Abstract
In this study, using fluid-structure interaction (FSI), 3-dimensional blood flow in an aneurysm in the circle of Willis – which is located in the middle cerebral artery (MCA) – has been simulated. The purpose of this study is to evaluate the effect of a partly blocked vessel on an aneurysm. To achieve this purpose, two cases have been investigated using the FSI method: in the first case, an ideal geometry of aneurysm in the MCA has been simulated; in the second case, modeling is performed for an ideal geometry of the aneurysm in the MCA with a partly blocked vessel. All boundary conditions, properties and modeling methods were considered the same for both cases. The only difference between the two cases was that part of the MCA parent artery was blocked in the second case. In order to consider the hyperelastic property of the wall and the non-Newtonian properties of the blood, the Mooney-Rivlin model and the Carreau model have been used, respectively. In the second case, the Von Mises stress in the peak systole is 26% higher than in the first case. With regard to the high amount of Von Mises stress, the risk of rupture of the aneurysm is higher in this case. In the second case, the maximum wall shear stress (WSS) is 12% higher than in the first case. And maximum displacement in the second case is also higher than in the first. So, the risk of growth of the aneurysm is higher in cases with a partly blocked vessel.
References
1.
Gay
M
, Zhang
L
. Numerical studies on fluid–structure interactions of stent deployment and stented arteries
. Eng Comput
. 2009
;25
(1
):61
–72
. 0264-44012.
van Gijn
J
, Rinkel
GJ
. Subarachnoid haemorrhage: diagnosis, causes and management
. Brain
. 2001
Feb
;124
(Pt 2
):249
–78
.
[PubMed]
0006-89503.
Meng
H
, Tutino
VM
, Xiang
J
, Siddiqui
A
. High WSS or low WSS? Complex interactions of hemodynamics with intracranial aneurysm initiation, growth, and rupture: toward a unifying hypothesis
. AJNR Am J Neuroradiol
. 2014
Jul
;35
(7
):1254
–62
.
[PubMed]
0195-61084.
Sekhar
LN
, Heros
RC
. Origin, growth, and rupture of saccular aneurysms: a review
. Neurosurgery
. 1981
Feb
;8
(2
):248
–60
.
[PubMed]
0148-396X5.
Wu
J
, Liu
G
, Huang
W
, Ghista
DN
, Wong
KK
. Transient blood flow in elastic coronary arteries with varying degrees of stenosis and dilatations: CFD modelling and parametric study
. Comput Methods Biomech Biomed Engin
. 2015
;18
(16
):1835
–45
.
[PubMed]
1025-58426.
Ahmadi
S
, Faridi
S
, Tahmasebi
S
. Calcium-dependent kinases in the brain have site-specific associations with locomotion and rearing impairments in rats with bile duct ligation
. Behav Brain Res
. 2019
Oct
;372
:112009
.
[PubMed]
0166-43287.
Tang
D
, Yang
C
, Kobayashi
S
, Ku
DN
. Effect of a lipid pool on stress/strain distributions in stenotic arteries: 3-D fluid-structure interactions (FSI) models
. J Biomech Eng
. 2004
Jun
;126
(3
):363
–70
.
[PubMed]
0148-07318.
Ricotta
JJ
, Pagan
J
, Xenos
M
, Alemu
Y
, Einav
S
, Bluestein
D
. Cardiovascular disease management: the need for better diagnostics
. Med Biol Eng Comput
. 2008
Nov
;46
(11
):1059
–68
.
[PubMed]
0140-01189.
Hoi
Y
, Meng
H
, Woodward
SH
, Bendok
BR
, Hanel
RA
, Guterman
LR
, et al Effects of arterial geometry on aneurysm growth: three-dimensional computational fluid dynamics study
. J Neurosurg
. 2004
Oct
;101
(4
):676
–81
.
[PubMed]
0022-308510.
Castro
MA
, Putman
CM
, Cebral
JR
. Computational fluid dynamics modeling of intracranial aneurysms: effects of parent artery segmentation on intra-aneurysmal hemodynamics
. AJNR Am J Neuroradiol
. 2006
Sep
;27
(8
):1703
–9
.
[PubMed]
0195-610811.
Sato
K
, Imai
Y
, Ishikawa
T
, Matsuki
N
, Yamaguchi
T
. The importance of parent artery geometry in intra-aneurysmal hemodynamics
. Med Eng Phys
. 2008
Jul
;30
(6
):774
–82
.
[PubMed]
1350-453312.
Kosierkiewicz
TA
, Factor
SM
, Dickson
DW
. Immunocytochemical studies of atherosclerotic lesions of cerebral berry aneurysms
. J Neuropathol Exp Neurol
. 1994
Jul
;53
(4
):399
–406
.
[PubMed]
0022-306913.
Killer-Oberpfalzer
M
, Aichholzer
M
, Weis
S
, Richling
B
, Jones
R
, Virmani
R
, et al Histological analysis of clipped human intracranial aneurysms and parent arteries with short-term follow-up
. Cardiovasc Pathol
. 2012
Jul-Aug
;21
(4
):299
–306
.
[PubMed]
1054-880714.
Greenhalgh
RM
, Laing
S
, Taylor
GW
. Risk factors in carotid artery stenosis and intracranial aneurysms
. J Cardiovasc Surg (Torino)
. 1980
Sep-Oct
;21
(5
):559
–67
.
[PubMed]
0021-950915.
Adamson
J
, Humphries
SE
, Ostergaard
JR
, Voldby
B
, Richards
P
, Powell
JT
. Are cerebral aneurysms atherosclerotic?
Stroke
. 1994
May
;25
(5
):963
–6
.
[PubMed]
0039-249916.
Shamloo
A
, Mohammadaliha
N
, Mohseni
M
. Integrative utilization of microenvironments, biomaterials and computational techniques for advanced tissue engineering
. J Biotechnol
. 2015
Oct
;212
:71
–89
.
[PubMed]
0168-165617.
Bazilevs
Y
, Calo
VM
, Zhang
Y
, Hughes
TJ
. Isogeometric fluid–structure interaction analysis with applications to arterial blood flow
. Comput Mech
. 2006
;38
(4-5
):310
–22
. 0178-767518.
Torii
R
, Oshima
M
, Kobayashi
T
, Takagi
K
, Tezduyar
TE
. Fluid–structure interaction modeling of blood flow and cerebral aneurysm: significance of artery and aneurysm shapes
. Comput Methods Appl Mech Eng
. 2009
;198
(45-46
):3613
–21
. 0045-782519.
Long
Q
, Xu
XY
, Ariff
B
, Thom
SA
, Hughes
AD
, Stanton
AV
. Reconstruction of blood flow patterns in a human carotid bifurcation: a combined CFD and MRI study
. J Magn Reson Imaging
. 2000
Mar
;11
(3
):299
–311
.
[PubMed]
1053-180720.
Fiorella
D
, Woo
H
. Method and apparatus for increasing blood flow through an obstructed blood vessel
. Google Patents
; 2011
.21.
Shamloo
A
, Nejad
MA
, Saeedi
M
. Fluid-structure interaction simulation of a cerebral aneurysm: effects of endovascular coiling treatment and aneurysm wall thickening
. J Mech Behav Biomed Mater
. 2017
Oct
;74
:72
–83
.
[PubMed]
1751-616122.
Shamloo
A
, Mohammadaliha
N
, Heilshorn
SC
, Bauer
AL
. A comparative study of collagen matrix density effect on endothelial sprout formation using experimental and computational approaches
. Ann Biomed Eng
. 2016
Apr
;44
(4
):929
–41
.
[PubMed]
0090-696423.
Meng
H
, Wang
Z
, Hoi
Y
, Gao
L
, Metaxa
E
, Swartz
DD
, et al Complex hemodynamics at the apex of an arterial bifurcation induces vascular remodeling resembling cerebral aneurysm initiation
. Stroke
. 2007
Jun
;38
(6
):1924
–31
.
[PubMed]
0039-249924.
Shojima
M
, Oshima
M
, Takagi
K
, Torii
R
, Hayakawa
M
, Katada
K
, et al Magnitude and role of wall shear stress on cerebral aneurysm: computational fluid dynamic study of 20 middle cerebral artery aneurysms
. Stroke
. 2004
Nov
;35
(11
):2500
–5
.
[PubMed]
0039-249925.
Nakatani
H
, Hashimoto
N
, Kang
Y
, Yamazoe
N
, Kikuchi
H
, Yamaguchi
S
, et al Cerebral blood flow patterns at major vessel bifurcations and aneurysms in rats
. J Neurosurg
. 1991
Feb
;74
(2
):258
–62
.
[PubMed]
0022-308526.
Fukuda
S
, Hashimoto
N
, Naritomi
H
, Nagata
I
, Nozaki
K
, Kondo
S
, et al Prevention of rat cerebral aneurysm formation by inhibition of nitric oxide synthase
. Circulation
. 2000
May
;101
(21
):2532
–8
.
[PubMed]
0009-732227.
ARANDA
. A. and A. VALENCIA, COMPUTATIONAL STUDY ON THE RUPTURE RISK IN REAL CEREBRAL ANEURYSMS WITH GEOMETRICAL AND FLUID-MECHANICAL PARAMETERS USING FSI SIMULATIONS AND MACHINE LEARNING ALGORITHMS
. J Mech Med Biol
. 2019
;•••
:1950014
.0219-519428.
Qiu
TL
, Jin
GL
, Bao
WQ
, Lu
HT
. Morphological Effect on Wall Shear Stress in Intracranial Aneurysms
. J Neurol Surg A Cent Eur Neurosurg
. 2018
Mar
;79
(2
):108
–15
.
[PubMed]
2193-631529.
Wang
Y
, Leng
X
, Zhou
X
, Li
W
, Siddiqui
AH
, Xiang
J
. Hemodynamics in a middle cerebral artery aneurysm before its growth and fatal rupture: case study and review of the literature
. World Neurosurg
. 2018
Nov
;119
:e395
–402
.
[PubMed]
1878-875030.
Razaghi
R
, Biglari
H
, Karimi
A
. Risk of rupture of the cerebral aneurysm in relation to traumatic brain injury using a patient-specific fluid-structure interaction model
. Comput Methods Programs Biomed
. 2019
Jul
;176
:9
–16
.
[PubMed]
0169-260731.
Torii
R
, Oshima
M
, Kobayashi
T
, Takagi
K
, Tezduyar
TE
. Fluid–structure interaction modeling of a patient-specific cerebral aneurysm: influence of structural modeling
. Comput Mech
. 2008
;43
(1
):151
–9
. 0178-767532.
Malvè
M
, García
A
, Ohayon
J
, Martínez
MA
. Unsteady blood flow and mass transfer of a human left coronary artery bifurcation: FSI vs. CFD
. Int Commun Heat Mass Transf
. 2012
;39
(6
):745
–51
. 0735-193333.
Shamloo
A
, Manuchehrfar
F
, Rafii-Tabar
H
. A viscoelastic model for axonal microtubule rupture
. J Biomech
. 2015
May
;48
(7
):1241
–7
.
[PubMed]
0021-929034.
Hamdan
MO
, et al CFD Investigation of the Effect of Cerebral Aneurysms Size on Wall Stresses and Strain. in 2019 Advances in Science and Engineering Technology International Conferences (ASET). 2019
. IEEE.35.
Kaku
, Y.
, et al, Treatment of cerebral aneurysms: surgical clipping and coil embolization.
Interventional Neuroradiology, 2007
. 13(1_suppl): p. 68-72. 36.
Lee
CJ
, Zhang
Y
, Takao
H
, Murayama
Y
, Qian
Y
. A fluid-structure interaction study using patient-specific ruptured and unruptured aneurysm: the effect of aneurysm morphology, hypertension and elasticity
. J Biomech
. 2013
Sep
;46
(14
):2402
–10
.
[PubMed]
0021-929037.
Jeong
, W.
and K.
Rhee
, Hemodynamics of cerebral aneurysms: computational analyses of aneurysm progress and treatment.
Computational and mathematical methods in medicine, 2012. 2012
. 38.
Babiker
MH
, Chong
B
, Gonzalez
LF
, Cheema
S
, Frakes
DH
. Finite element modeling of embolic coil deployment: multifactor characterization of treatment effects on cerebral aneurysm hemodynamics
. J Biomech
. 2013
Nov
;46
(16
):2809
–16
.
[PubMed]
0021-929039.
Tsang
AC
, Yiu
BY
, Tang
AY
, Chung
WC
, Leung
GK
, Poon
AK
, et al The effect of downstream resistance on flow diverter treatment of a cerebral aneurysm at a bifurcation: A joint computational-experimental study
. J Hydrodynam
. 2018
;30
(5
):803
–14
. 1001-605840.
Tang
D
, Yang
C
, Zheng
J
, Woodard
PK
, Sicard
GA
, Saffitz
JE
, et al 3D MRI-based multicomponent FSI models for atherosclerotic plaques
. Ann Biomed Eng
. 2004
Jul
;32
(7
):947
–60
.
[PubMed]
0090-696441.
Ivanov
D
, Dol
A
, Pavlova
O
, Aristambekova
A
. Modeling of human circle of Willis with and without aneurisms
. Acta Bioeng Biomech
. 2014
;16
(2
):121
–9
.
[PubMed]
1509-409X42.
Campo-Deaño
L
, Oliveira
MS
, Pinho
FT
. A review of computational hemodynamics in middle cerebral aneurysms and rheological models for blood flow
. Appl Mech Rev
. 2015
;67
(3
):030801
. 0003-690043.
Torii
R
, Oshima
M
, Kobayashi
T
, Takagi
K
, Tezduyar
TE
. Influence of wall thickness on fluid–structure interaction computations of cerebral aneurysms
. Int J Numer Methods Biomed Eng
. 2010
;26
(3‐4
):336
–47
. 2040-793944.
Thurston
GB
. Rheological parameters for the viscosity viscoelasticity and thixotropy of blood
. Biorheology
. 1979
;16
(3
):149
–62
.
[PubMed]
0006-355X45.
Walker
AM
, Johnston
CR
, Rival
DE
. On the characterization of a non-Newtonian blood analog and its response to pulsatile flow downstream of a simplified stenosis
. Ann Biomed Eng
. 2014
Jan
;42
(1
):97
–109
.
[PubMed]
0090-696446.
Valencia
A
, Zarate
A
, Galvez
M
, Badilla
L
. Non‐Newtonian blood flow dynamics in a right internal carotid artery with a saccular aneurysm
. Int J Numer Methods Fluids
. 2006
;50
(6
):751
–64
. 0271-209147.
Cho
YI
, Kensey
KR
. Effects of the non-Newtonian viscosity of blood on flows in a diseased arterial vessel. Part 1: steady flows
. Biorheology
. 1991
;28
(3-4
):241
–62
.
[PubMed]
0006-355X48.
Mills
CJ
, Gabe
IT
, Gault
JH
, Mason
DT
, Ross
J
Jr, Braunwald
E
, et al Pressure-flow relationships and vascular impedance in man
. Cardiovasc Res
. 1970
Oct
;4
(4
):405
–17
.
[PubMed]
0008-636349.
Zulliger
MA
, Fridez
P
, Hayashi
K
, Stergiopulos
N
. A strain energy function for arteries accounting for wall composition and structure
. J Biomech
. 2004
Jul
;37
(7
):989
–1000
.
[PubMed]
0021-929050.
Gasser
TC
, Ogden
RW
, Holzapfel
GA
. Hyperelastic modelling of arterial layers with distributed collagen fibre orientations
. J R Soc Interface
. 2006
Feb
;3
(6
):15
–35
.
[PubMed]
1742-568951.
Lally
C
, Dolan
F
, Prendergast
PJ
. Cardiovascular stent design and vessel stresses: a finite element analysis
. J Biomech
. 2005
Aug
;38
(8
):1574
–81
.
[PubMed]
0021-929052.
Doost
SN
, Ghista
D
, Su
B
, Zhong
L
, Morsi
YS
. Heart blood flow simulation: a perspective review
. Biomed Eng Online
. 2016
Aug
;15
(1
):101
.
[PubMed]
1475-925X53.
Xiang
J
, Natarajan
SK
, Tremmel
M
, Ma
D
, Mocco
J
, Hopkins
LN
, et al Hemodynamic-morphologic discriminants for intracranial aneurysm rupture
. Stroke
. 2011
Jan
;42
(1
):144
–52
.
[PubMed]
0039-249954.
Ujiie
H
, Tachibana
H
, Hiramatsu
O
, Hazel
AL
, Matsumoto
T
, Ogasawara
Y
, et al Effects of size and shape (aspect ratio) on the hemodynamics of saccular aneurysms: a possible index for surgical treatment of intracranial aneurysms
. Neurosurgery
. 1999
Jul
;45
(1
):119
–29
.
[PubMed]
0148-396X55.
Biasetti
J
, Gasser
TC
, Auer
M
, Hedin
U
, Labruto
F
. Hemodynamics of the normal aorta compared to fusiform and saccular abdominal aortic aneurysms with emphasis on a potential thrombus formation mechanism
. Ann Biomed Eng
. 2010
Feb
;38
(2
):380
–90
.
[PubMed]
0090-696456.
Hoi
Y
, Woodward
SH
, Kim
M
, Taulbee
DB
, Meng
H
. Validation of CFD simulations of cerebral aneurysms with implication of geometric variations
. J Biomech Eng
. 2006
Dec
;128
(6
):844
–51
.
[PubMed]
0148-073157.
Lu
R
, Turco
RP
, Jacobson
MZ
. An integrated air pollution modeling system for urban and regional scales: 1. Structure and performance
. J Geophys Res D Atmospheres
. 1997
;102
D5
:6063
–79
. 0747-730958.
Rossitti
S
, Svendsen
P
. Shear stress in cerebral arteries supplying arteriovenous malformations
. Acta Neurochir (Wien)
. 1995
;137
(3-4
):138
–45
.
[PubMed]
0001-626859.
Cheng
C
, Helderman
F
, Tempel
D
, Segers
D
, Hierck
B
, Poelmann
R
, et al Large variations in absolute wall shear stress levels within one species and between species
. Atherosclerosis
. 2007
Dec
;195
(2
):225
–35
.
[PubMed]
0021-915060.
Yagi
T
, Sato
A
, Shinke
M
, Takahashi
S
, Tobe
Y
, Takao
H
, et al Experimental insights into flow impingement in cerebral aneurysm by stereoscopic particle image velocimetry: transition from a laminar regime
. J R Soc Interface
. 2013
Feb
;10
(82
):20121031
.
[PubMed]
1742-568961.
Malek
AM
, Alper
SL
, Izumo
S
. Hemodynamic shear stress and its role in atherosclerosis
. JAMA
. 1999
Dec
;282
(21
):2035
–42
.
[PubMed]
0098-748462.
Isaksen
JG
, Bazilevs
Y
, Kvamsdal
T
, Zhang
Y
, Kaspersen
JH
, Waterloo
K
, et al Determination of wall tension in cerebral artery aneurysms by numerical simulation
. Stroke
. 2008
Dec
;39
(12
):3172
–8
.
[PubMed]
0039-249963.
MacDonald
DJ
, Finlay
HM
, Canham
PB
. Directional wall strength in saccular brain aneurysms from polarized light microscopy
. Ann Biomed Eng
. 2000
May
;28
(5
):533
–42
.
[PubMed]
0090-6964
