Disturbance Measurements Through a Constricted Tube at Moderate Reynolds Numbers
,”
J. Biomech.
0021-9290,
16
(
12
), pp.
955
963
.
25.
Ahmed
,
S. A.
, 1998, “
An Experimental Investigation of Pulsatile Flow Through a Smooth Constriction
,”
Exp. Therm. Fluid Sci.
0894-1777,
17
(
4
), pp.
309
318
.
26.
Deshpande
,
M. D.
, and
Giddens
,
D. P.
, 1980, “
Turbulence Measurements in a Constricted Tube
,”
J. Fluid Mech.
0022-1120,
97
(
1
), pp.
65
89
.
27.
Menter
,
F. R.
, 1994, “
Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
,”
AIAA J.
0001-1452,
32
(
8
), pp.
1598
1605
.
28.
Barth
,
T.
, and
Jesperson
,
D.
, 1989, “
The Design and Application of Upwind Schemes on Unstructured Meshes
,” AIAA Paper No. 1989–0366.
29.
Ferziger
,
J. H.
, and
Peric
,
M.
, 1996,
Computational Methods for Fluid Dynamics
,
Springer
,
Berlin
.
30.
Hutchinson
,
B. R.
, and
Raithby
,
G. D.
, 1986, “
A Multigrid Method Based on the Additive Correction Strategy
,”
Numer. Heat Transfer
0149-5720,
9
, pp.
511
537
.
31.
Wilcox
,
D. C.
, 1993,
Turbulence Modeling for CFD
,
Griffin
,
CA
.
32.
Langtry
,
R.
, and
Menter
,
F. R.
, 2005, “
Transition Modeling for General CFD Applications in Aeronautics
,”
Proceedings of the 43rd AIAA Aerospace Sciences Meeting and Exhibit
, Reno, NV, Jan. 10–13, 2005,
ANSYS CFX
,
Otterfing, Germany
.
33.
Menter
,
F. R.
,
Langtry
,
R.
, and
Völker
,
S.
, 2006, “
Transition Modelling for General Purpose CFD Codes
,”
Flow, Turbul. Combust.
1386-6184,
77
, pp.
277
303
.
34.
Menter
,
F. R.
,
Langtry
,
R. B.
,
Likki
,
S. R.
,
Suzen
,
Y. B.
,
Huang
,
P. G.
, and
Völker
,
S.
, 2004, “
A Correlation Based Transition Model Using Local Variables Part I—Model Formulation
,” ASME Paper No. ASME-GT2004–53452.
35.
Menter
,
F. R.
, and
Egorov
,
Y.
, 2005, “
A Scale Adaptive Simulation Model Using Two-Equation Models
,”
Proceedings of the 43rd AIAA Aerospace Sciences Meeting and Exhibit
, Reno, NA, Jan. 10–13, 2005,
ANSYS CFX
,
Otterfing, Germany
.
36.
Davidson
,
L.
, 2006, “
Evaluation for the SST-SAS Model: Channel Flow, Asymmetric Diffuser and Axi-Symmetric Hill
,”
Proceedings of the European Conference on Computational Fluid Dynamics
,
ECCOMAS CFD
,
Egmond aan Zee, The Netherlands
, Sept. 5–8.
37.
Cebral
,
J. R.
,
Lohner
,
R.
,
Soto
,
O.
,
Choyke
,
P. L.
, and
Yim
,
P. J.
, 2002, “
Image-Based Finite Element Modeling of Hemodynamics in Stenosed Carotid Artery
,”
Proc. SPIE
0277-786X,
4683
, pp.
297
304
.
38.
Womersley
,
J. R.
, 1955, “
Method for the Calculation of Velocity, Rate of Flow and Viscous Drag in Arteries When the Pressure Gradient is Known
,”
J. Physiol. (London)
0022-3751,
127
, pp.
553
563
.
39.
Taylor
,
C. A.
,
Hughes
,
T. J. R.
, and
Zarins
,
C. K.
, 1998, “
Finite Element Modeling of Three-Dimensional Pulsatile Flow in the Abdominal Aorta: Relevance to Atherosclerosis
,”
Ann. Biomed. Eng.
0090-6964,
26
, pp.
975
987
.
40.
Taylor
,
C. A.
, and
Hughes
,
T. J. R.
, and
Zarins
,
C.
, 1999, “
Effect of Exercise on Hemodynamic Conditions in the Abdominal Aorta
,”
J. Vasc. Surg.
0741-5214,
29
(
6
), pp.
1077
1089
.
41.
Staikov
,
I. N.
,
Arnold
,
M.
,
Mattle
,
H. P.
,
Remonda
,
L.
,
Sturzenegger
,
M.
,
Baumgartner
,
R. W.
, and
Schroth
,
G.
, 2000, “
Comparison of the ECST, CC, and NASCET Grading Methods and Ultrasound for Assessing Carotid Stenosis. European Carotid Surgery Trial. North American Symptomatic Carotid Endarterectomy Trial
,”
J. Neurol.
0340-5354,
247
(
9
), pp.
681
686
.
42.
Ku
,
D.
,
Giddens
,
D.
,
Zarins
,
C.
, and
Glagov
,
S.
, 1985, “
Pulsatile Flow and Atherosclerosis in the Human Carotid Bifurcation. Positive Correlation Between Plaque Location and Low Oscillating Shear Stress
,”
Arterioscler., Thromb., Vasc. Biol.
1079-5642,
5
(
3
), pp.
293
302
.
43.
Sherwin
,
S. J.
, and
Blackburn
,
H. M.
, 2005, “
Three-Dimensional Instabilities and Transition of Steady and Pulsatile Axisymmetric Stenotic Flows
,”
J. Fluid Mech.
0022-1120,
533
, pp.
297
327
.
44.
Varghese
,
S. S.
,
Frankel
,
S. H.
, and
Fisher
,
P. F.
, 2007, “
Direct Numerical Simulation of Stenotic Flows. Part 2. Pulsatile Flow
,”
J. Fluid Mech.
0022-1120,
582
, pp.
281
318
.
45.
Akhavan
,
R.
,
Kamm
,
R. D.
, and
Shapiro
,
A. H.
, 1991, “
Investigation of Transition to Turbulence in Bounded Oscillatory Stokes Flows Part 2. Numerical Simulations
,”
J. Fluid Mech.
0022-1120,
225
, pp.
423
444
.
46.
Wood
,
N. B.
, 1999, “
Aspects of Fluid Dynamics Applied to the Larger Arteries
,”
J. Theor. Biol.
0022-5193,
199
(
2
), pp.
137
161
.
47.
Giddens
,
D. P.
,
Mabon
,
R. F.
, and
Cassanova
,
R. A.
, 1976, “
Measurements of Disordered Flows Distal to Subtotal Vascular Stenoses in the Thoracic Aortas of Dogs
,”
Circ. Res.
0009-7330,
39
, pp.
112
119
.
48.
Nerem
,
R. M.
,
Seed
,
W. A.
, and
Wood
,
N. B.
, 1972, “
An Experimental Study of the Velocity Distribution and Transition to Turbulence in the Aorta
,”
J. Fluid Mech.
0022-1120,
52
(
1
), pp.
137
160
.
49.
Stein
,
P. D.
, and
Sabbah
,
H. N.
, 1976, “
Turbulent Blood Flow in the Ascending Aorta of Humans With Normal and Diseased Aortic Valves
,”
Circ. Res.
0009-7330,
39
, pp.
58
65
.
50.
ANSYS CFX, 2007, ANSYS CFX 11 Users Manual.
51.
Wilcox
,
D. C.
, 1988, “
Multiscale Model for Turbulent Flows
,”
AIAA J.
0001-1452,
2
(
11
), pp.
1311
1320
.
52.
Wilcox
,
D. C.
, 1988, “
Reassessment of the Scale Determining Equation for Advanced Turbulence Models
,”
AIAA J.
0001-1452,
25
(
11
), pp.
1299
1310
.
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