https://orcid.org/0000-0001-9469-9526
Abstract
This study utilizes computational tools to analyze the hemodynamic effects of a hypoplastic/stenotic A1 segment in the anterior cerebral artery (ACA) on the circle of Willis (CoW). The objective is to investigate how variations in ACA A1 diameter affect flow dynamics, wall shear stress (WSS), and the initiation of aneurysms within the CoW. An idealized CoW geometry is employed, incorporating hypoplastic ACA A1 segments with reductions of 25%, 50%, 75%, and 100% in diameter and a 50% constriction representing stenosis. A three-dimensional (3D) computational fluid dynamics (CFD) model explores flow dynamics and WSS distribution. The computational methodology is validated against experimental data from existing literature. The study demonstrates the resilience of overall brain perfusion despite a hypoplastic ACA A1 segment. Significant alterations and diversions in flow, particularly at the anterior communicating artery-anterior cerebral artery (ACoM-ACA) junction, are observed under varying degrees of hypoplasticity. The analysis of radial velocity profiles reveals asymmetry in flow distribution, exacerbating risks of arterial diseases such as atherosclerosis and thrombosis. Distinct patterns of WSS distribution during peak systole in the ACA A2 segment highlight the influence of hypoplasticity on vascular health, with implications for structural aberrations and aneurysm formation, particularly in the posterior cerebral artery (PCA). A comparison study of rigid wall cases with elastic walls using a fluid-structure interaction (FSI) model is also done to understand the applicability of FSI. Insights gained from this research contribute to comprehending CoW anomalies' pathophysiology and offer guidance for developing effective treatment strategies.
References
1.
Darvish
,
H.
,
Fatouraee
,
N.
, and
Nabaei
,
M.
, 2021
, “
Numerical Investigation of Perfusion Rates in the Circle of Willis in Different Anatomical Variations and Ischemic Stroke
,” Phys. Fluids
,
33
(4
), p. 041901
.10.1063/5.00403482.
Jones
,
J. D.
,
Castanho
,
P.
,
Bazira
,
P.
, and
Sanders
,
K.
, 2021
, “
Anatomical Variations of the Circle of Willis and Their Prevalence, With a Focus on the Posterior Communicating Artery: A Literature Review and Meta-Analysis
,” Clin. Anat.
,
34
(7
), pp. 978
–990
.10.1002/ca.236623.
Shatri
,
J.
,
Cerkezi
,
S.
,
Ademi
,
V.
,
Reci
,
V.
, and
Bexheti
,
S.
, 2019
, “
Anatomical Variations and Dimensions of Arteries in the Anterior Part of the Circle of Willis
,” Folia Morphol.
,
78
(2
), pp. 259
–266
.10.5603/FM.a2018.00954.
Golshani
,
K.
,
Ferrell
,
A.
,
Zomorodi
,
A.
,
Smith
,
T. P.
, and
Britz
,
G. W.
, 2010
, “
A Review of the Management of Posterior Communicating Artery Aneurysms in the Modern Era
,” Surg. Neurol. Int.
,
1
(1
), p. 88
.10.4103/2152-7806.741475.
Capone
,
S.
,
Shah
,
N.
, and
George-St Bernard
,
R. R.
, 2019
, “
A Fetal-Type Variant Posterior Communicating Artery and Its Clinical Significance
,” Cureus
,
11
(7
), p. e5064
.https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6721919/6.
Hindenes
,
L. B.
,
Haberg
,
A. K.
,
Johnsen
,
L. H.
,
Mathiesen
,
E. B.
,
Robben
,
D.
, and
Vang-Berg
,
T. R.
, 2020
, “
Variations in the Circle of Willis in a Large Population Sample Using 3D TOF Angiography: The Tromsø Study
,” PLoS One
,
15
(11
), p. e0241373
.10.1371/journal.pone.02413737.
Hindenes
,
L. B.
,
Ingebrigtsen
,
T.
,
Isaksen
,
J. G.
,
Haberg
,
A. K.
,
Johnsen
,
L.-H.
,
Herder
,
M.
,
Mathiesen
,
E. B.
, and
Vangberg
,
T. R.
, 2023
, “
Anatomical Variations in the Circle of Willis Are Associated With Increased Odds of Intracranial Aneurysms: The Tromsø Study
,” J. Neurol. Sci.
,
452
, p. 120740
.10.1016/j.jns.2023.1207408.
Battacharji
,
S.
,
Hutchinson
,
E.
, and
McCall
,
A.
, 1967
, “
The Circle of Willis—The Incidence of Developmental Abnormalities in Normal and Infarcted Brains
,” Brain
,
90
(4
), pp. 747
–758
.10.1093/brain/90.4.7479.
Powers
,
W. J.
, 1991
, “
Cerebral Hemodynamics in Ischemic Cerebrovascular Disease
,” Ann. Neurol.
,
29
(3
), pp. 231
–240
.10.1002/ana.41029030210.
DeVault
,
K.
,
Gremaud
,
P. A.
,
Novak
,
V.
,
Olufsen
,
M. S.
,
Vernieres
,
G.
, and
Zhao
,
P.
, 2008
, “
Blood Flow in the Circle of Willis: Modeling and Calibration
,” Multiscale Model. Simul.
,
7
(2
), pp. 888
–909
.10.1137/07070231X11.
Hillen
,
B.
,
Hoogstraten
,
H. W.
, and
Post
,
L.
, 1986
, “
A Mathematical Model of the Flow in the Circle of Willis
,” J. Biomech.
,
19
(3
), pp. 187
–194
.10.1016/0021-9290(86)90151-X12.
Wellnhofer
,
E.
,
Osman
,
J.
,
Kertzscher
,
U.
,
Affeld
,
K.
,
Fleck
,
E.
, and
Goubergrits
,
L.
, 2010
, “
Flow Simulation Studies in Coronary Arteries—Impact of Side-Branches
,” Atherosclerosis
,
213
(2
), pp. 475
–481
.10.1016/j.atherosclerosis.2010.09.00713.
Borazjani
,
I.
,
Ge
,
L.
,
Le
,
T.
, and
Sotiropoulos
,
F.
, 2013
, “
A Parallel Overset-Curvilinear immersed Boundary Framework for Simulating Complex 3D Incompressible Flows
,” Comput. Fluids
,
77
, pp. 76
–96
.10.1016/j.compfluid.2013.02.01714.
Krabbe-Hartkamp
,
M. J.
,
Van der Grond
,
J.
,
De Leeuw
,
F.
,
De Groot
,
J.
,
Algra
,
A.
,
Hillen
,
B.
,
Breteler
,
M.
, and
Mali
,
W.
, 1998
, “
Circle of Willis: Morphologic Variation on Three-Dimensional Time-of-Flight MR Angiograms
,” Radiology
,
207
(1
), pp. 103
–111
.10.1148/radiology.207.1.953030515.
Rezaie
,
H.
,
Ashrafizadeh
,
A.
, and
Mojra
,
A.
, 2017
, “
A Patient-Specific Three-Dimensional Hemodynamic Model of the Circle of Willis
,” Cardiovasc. Eng. Technol.
,
8
(4
), pp. 495
–504
.10.1007/s13239-017-0330-116.
Zhu
,
G.
,
Yuan
,
Q.
,
Yang
,
J.
, and
Yeo
,
J. H.
, 2015
, “
The Role of the Circle of Willis in Internal Carotid Artery Stenosis and Anatomical Variations: A Computational Study Based on a Patient specific Three-Dimensional Model
,” Biomed. Eng. Online
,
14
(1
), pp. 1
–19
.10.1186/s12938-015-0105-617.
Ren
,
Y.
,
Chen
,
Q.
, and
Li
,
Z.-Y.
, 2015
, “
A 3D Numerical Study of the Collateral Capacity of the Circle of Willis With Anatomical Variation in the Posterior Circulation
,” Biomed. Eng. Online
,
14
(S1
), pp. 1
–12
.10.1186/1475-925X-14-S1-S1118.
Lippert
,
H.
, and
Pabst
,
R.
, 1985
, Arterial Variations in Man: Classification and Frequency
, JF Bergmann Verlag, Munich, Germany
.19.
Cassot
,
F.
,
Vergeur
,
V.
,
Bossuet
,
P.
,
Hillen
,
B.
,
Zagzoule
,
M.
, and
Marc-Vergnes
,
J.-P.
, 1995
, “
Effects of Anterior Communicating Artery Diameter on Cerebral Hemodynamics in Internal Carotid Artery Disease: A Model Study
,” Circulation
,
92
(10
), pp. 3122
–3131
.10.1161/01.CIR.92.10.312220.
Viedma
,
A.
,
Jimenez-Ortiz
,
C.
, and
Marco
,
V.
, 1997
, “
Extended Willis Circle Model to Explain Clinical Observations in Periorbital Arterial Flow
,” J. Biomech.
,
30
(3
), pp. 265
–272
.10.1016/S0021-9290(96)00143-121.
Moorhead
,
K.
,
Doran
,
C.
,
Chase
,
J.
, and
David
,
T.
, 2004
, “
Lumped Parameter and Feedback Control Models of the Auto-Regulatory Response in the Circle of Willis
,” Comput. Methods Biomech. Biomed. Eng.
,
7
(3
), pp. 121
–130
.10.1080/1025584041000171089422.
Cornelissen
,
B. M. W.
,
Schneiders
,
J. J.
,
Sprengers
,
M. E.
,
van den Berg
,
R.
,
van Ooij
,
P.
,
Nederveen
,
A. J.
,
van Bavel
,
E.
, et al., 2018
, “
Aneurysmal Parent Artery–Specific Inflow Conditions for Complete and Incomplete Circle of Willis Configurations
,” Am. J. Neuroradiol.
,
39
(5
), pp. 910
–915
.10.3174/ajnr.A560223.
Berg
,
P.
,
Stucht
,
D.
,
Janiga
,
G.
,
Beuing
,
O.
,
Speck
,
O.
, and
Thévenin
,
D.
, 2014
, “
Cerebral Blood Flow in a Healthy Circle of Willis and Two Intracranial Aneurysms: Computational Fluid Dynamics Versus Four-Dimensional Phase-Contrast Magnetic Resonance Imaging
,” ASME J. Biomech. Eng.
,
136
(4
), p. 041003
.10.1115/1.402610824.
Philip
,
N. T.
,
Bolem
,
S.
,
Sudhir
,
B.
, and
Patnaik
,
B.
, 2022
, “
Hemodynamics and Biomechanics of Morphologically Distinct Saccular Intracranial Aneurysms at Bifurcations: Idealised vs Patient-Specific Geometries
,” Comput. Methods Prog. Biomed.
,
227
, p. 107237
.10.1016/j.cmpb.2022.10723725.
Saha
,
S.
,
Harshavardhan
,
E.
, and
Sudhir
,
B. J.
, 2022
, “
Fluid–Structure Interaction Model for Assessing Aneurysm Initiation at the Circle of Willis
,” ASME J. Eng. Sci. Med. Diagn. Ther.
,
5
(3
), p. 031101
.10.1115/1.405384326.
Mamatyukov
,
M.
,
Mikheev
,
I.
,
Parshin
,
D.
,
Khe
,
A.
,
Cherevko
,
A.
,
Orlov
,
K.
, and
Chupakhin
,
A.
, 2018
, “
Comprehensive Research of Human Brain Hemodynamics: Clinical Monitoring and Computer Simulations
,” AIP Conf. Proc.
,
2027
, p. 020009
.10.1063/1.506508727.
Piechna
,
A.
, and
Cieslicki
,
K.
, 2017
, “
Reversed Robin Hood Syndrome in the Light of Nonlinear Model of Cerebral Circulation
,” Int. J. Appl. Mech. Eng.
,
22
(2
), pp. 459
–464
.10.1515/ijame-2017-002928.
Zhu
,
F.
,
Qian
,
Y.
,
Xu
,
B.
,
Gu
,
Y.
,
Karunanithi
,
K.
,
Zhu
,
W.
,
Chen
,
L.
,
Mao
,
Y.
, and
Morgan
,
M. K.
, 2018
, “
Quantitative Assessment of Changes in Hemodynamics of the Internal Carotid Artery After Bypass Surgery for Moyamoya Disease
,” J. Neurosurg.
,
129
(3
), pp. 677
–683
.10.3171/2017.5.JNS16311229.
Razaghi
,
R.
,
Biglari
,
H.
, and
Karimi
,
A.
, 2019
, “
Risk of Rupture of the Cerebral Aneurysm in Relation to Traumatic Brain Injury Using a Patient-Specific Fluid-Structure Interaction Model
,” Comput. Methods Prog. Biomed.
,
176
, pp. 9
–16
.10.1016/j.cmpb.2019.04.01530.
Xie
,
J.
,
Cheng
,
Z.
,
Gu
,
L.
,
Wu
,
B.
,
Zhang
,
G.
,
Shiu
,
W.
,
Chen
,
R.
, et al., 2022
, “
Evaluation of Cerebrovascular Hemodynamics in Vascular Dementia Patients With a New Individual Computational Fluid Dynamics Algorithm
,” Comput. Methods Prog. Biomed.
,
213
, p. 106497
.10.1016/j.cmpb.2021.10649731.
Sun
,
H.
,
Li
,
B.
,
Zhang
,
L.
,
Zhang
,
Y.
,
Liu
,
J.
,
Huang
,
S.
,
Xi
,
X.
, and
Liu
,
Y.
, 2024
, “
Numerical Study of Hemodynamic Changes in the Circle of Willis After Stenosis of the Internal Carotid Artery
,” Comput. Methods Prog. Biomed.
,
243
, p. 107881
.10.1016/j.cmpb.2023.10788132.
Zhang
,
J.-M.
,
Chua
,
L. P.
,
Ghista
,
D. N.
,
Yu
,
S. C. M.
, and
Tan
,
Y. S.
, 2008
, “
Numerical Investigation and Identification of Susceptible Sites of Atherosclerotic Lesion Formation in a Complete Coronary Artery Bypass Model
,” Med. Biol. Eng. Comput.
,
46
(7
), pp. 689
–699
.10.1007/s11517-008-0320-433.
Zhang
,
J.-M.
,
Zhong
,
L.
,
Su
,
B.
,
Wan
,
M.
,
Yap
,
J. S.
,
Tham
,
J. P.
,
Chua
,
L. P.
,
Ghista
,
D. N.
, and
Tan
,
R. S.
, 2014
, “
Perspective on CFD Studies of Coronary Artery Disease Lesions and Hemodynamics: A Review
,” Int. J. Numer. Methods Biomed. Eng.
,
30
(6
), pp. 659
–680
.10.1002/cnm.262534.
Šutalo
,
I. D.
,
Bui
,
A. V.
,
Ahmed
,
S.
,
Liffman
,
K.
, and
Manasseh
,
R.
, 2014
, “
Modeling of Flow Through the Circle of Willis and Cerebral Vasculature to Assess the Effects of Changes in the Peripheral Small Cerebral Vasculature on the Inflows
,” Eng. Appl. Comput. Fluid Mech.
,
8
(4
), pp. 609
–622
.https://www.tandfonline.com/doi/abs/10.1080/19942060.2014.1108331135.
Ford
,
M. D.
,
Alperin
,
N.
,
Lee
,
S. H.
,
Holdsworth
,
D. W.
, and
Steinman
,
D. A.
, 2005
, “
Characterization of Volumetric Flow Rate Waveforms in the Normal Internal Carotid and Vertebral Arteries
,” Physiol. Meas.
,
26
(4
), pp. 477
–488
.10.1088/0967-3334/26/4/01336.
Helfrich
,
H.-P.
, and
Zwick
,
D.
, 1996
, “
A Trust Region Algorithm for Parametric Curve and Surface Fitting
,” J. Comput. Appl. Math.
,
73
(1–2
), pp. 119
–134
.10.1016/0377-0427(96)00039-837.
Cho
,
Y. I.
, and
Kensey
,
K. R.
, 1991
, “
Effects of the Non-Newtonian Viscosity of Blood on Flows in a Diseased Arterial Vessel. Part 1: Steady Flows
,” Biorheology
,
28
(3–4
), pp. 241
–262
.10.3233/BIR-1991-283-41538.
Mendieta
,
J. B.
,
Fontanarosa
,
D.
,
Wang
,
J.
,
Paritala
,
P. K.
,
McGahan
,
T.
,
Lloyd
,
T.
, and
Li
,
Z.
, 2020
, “
The Importance of Blood Rheology in Patient-Specific Computational Fluid Dynamics Simulation of Stenotic Carotid Arteries
,” Biomech. Model. Mechanobiol.
,
19
(5
), pp. 1477
–1490
.10.1007/s10237-019-01282-739.
Wu
,
J.
,
Liu
,
G.
,
Huang
,
W.
,
Ghista
,
D. N.
, and
Wong
,
K. K.
, 2015
, “
Transient Blood Flow in Elastic Coronary Arteries With Varying Degrees of Stenosis and Dilatations: CFD Modelling and Parametric Study
,” Comput. Methods Biomech. Biomed. Eng.
,
18
(16
), pp. 1835
–1845
.10.1080/10255842.2014.97681240.
Franquet
,
A.
,
Avril
,
S.
,
Le Riche
,
R.
,
Badel
,
P.
,
Schneider
,
F.
,
Boissier
,
C.
, and
Favre
,
J.-P.
, 2013
, “
Identification of the In Vivo Elastic Properties of Common Carotid Arteries From MRI: A Study on Subjects With and Without Atherosclerosis
,” J. Mech. Behav. Biomed. Mater.
,
27
, pp. 184
–203
.10.1016/j.jmbbm.2013.03.01641.
Ojha
,
M.
,
Cobbold
,
R. S.
,
Johnston
,
K. W.
, and
Hummel
,
R. L.
, 1989
, “
Pulsatile Flow Through Constricted Tubes: An Experimental Investigation Using Photochromic Tracer Methods
,” J. Fluid Mech.
,
203
, pp. 173
–197
.10.1017/S002211208900142442.
Xu
,
L.
,
Sugawara
,
M.
,
Tanaka
,
G.
,
Ohta
,
M.
,
Liu
,
H.
, and
Yamaguchi
,
R.
, 2016
, “
Effect of Elasticity on Wall Shear Stress Inside Cerebral Aneurysm at Anterior Cerebral Artery
,” Technol. Health Care
,
24
(3
), pp. 349
–357
.10.3233/THC-16113543.
Razavi
,
S. E.
, and
Sahebjam
,
R.
, 2014
, “
Numerical Simulation of the Blood Flow Behavior in the Circle of Willis
,” BioImpacts: BI
,
4
(2
), pp. 89
–94
.10.5681/bi.2014.00844.
Zheng
,
R.
,
Han
,
Q.
,
Hong
,
W.
,
Yi
,
X.
,
He
,
B.
, and
Liu
,
Y.
, 2024
, “
Hemodynamic Characteristics and Mechanism for Intracranial Aneurysms Initiation With the Circle of Willis Anomaly
,” Comput. Methods Biomech. Biomed. Eng.
,
27
(6
), pp. 727
–735
.10.1080/10255842.2023.219990245.
van Tuijl
,
R.
,
Ruigrok
,
Y.
,
Ophelders
,
M.
,
Vos
,
I.
,
van der Schaaf
,
I.
,
Zwanenburg
,
J.
, and
Velthuis
,
B.
, 2023
, “
Relationship Between Diameter Asymmetry and Blood Flow in the Precommunicating (a1) Segment of the Anterior Cerebral Arteries
,” J. Neuroradiol.
,
50
(4
), pp. 402
–406
.10.1016/j.neurad.2022.10.00446.
Moore
,
S.
,
David
,
T.
,
Chase
,
J.
,
Arnold
,
J.
, and
Fink
,
J.
, 2006
, “
3D Models of Blood Flow in the Cerebral Vasculature
,” J. Biomech.
,
39
(8
), pp. 1454
–1463
.10.1016/j.jbiomech.2005.04.00547.
Yang
,
H.
,
Cho
,
K.-C.
,
Hong
,
I.
,
Kim
,
Y.
,
Kim
,
Y. B.
,
Kim
,
J.-J.
, and
Oh
,
J. H.
, 2024
, “
Influence of Circle of Willis modeling on Hemodynamic Parameters in Anterior Communicating Artery Aneurysms and Recommendations for Model Selection
,” Sci. Rep.
,
14
(1
), p. 8476
.10.1038/s41598-024-59042-248.
Malek
,
A. M.
,
Alper
,
S. L.
, and
Izumo
,
S.
, 1999
, “
Hemodynamic Shear Stress and Its Role in Atherosclerosis
,” Jama
,
282
(21
), pp. 2035
–2042
.10.1001/jama.282.21.203549.
Chen
,
Y.
,
Yang
,
X.
,
Iskander
,
A. J.
, and
Wang
,
P.
, 2020
, “
On the Flow Characteristics in Different Carotid Arteries
,” Phys. Fluids
,
32
(10
), p. 101902
.10.1063/5.002209250.
Sekhane
,
D.
, 2016
, “
Image-Based Computational Fluid Dynamics (CFD) Modeling Cerebral Blood Flow in the Circle of Willis
,” J. Adv. Res. Phys.
,
6
(2
), pp. 1
–6
.https://www.researchgate.net/publication/312028337_Imagebased_Computational_fluid_dynamics_CFD_Modeling_cerebral_blood_flow_in_the_Circle_of_Willis51.
Zhang
,
Z-Q.
,
Xu
,
L-J.
,
Liu
,
R.
,
Liu
,
X-S.
,
Zhao
,
B.
, and
Liang
,
F-y.
, 2020
, “
Importance of Incorporating Systemic Cerebroarterial hemodynamics Into Computational Modeling of Blood Flow in Intracranial Aneurysm
,” J. Hydrodyn.
,
32
(3
), pp. 510
–522
.10.1007/s42241-019-0038-952.
Khodaee
,
F.
,
Vahidi
,
B.
, and
Fatouraee
,
N.
, 2016
, “
Analysis of Mechanical Parameters on the Thromboembolism Using a Patient-Specific Computational Model
,” Biomech. Model. Mechanobiol.
,
15
(5
), pp. 1295
–1305
.10.1007/s10237-016-0762-953.
Fabbri
,
D.
,
Long
,
Q.
,
Das
,
S.
, and
Pinelli
,
M.
, 2014
, “
Computational Modelling of Emboli Travel Trajectories in Cerebral Arteries: Influence of Microembolic Particle Size and Density
,” Biomech. Model. Mechanobiol.
,
13
(2
), pp. 289
–302
.10.1007/s10237-014-0561-054.
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 Prog. Biomed.
,
243
, p. 107916
.10.1016/j.cmpb.2023.107916
