The incidence of stent late restenosis is high (Zwart et al., 2010, “Coronary Stent Thrombosis in the Current Era: Challenges and Opportunities for Treatment,” Curr. Treat. Options Cardiovasc. Med., 12(1), pp. 46–57) despite the extensive use of stents, and is most prevalent at the proximal and distal ends of the stent. Elastic modulus change in stented coronary arteries subject to the motion of the myocardium is not studied extensively. It is our objective to understand and reveal the mechanism by which changes in elastic modulus and geometry contribute to the generation of nonphysiological wall shear stress (WSS). Such adverse hemodynamic conditions could have an effect on the onset of restenosis. Three-dimensional (3D), spatiotemporally resolved computational fluid dynamics (CFD) simulations of pulsatile flow with moving wall boundaries and fluid structure interaction (FSI) were carried out for a helical artery with physiologically relevant flow parameters. To study the effect of coronary artery (CA) geometry change on stent elastic modulus mismatch, models where the curvature, torsion and both curvature and torsion change were examined. The elastic modulus is increased by a factor of two, five, and ten in the stented section for all three modes of motion. The changes in elastic modulus and arterial geometry cause critical variations in the local pressure and velocity gradients and secondary flow patterns. The pressure gradient change is  47%, with respect to the unstented baseline when the elastic modulus is increased to 10. The corresponding WSS change is 15.4%. We demonstrate that these changes are attributed to the production of vorticity (vorticity flux) caused by the wall movement and elastic modulus discontinuity. The changes in curvature dominate torsion changes in terms of the effects to local hemodynamics. The elastic modulus discontinuities along with the dynamic change in geometry affected the secondary flow patterns and vorticity flux, which in turn affects the WSS.

References

References
1.
Berry
,
J. L.
,
Moore
, Jr.,
J. E.
,
Newman
,
V. S.
, and
Routh
,
W. D.
, 1995, “
In Vitro Flow Visualization in Stented Arterial Segments
,”
J Vasc Invest
,
3
(2), pp.
63
68
.
2.
Rachev
,
A.
,
Manoach
,
E.
,
Berry
,
J.
, and
Moore
,
J. E.
,
2000
, “
Model of Stress-Induced Geometrical Remodeling of Vessel Segments Adjacent to Stents and Artery/Graft Anastomoses
,”
J. Theor. Biol.
,
206
(
3
), pp.
429
443
.10.1006/jtbi.2000.2143
3.
Rolland
,
P. H.
,
Charifi
,
A. B.
,
Verrier
,
C.
,
Bodard
,
H.
,
Friggi
,
A.
,
Piquet
,
P.
,
Moulin
,
G.
, and
Bartoli
,
J. M.
,
1999
, “
Hemodynamics and Wall Mechanics After Stent Placement in Swine Iliac Arteries: Comparative Results From Six Stent Designs
,”
Radiology
,
213
(
1
), pp.
229
246
.10.1148/radiology.213.1.r99oc26229
4.
Berger
,
S. A.
, and
Jou
,
L. D.
,
2000
, “
Flows in Stenotic Vessels
,”
Ann. Rev. Fluid Mech.
,
32
, pp.
347
382
.10.1146/annurev.fluid.32.1.347
5.
Ku
,
D. N.
,
1997
, “
Blood Flow in Arteries
,”
Ann. Rev. Fluid Mech.
,
29
, pp.
399
434
.10.1146/annurev.fluid.29.1.399
6.
Caro
,
C. G.
,
Fitz-Gerald
,
J. M.
, and
Schroter
,
R. C.
,
1971
, “
Atheroma and Arterial Wall Shear Observation Correlation and Proposal of a Shear Dependant Mass Transfer Mechanism for Atherogenesis
,”
Proc. R. Soc. London, Ser. B
,
177
(
1046
), pp.
109
159
.10.1098/rspb.1971.0019
7.
Wootton
,
D. M.
, and
Ku
,
D. N.
,
1999
, “
Fluid Mechanics of Vascular Systems, Diseases, and Thrombosis
,”
Ann. Rev. Biomed. Eng.
,
1
, pp.
299
329
.10.1146/annurev.bioeng.1.1.299
8.
Selvarasu
,
N. K. C.
, and
Tafti
,
D. K.
,
2012
, “
Investigation of the Effects of Dynamic Change in Curvature and Torsion on Pulsatile Flow in a Helical Tube
,”
ASME J. Biomech. Eng.
,
134
(
7
), p.
071005
.10.1115/1.4006984
9.
Wang
,
C. Y.
,
1981
, “
On the Low-Reynolds-Number Flow in a Helical Pipe
,”
J. Fluid Mech.
,
108
, pp.
185
194
.10.1017/S0022112081002073
10.
Germano
,
M.
,
1982
, “
On the Effect of Torsion on a Helical Pipe Flow
,”
J. Fluid Mech.
,
125
, pp.
1
8
.10.1017/S0022112082003206
11.
Kao
,
H. C.
,
1987
, “
Torsion Effect on Fully Developed Flow in a Helical Pipe
,”
J. Fluid Mech.
,
184
, pp.
335
356
.10.1017/S002211208700291X
12.
Yamamoto
,
K.
,
Yanase
,
S.
, and
Yoshida
,
T.
,
1994
, “
Torsion Effect on the Flow in a Helical Pipe
,”
Fluid Dyn. Res.
,
14
, pp.
259
273
.10.1016/0169-5983(94)90035-3
13.
Berger
,
S. A.
,
Talbot
,
L.
, and
Yao
,
L. S.
,
1983
, “
Flow in Curved Pipes
,”
Annual Review of Fluid Mechanics, Annual Reviews, Palo Alto, CA
, Vol.
15
, pp.
461
512
.10.1146/annurev.fl.15.010183.002333
14.
Moore
, Jr.,
J. E.
,
Guggenheim
,
N.
,
Delfino
,
A.
,
Doriot
,
P. A.
,
Dorsaz
,
P. A.
,
Rutishhauser
,
W.
, and
Meister
,
J. J.
,
1994
, “
Preliminary Analysis of the Effects of Blood Vessel Movement on Blood Flow Patterns in the Coronary Arteries
,”
ASME J. Biomech. Eng.
,
116
(
3
), pp.
302
306
.10.1115/1.2895734
15.
Santamarina
,
A.
,
Weydahl
,
E.
,
Siegel
,
J. M.
, Jr.
, and
Moore
,
J. E.
, Jr.
,
1998
, “
Computational Analysis of Flow in a Curved Tube Model of the Coronary Arteries: Effects of Time-Varying Curvature
,”
Ann. Biomed. Eng.
,
26
, pp.
944
954
.10.1114/1.113
16.
Moore
,
J. E.
,
Weydahl
,
E. S.
, and
Santamarina
,
A.
,
2001
, “
Frequency Dependence of Dynamic Curvature Effects on Flow Through Coronary Arteries
,”
ASME J. Biomech. Eng.
,
123
(
2
), pp.
129
133
.10.1115/1.1351806
17.
Prosi
,
M.
,
Perktold
,
K.
,
Ding
,
Z.
, and
Friedman
,
M. H.
,
2004
, “
Influence of Curvature Dynamics on Pulsatile Coronary Artery Flow in a Realistic Bifurcation Model
,”
J. Biomech.
,
37
, pp.
1767
1775
.10.1016/j.jbiomech.2004.01.021
18.
Zeng
,
D.
,
Ding
,
Z.
,
Friedman
,
M. H.
, and
Ethier
,
C. R.
,
2003
, “
Effects of Cardiac Motion on Right Coronary Artery Hemodynamics
,”
Ann. Biomed. Eng.
,
31
, pp. 420–429.10.1114/1.1560631
19.
Theodorakakos
,
A.
,
2008
, “
Simulation of Cardiac Motion on Non-Newtonian, Pulsating Flow Development in the Human Left Anterior Descending Coronary Artery
,”
Phys. Med. Biol.
,
53
(
18
), pp.
4875
4892
.10.1088/0031-9155/53/18/002
20.
Torii
,
R.
,
2009
, “
The Effect of Dynamic Vessel Motion on Haemodynamic Parameters in the Right Coronary Artery: A Combined MR and CFD Study
,”
Br. J. Radiol.
,
82
(
1
), pp.
S24
S32
.10.1259/bjr/62450556
21.
Prosi
,
M.
,
Perktold
,
K.
,
Ding
,
Z.
, and
Friedman
,
M. H.
,
2004
, “
Influence of Curvature Dynamics on Pulsatile Coronary Artery Flow in a Realistic Bifurcation Model
,”
J. Biomech.
,
37
, pp.
1767
1775
.10.1016/j.jbiomech.2004.01.021
22.
Ding
,
Z. H.
, and
Friedman
,
M. H.
,
2000
, “
Dynamics of Human Coronary Arterial Motion and Its Potential Role in Coronary Atherogenesis
,”
ASME J. Biomech. Eng.
,
122
(
5
), pp.
488
492
.10.1115/1.1289989
23.
Ding
,
Z. H.
, and
Friedman
,
M. H.
,
2000
, “
Quantification of 3D Coronary Arterial Motion Using Clinical Biplane Cineangiograms
,”
Int. J. Card. Imaging
,
16
(
5
), pp.
331
346
.10.1023/A:1026590417177
24.
Brinkman
,
A. M.
,
Baker
,
P. B.
,
Newman
,
W. P.
,
Vigorito
,
R.
, and
Friedman
,
M. H.
,
1994
, “
Variability of Human Coronary-Artery Geometry—An Angiographic Study of the Left Anterior Descending Arteries of 30 Autopsy Hearts
,”
Ann. Biomed. Eng.
,
22
(
1
), pp.
34
44
.10.1007/BF02368220
25.
Zhu
,
H.
,
Ding
,
Z. H.
,
Piana
,
R. N.
,
Gehrig
,
T. R.
, and
Friedman
,
M. H.
,
2009
, “
Cataloguing the Geometry of the Human Coronary Arteries: A Potential Tool for Predicting Risk of Coronary Artery Disease
,”
Int. J. Cardiol.
,
135
(
1
), pp.
43
52
.10.1016/j.ijcard.2008.03.087
26.
Duraiswamy
,
N.
,
Schoephoerster
,
R. T.
,
Moreno
,
M. R.
, and
Moore
,
J. E.
, Jr
.,
2007
, “
Stented Artery Flow Patterns and Their Effects on the Artery Wall
,”
Ann. Rev. Fluid Mech.
,
39
, pp.
357
382
.10.1146/annurev.fluid.39.050905.110300
27.
Zwart
,
B.
,
van Werkum
,
J.
,
Heestermans
,
A.
, and
ten Berg
,
J.
,
2010
, “
Coronary Stent Thrombosis in the Current Era: Challenges and Opportunities for Treatment
,”
Curr. Treat. Options Cardiovasc. Med.
,
12
(
1
), pp.
46
57
.10.1007/s11936-009-0055-z
28.
Pache
,
J.
,
Kastrati
,
A.
,
Mehilli
,
J.
,
Schuhlen
,
H.
,
Dotzer
,
F.
,
Hausleiter
,
J.
,
Fleckenstein
,
M.
,
Neumann
,
F. J.
,
Sattelberger
,
U.
,
Schmitt
,
C.
,
Muller
,
M.
,
Dirschinger
,
J.
, and
Schomig
,
A.
, “
Intracoronary Stenting and Angiographic Results: Strut Thickness Effect on Restenosis Outcome (ISAR-STEREO-2) Trial
,”
Proceedings of 51st Annual Scientific Session of the American College of Cardiology
, pp.
1283
1288
.
29.
Ojha
,
M.
,
1994
, “
Wall Shear-Stress Temporal Gradient and Anastomotic Intimal Hyperplasia
,”
Circ. Res.
,
74
(
6
), pp.
1227
1231
.10.1161/01.RES.74.6.1227
30.
Leask
,
R. L.
,
Butany
,
J.
,
Johnston
,
K. W.
,
Ethier
,
C. R.
, and
Ojha
,
M.
,
2005
, “
Human Saphenous Vein Coronary Artery Bypass Graft Morphology, Geometry and Hemodynamics
,”
Ann. Biomed. Eng.
,
33
(
3
), pp.
301
309
.10.1007/s10439-005-1732-z
31.
Fry
,
D. L.
,
1968
, “
Acute Vascular Endothelial Changes Associated With Increased Blood Velocity Gradients
,”
Circ. Res.
,
22
(
2
), pp.
165
197
.10.1161/01.RES.22.2.165
32.
Baird
,
R. N.
, and
Abbott
,
W. M.
,
1976
, “
Pulsatile Blood-Flow in Arterial Grafts
,”
Lancet
,
2
(
7992
), pp.
948
949
.10.1016/S0140-6736(76)90906-5
33.
Abbott
,
W. M.
,
Megerman
,
J.
,
Hasson
,
J. E.
,
Litalien
,
G.
, and
Warnock
,
D. F.
,
1987
, “
Effect of Compliance Mismatch on Vascular Graft Patency
,”
J. Vasc. Surg.
,
5
(
2
), pp.
376
382
.10.1016/0741-5214(87)90148-0
34.
Charonko
,
J. J.
,
Ragab
,
S. A.
, and
Vlachos
,
P. P.
,
2009
, “
A Scaling Parameter for Predicting Pressure Wave Reflection in Stented Arteries
,”
ASME J. Med. Devices
,
3
(
1
), p.
011006
.10.1115/1.3089140
35.
Charonko
,
J.
,
Karri
,
S.
,
Schmieg
,
J.
,
Prabhu
,
S.
, and
Vlachos
,
P.
,
2009
, “
in vitro, Time-Resolved PIV Comparison of the Effect of Stent Design on Wall Shear Stress
,”
Ann. Biomed. Eng.
,
37
(
7
), pp.
1310
1321
.10.1007/s10439-009-9697-y
36.
Charonko
,
J.
,
Karri
,
S.
,
Schmieg
,
J.
,
Prabhu
,
S.
, and
Vlachos
,
P.
, “
In Vitro Comparison of the Effect of Stent Configuration on Wall Shear Stress Using Time-resolved Particle Image Velocimetry
,”
Ann. Biomed. Eng.
,
38
(
3
), pp.
1
14
.10.1007/s10439-010-9915-7
37.
Yazdani
,
S. K.
,
Moore
,
J. E.
,
Berry
,
J. L.
, and
Vlachos
,
P. P.
,
2004
, “
DPIV Measurements of Flow Disturbances in Stented Artery Models: Adverse Affects of Compliance Mismatch
,”
ASME J. Biomech. Eng.
,
126
(
5
), pp.
559
566
.10.1115/1.1797904
38.
Selvarasu
,
N. K. C.
,
Tafti
,
D. K.
, and
Vlachos
,
P. P.
,
2011
, “
Hydrodynamic Effects of Compliance Mismatch in Stented Arteries
,”
ASME J. Biomech. Eng.
,
133
(
2
), p.
021008
.10.1115/1.4003319
39.
Canic
,
S.
,
Lamponi
,
D.
,
Mikelic
,
A.
, and
Tambaca
,
J.
,
2005
, “
Self-Consistent Effective Equations Modeling Blood Flow in Medium-to-Large Compliant Arteries
,”
Multiscale Model. Simul.
,
3
(
3
), pp.
559
596
.10.1137/030602605
40.
Causin
,
P.
,
Gerbeau
,
J. F.
, and
Nobile
,
F.
,
2005
, “
Added-Mass Effect in the Design of Partitioned Algorithms for Fluid-Structure Problems
,”
Comput. Methods Appl. Mech. Eng.
,
194
(
42–44
), pp.
4506
4527
.10.1016/j.cma.2004.12.005
41.
Weber
,
T.
,
Auer
,
J.
,
O'Rourke
,
M. F.
,
Kvas
,
E.
,
Lassnig
,
E.
,
Berent
,
R.
, and
Eber
,
B.
,
2004
, “
Arterial Stiffness, Wave Reflections, and the Risk of Coronary Artery Disease
,”
Circulation
,
109
(
2
), pp.
184
189
.10.1161/01.CIR.0000105767.94169.E3
42.
Gopalakrishnan
,
P.
, and
Tafti
,
D. K.
,
2009
, “
A Parallel Boundary Fitted Dynamic Mesh Solver for Applications to Flapping Flight
,”
Comput. Fluids
,
38
(
8
), pp.
1592
1607
.10.1016/j.compfluid.2009.01.006
43.
Charonko
,
J.
,
Karri
,
S.
,
Schmieg
,
J.
,
Prabhu
,
S.
, and
Vlachos
,
P.
, “
In Vitro Comparison of the Effect of Stent Configuration on Wall Shear Stress Using Time-Resolved Particle Image Velocimetry
,”
Ann. Biomed. Eng.
,
38
(
3
), pp.
889
902
.10.1007/s10439-010-9915-7
44.
Karri
,
S.
,
2009
, “
Laminar and Transitional Flow Disturbances in Diseased and Stented Arteries
,” Ph.D dissertation, Virginia Tech, Blacksburg, VA.
45.
Vernhet
,
H.
,
Demaria
,
R.
,
Perez-Martin
,
A.
,
Juan
,
J. M.
,
Oliva-Lauraire
,
M. C.
,
Marty-Double
,
C.
,
Senac
,
J. P.
, and
Dauzat
,
M.
,
2003
, “
Wall Mechanics of the Stented Rabbit Aorta: Long-Term Study and Correlation With Histological Findings
,”
J. Endovascular Therapy
,
10
(
3
), pp.
577
584
.10.1583/1545-1550(2003)010<0577:WMOTSR>2.0.CO;2
46.
Kim
,
H. J.
,
Vignon-Clementel
, I
. E.
,
Coogan
,
J. S.
,
Figueroa
,
C. A.
,
Jansen
,
K. E.
, and
Taylor
,
C. A.
,
2010
, “
Patient-Specific Modeling of Blood Flow and Pressure in Human Coronary Arteries
,”
Ann. Biomed. Eng.
,
38
(
10
), pp.
3195
3209
.10.1007/s10439-010-0083-6
47.
Santamarina
,
A.
,
Weydahl
,
E.
,
Siegel
,
J. M.
, Jr.
, and
Moore
,
J. E.
, Jr.
,
1998
, “
Computational Analysis of Flow in a Curved Tube Model of the Coronary Arteries: Effects of Time-Varying Curvature
,”
Ann. Biomed. Eng.
,
26
, pp.
944
954
.10.1114/1.113
48.
Zamir
,
M.
,
2000
,
The Physics of Pulsatile Flow
,
Springer-Verlag
,
New York
.
49.
Yamamoto
,
K.
,
Aribowo
,
A.
,
Hayamizu
,
Y.
,
Hirose
,
T.
, and
Kawahara
,
K.
,
2002
, “
Visualization of the Flow in a Helical Pipe
,”
Fluid Dyn. Res.
,
30
, pp.
251
267
.10.1016/S0169-5983(02)00043-6
50.
Patel
,
D. J.
, and
Vaishnav
,
R. N. J. A.
,
1980
, “
Basic Hemodynamics and Its Role in Disease Processes/by Dali
,” University Park Press, Baltimore.
51.
Giddens
,
D. P.
,
Zarins
,
C. K.
, and
Glagov
,
S.
,
1993
, “
The Role of Fluid-Mechanics in the Localization and Detection of Atherosclerosis
,”
ASME J. Biomech. Eng.
,
115
(
4B
), pp.
588
594
.10.1115/1.2895545
52.
Kamiya
,
A.
,
Bukhari
,
R.
, and
Togawa
,
T.
,
1984
, “
Adaptive Regulation of Wall Shear-Stress Optimizing Vascular Tree Function
,”
Bull. Math. Biol.
,
46
(
1
), pp.
127
137
.10.1007/BF02463726
53.
Kamiya
,
A.
, and
Togawa
,
T.
,
1980
, “
Adaptive Regulation of Wall Shear-Stress to Flow Change in the Canine Carotid Artery
,”
Am. J. Physiol.
,
239
(
1
), pp.
H14
H21
.
54.
Lei
,
M.
,
Kleinstreuer
,
C.
, and
Truskey
,
G. A.
,
1995
, “
Numerical Investigation and Prediction of Atherogenic Sites in Branching Arteries
,”
ASME J. Biomech. Eng.
,
117
(
3
), pp.
350
357
.10.1115/1.2794191
55.
Ojha
,
M.
,
Leask
,
R. L.
,
Butany
,
J.
, and
Johnston
,
K. W.
,
2001
, “
Distribution of Intimal and Medial Thickening in the Human Right Coronary Artery: A Study of 17 RCAs
,”
Atherosclerosis
,
158
(
1
), pp.
147
153
.10.1016/S0021-9150(00)00759-0
56.
Bleasdale
,
R. A.
,
Parker
,
K. H.
, and
Jones
,
C. J. H.
,
2003
, “
Chasing the Wave. Unfashionable But Important New Concepts in Arterial Wave Travel
,”
Am. J. Physiol.-Heart Circ. Physiol.
,
284
(
6
), pp.
H1879
H1885
.10.1152/ajpheart.00070.2003
57.
Friedman
,
M. H.
,
Deters
,
O. J.
,
Bargeron
,
C. B.
,
Hutchins
,
G. M.
, and
Mark
,
F. F.
,
1986
, “
Shear-Dependent Thickening of the Human Arterial Intima
,”
Atherosclerosis
,
60
(
2
), pp.
161
171
.10.1016/0021-9150(86)90008-0
58.
Shijie
,
L.
, and
Masliyah
,
J. H.
,
1993
, “
Axially Invariant Laminar Flow in Helical Pipes With a Finite Pitch
,”
J. Fluid Mech.
,
251
, pp.
315
353
.10.1017/S002211209300343X
59.
Lighthill
,
M. J.
,
1963
,
Laminar Boundary Layers
,
Dover Publications Inc.
,
New York
.
60.
Germano
,
M.
,
1982
, “
On the Effect of Torsion on a Helical Pipe Flow
,”
J. Fluid Mech.
,
125
, pp.
1
8
.10.1017/S0022112082003206
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