Abstract

The carotid arteries (CAs) and vertebral arteries (VAs) are principal conduits for cerebral blood supply and are common sites for atherosclerotic plaque formation. To date, there has been extensive clinical and hemodynamic reporting on carotid arteries; however, studies focusing on the hemodynamic characteristics of the VA are notably scarce. This article presents a systematic analysis of the impact of VA diameter and the angle of divergence from the subclavian artery (SA) on hemodynamic properties, facilitated by the construction of an idealized VA geometric model. Research indicates that the increase in the diameter of the VA is associated with a corresponding increase in the complexity of the vortex structures at the bifurcation with the SA. When the VA diameter is constant, a 30deg VA–SA angle yields better hemodynamic capacity than 45deg and 60deg angles, and the patterns of blood flow and helicity values are consistent across different angles. Elevated oscillatory shear index (OSI) zones are mainly at the origin of the VA, with an elliptical low OSI region within. As the diameter increases, the high OSI region spreads downstream. Increasing the bifurcation angle decreases OSI values in and below the elliptical low OSI region. These findings are valuable for studying the physiological and pathological mechanisms of VA atherosclerosis.

References

1.
Moghadasi
,
K.
,
Ghayesh
,
M. H.
,
Hu
,
E.
, and
Li
,
J.
,
2024
, “
Nonlinear Biomechanics of Diseased Carotid Arteries
,”
Int. J. Eng. Sci.
,
199
, p.
104070
.10.1016/j.ijengsci.2024.104070
2.
Sun
,
H.
,
Li
,
B.
,
Liu
,
J.
,
Xi
,
X.
,
Zhang
,
L.
,
Zhang
,
Y.
,
Li
,
G.
, et al.,
2024
, “
Real-Time Model-Based Cerebral Perfusion Calculation for Ischemic Stroke
,”
Comput. Methods Programs Biomed.
,
243
, p.
107916
.10.1016/j.cmpb.2023.107916
3.
Papadopoulos
,
K. P.
,
Gavaises
,
M.
,
Pantos
,
I.
,
Katritsis
,
D. G.
, and
Mitroglou
,
N.
,
2016
, “
Derivation of Flow Related Risk Indices for Stenosed Left Anterior Descending Coronary Arteries With the Use of Computer Simulations
,”
Med. Eng. Phys.
,
38
(
9
), pp.
929
939
.10.1016/j.medengphy.2016.05.016
4.
Hurd
,
E. R.
,
Han
,
M.
,
Mendes
,
J. K.
,
Hadley
,
J. R.
,
Johnson
,
C. R.
,
DiBella
,
E. V. R.
,
Oshinski
,
J. N.
, and
Timmins
,
L. H.
,
2023
, “
Comparison of Prospective and Retrospective Gated 4D Flow Cardiac MR Image Acquisitions in the Carotid Bifurcation
,”
Cardiovasc. Eng. Technol.
,
14
(
1
), pp.
1
12
.10.1007/s13239-022-00630-6
5.
Meng
,
H.
,
Wang
,
Z.
,
Hoi
,
Y.
,
Gao
,
L.
,
Metaxa
,
E.
,
Swartz
,
D. D.
, and
Kolega
,
J.
,
2007
, “
Complex Hemodynamics at the Apex of an Arterial Bifurcation Induces Vascular Remodeling Resembling Cerebral Aneurysm Initiation
,”
Stroke
,
38
(
6
), pp.
1924
1931
.10.1161/STROKEAHA.106.481234
6.
Benson
,
J. C.
,
Shahid
,
A.
,
Larson
,
A.
,
Brinjikji
,
W.
,
Nasr
,
D.
,
Saba
,
L.
,
Lanzino
,
G.
, and
Savastano
,
L. E.
,
2023
, “
Carotid Artery Tortuosity and Internal Carotid Artery Plaque Composition
,”
Clin. Neuroradiol.
,
33
(
4
), pp.
1017
1021
.10.1007/s00062-023-01302-1
7.
Thomas
,
J. B.
,
Antiga
,
L.
,
Che
,
S. L.
,
Milner
,
J. S.
,
Hangan Steinman
,
D. A.
,
Spence
,
J. D.
,
Rutt
,
B. K.
, and
Steinman
,
D. A.
,
2005
, “
Variation in the Carotid Bifurcation Geometry of Young Versus Older Adults
,”
Stroke
,
36
(
11
), pp.
2450
2456
.10.1161/01.STR.0000185679.62634.0a
8.
Morbiducci
,
U.
,
Kok
,
A. M.
,
Kwak
,
B. R.
,
Stone
,
P. H.
,
Steinman
,
D. A.
, and
Wentzel
,
J. J.
,
2016
, “
Atherosclerosis at Arterial Bifurcations: Evidence for the Role of Haemodynamics and Geometry
,”
Thromb. Haemostasis
,
115
(
3
), pp.
484
492
.10.1160/th15-07-0597
9.
Domanin
,
M.
,
Gallo
,
D.
,
Vergara
,
C.
,
Biondetti
,
P.
,
Forzenigo
,
L. V.
, and
Morbiducci
,
U.
,
2019
, “
Prediction of Long Term Restenosis Risk After Surgery in the Carotid Bifurcation by Hemodynamic and Geometric Analysis
,”
Ann. Biomed. Eng.
,
47
(
4
), pp.
1129
1140
.10.1007/s10439-019-02201-8
10.
Wang
,
S.
,
Wu
,
D.
,
Li
,
G.
,
Zhang
,
Z.
,
Xiao
,
W.
,
Li
,
R.
,
Qiao
,
A.
,
Jin
,
L.
, and
Liu
,
H.
,
2023
, “
Deep Learning-Based Hemodynamic Prediction of Carotid Artery Stenosis Before and After Surgical Treatments
,”
Front. Physiol.
,
13
, p.
1094743
.10.3389/fphys.2022.1094743
11.
Zhang
,
Z.
,
Ai
,
X.
,
Xu
,
Y.
,
Wang
,
Y.
,
Zhang
,
S.
,
Zhao
,
Y.
,
Zhou
,
R.
,
Tang
,
R.
,
Wang
,
L.
, and
Liu
,
Y.
,
2024
, “
Impact of Craniocervical Junction Abnormality on Vertebral Artery Hemodynamics: Based on Computational Fluid Dynamics Analysis
,”
Front. Neurol.
,
14
, p.
1244327
.10.3389/fneur.2023.1244327
12.
Jiang
,
Y.
,
Ge
,
L.
,
Lu
,
G.
,
Wan
,
H.
,
Chen
,
Q.
,
Zou
,
R.
,
Leng
,
X.
,
Xiang
,
J.
, and
Zhang
,
X.
,
2023
, “
Wall Enhancement Predictive of Abnormal Hemodynamics and Ischemia in Vertebrobasilar Non-Saccular Aneurysms: A Pilot Study
,”
Front. Neurol.
,
14
(
6
), p.
1108904
.10.3389/fneur.2023.1108904
13.
Su
,
H.
,
Yu
,
S.
,
Tian
,
C.
,
Du
,
Z.
,
Liu
,
X.
,
Wang
,
J.
, and
Cao
,
X.
,
2021
, “
Effects of the Vertebral Artery Ostium/Subclavian Artery Angle on In-Stent Restenosis After Vertebral Artery Ostium Stenting
,”
Biomed. Res. Int.
,
2021
, p.
e5527988
.10.1155/2021/5527988
14.
Burle
,
V. S.
,
Panjwani
,
A.
,
Mandalaneni
,
K.
,
Kollu
,
S.
, and
Gorantla
,
V. R.
,
2022
, “
Vertebral Artery Stenosis: A Narrative Review
,”
Cureus
,
14
(
8
), p.
e28068
.10.7759/cureus.28068
15.
Suzuki
,
T.
,
Takao
,
H.
,
Suzuki
,
T.
,
Kambayashi
,
Y.
,
Watanabe
,
M.
,
Shinohara
,
K.
,
Fujiwara
,
H.
, et al.,
2015
, “
Fluid Structure Interaction Analysis Reveals Facial Nerve Palsy Caused by Vertebral-Posterior Inferior Cerebellar Artery Aneurysm
,”
Comput. Biol. Med.
,
66
, pp.
263
268
.10.1016/j.compbiomed.2015.09.016
16.
Tong
,
X.
,
Dong
,
J.
,
Zhou
,
G.
,
Zhang
,
X.
,
Wang
,
A.
,
Ji
,
Z.
,
Jiao
,
L.
,
Mei
,
Y.
, and
Chen
,
D.
,
2021
, “
Hemodynamic Effects of Size and Location of Basilar Artery Fenestrations Associated to Pathological Implications
,”
Int. J. Numer. Methods Biomed. Eng.
,
37
(
9
), p.
e3507
.10.1002/cnm.3507
17.
Niu
,
J.
,
Qiao
,
A.-K.
, and
Jiao
,
L.-Q.
,
2013
, “
Hemodynamic Analysis of Stent Expansion Ratio for Vertebral Artery Ostial Stenosis Intervention
,”
J. Mech. Med. Biol.
,
13
(
4
), p.
1350058
.10.1142/S0219519413500589
18.
Qiao
,
A.
,
Dai
,
X.
,
Niu
,
J.
, and
Jiao
,
L.
,
2016
, “
Hemodynamics in Stented Vertebral Artery Ostial Stenosis Based on Computational Fluid Dynamics Simulations
,”
Comput. Methods Biomech. Biomed. Eng.
,
19
(
11
), pp.
1190
1200
.10.1080/10255842.2015.1123253
19.
Wake-Buck
,
A. K.
,
Gatenby
,
J. C.
, and
Gore
,
J. C.
,
2012
, “
Hemodynamic Characteristics of the Vertebrobasilar System Analyzed Using MRI-Based Models
,”
PLoS One
,
7
(
12
), p.
e51346
.10.1371/journal.pone.0051346
20.
Madonis
,
S. M.
, and
Jenkins
,
J. S.
,
2021
, “
Vertebral Artery Stenosis
,”
Prog. Cardiovasc. Dis.
,
65
, pp.
55
59
.10.1016/j.pcad.2021.02.006
21.
Mukherjee
,
D.
, and
Pineda
,
G.
,
2007
, “
Extracranial Vertebral Artery Intervention
,”
J. Interventional Cardiol.
,
20
(
6
), pp.
409
416
.10.1111/j.1540-8183.2007.00289.x
22.
Cramer
,
G. D.
,
2014
, “Chapter 5 -
The Cervical Region
,”
Clinical Anatomy of the Spine, Spinal Cord, and ANS (Third Edition)
,
Elsevier
, Saint Louis, MO, pp.
135
209
.
23.
Dodevski
,
A.
,
Lazareska
,
M.
,
Tosovska-Lazarova
,
D.
,
Zhivadinovik
,
J.
, and
Aliji
,
V.
,
2011
, “
Morphological Characteristics of the First Part of the Vertebral Artery
,”
Prilozi
,
32
(
1
), pp.
173
188
.http://www.manu.edu.mk/prilozi/12do.pdf
24.
Qtaish
,
I.
,
Ayasrah
,
M.
, and
Qtaish
,
N. R.
,
2024
, “
Retrospective Cohort Angiographic Analysis of Vertebral Artery Dominance, Stenosis Patterns, and Demographic Correlations
,”
Vasc. Health Risk Manage.
,
20
, pp.
207
214
.10.2147/VHRM.S453352
25.
Szárazová
,
A. S.
,
Bartels
,
E.
, and
Turčáni
,
P.
,
2012
, “
Vertebral Artery Hypoplasia and the Posterior Circulation Stroke
,”
Perspect. Med.
,
1
(
1–12
), pp.
198
202
.10.1016/j.permed.2012.02.063
26.
Xiang
,
Y.
,
Huang
,
X.
,
Benitez Mendieta
,
J.
,
Wang
,
J.
,
Paritala
,
P. K.
,
Lloyd
,
T.
, and
Li
,
Z.
,
2022
, “
The Need to Shift From Morphological to Structural Assessment for Carotid Plaque Vulnerability
,”
Biomedicines
,
10
(
12
), p.
3038
.10.3390/biomedicines10123038
27.
Zhang
,
X.
,
Fan
,
Z.
,
Zhao
,
P.
,
Ye
,
X.
,
Deng
,
X.
,
Guidoin
,
R.
, and
Liu
,
M.
,
2024
, “
Elucidating the Hemodynamic Impact of Residual Stenosis Post-Carotid Artery Stenting: A Numerical Study
,”
Med. Phys.
,
51
(
12
), pp.
9303
9317
.10.1002/mp.17386
28.
Singhal
,
M.
,
Gupta
,
R.
,
Saikia
,
B.
,
Malviya
,
A.
,
Sarma
,
A.
,
Phukan
,
P.
, and
Lynser
,
D.
,
2024
, “
Hemodynamics in Left Coronary Artery With Ramus Intermedius: A Patient-Specific Computational Study
,”
Phys. Fluids
,
36
(
3
), p.
031911
.10.1063/5.0187790
29.
Chen
,
Y.
,
Huang
,
K.
,
Cheng
,
Y.
,
Luo
,
K.
,
Fan
,
J.
, and
Zhan
,
R.
,
2024
, “
Hemodynamic Assessment of Severely Stenotic Carotid Arteries
,”
Phys. Fluids
,
36
(
5
), p.
051911
.10.1063/5.0206906
30.
Albadawi
,
M.
,
Abuouf
,
Y.
,
Elsagheer
,
S.
,
Ookawara
,
S.
, and
Ahmed
,
M.
,
2021
, “
Predicting the Onset of Consequent Stenotic Regions in Carotid Arteries Using Computational Fluid Dynamics
,”
Phys. Fluids
,
33
(
12
), p.
123106
.10.1063/5.0068998
31.
Martin
,
D. M.
,
Murphy
,
E. A.
, and
Boyle
,
F. J.
,
2014
, “
Computational Fluid Dynamics Analysis of Balloon-Expandable Coronary Stents: Influence of Stent and Vessel Deformation
,”
Med. Eng. Phys.
,
36
(
8
), pp.
1047
1056
.10.1016/j.medengphy.2014.05.011
32.
Martínez
,
A.
,
Hoeijmakers
,
M.
,
Geronzi
,
L.
,
Morgenthaler
,
V.
,
Tomasi
,
J.
,
Rochette
,
M.
, and
Biancolini
,
M. E.
,
2023
, “
Effect of Turbulence and Viscosity Models on Wall Shear Stress Derived Biomarkers for Aorta Simulations
,”
Comput. Biol. Med.
,
167
, p.
107603
.10.1016/j.compbiomed.2023.107603
33.
Bantwal
,
A.
,
Singh
,
A.
,
Menon
,
A. R.
, and
Kumar
,
N.
,
2021
, “
Pathogenesis of Atherosclerosis and Its Influence on Local Hemodynamics: A Comparative FSI Study in Healthy and Mildly Stenosed Carotid Arteries
,”
Int. J. Eng. Sci.
,
167
, p.
103525
.10.1016/j.ijengsci.2021.103525
34.
Oliveira
,
D.
,
Rosa
,
S. A.
,
Tiago
,
J.
,
Ferreira
,
R. C.
,
Agapito
,
A. F.
, and
Sequeira
,
A.
,
2019
, “
Bicuspid Aortic Valve Aortopathies: An Hemodynamics Characterization in Dilated Aortas
,”
Comput. Methods Biomech. Biomed. Eng.
,
22
(
8
), pp.
815
826
.10.1080/10255842.2019.1597860
35.
Shakya
,
K.
, and
Chowdhury
,
S. R.
,
2024
, “
A Fluid–Structure Interaction Study to Analyze the Severity of Carotid Artery Stenosis at Different Locations and Its Effect on Various Hemodynamic Biomarkers
,”
Eur. J. Mech. B/Fluids
,
106
, pp.
227
237
.10.1016/j.euromechflu.2024.04.006
36.
Pirola
,
S.
,
Cheng
,
Z.
,
Jarral
,
O. A.
,
O'Regan
,
D. P.
,
Pepper
,
J. R.
,
Athanasiou
,
T.
, and
Xu
,
X. Y.
,
2017
, “
On the Choice of Outlet Boundary Conditions for Patient-Specific Analysis of Aortic Flow Using Computational Fluid Dynamics
,”
J. Biomech.
,
60
, pp.
15
21
.10.1016/j.jbiomech.2017.06.005
37.
Lopes
,
D.
,
Puga
,
H.
,
Teixeira
,
J. C.
, and
Teixeira
,
S. F.
,
2019
, “
Influence of Arterial Mechanical Properties on Carotid Blood Flow: Comparison of CFD and FSI Studies
,”
Int. J. Mech. Sci.
,
160
, pp.
209
218
.10.1016/j.ijmecsci.2019.06.029
38.
Qiao
,
Y.
,
Fan
,
J.
,
Ding
,
Y.
,
Zhu
,
T.
, and
Luo
,
K.
,
2019
, “
A Primary Computational Fluid Dynamics Study of Pre- and Post-TEVAR With Intentional Left Subclavian Artery Coverage in a Type B Aortic Dissection
,”
ASME J. Biomech. Eng.
,
141
(
11
), p.
111002
.10.1115/1.4043881
39.
Oyejide
,
A. J.
,
Awonusi
,
A. A.
, and
Ige
,
E. O.
,
2023
, “
Fluid-Structure Interaction Study of Hemodynamics and Its Biomechanical Influence on Carotid Artery Atherosclerotic Plaque Deposits
,”
Med. Eng. Phys.
,
117
, p.
103998
.10.1016/j.medengphy.2023.103998
40.
Gallo
,
D.
,
Lefieux
,
A.
,
Morganti
,
S.
,
Veneziani
,
A.
,
Reali
,
A.
,
Auricchio
,
F.
,
Conti
,
M.
, and
Morbiducci
,
U.
,
2016
, “
A Patient-Specific Follow Up Study of the Impact of Thoracic Endovascular Repair (TEVAR) on Aortic Anatomy and on Post-Operative Hemodynamics
,”
Comput. Fluids
,
141
, pp.
54
61
.10.1016/j.compfluid.2016.04.025
41.
Chiastra
,
C.
,
Gallo
,
D.
,
Tasso
,
P.
,
Iannaccone
,
F.
,
Migliavacca
,
F.
,
Wentzel
,
J. J.
, and
Morbiducci
,
U.
,
2017
, “
Healthy and Diseased Coronary Bifurcation Geometries Influence Near-Wall and Intravascular Flow: A Computational Exploration of the Hemodynamic Risk
,”
J. Biomech.
,
58
, pp.
79
88
.10.1016/j.jbiomech.2017.04.016
42.
Wen
,
J.
,
Gao
,
Q.
,
Chen
,
J.
,
Li
,
X.
,
Zhang
,
K.
,
He
,
G.
,
Dai
,
M.
, and
Song
,
P.
,
2023
, “
Risk Evaluation of Adverse Aortic Events in Patients With Non-Circular Aortic Annulus After Transcatheter Aortic Valve Implantation: A Numerical Study
,”
Biomech. Model. Mechanobiol.
,
22
(
4
), pp.
1379
1394
.10.1007/s10237-023-01725-2
43.
Mei
,
C. C.
, and
Jing
,
H.
,
2016
, “
Pressure and Wall Shear Stress in Blood Hammer—Analytical Theory
,”
Math. Biosci.
,
280
, pp.
62
70
.10.1016/j.mbs.2016.07.007
44.
Malik
,
J.
,
Novakova
,
L.
,
Valerianova
,
A.
,
Chytilova
,
E.
,
Lejsek
,
V.
,
Buryskova Salajova
,
K.
,
Lambert
,
L.
,
Grus
,
T.
,
Porizka
,
M.
, and
Michalek
,
P.
,
2022
, “
Wall Shear Stress Alteration: A Local Risk Factor of Atherosclerosis
,”
Curr. Atheroscler. Rep.
,
24
(
3
), pp.
143
151
.10.1007/s11883-022-00993-0
45.
Liu
,
X.
,
Song
,
P.
,
Gao
,
Q.
,
Dai
,
M.
,
Rao
,
J.
, and
Wen
,
J.
,
2024
, “
Impact on Hemodynamics in Carotid Arteries With Carotid Webs at Different Locations: A Numerical Study Integrating Thrombus Growth Model
,”
Comput. Methods Programs Biomed.
,
243
, p.
107926
.10.1016/j.cmpb.2023.107926
46.
Zhao
,
X.
,
Liu
,
Y.
,
Li
,
L.
,
Wang
,
W.
,
Xie
,
J.
, and
Zhao
,
Z.
,
2016
, “
Hemodynamics of the String Phenomenon in the Internal Thoracic Artery Grafted to the Left Anterior Descending Artery With Moderate Stenosis
,”
J. Biomech.
,
49
(
7
), pp.
983
991
.10.1016/j.jbiomech.2015.11.044
47.
Jack
,
J. T.
,
Jensen
,
M.
,
Collins
,
R. T.
,
Chan
,
F. P.
, and
Millett
,
P. C.
,
2024
, “
Numerical Study of Hemodynamic Flow in the Aortic Vessel of Williams Syndrome Patient With Congenital Heart Disease
,”
J. Biomech.
,
168
, p.
112124
.10.1016/j.jbiomech.2024.112124
48.
Chen
,
Y.
,
Xu
,
B.
,
Cheng
,
Y.
,
Luo
,
K.
,
Fan
,
J.
, and
Xiang
,
M.
,
2023
, “
Hemodynamic Differences Caused by Left Atrial Appendage Modeling Contours
,”
Phys. Fluids
,
35
(
11
), p.
111904
.10.1063/5.0172261
49.
Wang
,
Y.
,
Meng
,
R.
,
Liu
,
G.
,
Cao
,
C.
,
Chen
,
F.
,
Jin
,
K.
,
Ji
,
X.
, and
Cao
,
G.
,
2019
, “
Intracranial Atherosclerotic Disease
,”
Neurobiol. Dis.
,
124
, pp.
118
132
.10.1016/j.nbd.2018.11.008
50.
Cilla
,
M.
,
Casales
,
M.
,
Peña
,
E.
,
Martínez
,
M.
, and
Malvè
,
M.
,
2020
, “
A Parametric Model for Studying the Aorta Hemodynamics by Means of the Computational Fluid Dynamics
,”
J. Biomech.
,
103
, p.
109691
.10.1016/j.jbiomech.2020.109691
51.
Tzirakis
,
K.
,
Kamarianakis
,
Y.
,
Kontopodis
,
N.
, and
Ioannou
,
C. V.
,
2023
, “
Selection of Bifurcated Grafts' Dimensions During Aorto-Iliac Vascular Reconstruction Based on Their Hemodynamic Performance
,”
Bioengineering
,
10
(
7
), p.
776
.10.3390/bioengineering10070776
52.
Qiao
,
Y.
,
Mao
,
L.
,
Zhu
,
T.
,
Fan
,
J.
, and
Luo
,
K.
,
2020
, “
Biomechanical Implications of the Fenestration Structure After Thoracic Endovascular Aortic Repair
,”
J. Biomech.
,
99
, p.
109478
.10.1016/j.jbiomech.2019.109478
53.
Zhou
,
M.
,
Yu
,
Y.
,
Chen
,
R.
,
Liu
,
X.
,
Hu
,
Y.
,
Ma
,
Z.
,
Gao
,
L.
,
Jian
,
W.
, and
Wang
,
L.
,
2023
, “
Wall Shear Stress and Its Role in Atherosclerosis
,”
Front. Cardiovasc. Med.
,
10
, p.
1083547
.10.3389/fcvm.2023.1083547
54.
Vorobtsova
,
N.
,
Chiastra
,
C.
,
Stremler
,
M. A.
,
Sane
,
D. C.
,
Migliavacca
,
F.
, and
Vlachos
,
P.
,
2016
, “
Effects of Vessel Tortuosity on Coronary Hemodynamics: An Idealized and Patient-Specific Computational Study
,”
Ann. Biomed. Eng.
,
44
(
7
), pp.
2228
2239
.10.1007/s10439-015-1492-3
You do not currently have access to this content.