Abstract

Blood flow dynamics in a stenosed, subject-specific carotid bifurcation is numerically simulated using direct numerical simulation (DNS) and Reynolds-averaged Navier–Stokes (RANS) equations closed with turbulence models. DNS is meant to provide a term of comparison for the RANS calculations, which include classic two-equations models (k–ε and k–ω) as well as a transitional three-equations eddy-viscosity model (kTkLω). Pulsatile inlet conditions based on in vivo ultrasound measurements of blood velocity are used. The blood is modeled as a Newtonian fluid, and the vessel walls are rigid. The main purpose of this work is to highlight the problems related to the use of classic RANS models in the numerical simulation of such flows. The time-averaged DNS results, interpreted in view of their finite-time averaging error, are used to demonstrate the superiority of the transitional RANS model, which is found to provide results closer to DNS than those of conventional models. The transitional model shows better predictive capabilities in terms of turbulence intensity, temporal evolution of the pressure along the cardiac cycle, and the oscillatory shear index (OSI). Indeed, DNS brings to light the locally transitional or weakly turbulent state of the blood flow, which presents velocity and pressure fluctuations only in the poststenotic region of the internal carotid artery during systole, while the flow is laminar during diastole.

References

References
1.
Ross
,
R.
,
1993
, “
The Pathogenesis of Atherosclerosis: A Perspective for the 1990s
,”
Nature
,
362
(
6423
), pp.
801
809
.10.1038/362801a0
2.
GBD 2013 Mortality and Causes of Death Collaborators
,
2014
, “
Global, Regional, and National Age-Sex Specific All-Cause and Cause-Specific Mortality for 240 Causes of Death, 1990–2013: A Systematic Analysis for the Global Burden of Disease Study 2013
,”
The Lancet
,
385
(
9963
), pp.
117
171
.10.1016/S0140-6736(14)61682-2
3.
Towfighi
,
A.
, and
Saver
,
J. L.
,
2011
, “
Stroke Declines From Third to Fourth Leading Cause of Death in the United States: Historical Perspective and Challenges Ahead
,”
Stroke
,
42
(
8
), pp.
2351
2355
.10.1161/STROKEAHA.111.621904
4.
Go
,
A. S.
,
2013
, “
Heart Disease and Stroke Statistics–2013 Update
,”
Circulation
,
127
(
1
), pp.
e6
e245
.10.1161/CIR.0b013e31828124ad
5.
Shaaban
,
A. M.
, and
Duerinckx
,
A. J.
,
2000
, “
Wall Shear Stress and Early Atherosclerosis
,”
Am. J. Roentgenol.
,
174
(
6
), pp.
1657
1665
.10.2214/ajr.174.6.1741657
6.
Gimbrone
,
M. J.
,
Resnick
,
N.
,
Nagel
,
T.
,
Khachigian
,
L. M.
,
Collins
,
T.
, and
Topper
,
J. N.
,
1997
, “
Hemodynamics, Endothelial Gene Expression, and Atherogenesis
,”
Ann. N. Y. Acad. Sci.
,
811
, pp.
1
10
.10.1111/j.1749-6632.1997.tb51983.x
7.
Malek
,
A. M.
,
Alper
,
S. L.
, and
Izumo
,
S.
,
1999
, “
Hemodynamic Shear Stress and Its Role in Atherosclerosis
,”
J. Am. Med. Assoc.
,
282
(
21
), pp.
2035
2042
.10.1001/jama.282.21.2035
8.
Birchall
,
D.
,
Zaman
,
A.
,
Hacker
,
J.
,
Davies
,
G.
, and
Mendelow
,
D.
,
2006
, “
Analysis of Haemodynamic Disturbance in the Atherosclerotic Carotid Artery Using Computational Fluid Dynamics
,”
Eur. Radiol.
,
16
(
5
), pp.
1074
1083
.10.1007/s00330-005-0048-6
9.
Cibis
,
M.
,
Potters
,
W. V.
,
Selwaness
,
M.
,
Gijsen
,
F. J.
,
Franco
,
O. H.
,
Arias Lorza
,
A. M.
,
de Bruijne
,
M.
,
Hofman
,
A.
,
van der Lugt
,
A.
,
Nederveen
,
A. J.
, and
Wentzel
,
J. J.
,
2016
, “
Relation Between Wall Shear Stress and Carotid Artery Wall Thickening MRI Versus CFD
,”
J. Biomech.
,
49
(
5
), pp.
735
741
.10.1016/j.jbiomech.2016.02.004
10.
Groen
,
H. C.
,
Gijsen
,
F. J. H.
,
van der Lugt
,
A.
,
Ferguson
,
M. S.
,
Hatsukami
,
T. S.
,
van der Steen
,
A. F. W.
,
Yuan
,
C.
, and
Wentzel
,
J. J.
,
2007
, “
Plaque Rupture in the Carotid Artery Is Localized at the High Shear Stress Region
,”
Stroke
,
38
(
8
), p.
2379
.10.1161/STROKEAHA.107.484766
11.
Executive Committee for the Asymptomatic Carotid Atherosclerosis Study
,
1995
, “
Endarterectomy for Asymptomatic Carotid Artery Stenosis
,”
J. Am. Med. Assoc.
,
273
(
18
), pp.
1421
1428
.10.1001/jama.1995.03520420037035
12.
Tuenter
,
A.
,
Selwaness
,
M.
,
Arias Lorza
,
A.
,
Schuurbiers
,
J. C. H.
,
Speelman
,
L.
,
Cibis
,
M.
,
van der Lugt
,
A.
,
de Bruijne
,
M.
,
van der Steen
,
A. F. W.
,
Franco
,
O. H.
,
Vernooij
,
M. W.
, and
Wentzel
,
J. J.
,
2016
, “
High Shear Stress Relates to Intraplaque Haemorrhage in Asymptomatic Carotid Plaques
,”
Atherosclerosis
,
251
, pp.
348
354
.10.1016/j.atherosclerosis.2016.05.018
13.
Slack
,
S. M.
,
Cui
,
Y.
, and
Turitto
,
V. T.
,
1993
, “
The Effects of Flow on Blood Coagulation and Thrombosis
,”
J. Thromb. Haemostasis
,
70
(
1
), pp.
129
134
.
14.
Affeld
,
K.
,
Reininger
,
A. J.
,
Gadischke
,
J.
,
Grunert
,
K.
,
Schmidt
,
S.
, and
Thiele
,
F.
,
1995
, “
Fluid Mechanics of the Stagnation Point Flow Chamber and Its Platelet Deposition
,”
Artif. Organs
,
19
(
7
), pp.
597
602
.10.1111/j.1525-1594.1995.tb02387.x
15.
Paul
,
M. C.
,
Molla
,
M. M.
, and
Roditi
,
G.
,
2009
, “
Large–Eddy Simulation of Pulsatile Blood Flow
,”
Med. Eng. Phys.
,
31
(
1
), pp.
153
159
.10.1016/j.medengphy.2008.04.014
16.
Varghese
,
S. S.
, and
Frankel
,
S. H.
,
2003
, “
Numerical Modeling of Pulsatile Turbulent Flow in Stenotic Vessels
,”
ASME J. Biomech. Eng.
,
125
(
4
), pp.
445
460
.10.1115/1.1589774
17.
Gharahi
,
H.
,
Zambrano
,
B. A.
,
Zhu
,
D. C.
,
DeMarco
,
J. K.
, and
Baek
,
S.
,
2016
, “
Computational Fluid Dynamic Simulation of Human Carotid Artery Bifurcation Based on Anatomy and Volumetric Blood Flow Rate Measured With Magnetic Resonance Imaging
,”
Int. J. Adv. Eng. Sci. Appl. Math.
,
8
(
1
), pp.
46
60
.10.1007/s12572-016-0161-6
18.
Khodarahmi
,
I.
,
2015
, “
Comparing Velocity and Fluid Shear Stress in a Stenotic Phantom With Steady Flow: Phase-Contrast MRI, Particle Image Velocimetry and Computational Fluid Dynamics
,”
Magma Magn. Reson. Mater. Phys., Biol. Med.
,
28
(
4
), pp.
385
393
.10.1007/s10334-014-0476-x
19.
Mittal
,
R.
,
Simmons
,
S. P.
, and
Udaykumar
,
H. S.
,
2001
, “
Application of Large-Eddy Simulation to the Study of Pulsatile Flow in a Modeled Arterial Stenosis
,”
ASME J. Biomech. Eng.
,
123
(
4
), pp.
325
332
.10.1115/1.1385840
20.
Molla
,
M. M.
,
Wang
,
B.-C.
, and
Kuhn
,
D. C. S.
,
2012
, “
Numerical Study of Pulsatile Channel Flows Undergoing Transition Triggered by a Modelled Stenosis
,”
Phys. Fluids
,
24
(
12
), p.
121901
.10.1063/1.4771604
21.
Beratlis
,
N.
,
Balaras
,
E.
, and
Kiger
,
K.
,
2007
, “
Direct Numerical Simulations of Transitional Pulsatile Flow Through a Constriction
,”
J. Fluid Mech.
,
587
, pp.
425
451
.10.1017/S0022112007007380
22.
Mittal
,
R.
,
Simmons
,
S. P.
, and
Najjar
,
F.
,
2003
, “
Numerical Study of Pulsatile Flow in a Constricted Channel
,”
J. Fluid Mech.
,
485
, pp.
337
378
.10.1017/S002211200300449X
23.
Beratlis
,
N.
,
Balaras
,
E.
,
Parvinian
,
B.
, and
Kiger
,
K.
,
2005
, “
A Numerical and Experimental Investigation of Transitional Pulsatile Flow in a Stenosed Channel
,”
ASME J. Biomech. Eng.
,
127
(
7
), pp.
1147
1157
.10.1115/1.2073628
24.
Varghese
,
S. S.
,
Frankel
,
S. H.
, and
Fischer
,
P. F.
,
2007
, “
Direct Numerical Simulation of Stenotic Flows—Part 1: Steady Flow
,”
J. Fluid Mech.
,
582
, pp.
253
280
.10.1017/S0022112007005848
25.
Varghese
,
S. S.
,
Frankel
,
S. H.
, and
Fischer
,
P. F.
,
2007
, “
Direct Numerical Simulation of Stenotic Flows—Part 2: Pulsatile Flow
,”
J. Fluid Mech.
,
582
, pp.
281
318
.10.1017/S0022112007005836
26.
Varghese
,
S. S.
,
Frankel
,
S. H.
, and
Fischer
,
P. F.
,
2008
, “
Modeling Transition to Turbulence in Eccentric Stenotic Flows
,”
ASME J. Biomech. Eng.
,
130
(
1
), p.
014503
.10.1115/1.2800832
27.
Tan
,
F. P. P.
,
Wood
,
N. B.
,
Tabor
,
G.
, and
Xu
,
X. Y.
,
2011
, “
Comparison of LES of Steady Transitional Flow in an Idealized Stenosed Axisymmetric Artery Model With a RANS Transitional Model
,”
ASME J. Biomech. Eng.
,
133
(
5
), p.
051001
.10.1115/1.4003782
28.
Banks
,
J.
, and
Bressloff
,
N. W.
,
2007
, “
Turbulence Modeling in Three-Dimensional Stenosed Arterial Bifurcations
,”
ASME J. Biomech. Eng.
,
129
(
1
), pp.
40
50
.10.1115/1.2401182
29.
Banks
,
J.
,
Bressloff Ghalichi
,
F.
, and
Deng
,
X.
,
2003
, “
Turbulence Detection in a Stenosed Artery Bifurcation by Numerical Simulation of Pulsatile Blood Flow Using the low-Reynolds Number Turbulence Model
,”
Biorheology
,
40
(
6
), pp.
637
654
.
30.
Kaazempur-Mofrad
,
M.
,
Isasi
,
A. G.
,
Younis
,
H. F.
,
Chan
,
R. C.
,
Hinton
,
D. P.
,
Sukhova
,
G.
,
LaMuraglia
,
G. M.
,
Lee
,
R. T.
, and
Kamm
,
R. D.
,
2004
, “
Characterization of the Atherosclerotic Carotid Bifurcation Using MRI, Finite Element Modeling, and Histology
,”
Ann. Biomed. Eng.
,
32
(
7
), pp.
932
946
.10.1023/B:ABME.0000032456.16097.e0
31.
Schirmer
,
C. M.
, and
Malek
,
A. M.
,
2012
, “
Computational Fluid Dynamic Characterization of Carotid Bifurcation Stenosis in Patient-Based Geometries
,”
Brain Behav.
,
2
(
1
), pp.
42
52
.10.1002/brb3.25
32.
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.
,
124
(
1
), pp.
9
20
.10.1115/1.1427042
33.
Tan
,
F. P.
,
Soloperto
,
G.
,
Bashford
,
S.
,
Wood
,
N. B.
,
Thom
,
S.
,
Hughes
,
A.
, and
Xu
,
X. Y.
,
2008
, “
Analysis of Flow Disturbance in a Stenosed Carotid Artery Bifurcation Using Two-Equation Transitional and Turbulence Models
,”
ASME J. Biomech. Eng.
,
130
(
6
), p.
061008
.10.1115/1.2978992
34.
Dong
,
J.
,
Inthavong
,
K.
, and
Tu
,
J.
,
2013
, “
Image-Based Computational Hemodynamics Evaluation of Atherosclerotic Carotid Bifurcation Models
,”
Comput. Biol. Med.
,
43
(
10
), pp.
1353
1362
.10.1016/j.compbiomed.2013.06.013
35.
Rayz
,
V. L.
,
Berger
,
S. A.
, and
Saloner
,
D.
,
2007
, “
Transitional Flows in Arterial Fluid Dynamics
,”
Comput. Meth. Appl. Mech. Eng.
,
196
(
31–32
), pp.
3043
3048
.10.1016/j.cma.2006.10.014
36.
Lee
,
S. E.
,
Lee
,
S.-W.
,
Fischer
,
P. F.
,
Bassiouny
,
H. S.
, and
Loth
,
F.
,
2008
, “
Direct Numerical Simulation of Transitional Flow in a Stenosed Carotid Bifurcation
,”
J. Biomech.
,
41
(
11
), pp.
2551
2561
.10.1016/j.jbiomech.2008.03.038
37.
Kikinis
,
R.
,
Pieper
,
S. D.
, and
Vosburgh
,
K. G.
,
2014
,
3D Slicer: A Platform for Subject-Specific Image Analysis, Visualization, and Clinical Support
,
Springer
,
New York
, pp.
277
289
.
38.
Ballyk
,
P. D.
,
Steinman
,
D. A.
, and
Ethier
,
C. R.
,
1994
, “
Simulation of Non-Newtonian Blood Flow in an End-to-Side Anastomosis
,”
Biorheology
,
31
(
5
), pp.
565
586
.10.3233/BIR-1994-31505
39.
Sharp
,
M. K.
,
Thurston
,
G. B.
, and
Moore
,
J. E.
,
1996
, “
The Effect of Blood Viscoelasticity on Pulsatile Flow in Stationary and Axially Moving Tubes
,”
Biorheology
,
33
(
3
), pp.
185
208
.10.3233/BIR-1996-33301
40.
Gijsen
,
F. J.
,
van de Vosse
,
F. N.
, and
Janssen
,
J. D.
,
1999
, “
The Influence of the Non-Newtonian Properties of Blood on the Flow in Large Arteries: Steady Flow in a Carotid Bifurcation Model
,”
J. Biomech.
,
32
(
6
), pp.
601
608
.10.1016/S0021-9290(99)00015-9
41.
Ambrosi
,
D.
,
Quarteroni
,
A.
, and
Rozza
,
G.
,
2012
,
Modeling of Physiological Flows
,
Springer
,
Berlin
.
42.
Lee
,
S.-W.
, and
Steinman
,
D. A.
,
2007
, “
On the Relative Importance of Rheology for Image-Based CFD Models of the Carotid Bifurcation
,”
ASME J. Biomech. Eng.
,
129
(
2
), pp.
273
278
.10.1115/1.2540836
43.
Thomas
,
J. B.
,
Milner
,
J. S.
,
Rutt
,
B. K.
, and
Steinman
,
D. A.
,
2003
, “
Reproducibility of Image-Based Computational Fluid Dynamics Models of the Human Carotid Bifurcation
,”
Ann. Biomed. Eng.
,
31
(
2
), pp.
132
141
.10.1114/1.1540102
44.
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.
,
127
(
3
), pp.
553
563
.10.1113/jphysiol.1955.sp005276
45.
Komen
,
E.
,
Shams
,
A.
,
Camilo
,
L.
, and
Koren
,
B.
,
2014
, “
Quasi-DNS Capabilities of openFOAM for Different Mesh Types
,”
Comput. Fluid
,
96
, pp.
87
104
.10.1016/j.compfluid.2014.02.013
46.
Eckhardt
,
B.
,
Schneider
,
T.
,
Hof
,
B.
, and
Westerweel
,
J.
,
2007
, “
Turbulence Transition in Pipe Flow
,”
Annu. Rev. Fluid Mech.
,
39
(
1
), pp.
447
468
.10.1146/annurev.fluid.39.050905.110308
47.
Orlandi
,
P.
, and
Fatica
,
M.
,
1997
, “
Direct Simulations of Turbulent Flow in a Pipe Rotating About Its Axis
,”
J. Fluid Mech.
,
343
, pp.
43
72
.10.1017/S0022112097005715
48.
Quadrio
,
M.
, and
Sibilla
,
S.
,
2000
, “
Numerical Simulation of Turbulent Flow in a Pipe Oscillating Around Its Axis
,”
J. Fluid Mech.
,
424
, pp.
217
241
.10.1017/S0022112000001889
49.
Smagorinsky
,
J.
,
1963
, “
General Circulation Experiments With the Primitive Equations
,”
Mon. Weather Rev.
,
91
(
3
), pp.
99
164
.10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2
50.
Launder
,
B. E.
, and
Sharma
,
B. I.
,
1974
, “
Application of the Energy-Dissipation Model of Turbulence to the Calculation of Flow Near a Spinning Disc
,”
Lett. Heat Mass Transfer
,
1
(
2
), pp.
131
137
.10.1016/0094-4548(74)90150-7
51.
Jones
,
W. P.
, and
Launder
,
B. E.
,
1972
, “
The Prediction of Laminarization With a Two-Equation Model of Turbulence
,”
Int. J. Heat Mass Transfer
,
15
(
2
), pp.
301
314
.10.1016/0017-9310(72)90076-2
52.
Wilcox
,
D. C.
,
1988
, “
Reassessment of the Scale-Determining Equation for Advanced Turbulence Models
,”
AIAA J.
,
26
(
11
), pp.
1299
1310
.10.2514/3.10041
53.
Walters
,
D. K.
, and
Cokljat
,
D.
,
2008
, “
A Three-Equation Eddy-Viscosity Model for Reynolds-Averaged Navier-Stokes Simulations of Transitional Flow
,”
ASME J. Fluids Eng.
,
130
(
12
), p.
121401
.10.1115/1.2979230
54.
Walters
,
D. K.
, and
Leylek
,
J. H.
,
2004
, “
A New Model for Boundary Layer Transition Using a Single-Point RANS Approach
,”
ASME J. Turbomach.
,
126
(
1
), pp.
193
202
.10.1115/1.1622709
55.
Jacobs
,
R. G.
, and
Durbin
,
P. A.
,
2001
, “
Simulations of Bypass Transition
,”
J. Fluid Mech.
,
428
, pp.
185
212
.10.1017/S0022112000002469
56.
Loeve
,
M.
,
1977
,
Probability Theory
,
Springer
,
Berlin
.
57.
O'Donnell
,
T. F.
,
1986
, “
Pulsatile Flow and Atherosclerosis in the Human Carotid Bifurcation: Positive Correlation Between Plaque Location and Low and Oscillating Shear Stress
,”
J. Vasc. Surg.
,
3
(
6
), p.
944
.10.1016/0741-5214(86)90448-9
58.
He
,
X.
, and
Ku
,
D. N.
,
1996
, “
Pulsatile Flow in the Human Left Coronary Artery Bifurcation: Average Conditions
,”
ASME J. Biomech. Eng.
,
118
(
1
), pp.
74
82
.10.1115/1.2795948
59.
Basavaraja
,
P.
,
Surendran
,
A.
,
Gupta
,
A.
,
Saba
,
L.
,
Laird
,
J. R.
,
Nicolaides
,
A.
,
Mtui
,
E. E.
,
Baradaran
,
H.
,
Lavra
,
F.
, and
Suri
,
J. S.
,
2017
, “
Wall Shear Stress and Oscillatory Shear Index Distribution in Carotid Artery With Varying Degree of Stenosis: A Hemodinamic Study
,”
J. Mech. Med. Biol.
,
17
(
2
), p.
1750037
.10.1142/S0219519417500373
60.
Jeong
,
J.
, and
Hussain
,
F.
,
1995
, “
On the Identification of a Vortex
,”
J. Fluid Mech.
,
285
(
1
), pp.
69
94
.10.1017/S0022112095000462
61.
Chakraborty
,
P.
,
Balachandar
,
S.
, and
Adrian
,
R. J.
,
2005
, “
On the Relationships Between Local Vortex Identification Schemes
,”
J. Fluid Mech.
,
535
, pp.
189
214
.10.1017/S0022112005004726
62.
Lopez
,
M.
, and
Walters
,
D. K.
,
2016
, “
Prediction of Transitional and Fully Turbulent Flow Using an Alternative to the Laminar Kinetic Energy Approach
,”
J. Turbul.
,
17
(
3
), pp.
253
273
.10.1080/14685248.2015.1062509
You do not currently have access to this content.