A one-dimensional finite-difference model was developed to predict pressure wave reflections in stented arteries, and a parametric study of variations in stent and vessel properties was performed, including stent stiffness, length, and compliance transition region, as well as vessel radius and wall thickness. The model was solved using a combination of weighted essentially nonoscillatory and Runge–Kutta methods. Over 100 cases were tested and the magnitudes of the predicted waves were less than 0.5mmHg for all cases, less than 1% of the normal pulse pressure of 40mmHg. It was also shown that reasonable variations in these parameters could induce changes in reflection magnitude of up to ±50%. The relationship between each of these properties and the resulting wave reflection could be described in a simple manner, and the effect of all of them together could, in fact, be encompassed by a single nondimensional parameter titled “stent authority.” It is believed that stent authority is a novel way of relating the energy imposed upon the arterial wall by the stent to the fraction of the incident pressure energy that is reflected from the stented region. Based on these results, it is believed that stent design can have a significant effect on pressure wave reflections; however, it was concluded that their small magnitudes make clinical relevance of these waves unlikely, regardless of design.

1.
American Heart Association
, 2004, “Heart Disease and Stroke Statistics—2004 Update.”
2.
American Heart Association
, 2004, “International Cardiovascular Disease Statistics.”
3.
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
0009-7322,
109
, pp.
184
189
.
4.
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
, pp.
H1879
H1885
. 0363-6135
5.
Knight
,
C. J.
,
Curzen
,
N. P.
,
Groves
,
P. H.
,
Patel
,
D. J.
,
Goodall
,
A. H.
,
Wright
,
C.
,
Clarke
,
D.
,
Oldershaw
,
P. J.
, and
Fox
,
K. M.
, 1999, “
Stent Implantation Reduces Restenosis in Patients With Suboptimal Results Following Coronary Angioplasty
,”
Eur. Heart J.
,
20
(
24
), pp.
1783
1790
. 0195-668X
6.
Edelman
,
E. R.
, and
Rogers
,
C.
, 1998, “
Pathobiological Responses to Stenting
,”
Am. J. Cardiol.
0002-9149,
81
, (7A), pp.
4E
6E
.
7.
Babapulle
,
M. N.
, and
Eisenberg
,
M. J.
, 2002, “
Coated Stents for the Prevention of Restenosis: Part I
,”
Circulation
,
106
, pp.
2734
2740
. 0009-7322
8.
Berry
,
J. L.
,
Manoach
,
E.
,
Mekkaoui
,
C.
,
Rolland
,
P. H.
,
Moore
,
J. E.
, and
Rachev
,
A.
, 2002, “
Hemodynamics and Wall Mechanics of a Compliance Matching Stent: In Vitro and In Vivo Analysis
,”
J. Vasc. Interv. Radiol.
,
13
, pp.
97
105
. 1051-0443
9.
Berry
,
J. L.
,
Santamarina
,
A.
,
Moore
,
J. E.
,
Roychowdhury
,
S.
, and
Routh
,
W. D.
, 2000, “
Experimental and Computational Flow Evaluation of Coronary Stents
,”
Ann. Biomed. Eng.
0090-6964,
28
(
4
), pp.
386
398
.
10.
Kinlay
,
S.
,
Grewal
,
J.
,
Manuelin
,
D.
,
Fang
,
J. C.
,
Selwyn
,
A. P.
,
Bittle
,
J. A.
, and
Ganz
,
P.
, 2002, “
Coronary Flow Velocity and Disturbed Flow Predict Adverse Clinical Outcome After Coronary Angioplasty
,”
Arterioscler., Thromb., Vasc. Biol.
,
22
, pp.
1334
1340
. 1079-5642
11.
Wentzel
,
J. J.
,
Gijsen
,
F. J. H.
,
Stergiopulos
,
N.
,
Serruys
,
P. W.
,
Slager
,
C. J.
, and
Krams
,
R.
, 2003, “
Shear Stress, Vascular Remodeling and Neointimal Formation
,”
J. Biomech.
0021-9290,
36
, pp.
681
688
.
12.
Benard
,
N.
,
Coisne
,
D.
,
Donal
,
E.
, and
Perrault
,
R.
, 2003, “
Experimental Study of Laminar Blood Flow Through an Artery Treated by a Stent Implantation: Characterization of Intra-Stent Wall Shear Stress
,”
J. Biomech.
0021-9290,
36
, pp.
991
998
.
13.
Babapulle
,
M. N.
, and
Eisenberg
,
M. J.
, 2002, “
Coated Stents for the Prevention of Restenosis: Part II
,”
Circulation
,
106
(
22
), pp.
2859
2866
. 0009-7322
14.
O’Neill
,
W. W.
, and
Leon
,
M. B.
, 2003, “
Drug-Eluting Stents: Costs Versus Clinical Benefit
,”
Circulation
,
107
(
24
), pp.
3008
3011
. 0009-7322
15.
Orlic
,
D.
,
Bonizzoni
,
E.
,
Stankovic
,
G.
,
Airoldi
,
F.
,
Chieffo
,
A.
,
Corbaja
,
N.
,
Sangiorgi
,
G.
,
Ferror
,
M.
,
Briguori
,
C.
,
Montorfano
,
M.
,
Calino
,
M.
, and
Colombo
,
A.
, 2004, “
Treatment of Multivessel Coronary Artery Disease With Sirolimus-Eluting Stent Implantation: Immediate and Mid-Term Results
,”
J. Am. Coll. Cardiol.
,
43
(
7
), pp.
1154
1160
. 0735-1097
16.
Rogers
,
C.
, and
Edelman
,
E. R.
, 1995, “
Endovascular Stent Design Dictates Experimental Restensois and Thrombosis
,”
Circulation
,
91
(
12
), pp.
2995
3001
. 0009-7322
17.
Hausleiter
,
J.
,
Kastrati
,
A.
,
Mehilli
,
J.
,
Schühlen
,
H.
,
Pache
,
J.
,
Dotzer
,
F.
,
Dirschinger
,
J.
, and
Schömig
,
A.
, 2002, “
Predictive Factors for Early Cardiac Events and Angiographic Restenosis After Coronary Stent Placement in Small Coronary Arteries
,”
J. Am. Coll. Cardiol.
,
40
(
5
), pp.
882
889
. 0735-1097
18.
Kastrati
,
A.
,
Mehilli
,
J.
,
Dirschinger
,
J.
,
Dotzer
,
F.
,
Schühlen
,
H.
,
Neumann
,
F. -J.
,
Fleckenstein
,
M.
,
Pfafferott
,
C.
,
Seyfarth
,
M.
, and
Schömig
,
A.
, 2001, “
Intracoronary Stenting and Angiographic Results: Strut Thickness Effect on Restenosis Outcome (ISAR-STEREO) Trial
,”
Circulation
,
103
, pp.
2816
2821
. 0009-7322
19.
Pache
,
J.
,
Kastrati
,
A.
,
Mehilli
,
J.
,
Schühlen
,
H.
,
Dotzer
,
F.
,
Hausleiter
,
J.
,
Fleckenstein
,
M.
,
Neumann
,
F. -J.
,
Sattelberger
,
U.
,
Schmitt
,
C.
,
Müller
,
M.
,
Dirschinger
,
J.
, and
Schömig
,
A.
, 2003, “
Intracoronary Stenting and Angiographic Results: Strut Thickness Effect on Restenosis Outcome (ISAR-STEREO-2) Trial
,”
J. Am. Coll. Cardiol.
0735-1097,
41
(
8
), pp.
1283
1288
.
20.
Orlic
,
D.
,
Bonizzoni
,
E.
,
Stankovic
,
G.
,
Airoldi
,
F.
,
Chieffo
,
A.
,
Corvaja
,
N.
,
Sangiorgi
,
G.
,
Ferraro
,
M.
,
Briguori
,
C.
,
Montofrano
,
M.
,
Calino
,
M.
, and
Colombo
,
A.
, 2004, “
Treatment of Multivessel Coronary Artery Disease With Sirolimus-Eluting Stent Implantation: Immediate and Mid-Term Results
,”
J. Am. Coll. Cardiol.
,
43
(
7
), pp.
1154
1160
. 0735-1097
21.
Chua
,
S. N. D.
,
MacDonald
,
B. J.
, and
Hashmi
,
M. S. J.
, 2002, “
Finite-Element Simulation of Stent Expansion
,”
J. Mater. Process. Technol.
0924-0136,
120
, pp.
335
340
.
22.
Petrini
,
L.
,
Migliavacca
,
F.
,
Auricchio
,
F.
, and
Dubini
,
G.
, 2004, “
Numerical Investigation of the Intravascular Coronary Stent Flexibility
,”
J. Biomech.
0021-9290,
37
, pp.
495
501
.
23.
LaDisa
,
J. F.
, Jr.
,
Guler
,
I.
,
Olson
,
L. E.
,
Hettrick
,
D. A.
,
Kersten
,
J. R.
,
Warltier
,
D. C.
, and
Pagel
,
P. S.
, 2003, “
Three-Dimensional Computational Fluid Dynamics Modeling of Alterations in Coronary Wall Shear Stress Produced by Stent Implantation
,”
Ann. Biomed. Eng.
0090-6964,
31
, pp.
972
980
.
24.
La Disa
,
J. F.
, Jr.
,
Olson
,
L. E.
,
Guler
,
I.
,
Hettrick
,
D. A.
,
Kersten
,
J. R.
,
Warltier
,
D. C.
, and
Pagel
,
P. S.
, 2004, “
Circumferential Vascular Deformation After Stent Implantation Alters Wall Shear Stress Evaluated With Time-Dependent 3D Computational Fluid Dynamics Models
,”
J. Appl. Physiol.
,
98
, pp.
947
957
. 0021-8987
25.
Banerjee
,
R. K.
,
Devarakonda
,
S. B.
,
Rajamohan
,
D.
, and
Back
,
L. H.
, 2007, “
Developed Pulsatile Flow in a Deployed Coronary Stent
,”
Biorheology
,
44
(
2
), pp.
91
102
. 0006-355X
26.
Balossino
,
R.
,
Gervaso
,
F.
,
Migliavacca
,
F.
, and
Dubini
,
G.
, 2008, “
Effects of Different Stent Designs on Local Hemodynamics in Stented Arteries
,”
J. Biomech.
,
41
, pp.
1053
1061
. 0021-9290
27.
Tortoriello
,
A.
, and
Pedrizzetti
,
G.
, 2004, “
Flow-Tissue Interaction With Compliance Mismatch in a Model Stented Artery
,”
J. Biomech.
,
37
, pp.
1
11
. 0021-9290
28.
Alderson
,
H.
, and
Zamir
,
M.
, 2004, “
Effects of Stent Stiffness on Local Haemodynamics With Particular Reference to Wave Reflections
,”
J. Biomech.
,
37
, pp.
339
348
. 0021-9290
29.
Formaggia
,
L.
,
Nobile
,
F.
, and
Quarteroni
,
A.
, 2001, “
A One-Dimensional Model for Blood Glow: Application to Vascular Prosthesis
,” EPFL Report No. 02.2001.
30.
Pontrelli
,
G.
, and
Rossoni
,
E.
, 2003, “
Numerical Modelling of the Pressure Wave Propagation in the Arterial Flow
,”
Int. J. Numer. Methods Fluids
0271-2091,
43
, pp.
651
671
.
31.
Sherwin
,
S. J.
,
Formaggia
,
L.
,
Peiro
,
J.
, and
Franke
,
V.
, 2003, “
Computational Modelling of 1D Blood Flow With Variable Mechanical Properties and Its Application to the Simulation of Wave Propagation in the Human Arterial System
,”
Int. J. Numer. Methods Fluids
0271-2091,
43
, pp.
673
700
.
32.
Sherwin
,
S. J.
,
Franke
,
V.
,
Peiro
,
J.
, and
Parker
,
K.
, 2003, “
One-Dimensional Modelling of a Vascular Network in Space-Time Variables
,”
J. Eng. Math.
0022-0833,
47
, pp.
217
250
.
33.
Timoshenko
,
S.
, and
Woinowski-Krieger
,
S.
, 1959,
Theory of Plates and Shells
,
2nd ed.
,
McGraw-Hill
,
New York
, Chap. 15.
34.
Kassab
,
G. S.
, and
Molloi
,
S.
, 2001, “
Cross-Sectional Area and Volume Compliance of Porcine Left Coronary Arteries
,”
Am. J. Physiol. Heart Circ. Physiol.
,
281
, pp.
H623
H628
. 0363-6135
35.
Liu
,
X. -D.
,
Osher
,
S.
, and
Chan
,
T.
, 1994, “
Weighted Essentially Nonoscillatory Schemes
,”
J. Comput. Phys.
0021-9991,
115
, pp.
200
212
.
36.
Jiang
,
G. -S.
, and
Shu
,
C. -W.
, 1996, “
Efficient Implementation of Weighted ENO Schemes
,”
J. Comput. Phys.
0021-9991,
126
, pp.
202
228
.
37.
Balsara
,
D. S.
, and
Shu
,
C. -W.
, 2000, “
Monotonicity Preserving Weighting Essentially Non-Oscillatory Schemes With increasingly High Order of Accuracy
,”
J. Comput. Phys.
0021-9991,
160
(
2
), pp.
405
452
.
38.
Shu
,
C. -W.
, 2001, “
High Order Finite Difference and Finite Volume WENO Schemes and Discontinuous Galerkin Methods for CFD
,”
NASA
Report No. CR-2001-210865.
39.
Carpenter
,
M. H.
, and
Kennedy
,
L. A.
, 1994, “
Fourth-Order, 2n-Storage Runge–Kutta Schemes
,”
NASA
Report No. TM 109112.
40.
Wilson
,
R. V.
,
Demurren
,
A. O.
, and
Carpenter
,
M. H.
, 1998, “
Higher-Order Compact Schemes for Numerical Simulation of Incompressible Flows
,”
NASA
Report No. CR-1998-206922.
41.
Rumberger
,
J. A.
, and
Nerem
,
R. M.
, 1977, “
A Method-of-Characteristics Calculation of Coronary Blood Flow
,”
J. Fluid Mech.
,
82
(
3
), pp.
429
448
. 0022-1120
42.
Ozolanta
,
I.
,
Tetere
,
G.
,
Purinya
,
B.
, and
Kasyanov
,
V.
, 1998, “
Changes in the Mechanical Properties, Biochemical Contents, and Wall Structure of the Human Coronary Arteries With Age and Sex
,”
Med. Eng. Phys.
1350-4533,
20
, pp.
523
533
.
43.
Cordis Corporation
, 1998, “
Information for Prescribers: PALMAZ-SCHATZ CROWN Balloon-Expandable Stent With PowerGrip Over-the-Wire Delivery System
,” Cordis Corporation, a Johnson & Johnson Company.
44.
Schrader
,
S. C.
, and
Beyar
,
R.
, 1998, “
Evaluation of the Compressive Mechanical Properties of Endoluminal Metal Stents
,”
Cathet. Cardiovasc. Diagn.
,
44
(
2
), pp.
179
187
. 0098-6569
45.
Charonko
,
J.
,
Etebari
,
A.
,
Akle
,
B.
,
Vlachos
,
P.
, and
Leo
,
D.
, 2003. “
Novel Non-Invasive Methods for In-Vitro or Ex-Vivo Vessel Compliance Measurements
,”
2003 BMES Annual Fall Meeting
, Oct.
You do not currently have access to this content.