Cerebrovascular accidents are the third most common cause of death in developed countries. Over recent years, CFD simulations using medical image-based anatomical vascular geometries have been shown to have great potential as a tool for diagnostic and treatment of brain aneurysms, in particular to help advise on the best treatment options. This work aims to present a state of the art review of the different models used in CFD, focusing in particular on modeling blood as a viscoelastic non-Newtonian fluid in order to help understand the role of the complex rheological nature of blood upon the dynamics of middle cerebral aneurysms. Moreover, since the mechanical properties of the vessel walls also play an important role in the cardiovascular system, different models for the arterial structure are reviewed in order to couple CFD and computational solid dynamics to allow the study of the fluidstructure interaction (FSI).

References

1.
Deaton
,
C.
,
Froelicher
,
E. S.
,
Wu
,
L. H.
,
Ho
,
C.
,
Shishani
,
K.
, and
Jaarsma
,
T.
,
2011
, “
The Global Burden of Cardiovascular Disease
,”
J. Cardiovasc. Nurs.
,
26
, pp.
S5
S14
.10.1097/JCN.0b013e318213efcf
2.
Zarins
,
C. K.
,
Giddens
,
D. P.
,
Bharadvaj
,
B. K.
,
Sottiurai
,
V. S.
,
Mabon
,
R. F.
, and
Glagov
,
S.
,
1983
, “
Carotid Bifurcation Atherosclerosis: Quantitative Correlation of Plaque Localization With Flow Velocity Profiles and Wall Shear Stress
,”
Circ. Res.
,
53
(
4
), pp.
502
514
.10.1161/01.RES.53.4.502
3.
Thubrikar
,
M. J.
,
Al-Soudi
,
J.
, and
Robicsek
,
F.
,
2001
, “
Wall Stress Studies of Abdominal Aortic Aneurysm in a Clinical Model
,”
Ann. Vasc. Surg.
,
15
(
3
), pp.
355
366
.10.1007/s100160010080
4.
Ujiie
,
H.
,
Tamano
,
Y.
,
Sasaki
,
K.
, and
Hori
,
T.
,
2001
, “
Is the Aspect Ratio a Reliable Index for Predicting the Rupture of a Saccular Aneurysm?
,”
Neurosurgery
,
48
(
3
), pp.
495
502
.10.1097/00006123-200103000-00007
5.
Szikora
,
I.
,
Páal
,
G.
, and
Ugron
,
A.
,
2008
, “
Impact of Aneurysmal Geometry on Intraaneurysmal Flow: A Computerized Flow Simulation Study
,”
Neuroradiology
,
50
(
5
), pp.
411
421
.10.1007/s00234-007-0350-x
6.
Imbesi
,
S. G.
, and
Kerber
,
C. W.
,
1999
, “
Analysis of Slipstream Flow in Two Tuptured Intracranial Cerebral Aneurysms
,”
Am. J. Neuroradiol.
,
20
(
9
), pp.
1703
1705
.
7.
Moyers-Gonzalez
,
M.
,
Owens
,
R. G.
, and
Fang
,
J.
,
2008
, “
A Non-Homogeneous Constitutive Model for Human Blood. Part III. Oscillatory Flow
,”
J. Non-Newtonian Fluid Mech.
,
155
(
3
), pp.
161
173
.10.1016/j.jnnfm.2008.04.001
8.
Eckmann
,
D. M.
,
Bowers
,
S.
,
Stecker
,
M.
, and
Cheung
,
A. T.
,
2000
, “
Hematocrit, Volume Expander, Temperature, and Shear Rate Effects on Blood Viscosity
,”
Anesth. Analg.
,
91
(
3
), pp.
539
545
.10.1213/00000539-200009000-00007
9.
Merrill
,
E. W.
,
1969
, “
Rheology of Blood
,”
Physiol. Rev.
,
49
, pp.
863
888
.
10.
Thurston
,
G. B.
,
1979
, “
Rheological Parameters for the Viscosity, Viscoelasticity and Thixotropy of Blood
,”
Biorheology
,
16
, pp.
149
162
.
11.
Dintenfass
,
L.
,
1963
, “
Blood Rheology in Cardio-Vascular Diseases
,”
Nature
,
199
, pp.
813
815
.10.1038/199813a0
12.
Langstroth
,
L.
,
1919
, “
Blood Viscosity. I Conditions Affecting the Viscosity of Blood After Withdrawal From the Body
,”
J. Exp. Med.
,
30
(
6
), pp.
597
606
.10.1084/jem.30.6.597
13.
Chien
,
S.
,
Usami
,
S.
,
Dellenback
,
R. J.
, and
Gregersen
,
M. I.
,
1967
, “
Blood Viscosity: Influence of Erythrocyte Deformation
,”
Science
,
157
(
3790
), pp.
827
829
.10.1126/science.157.3790.827
14.
Chien
,
S.
,
Usami
,
S.
,
Dellenback
,
R. J.
,
Gregersen
,
M. I.
,
Nanninga
,
L. B.
, and
Guest
,
M. M.
,
1967
, “
Blood Viscosity: Influence of Erythrocyte Aggregation
,”
Science
,
157
(
3790
), pp.
829
831
.10.1126/science.157.3790.829
15.
Morrison
,
F. A.
,
2001
,
Understanding Rheology
,
Oxford University, Inc.
, New York.
16.
Campo-Deaño
,
L.
,
Dullens
,
R. P. A.
,
Aarts
,
D. G. L. A.
,
Pinho
,
F. T.
, and
Oliveira
,
M. S. N.
,
2013
, “
Viscoelasticity of Blood and Viscoelastic Blood Analogues for Use in Polydymethylsiloxane in Vitro Models of the Circulatory System
,”
Biomicrofluidics
,
7
(
3
), p.
034102
.10.1063/1.4804649
17.
Poole
,
R. J.
,
2012
, “
The Deborah and Weissenberg Numbers
,”
British Soc. Rheol. Rheol. Bull.
,
53
, pp.
32
39
.
18.
Galindo-Rosales
,
F. J.
,
Campo-Deaño
,
L.
,
Sousa
,
P. C.
,
Ribeiro
,
V. M.
,
Oliveira
,
M. S. N.
,
Alves
,
M. A.
, and
Pinho
,
F. T.
,
2014
, “
Viscoelastic Instabilities in Micro-Scale Flows
,”
Experimental Thermal and Fluid Science
,
59
, pp.
128
129
.10.1016/j.expthermflusci.2014.03.004
19.
Gijsen
,
F. J. H.
,
van de Vosse
,
F. N.
, and
Janssen
,
J. D.
,
1999
, “
The Influence of the Non-Newtonian Properties of Blood on the Flow in Large Arteries: Steady Flow in a Carotid Bifurcation Model
,”
J. Biomech.
,
32
(
6
), pp.
601
608
.10.1016/S0021-9290(99)00015-9
20.
Owens
,
R. G.
,
2006
, “
A New Microstructure-Based Constitutive Model for Human Blood
,”
J. Non-Newtonian Fluid Mech.
,
140
(
1–3
), pp.
57
70
.10.1016/j.jnnfm.2006.01.015
21.
Moyers-Gonzalez
,
M.
,
Owens
,
R. G.
, and
Fang
,
J.
,
2008
, “
A Non-Homogeneous Constitutive Model for Human Blood. Part I. Model Derivation and Steady Flow
,”
J. Fluid Mech.
,
617
, pp.
327
354
.10.1017/S002211200800428X
22.
Moyers-Gonzalez
,
M.
, and
Owens
,
R. G.
,
2008
, “
A Non-Homogeneous Constitutive Model for Human Blood. Part II. Asymptotic Solution for Large Péclet Numbers
,”
J. Non-Newtonian Fluid Mech.
,
155
(
3
), pp.
146
160
.10.1016/j.jnnfm.2008.06.009
23.
Sforza
,
D. M.
,
Putman
,
C. M.
, and
Cebral
,
J. R.
,
2012
, “
Computational Fluid Dynamics in Brain Aneurysms
,”
Int. J. Numer. Methods Biomed. Eng.
,
28
(
6–7
), pp.
801
808
.10.1002/cnm.1481
24.
Markwalder
,
T. M.
,
Grolimund
,
P.
,
Seiler
,
R. W.
,
Roth
,
F.
, and
Aaslid
,
R.
,
1984
, “
Dependency of Blood Flow Velocity in the Middle Cerebral Artery on End-Tidal Carbon Dioxide Partial Pressure- A Transcranial Ultrasound Doppler Study
,”
J. Cereb. Blood Flow Metab.
,
4
(
3
), pp.
368
372
.10.1038/jcbfm.1984.54
25.
Vlachos
,
N. S.
, and
Whitelaw
,
J. H.
,
1974
, “
The Measurement of Blood Velocity With Laser Anemometry
,”
Proceedings
, Volume
1
, No. A76-10426 01-35, Purdue University, West Lafayette, IN, pp.
521
540
., In: International Workshop on Laser Velocimetry, 2nd, West Lafayette, Ind., March 27–29, 1974.
26.
Lasheras
,
J. C.
,
2007
, “
The Biomechanics of Arterial Aneurysms
,”
Annu. Rev. Fluid Mech.
,
39
(
1
), pp.
293
319
.10.1146/annurev.fluid.39.050905.110128
27.
Sforza
,
D. M.
,
Putman
,
C. M.
, and
Cebral
,
J. R.
,
2009
, “
Hemodynamics of Cerebral Aneurysms
,”
Annu. Rev. Fluid Mech.
,
41
, pp.
91
107
.10.1146/annurev.fluid.40.111406.102126
28.
Withers
,
K.
,
Carolan-Rees
,
G.
, and
Dale
,
M.
,
2013
, “
PipelineTM Embolization Device for the Treatment of Complex Intracranial Aneurysms. A NICE Medical Technology Guidance
,”
Appl. Health Econ. Health Policy
,
11
, pp.
5
13
.10.1007/s40258-012-0005-x
29.
Foutrakis
,
G. N.
,
Yonas
,
H.
, and
Sclabassi
,
R. J.
,
1999
, “
Saccular Aneurysm Formation in Curved and Bifurcating Arteries
,”
Am. J. Neuroradiol.
,
20
(
7
), pp.
1309
1317
.
30.
Massoud
,
T. F.
,
Turjman
,
F.
,
Ji
,
C.
,
Viũela
,
F.
,
Guglielmi
,
G.
,
Gobin
,
Y. P.
, and
Duckwiler
,
G. R.
,
1995
, “
Endovascular Treatment of Fusiform Aneurysms With Stents and Coils: Technical Feasibility in a Swine Model
,”
Am. J. Neuroradiol.
,
16
(
10
), pp.
1953
1963
.
31.
Raghavan
,
M. L.
,
Ma
,
B.
, and
Harbaugh
,
R. E.
,
2005
, “
Quantified Aneurysm Shape and Rupture Risk
,”
J. Neurosurg.
,
102
(
2
), pp.
355
362
.10.3171/jns.2005.102.2.0355
32.
Parlea
,
L.
,
Fahrig
,
R.
,
Holdsworth
,
D. W.
, and
Lownie
,
S. P.
,
1999
, “
An Analysis of the Geometry of Saccular Intracranial Aneurysms
,”
Am. J. Neuroradiol.
,
20
(
6
), pp.
1079
1089
.
33.
Ma
,
B.
,
Harbaugh
,
R. B.
, and
Raghavan
,
M. L.
,
2004
, “
Three-Dimensional Geometrical Characterization of Cerebral Aneurysms
,”
Ann. Biomed. Eng.
,
32
(
2
), pp.
264
273
.10.1023/B:ABME.0000012746.31343.92
34.
Lauric
,
A.
,
Miller
,
E. L.
,
Baharoglu
,
M. I.
, and
Malek
,
A. M.
,
2011
, “
3D Shape Analysis of Intracranial Aneurysms Using the Writhe Number as a Discriminant for Rupture
,”
Ann. Biomed. Eng.
,
39
(
5
), pp.
1457
1469
.10.1007/s10439-010-0241-x
35.
Hoh
,
B. L.
,
Sistrom
,
C. L.
,
Firment
,
C. S.
,
Fautheree
,
G. L.
,
Velat
,
G. J.
,
Whiting
,
J. H.
,
Reavey-Cantwell
,
J. F.
, and
Lewis
,
S. B.
,
2007
, “
Bottleneck Factor and Height-Width Ratio: Association With Ruptured Aneurysms in Patients With Multiple Cerebral Aneurysms
,”
Neurosurgery
,
61
(
4
), pp.
716
723
.10.1227/01.NEU.0000298899.77097.BF
36.
Ujiie
,
H.
,
Tachibana
,
H.
,
Hiramatsu
,
O.
,
Hazel
,
A. L.
,
Matsumoto
,
T.
,
Ogasawara
,
Y.
,
Nakajima
,
H.
,
Hori
,
T.
,
Takakura
,
K.
, and
Kajiya
,
F.
,
1999
, “
Effects of Size and Shape (Aspect Ratio) on the Hemodynamics of Saccular Aneurysms: A Possible Index for Surgical Treatment of Intracranial Aneurysms
,”
Neurosurgery
,
45
(
1
), pp.
119
130
.10.1097/00006123-199907000-00028
37.
Fuller
,
F. B.
,
1971
, “
The Writhing Number of a Space Curve
,”
Proc. Natl. Acad. Sci. U.S.A.
,
68
(
4
), pp.
815
819
.10.1073/pnas.68.4.815
38.
Tremmel
,
M.
,
Dhar
,
S.
,
Levy
,
E.
,
Mocco
,
J.
, and
Meng
,
H.
,
2009
, “
Influence of Intracranial Aneurysms-to-Parent Vessel Size Ratio on Hemodynamics and Implication for Rupture: Results From a Virtual Experimental Study
,”
Neurosurgery
,
64
(
4
), pp.
622
631
.10.1227/01.NEU.0000341529.11231.69
39.
Ku
,
D. N.
,
Giddens
,
D. P.
,
Zarins
,
C. K.
, and
Glagov
,
S.
,
1985
, “
Pulsatile Flow and Atherosclerosis in the Human Carotid Bifurcation. Positive Correlation Between Plaque Location and Low and Oscillating Shear Stress
,”
Arterioscler., Thromb., Vasc. Biol.
,
5
(
3
), pp.
293
302
.10.1161/01.ATV.5.3.293
40.
Mantha
,
A.
,
Karmonik
,
C.
,
Benndorf
,
G.
,
Strother
,
C.
, and
Metcalfe
,
R.
,
2006
, “
Hemodynamics in a Cerebral Artery Before and After the Formation of an Aneurysm
,”
Am. J. Neuroradiol.
,
27
(
5
), pp.
1113
1118
.
41.
Shimogonya
,
Y.
,
Ishikawa
,
T.
,
Imai
,
Y.
,
Matsuki
,
N.
, and
Yamaguchi
,
T.
,
2009
, “
Can Temporal Fluctuation in Spatial Wall Shear Stress Gradient Initiate a Cerebral Aneurysm? A Proposed Novel Hemodynamic Index, the Gradient Oscillatory Number (GON)
,”
J. Biomech.
,
42
(
4
), pp.
550
554
.10.1016/j.jbiomech.2008.10.006
42.
Jou
,
L.-D.
, and
Mawad
,
M. E.
,
2011
, “
Timing and Size of Flow Impingement in a Giant Intracranial Aneurysm at the Internal Carotid Artery
,”
Med. Biol. Eng. Comput.
,
49
(
8
), pp.
891
899
.10.1007/s11517-010-0727-6
43.
Zuleger
,
D. I.
,
Poulikakos
,
D.
,
Valavanis
,
A.
, and
Kollias
,
S. S.
,
2010
, “
Combining Magnetic Resonance Measurements With Numerical Simulations – Extracting Blood Flow Physiology Information Relevant to the Investigation of Intracranial Aneurysms in the Circle of Willis
,”
Int. J. Heat Fluid Flow
,
31
(
6
), pp.
1032
1039
.10.1016/j.ijheatfluidflow.2010.07.003
44.
Kojima
,
M.
,
Irie
,
K.
,
Keda
,
S.
,
Fukuda
,
T.
,
Arai
,
F.
,
Hirose
,
Y.
, and
Negoro
,
M.
,
2012
, “
The Hemodynamic Study for Growth Factor Evaluation of Rupture Cerebral Aneurysm Followed up for Five Years
,”
J. Biomed. Sci. Eng.
,
5
(
12A
), pp.
884
891
.10.4236/jbise.2012.512A112
45.
Irie
,
K.
,
Anzai
,
H.
,
Kojima
,
M.
,
Honjo
,
N.
,
Ohta
,
M.
,
Hirose
,
Y.
, and
Negoro
,
M.
,
2012
, “
Computational Fluid Dynamic Analysis Following Recurrence of Cerebral Aneurysm After Coil Embolization
,”
Asian J. Neurosurg.
,
7
(
3
), pp.
109
115
.10.4103/1793-5482.103706
46.
Sforza
,
D. M.
,
Putman
,
C. M.
,
Tateshima
,
S.
,
Viñuela
,
F.
, and
Cebral
,
J. R.
,
2012
, “
Effects of Perianeurysmal Environment During the Growth of Cerebral Aneurysms: A Case Study
,”
Am. J. Neuroradiol.
,
33
(
6
), pp.
1115
1120
.10.3174/ajnr.A2908
47.
Tanoue
,
T.
,
Tateshima
,
S.
,
Villablanca
,
J. P.
,
Viñuela
,
F.
, and
Tanishita
,
K.
,
2011
, “
Wall Shear Stress Distribution Inside Growing Cerebral Aneurysm
,”
Am. J. Neuroradiol.
,
32
(
9
), pp.
1732
1737
.10.3174/ajnr.A2607
48.
Boussel
,
L.
,
Rayz
,
V.
,
McCulloch
,
C.
,
Martin
,
A.
,
Acevedo-Bolton
,
G.
,
Lawton
,
M.
,
Higashida
,
R.
,
Smith
,
W. S.
,
Young
,
W. L.
, and
Saloner
,
D.
,
2008
, “
Aneurysm Growth Occurs at Region of Low Wall Shear Stress: Patient-Specific Correlation of Hemodynamics and Growth in a Longitudinal Study
,”
Stroke
,
39
(
11
), pp.
2997
3002
.10.1161/STROKEAHA.108.521617
49.
Jou
,
L.-D.
,
Wong
,
G.
,
Dispensa
,
B.
,
Lawton
,
M. T.
,
Higashida
,
R. T.
,
Young
,
W. L.
, and
Saloner
,
D.
,
2005
, “
Correlation Between Lumenal Geometry Changes and Hemodynamics in Fusiform Intracranial Aneurysms
,”
Am. J. Neuroradiol.
,
26
(
9
), pp.
2357
2363
.
50.
Rayz
,
V. L.
,
Boussel
,
L.
,
Ge
,
L.
,
Leach
,
J. R.
,
Martin
,
A. J.
,
Lawton
,
M. T.
,
McCulloch
,
C.
, and
Saloner
,
D.
,
2010
, “
Flow Residence Time and Regions of Intraluminal Thrombus Deposition in Intracranial Aneurysms
,”
Ann. Biomed. Eng.
,
38
(
10
), pp.
3058
3069
.10.1007/s10439-010-0065-8
51.
Valant
,
A. Z.
,
Ziberna
,
L.
,
Papaharilaou
,
Y.
,
Anayiotos
,
A.
, and
Georgiou
,
G. C.
,
2011
, “
The Influence of Temperature on Rheological Properties of Blood Mixtures With Different Volume Expanders—Implications in Numerical Arterial Hemodynamics Simulations
,”
Rheol. Acta
,
50
(
4
), pp.
389
402
.10.1007/s00397-010-0518-x
52.
Caro
,
C. G.
,
Pedley
,
T. J.
,
Schroter
,
R. C.
, and
Seed
,
W. A.
,
2012
,
The Mechanics of the Circulation
,
Cambridge University
,
New York
.10.1017/CBO9781139013406
53.
Vlastos
,
G.
,
Lerche
,
D.
,
Koch
,
B.
,
Samba
,
O.
, and
Pohl
,
M.
,
1997
, “
The Effect of Parallel Combined Steady and Oscillatory Shear Flows on Blood and Polymer Solutions
,”
Rheol. Acta
,
36
(
2
), pp.
160
172
.10.1007/BF00366822
54.
Sousa
,
P. C.
,
Carneiro
,
J.
,
Vaz
,
R.
,
Cerejo
,
A.
,
Pinho
,
F. T.
,
Alves
,
M. A.
, and
Oliveira
,
M. S. N.
,
2013
, “
Shear Viscosity and Nonlinear Behavior of Whole Blood Under Large Amplitude Oscillatory Shear
,”
Biorheology
,
50
(
5–6
), pp.
269
282
.
55.
Boyd
,
J.
,
Buick
,
J. M.
, and
Green
,
S.
,
2007
, “
Analysis of the Casson and Carreau-Yasuda Non-Newtonian Blood Models in Steady and Oscillatory Flows Using the Lattice Boltzmann Method
,”
Phys. Fluids
,
19
(
9
), p.
093103
.10.1063/1.2772250
56.
Razavi
,
A.
,
Shirani
,
E.
, and
Sadeghi
,
M. R.
,
2011
, “
Numerical Simulation of Blood Pulsatile Flow in a Stenosed Carotid Artery Using Different Rheological Models
,”
J. Biomech.
,
44
(
11
), pp.
2021
2030
.10.1016/j.jbiomech.2011.04.023
57.
Molla
,
M. M.
, and
Paul
,
M. C.
,
2012
, “
LES of Non-Newtonian Physiological Blood Flow in a Model of Arterial Stenosis
,”
Med. Eng. Phys.
,
34
(
8
), pp.
1079
1087
.10.1016/j.medengphy.2011.11.013
58.
Valencia
,
A.
,
Morales
,
H.
,
Rivera
,
R.
,
Bravo
,
E.
, and
Galvez
,
M.
,
2008
, “
Blood Flow Dynamics in Patient-Specific Cerebral Aneurysm Models: The Relationship Between Wall Shear Stress and Aneurysm Area Index
,”
Med. Eng. Phys.
,
30
(
3
), pp.
329
340
.10.1016/j.medengphy.2007.04.011
59.
Amornsamankul
,
S.
,
Wiwatanapataphee
,
B.
,
Wu
,
Y. H.
, and
Lenbury
,
Y.
,
2005
, “
Effect of Non-Newtonian Behavior of Blood on Pulsatile Flows in Stenotic Arteries
,”
Int. J. Biol. Life Sci.
,
1
, pp.
42
46
.
60.
Anand
,
M.
, and
Rajagopal
,
K. R.
,
2004
, “
A Shear-Thinning Viscoelastic Fluid Model for Describing the Flow of Blood
,”
Int. J. Cardiovasc. Med. Sci.
,
4
, pp.
59
68
.
61.
Robertson
,
A. M.
,
Sequeira
,
A.
, and
Owens
,
R. G.
,
2009
, “
Rheological Models for Blood
,”
Cardiovascular Mathematics: Modeling and Simulation of the Circulatory System
,
L.
Formaggia
,
A.
Quarteroni
,
A.
Veneziani
, eds.,
Springer-Verlag
,
Milano, Italy
.10.1007/978-88-470-1152-6_6
62.
Bodnár
,
T.
,
Sequeira
,
A.
, and
Pirkl
,
L.
,
2009
, “
Numerical Simulations of Blood Flow in a Stenosed Vessel Under Different Flow Rates Using a Generalized Oldroyd-B Model
,”
International Conference on Numerical Analysis and Applied Mathematics
, Rethymno, Crete, Sept. 18–22, Vol.
2
, pp.
645
648
. 10.1063/1.3241546
63.
Yilmaz
,
F.
, and
Gundogdu
,
M. Y.
,
2008
, “
A Critical Review on Blood Flow in Large Arteries; Relevance to Blood Rheology, Viscosity Models, and Physiologic Conditions
,”
Korea-Australia Rheol. J.
,
20
, pp.
197
211
.
64.
Stuart
,
J.
, and
Kenny
,
M. W.
,
1980
, “
Blood Rheology
,”
J. Clin. Pathol.
,
33
(
5
), pp.
417
429
.10.1136/jcp.33.5.417
65.
Antonova
,
N.
,
2012
, “
On Some Mathematical Models in Hemorheology
,”
Biotechnol. Biotechnol. Equip.
,
26
(
5
), pp.
3286
3291
.10.5504/BBEQ.2012.0069
66.
Giesekus
,
H.
,
1982
, “
A Simple Constitutive Equation for Polymer Fluids Based on the Concept of Deformation-Dependent Tensorial Mobility
,”
J. Non-Newtonain Fluid Mech.
,
11
(
1–2
), pp.
69
109
.10.1016/0377-0257(82)85016-7
67.
Phan-Thien
,
N.
, and
Tanner
,
R. I.
,
1977
, “
A New Constitutive Equation Derived From Network Theory
,”
J. Non-Newtonain Fluid Mech.
,
2
(
4
), pp.
353
365
.10.1016/0377-0257(77)80021-9
68.
Bureau
,
M.
,
Healy
,
J. C.
,
Bourgoin
,
D.
, and
Joly
,
M.
,
1980
, “
Rheological Hysteresis of Blood at Low Shear Rate
,”
Biorheology
,
17
(
1–2
), pp.
191
203
.
69.
Oldroyd
,
J. G.
,
1950
, “
On the Formulation of Rheological Equation of State
,”
Proc. R. Soc. London, Ser. A.
,
200
(
1063
), pp.
523
541
.10.1098/rspa.1950.0035
70.
Javadzadegan
,
J.
,
Esmaeili
,
M.
,
Majidi
,
S.
, and
Fakhimghanbarzadeh
,
B.
,
2009
, “
Pulsatile Flow of Viscous and Viscoelastic Fluids in Constricted Tubes
,”
J. Mech. Sci. Technol.
,
23
(
9
), pp.
2456
2467
.10.1007/s12206-009-0713-9
71.
Yeleswarapu
,
K. K.
,
Kameneva
,
M. V.
,
Rajagopal
,
K. R.
, and
Antaki
,
J. F.
,
1998
, “
The Flow of Blood in Tubes: Theory and Experiment
,”
Mech. Res. Commun.
,
25
(
3
), pp.
257
262
.10.1016/S0093-6413(98)00036-6
72.
Ku
,
D. N.
,
1997
, “
Blood Flow in Arteries
,”
Annu. Rev. Fluid Mech.
,
29
(
1
), pp.
399
434
.10.1146/annurev.fluid.29.1.399
73.
Elad
,
D.
, and
Einav
,
S.
,
2004
, “
Physical and Flow Properties of Blood. Source
,”
Standard Handbook of Biomedical Engineering and Design
, pp.
1
25
.
74.
Xiao
,
N.
,
Humphrey
,
J. D.
, and
Figueroa
,
C. A.
,
2013
, “
Multi-Scale Computational Model of Three-Dimensional Hemodynamics Within a Deformable Full-Body Arterial Network
,”
J. Comput. Phys.
,
244
, pp.
22
40
.10.1016/j.jcp.2012.09.016
75.
Smith
,
N. P.
,
Pullan
,
A. J.
, and
Hunter
,
P. J.
,
2002
, “
An Anatomically Based Model of Transient Coronary Blood Flow in the Heart
,”
SIAM J. Appl. Math.
,
62
(
3
), pp.
990
1018
.10.1137/S0036139999355199
76.
Womersley
,
J. R.
,
1955
, “
Method for the Calculation of Velocity, Rate of Flow and Viscous Drag in Arteries When the Pressure Gradient is Known
,”
J. Physiol.
,
127
(
2
), pp.
553
563
.
77.
Fung
,
Y.
,
1996
,
Biomechanics Circulation
,
Springer
,
Berlin, Germany
.
78.
Banerjee
,
M. K.
,
Ganguly
,
R.
, and
Datta
,
A.
,
2012
, “
Effect of Pulsatile Flow Waveform and Womersley Number on the Flow in Stenosed Arterial Geometry
,”
ISRN Biomath.
,
2012
, p.
853056
.10.5402/2012/853056
79.
Campbell
,
I. C.
,
Ries
,
J.
,
Dhawan
,
S. S.
,
Quyyumi
,
A. A.
,
Taylor
,
W. R.
, and
Oshinski
,
J. N.
,
2012
, “
Effect of Inlet Velocity Profiles on Patient-Specific Computational Fluid Dynamics Simulations of the Carotid Bifurcation
,”
ASME J. Biomech. Eng.
,
134
(
5
), p.
051001
.10.1115/1.4006681
80.
Grinberg
,
L.
, and
Karniadakis
,
G.
,
2008
, “
Outflow Boundary Conditions for Arterial Networks With Multiple Outlets
,”
Ann. Biomed. Eng.
,
36
(
9
), pp.
1496
1514
.10.1007/s10439-008-9527-7
81.
Ramalho
,
S.
,
Moura
,
A.
,
Gambaruto
,
A. M.
, and
Sequeira
,
A.
,
2012
, “
Sensitivity to Outflow Boundary Conditions and Level of Geometry Description for a Cerebral Aneurysm
,”
Int. J. Numer. Methods Biomed. Eng.
,
28
(
6–7
), pp.
697
713
.10.1002/cnm.2461
82.
Papanastasiou
,
T. C.
,
Malamataris
,
N.
, and
Ellwood
,
K.
,
1992
, “
A New Outflow Boundary Condition
,”
Int. J. Numer. Methods Fluids
,
14
(
5
), pp.
587
608
.10.1002/fld.1650140506
83.
Malamataris
,
N. T.
, and
Papanastasiou
,
T. C.
,
1991
, “
Unsteady Free Surface Flows on Truncated Domains
,”
Ind. Eng. Chem. Res.
,
30
(
9
), pp.
2211
2219
.10.1021/ie00057a025
84.
Griffiths
,
D. F.
,
1997
, “
The ‘No Boundary Condition’ Outflow Boundary Condition
,”
Int. J. Numer. Methods Fluids
,
24
(
4
), pp.
393
411
.10.1002/(SICI)1097-0363(19970228)24:4<393::AID-FLD505>3.0.CO;2-O
85.
Renardy
,
M.
,
1997
, “
Imposing No Boundary Condition at Outflow: Why Does It Work?
,”
Int. J. Numer. Methods Fluids
,
24
(
4
), pp.
413
417
.10.1002/(SICI)1097-0363(19970228)24:4<413::AID-FLD507>3.0.CO;2-N
86.
Park
,
S. J.
, and
Lee
,
S. J.
,
1999
, “
On the Use of the Open Boundary Condition Method in the Numerical Simulation of Nonisothermal Viscoelastic Flow
,”
J. Non-Newtonian Fluid Mech.
,
87
(
2–3
), pp.
197
214
.10.1016/S0377-0257(99)00064-6
87.
Moon
,
J. Y.
,
Suh
,
D. C.
,
Lee
,
Y. S.
,
Kim
,
Y. W.
, and
Lee
,
J. S.
,
2014
, “
Considerations of Blood Properties, Outlet Boundary Conditions and Energy Loss Approaches in Computational Fluid Dynamics Modeling
,”
Neurointervention
,
9
(
1
), pp.
1
8
.10.5469/neuroint.2014.9.1.1
88.
Vignon-Clementel
,
I. E.
,
Figueroa
,
C. A.
,
Jansen
,
K. E.
, and
Taylor
,
C. A.
,
2006
, “
Outflow Boundary Conditions for Three-Dimensional Finite Element Modeling of Blood Flow and Pressure in Arteries
,”
Comput. Methods Appl. Mech. Eng.
,
195
(
29–32
), pp.
3776
3796
.10.1016/j.cma.2005.04.014
89.
Vignon
,
I. E.
, and
Taylor
,
C. A.
,
2004
, “
Outflow Boundary Conditions for One-Dimensional Finite Element Modeling of Blood Flow and Pressure Waves in Arteries
,”
Wave Motion
,
39
(
4
), pp.
361
374
.10.1016/j.wavemoti.2003.12.009
90.
Figueroa
,
C. A.
,
Vignon-Clementel
,
I. E.
,
Jansen
,
K. E.
,
Hughes
,
T. J. R.
, and
Taylor
,
C. A.
,
2006
, “
A Coupled Momentum Method for Modeling Blood Flow in Three-Dimensional Deformable Arteries
,”
Comput. Methods Appl. Mech. Eng.
,
195
(
41–43
), pp.
5685
5706
.10.1016/j.cma.2005.11.011
91.
Westerhof
,
N.
,
Bosman
,
F.
,
DeVries
,
C. J.
, and
Noordergraaf
,
A.
,
1969
, “
Analogue Studies of the Human Systemic Arterial Tree
,”
J. Biomech.
,
2
(
2
), pp.
121
143
.10.1016/0021-9290(69)90024-4
92.
Olufsen
,
M. S.
, and
Nadim
,
A.
,
2004
, “
On Deriving Lumped Models for Blood Flow and Pressure in the Systemic Arteries
,”
Math. Biosci. Eng.
,
1
(
1
), pp.
61
80
.10.3934/mbe.2004.1.61
93.
Vignon-Clementel
,
I. E.
,
Figueroa
,
C. A.
,
Jansen
,
K. E.
, and
Taylor
,
C. A.
,
2010
, “
Outflow Boundary Conditions for 3D Simulations of Non-Periodic Blood Flow and Pressure Fields in Deformable Arteries
,”
Comput. Methods Biomech. Biomed. Eng.
,
13
(
5
), pp.
625
640
.10.1080/10255840903413565
94.
Esmaily-Moghadam
,
M.
,
Vignon-Clementel
,
I. E.
,
Figliola
,
R.
, and
Marsden
,
A. L.
, f. t. M. O. C. H. A. M. I.,
2013
, “
A Modular Numerical Method for Implicit 0D/3D Coupling in Cardiovascular Finite Element Simulations
,”
J. Comput. Phys.
,
244
, pp.
63
79
.10.1016/j.jcp.2012.07.035
95.
O'Rourke
,
M. F.
,
Staessen
,
J. A.
,
Vlachopoulos
,
C.
,
Duprez
,
D.
, and
Plante
,
G. E.
,
2002
, “
Clinical Applications of Arterial Stiffness; Definitions and Reference Values
,”
Am. J. Hypertens.
,
15
(
5
), pp.
426
444
.10.1016/S0895-7061(01)02319-6
96.
Couade
,
M.
,
Pernot
,
M.
,
Prada
,
C.
,
Messas
,
E.
,
Emmerich
,
J.
,
Bruneval
,
P.
,
Criton
,
A.
,
Fink
,
M.
, and
Tanter
,
M.
,
2010
, “
Quantitative Assessment of Arterial Wall Biomechanical Properties Using Shear Wave Imaging
,”
Ultrasound Med. Biol.
,
36
(
10
), pp.
1662
1676
.10.1016/j.ultrasmedbio.2010.07.004
97.
Deng
,
S. X.
,
Tomioka
,
J.
,
Debes
,
J. C.
, and
Fung
,
Y. C.
,
1994
, “
New Experiments on Shear Modulus of Elasticity of Arteries
,”
Am. J. Physiol. Heart Circ. Physiol.
,
266
(
1 Pt 2
), pp.
H1
H10
.
98.
Balzani
,
D.
,
Brinkhues
,
S.
, and
Holzapfel
,
G. A.
,
2012
, “
Constitutive Framework for the Modeling of Damage in Collagenous Soft Tissues With Application to Arterial Walls
,”
Comput. Methods Appl. Mech. Eng.
,
213–216
, pp.
139
151
.10.1016/j.cma.2011.11.015
99.
Tezduyar
,
T. E.
, and
Sathe
,
S.
,
2007
, “
Modeling of Fluid-Structure Interactions With Space-Time Finite Elements: Solution Techniques
,”
Int. J. Numer. Methods Fluids
,
54
(
6–8
), pp.
855
900
.10.1002/fld.1430
100.
Tezduyar
,
T. E.
,
Sathe
,
S.
,
Schwaab
,
M.
, and
Conklin
,
B. S.
,
2008
, “
Arterial Fluid Mechanics Modeling With the Stabilized Space-Time Fluid-Structure Interaction Technique
,”
Int. J. Numer. Methods Fluids
,
57
(
5
), pp.
601
629
.10.1002/fld.1633
101.
Fung
,
Y.
,
1993
,
Biomechanics: Mechanical Properties of Living Tissues
, 2nd ed.,
Springer
,
Berlin
.
102.
Mooney
,
M.
,
1940
, “
A Theory of Large Elastic Deformation
,”
J. Appl. Phys.
,
11
(
9
), pp.
582
592
.10.1063/1.1712836
103.
Rivlin
,
R. S.
,
1948
, “
Large Elastic Deformations of Isotropic Materials. IV. Further Developments of the General Theory
,”
Philos. Trans. R. Soc. London, Ser. A
,
241
(
835
), pp.
379
397
.10.1098/rsta.1948.0024
104.
Torii
,
R.
,
Oshima
,
M.
,
Kobayashi
,
T.
,
Takagi
,
K.
, and
Tezduyar
,
T. E.
,
2008
, “
Fluid-Structure Interaction Modeling of a Patient-Specific Cerebral Aneurysm: Influence of Structural Modeling
,”
Comput. Mech.
,
43
(
1
), pp.
151
159
.10.1007/s00466-008-0325-8
105.
Hou
,
G.
,
Wang
,
J.
, and
Layton
,
A.
,
2012
, “
Numerical Methods for Fluid-Structure Interaction—A Review
,”
Commun. Comput. Phys.
,
12
(
2
), pp.
337
377
.10.4208/cicp.291210.290411s
106.
Valencia
,
A.
,
Burdiles
,
P.
,
Ignat
,
M.
,
Mura
,
J.
,
Bravo
,
E.
,
Rivera
,
R.
, and
Sordo
,
J.
,
2013
, “
Fluid Structural Analysis of Human Cerebral Aneurysm Using Their Own Wall Mechanical Properties
,”
Comput. Math. Method Med.
,
2013
(
5
), p.
293128
.10.1155/2013/293128
107.
Lee
,
C. J.
,
Zhang
,
Y.
,
Takao
,
H.
,
Murayama
,
Y.
, and
Qian
,
Y.
,
2013
, “
A Fluid-Structure Interaction Study Using Patient-Specific Ruptured and Unruptured Aneurysm: The Effect of Aneurysm Morphology, Hypertension and Elasticity
,”
J. Biomech.
,
46
(
14
), pp.
2402
2410
.10.1016/j.jbiomech.2013.07.016
108.
Valencia
,
A.
, and
Solis
,
F.
,
2006
, “
Blood Flow Dynamics and Arterial Wall Interaction in a Saccular Aneurysm Model of the Basilar Artery
,”
Comput. Struct.
,
84
(
21
), pp.
1326
1337
.10.1016/j.compstruc.2006.03.008
109.
Degroote
,
J.
,
Bathe
,
K.-J.
, and
Vierendeels
,
J.
,
2009
, “
Performance of a New Partitioned Procedure Versus a Monolithic Procedure in Fluid-Structure Interaction
,”
Comput. Struct.
,
87
(
11–12
), pp.
793
801
.10.1016/j.compstruc.2008.11.013
110.
Young
,
Y. L.
,
Chae
,
E. J.
, and
Akcabay
,
D. T.
,
2012
, “
Hybrid Algorithm for Modeling of Fluid-Structure Interaction in Incompressible, Viscous Flows
,”
Acta Mech. Sin.
,
28
(
4
), pp.
1030
1041
.10.1007/s10409-012-0118-3
111.
Peskin
,
C. S.
,
2002
, “
The Immersed Boundary Method
,”
Acta Numer.
,
11
, pp.
479
517
.10.1017/S0962492902000077
112.
Jendoubi
,
A.
,
Yakoubi
,
D.
,
Fortin
,
A.
, and
Tibirna
,
C.
,
2014
, “
An Immersed Boundary Method for Fluid Flows Around Rigid Objects
,”
Int. J. Numer. Methods Fluids
,
75
(
1
), pp.
63
80
.10.1002/fld.3884
113.
Mittal
,
R.
, and
Iaccarino
,
G.
,
2005
, “
Immersed Boundary Methods
,”
Annu. Rev. Fluid Mech.
,
37
(
1
), pp.
239
261
.10.1146/annurev.fluid.37.061903.175743
114.
Tezduyar
,
T. E.
,
Sathe
,
S.
,
Cragin
,
T.
,
Nanna
,
B.
,
Conklin
,
B. S.
,
Pausewang
,
J.
, and
Schwaab
,
M.
,
2007
, “
Modeling of Fluid-Structure Interactions With Space-Time Finite Elements: Arterial Fluid Mechanics
,”
Int. J. Numer. Methpds Fluids
,
54
(
6–8
), pp.
901
922
.10.1002/fld.1443
115.
Takizawa
,
K.
,
Moorman
,
C.
,
Wright
,
S.
,
Purdue
,
J.
,
Mcphail
,
T.
,
Chen
,
P. R.
,
Warren
,
J.
, and
Tezduyar
,
T. E.
,
2011
, “
Patient-Specific Arterial Fluid-Structure Interaction Modeling of Cerebral Aneurysms
,”
Int. J. Numer. Methods Fluids
,
65
(
1–3
), pp.
308
323
.10.1002/fld.2360
116.
Tezduyar
,
T. E.
, T. K.,
Brummer
,
T.
, and
Chen
,
P. R.
,
2011
, “
Space-Time Fluid-Structure Interaction Modeling of Patient-Specific Cerebral Aneurysms
,”
Int. J. Numer. Methods Biomed. Eng.
,
27
(
11
), pp.
1665
1710
.10.1002/cnm.1433
117.
Mittal
,
S.
, and
Tezduyar
,
T. E.
,
1995
, “
Parallel Finite Element Simulation of 3D Incompressible Flows-Fluid-Structure Interactions
,”
Int. J. Numer. Methods Fluids
,
21
(
10
), pp.
933
953
.10.1002/fld.1650211011
118.
Neal
,
M. L.
, and
Kerckhoffs
,
R.
,
2010
, “
Current Progress in Patient-Specific Modeling
,”
Briefings Bioinf.
,
11
(
1
), pp.
111
126
.10.1093/bib/bbp049
119.
Cebral
,
J. R.
,
Castro
,
M. A.
,
Burgess
,
J. E.
,
Pergolizzi
,
R. S.
,
Sheridan
,
M. J.
, and
Putman
,
C. M.
,
2005
, “
Characterization of Cerebral Aneurysms for Assessing Risk of Rupture by Using Patient-Specific Computational Hemodynamics Models
,”
Am. J. Neuroradiol.
,
26
(
10
), pp.
2550
2559
.
120.
Karmonik
,
C.
,
Klucznik
,
R.
, and
Benndorf
,
G.
,
2008
, “
Comparison of Velocity Patterns in an AComA Aneurysm Measured With 2D Phase Contrast MRI and Simulated With CFD
,”
Technol. Health Care
,
16
(
2
), pp.
119
128
.
121.
Ford
,
M. D.
,
Nikolov
,
H. N.
,
Milner
,
J. S.
,
Lownie
,
S. P.
,
DeMont
,
E. M.
,
Kalata
,
W.
,
Loth
,
F.
,
Holdsworth
,
D. W.
, and
Steinman
,
D. A.
,
2008
, “
PIV-Measured Versus CFD-Predicted Flow Dynamics in Anatomically Realistic Cerebral Aneurysm Models
,”
ASME J. Biomech. Eng.
,
130
(
2
), p.
021015
.10.1115/1.2900724
122.
Potočnik
,
B.
,
Heric
,
D.
,
Zazula
,
D.
,
Cigale
,
B.
, and
Bernad
,
D.
,
2005
, “
Construction of Patient Specific Virtual Models of Medical Phenomena
,”
Informatica
,
29
, pp.
209
218
.
123.
Augsburger
,
L.
,
Reymond
,
P.
,
Fonck
,
E.
,
Kulcsar
,
Z.
,
Farhat
,
M.
,
Ohta
,
M.
,
Stergiopulos
,
N.
, and
Rüfenacht
,
D. A.
,
2009
, “
Methodologies to Assess Blood Flow in Cerebral Aneurysms: Current State of Research and Perspectives
,”
J. Neuroradiol.
,
36
(
5
), pp.
270
277
.10.1016/j.neurad.2009.03.001
124.
Hollnagel
,
D. I.
,
Summers
,
P. E.
,
Poulikakos
,
D.
, and
Kollias
,
S. S.
,
2009
, “
Comparative Velocity Investigations in Cerebral Arteries and Aneurysms: 3D Phase-Contrast MR Angiography, Laser Doppler Velocimetry and Computational Fluid Dynamics
,”
NMR Biomed.
,
22
(
8
), pp.
795
808
.10.1002/nbm.1389
125.
Jeong
,
W.
, and
Rhee
,
K.
,
2012
, “
Hemodynamics of Cerebral Aneurysms: Computational Analyses of Aneurysm Progress and Treatment
,”
Comput. Math. Methods Med.
,
2012
(
4
), pp.
1
11
.10.1155/2012/782801
126.
Castro
,
M. A.
,
Putman
,
C. M.
, and
Cebral
,
J. R.
,
2006
, “
Patient-Specific Computational Modeling of Cerebral Aneurysms With Multiple Avenues of Flow From 3D Rotational Angiography Images
,”
Acad. Radiol.
,
13
(
7
), pp.
811
821
.10.1016/j.acra.2006.03.011
127.
Castro
,
M. A.
,
Putman
,
C. M.
, and
Cebral
,
J. R.
,
2006
, “
Computational Fluid Dynamics Modeling of Intracranial Aneurysms: Effects of Parent Artery Segmentation on Intra-Aneurysmal Hemodynamics
,”
Am. J. Neuroradiol.
,
27
(
8
), pp.
1703
1709
.
128.
Marzo
,
A.
,
Singh
,
P.
,
Reymond
,
P.
,
Stergiopulos
,
N.
,
Patel
,
U.
, and
Hose
,
R.
,
2009
, “
Influence of Inlet Boundary Conditions on the Local Haemodynamics of Intracranial Aneurysms
,”
Comput. Methods Biomech. Biomed. Eng.
,
12
(
4
), pp.
431
444
.10.1080/10255840802654335
129.
Marzo
,
A.
,
Singh
,
P.
,
Larrabide
,
I.
,
Radaelli
,
A.
,
Coley
,
S.
,
Gwilliam
,
M.
,
Wilkinson
,
I. D.
,
Lawford
,
P.
,
Reymond
,
P.
,
Patel
,
U.
,
Frangi
,
A.
, and
Hose
,
D. R.
,
2011
, “
Computational Hemodynamics in Cerebral Aneurysms: The Effects of Modeled Versus Measured Boundary Conditions
,”
Ann. Biomed. Eng.
,
39
(
2
), pp.
884
896
.10.1007/s10439-010-0187-z
130.
Shojima
,
M.
,
Oshima
,
M.
,
Takagi
,
K.
,
Torii
,
R.
,
Hayakawa
,
M.
,
Katada
,
K.
,
Morita
,
A.
, and
Kirino
,
T.
,
2004
, “
Magnitude and Role of Wall Shear Stress on Cerebral Aneurysm: Computational Fluid Dynamic Study of 20 Middle Cerebral Artery Aneurysms
,”
Stroke
,
35
(
11
), pp.
2500
2505
.10.1161/01.STR.0000144648.89172.0f
131.
Bazilevs
,
Y.
,
Hsu
,
M.-C.
,
Zhang
,
Y.
,
Wang
,
W.
,
Liang
,
X.
,
Kvamsdal
,
T.
,
Brekken
,
R.
, and
Isaksen
,
J. G.
,
2010
, “
A Fully-Coupled Fluid-Structure Interaction Simulation of Cerebral Aneurysms
,”
Comput. Mech.
,
46
(
1
), pp.
3
16
.10.1007/s00466-009-0421-4
132.
Raschi
,
M.
,
Mut
,
F.
,
Byrne
,
G.
,
Putman
,
C. M.
,
Tateshima
,
S.
,
Viñuela
,
F.
,
Tanoue
,
T.
, and
Tanishita
,
K.
,
2012
, “
CFD and PIV Analysis of Hemodynamics in a Growing Intracranial Aneurysm
,”
Int. J. Numer. Methods Biomed. Eng.
,
28
(
2
), pp.
214
228
.10.1002/cnm.1459
133.
Miura
,
Y.
,
Ishida
,
F.
,
Umeda
,
Y.
,
Tanemura
,
H.
,
Suzuki
,
H.
,
Matsushima
,
S.
,
Shimosaka
,
S.
, and
Taki
,
W.
,
2013
, “
Low Wall Shear Stress is Independently Associated With the Rupture Status of Middle Cerebral Artery Aneurysms
,”
Stroke
,
44
, pp.
519
521
.10.1161/STROKEAHA.112.675306
134.
Omodaka
,
S.
,
Sugiyama
,
S.-I.
,
Inoue
,
T.
,
Funamoto
,
K.
,
Fujimura
,
M.
,
Shimizu
,
H.
,
Hayase
,
T.
,
Takahashi
,
A.
, and
Tominaga
,
T.
,
2012
, “
Local Hemodynamics at the Rupture Point of Cerebral Aneurysms Determined by Computational Fluid Dynamics Analysis
,”
Cerebrovasc. Dis. (Basel, Switzerland)
,
34
(
2
), pp.
121
129
.10.1159/000339678
135.
Fisher
,
C.
, and
Rossmann
,
J. S.
,
2009
, “
Effect of Non-Newtonian Behavior on the Hemodynamics of Cerebral Aneurysm
,”
ASME J. Biomech. Eng.
,
131
(9), p.
091004
.10.1115/1.3148470
136.
Perktold
,
K.
,
Peter
,
R.
, and
Resch
,
M.
,
1989
, “
Pulsatile Non-Newtonian Blood Flow Simulation Through a Bifurcation With an Aneurysm
,”
Biorheology
,
26
, pp.
1011
1030
.
137.
Valencia
,
A.
,
Zarate
,
A.
,
Galvez
,
M.
, and
Badilla
,
L.
,
2006
, “
Non-Newtonian Blood Flow Dynamics in a Right Internal Carotid Artery With a Saccular Aneurysm
,”
Int. J. Numer. Methods Fluids
,
50
(
6
), pp.
751
764
.10.1002/fld.1078
138.
Wang
,
S. Z.
,
Chen
,
J. L.
,
Ding
,
G. H.
,
Lu
,
G.
, and
Zhang
,
X. L.
,
2010
, “
Non-Newtonian Computational Hemodynamics in Two Patient-Specific Cerebral Aneurysms With Daughter Saccules
,”
J. Hydrodyn.
,
22
(
5
), pp.
639
646
.10.1016/S1001-6058(09)60098-6
139.
Bernabeu
,
M. O.
,
Nash
,
R. W.
,
Groen
,
D.
,
Carver
,
H. B.
,
Hetherington
,
J.
,
Krüger
,
T.
, and
Coveney
,
P. T.
,
2013
, “
Impact of Blood Rheology on Wall Shear Stress in a Model of the Middle Cerebral Artery
,”
Interface Focus
,
3
(
3
), p.
20120094
.10.1098/rsfs.2012.0094
140.
Valencia
,
A.
,
Guzmán
,
A. M.
,
Finol
,
E. A.
, and
Amon
,
C. H.
,
2006
, “
Blood Flow Dynamics in Saccular Aneurysm Models of the Basilar Artery
,”
ASME J. Biomech. Eng.
,
128
(
4
), pp.
516
526
.10.1115/1.2205377
141.
Evju
,
O.
,
Valen-Sendstad
,
K.
, and
Mardal
,
K. A.
,
2013
, “
A Study of Wall Shear Stress in 12 Aneurysms With Respect to Different Viscosity Models and Flow Conditions
,”
J. Biomech.
,
46
(
16
), pp.
2802
2808
.10.1016/j.jbiomech.2013.09.004
142.
Dimakopoulos
,
Y.
,
Syrakos
,
A.
,
Georgios
,
G. C.
,
Papadopoulos
,
K.
, and
Tsamopoulos
,
J.
,
2014
, “
Effect of RBC Migration Phenomena on the Hemodynamics in Stenotic Microvessels Under Pulsating Flow Conditions
,”
Book of Abstracts of the 9th Annual European Rheology Conference
, Karlsruhe, Germany, Apr. 8–11, Vol.
75
, p.
58
.
143.
Steinman
,
D. A.
,
Hoi
,
Y.
,
Fahy
,
P.
,
Morris
,
L.
,
Walsh
,
M. T.
,
Aristokleous
,
N.
,
Anayiotos
,
A. S.
,
Papaharilaou
,
Y.
,
Arzani
,
A.
,
Shadden
,
S. C.
,
Berg
,
P.
,
Janiga
,
G.
,
Bols
,
J.
,
Segers
,
P.
,
Bressloff
,
N. W.
,
Cibis
,
M.
,
Gijsen
,
F. H.
,
Cito
,
S.
,
Pallarés
,
J.
,
Browne
,
L. D.
,
Costelloe
,
J. A.
,
Lynch
,
A. G.
,
Degroote
,
J.
,
Vierendeels
,
J.
,
Fu
,
W.
,
Qiao
,
A.
,
Hodis
,
S.
,
Kallmes
,
D. F.
,
Kalsi
,
H.
,
Long
,
Q.
,
Kheyfets
,
V. O.
,
Finol
,
E. A.
,
Kono
,
K.
,
Malek
,
A. M.
,
Lauric
,
A.
,
Menon
,
P. G.
,
Pekkan
,
K.
,
Moghadam
,
M. E.
,
Marsden
,
A. L.
,
Oshima
,
M.
,
Katagiri
,
K.
,
Peiffer
,
V.
,
Mohamied
,
Y.
,
Sherwin
,
S. J.
,
Schaller
,
J.
,
Goubergrits
,
L.
,
Usera
,
G.
,
Mendina
,
M.
,
Valen-Sendstad
,
K.
,
Habets
,
D. F.
,
Xiang
,
J.
,
Meng
,
H.
,
Yu
,
Y.
,
Karniadakis
,
G. E.
,
Shaffer
,
N.
, and
Loth
,
F.
,
2013
, “
Variability of Computational Fluid Dynamics Solutions for Pressure and Flow in a Giant Aneurysm: The ASME 2012 Summer Bioengineering Conference CFD Challenge
,”
ASME J. Biomech. Eng.
,
135
(
2
), p.
021016
.10.1115/1.4023382
144.
Valen-Sendstad
,
K.
, and
Steinman
,
D. A.
,
2014
, “
Mind the Gap: Impact of Computational Fluid Dynamics Solution Strategy on Prediction of Intracranial Aneurysm Hemodynamics and Rupture Status Indicators
,”
Am. J. Neuroradiol.
,
35
(
3
), pp.
544
545
.10.3174/ajnr.A3793
145.
Janela
,
J.
,
Moura
,
A.
, and
Sequeira
,
A.
,
2010
, “
Towards a Geometrical Multiscale Approach to Non-Newtonian Blood Flow Simulations
,” Advances in Mathematical Fluid Mechanics, R. Rannacher, A. Sequeira (eds) Springer, Berlin, pp. 295–09.
146.
Forsyth
,
A. M.
,
Wan
,
J.
,
Owrutsky
,
P. D.
,
Abkarian
,
M.
, and
Stone
,
H. A.
,
2011
, “
Multiscale Approach to Link Red Blood Cell Dynamics, Shear Viscosity, and ATP Release
,”
Proc. Natl. Acad. Sci. U.S.A
,
108
, pp.
10986
10991
.10.1073/pnas.1101315108
147.
Xu
,
Z.
,
Chen
,
N.
,
Shadden
,
S. C.
,
Marsden
,
J. E.
,
Kamocka
,
M. M.
,
Rosen
,
E. D.
, and
Alber
,
M.
,
2009
, “
Study of Blood Flow Impact on Growth of Thrombi Using a Multiscale Model
,”
Soft Matter
,
5
, pp.
769
779
.10.1039/b812429a
148.
Grinberg
,
L.
,
Fedosov
,
D. A.
, and
Karniadakis
,
G. E.
,
2013
, “
Parallel Multiscale Simulations of a Brain Aneurysm
,”
J. Comput. Phys.
,
244
, pp.
131
147
.10.1016/j.jcp.2012.08.023
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