The physiological mechanisms that give rise to the inception and development of a cerebral aneurysm are accepted to involve the interplay between the local mechanical forces acting on the arterial wall and the biological processes occurring at the cellular level. In fact, the wall shear stresses (WSSs) that act on the endothelial cells are thought to play a pivotal role. A computational framework is proposed to explore the link between the evolution of a cerebral aneurysm and the influence of hemodynamic stimuli that act on the endothelial cells. An aneurysm evolution model, which utilizes a realistic microstructural model of the arterial wall, is combined with detailed 3D hemodynamic solutions. The evolution of the blood flow within the developing aneurysm determines the distributions of the WSS and the spatial WSS gradient (WSSG) that act on the endothelial cell layer of the tissue. Two illustrative examples are considered: Degradation of the elastinous constituents is driven by deviations of WSS or the WSSG from normotensive values. This model provides the basis to further explore the etiology of aneurysmal disease.

1.
Brisman
,
J. L.
,
Song
,
J. K.
, and
Newell
,
D. W.
, 2006, “
Cerebral Aneurysms
,”
N. Engl. J. Med.
0028-4793,
355
, pp.
928
939
.
2.
Peters
,
D. G.
,
Kassam
,
A. B.
,
Feingold
,
E.
,
Heidrich-O’Hare
,
E.
,
Yonas
,
H.
,
Ferrell
,
R. E.
, and
Brufsky
,
A.
, 2001, “
Molecular Anatomy of an Intracranial Aneurysm Coordinated Expression of Genes Involved in Wound Healing and Tissue Remodeling
,”
Stroke
0039-2499,
32
, pp.
1036
1042
.
3.
Meng
,
H.
,
Wang
,
Z.
,
Hoi
,
Y.
,
Gao
,
L.
,
Metaxa
,
E.
,
Swart
,
D. D.
, and
Kolega
,
J.
, 2007, “
Complex Hemodynamics at the Apex of an Arterial Bifurcation Induces Vascular Remodelling Resembling Cerebral Aneurysm Initiation
,”
Stroke
0039-2499,
38
, pp.
1924
1931
.
4.
Kondo
,
S.
,
Hashoimotot
,
N.
,
Kikuchi
,
H.
,
Hazama
,
F.
,
Nagata
,
I.
, and
Kataoka
,
H.
, 1997, “
Cerebral Aneurysms Arising at Nonbranching Sites. An Experimental Study
,”
Stroke
0039-2499,
28
, pp.
398
404
.
5.
Ahn
,
S.
,
Shin
,
D.
,
Tateshima
,
S.
,
Tanishita
,
K.
,
Vinuela
,
F.
, and
Sinha
,
S.
, 2007, “
Fluid-Induced WSS in Anthropomorphic Brain Aneurysm Models: MR Phase-Contrast Study at 3T
,”
J. Magn. Reson Imaging
1053-1807,
25
, pp.
1120
1130
.
6.
Hoi
,
Y.
,
Meng
,
H.
,
Woodward
,
S. H.
,
Bendok
,
B. R.
,
Hamel
,
R. A.
,
Guterman
,
L. R.
, and
Hopkins
,
L. N.
, 2004, “
Effects of Arterial Geometry on Aneurysm Growth: Three Dimensional Computational Fluid Dynamics Study
,”
J. Neurosurg.
0022-3085,
101
, pp.
676
681
.
7.
Nakatani
,
H.
,
Hashimoto
,
N.
,
Kang
,
Y.
,
Yamazoe
,
N.
,
Kikuchi
,
H.
,
Yamaguchi
,
S.
, and
Niimi
,
H.
, 1991, “
Cerebral Blood Flow Patterns at Major Vessel Bifurcations and Aneurysms in Rats
,”
J. Neurosurg.
0022-3085,
74
, pp.
258
262
.
8.
Tateshima
,
S.
,
Murayama
,
Y.
,
Villablanca
,
J. P.
,
Morino
,
T.
,
Nomura
,
K.
,
Tanishita
,
K.
, and
Viuela
,
F.
, 2003, “
In Vitro Measurement of Fluid-Induced WSS in Unruptured Cerebral Aneurysms Harboring Blebs
,”
Stroke
0039-2499,
34
, pp.
187
192
.
9.
DePaola
,
N.
,
Gimbrone
, Jr.,
M. A.
,
Davies
,
P. F.
, and
Dewey
, Jr.,
C. F.
, 1992, “
Vascular Endothelium Responds to Fluid Shear Stress Gradients
,”
Arterioscler. Thromb.
1049-8834,
12
, pp.
1254
1257
.
10.
Shojima
,
M.
,
Oshima
,
M.
,
Takagi
,
K.
,
Torii
,
R.
,
Hayakawa
,
M.
,
Katada
,
K.
,
Morita
,
A.
, and
Kirino
,
T.
, 2004, “
Magnitude and Role of WSS on Cerebral Aneurysm: Computational Fluid Dynamic Study of 20 Middle Cerebral Artery Aneurysms
,”
Stroke
0039-2499,
35
, pp.
2500
2505
.
11.
Watton
,
P. N.
,
Hill
,
N. A.
, and
Heil
,
M.
, 2004, “
A Mathematical Model for the Growth of the Abdominal Aortic Aneurysm
,”
Biomech. Model. Mechanobiol.
1617-7959,
3
, pp.
98
113
.
12.
Baek
,
S.
,
Rajagopal
,
K. R.
, and
Humphrey
,
J. D.
, 2005, “
Competition Between Radial Expansion and Thickening in the Enlargement of an Intracranial Saccular Aneurysm
,”
J. Elast.
0374-3535,
80
, pp.
13
31
.
13.
Watton
,
P. N.
, and
Hill
,
N. A.
, 2009, “
Evolving Mechanical Properties of a Model of Abdominal Aortic Aneurysm
,”
Biomech. Model. Mechanobiol.
1617-7959,
8
, pp.
25
42
.
14.
Kroon
,
M.
, and
Holzapfel
,
G. A.
, 2007, “
A Model for Saccular Cerebral Aneurysm Growth by Collagen Fibre Remodelling
,”
J. Theor. Biol.
0022-5193,
247
, pp.
775
787
.
15.
Kroon
,
M.
, and
Holzapfel
,
G. A.
, 2009, “
A Theoretical Model for Fibroblast-Controlled Growth of Saccular Cerebral Aneurysms
,”
J. Theor. Biol.
0022-5193,
26
(
2
), pp.
133
164
.
16.
Watton
,
P. N.
,
Ventikos
,
Y.
, and
Holzapfel
,
G. A.
, 2009, “
Modelling the Growth and Stabilisation of Cerebral Aneurysms
,”
Math. Med. Biol.
,
26
(
2
), pp.
133
164
. 1477-8599
17.
Watton
,
P. N.
, and
Ventikos
,
Y.
, 2009, “
Modelling Evolution of Saccular Cerebral Aneurysms
,”
J. Strain Anal.
0022-4758,
44
(
5
), pp.
375
389
.
18.
Chatziprodromou
,
I.
,
Tricoli
,
A.
,
Poulikakos
,
D.
, and
Ventikos
,
Y.
, 2007, “
Haemodynamics and Wall Remodelling of a Growing Cerebral Aneurysm: A Computational Model
,”
J. Biomech.
0021-9290,
40
, pp.
412
426
.
19.
Feng
,
Y.
,
Wada
,
S.
,
Tsubota
,
K.
, and
Yamaguchi
,
T.
, 2004, “
Growth of Intracranial Aneurysms Arising From Curved Vessels Under the Influence of Elevated Wall Shear Stress—A Computer Simulation Study
,”
JSME Int. J., Ser. C
1340-8062,
47
, pp.
1035
1042
.
20.
Feng
,
Y.
,
Wada
,
S.
,
Ishikawa
,
T.
,
Tsubota
,
K.
, and
Yamaguchi
,
T.
, 2008, “
A Rule-Based Computational Study on the Early Progression of Intracranial Aneurysms Using Fluid-Structure Interaction: Comparison Between Straight Model and Curved Model
,”
J. Biomech. Sci. Eng.
,
3
, pp.
124
137
. 1880-9863
21.
Holzapfel
,
G. A.
,
Gasser
,
T. C.
, and
Ogden
,
R. W.
, 2000, “
A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models
,”
J. Elast.
0374-3535,
61
, pp.
1
48
.
22.
Wempner
,
G.
, 1973,
Mechanics of Solids
,
McGraw-Hill
,
New York
.
23.
Heil
,
M.
, 1996, “
The Stability of Cylindrical Shells Conveying Viscous Flow
,”
J. Fluids Struct.
0889-9746,
10
, pp.
173
196
.
24.
Holzapfel
,
G. A.
, 2000,
Nonlinear Solid Mechanics. A Continuum Approach for Engineering
,
Wiley
,
Chichester
.
25.
Watton
,
P. N.
, 2002, “
Mathematical Modelling of the Abdominal Aortic Aneurysm
,” Ph.D. thesis, University of Leeds, Leeds, UK.
26.
Humphrey
,
J. D.
, 1999, “
Remodelling of a Collagenous Tissue at Fixed Lengths
,”
ASME J. Biomech. Eng.
0148-0731,
121
, pp.
591
597
.
27.
Gundiah
,
N.
,
Ratcliffe
,
M. B.
, and
Pruitt
,
L. A.
, 2007, “
Determination of Strain Energy Function for Arterial Elastin: Experiments Using Histology and Mechanical Tests
,”
J. Biomech.
0021-9290,
40
, pp.
586
594
.
28.
Watton
,
P. N.
,
Ventikos
,
Y.
, and
Holzapfel
,
G. A.
, 2009, “
Modelling the Mechanical Response of Elastin for Arterial Tissue
,”
J. Biomech.
0021-9290,
42
, pp.
1320
1325
.
29.
Monson
,
K. L.
,
Goldsmith
,
W.
,
Barbaro
,
N. M.
, and
Manley
,
G. T.
, 2005, “
Significance of Source and Size in the Mechanical Response of Human Cerebral Blood Vessels
,”
J. Biomech.
0021-9290,
38
, pp.
737
744
.
30.
Monson
,
K. L.
,
Goldsmith
,
W.
,
Barbaro
,
N. M.
, and
Manley
,
G. T.
, 2003, “
Axial Mechanical Properties of Fresh Human Cerebral Blood Vessels
,”
ASME J. Biomech. Eng.
0148-0731,
125
, pp.
288
294
.
31.
Hansen
,
F.
,
Mangell
,
P.
,
Sonesson
,
B.
, and
Lanne
,
T.
, 1995, “
Diameter and Compliance in the Human Common Carotid Artery—Variations With Age and Sex
,”
Ultrasound Med. Biol.
0301-5629,
21
, pp.
1
99
.
32.
Patakar
,
H. S.
, 1980,
Numerical Heat Transfer and Fluid Flow
(
Hemisphere Series on Computational Methods in Mechanics and Thermal Science
),
Taylor & Francis
,
London
.
33.
Ferziger
,
J.
, and
Milovan
,
P.
, 2001,
Computational Methods for Fluid Dynamics
,
3rd ed.
,
Springer
,
New York
.
34.
Hutchinson
,
B. R.
, and
Raithby
,
G. D.
, 1986, “
A Multigrid Method Based on the Additive Correction Strategy
,”
Numer. Heat Transfer
0149-5720,
9
, pp.
511
537
.
35.
Oshima
,
M.
,
Torii
,
R.
,
Kobayashia
,
T.
,
Taniguchic
,
N.
, and
Takagid
,
K.
, 2001, “
Finite Element Simulation of Blood Flow in the Cerebral Artery
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
191
, pp.
661
671
.
36.
Albayrak
,
R.
,
Degirmenci
,
B.
,
Acar
,
M.
,
Haktanir
,
A.
,
Colbay
,
M.
, and
Yaman
,
M.
, 2007, “
Doppler Sonography Evaluation of Flow Velocity and Volume of the Extracranial Internal Carotid and Vertebral Arteries in Healthy Adults
,”
J. Clin. Ultrasound
0091-2751,
35
, pp.
27
33
.
37.
Nissen
,
R.
,
Cardinale
,
G. J.
, and
Udenfriend
,
S.
, 1978, “
Increased Turnover of Arterial Collagen in Hypertensive Rats
,”
Proc. Natl. Acad. Sci. U.S.A.
0027-8424,
75
, pp.
451
453
.
38.
Abdul-Hussien
,
H.
,
Soekhoe
,
R. G.
,
Weber
,
E.
,
von der Thüsen
,
J. H.
,
Kleemann
,
R.
,
Mulder
,
A.
,
van Bockel
,
J. H.
,
Hanemaaijer
,
R.
, and
Lindeman
,
J. H.
, 2007, “
Collagen Degradation in the Abdominal Aortic Aneurysm: A Conspiracy of Matrix Metalloproteinase and Cysteine Collagenases
,”
Am. J. Pathol.
0002-9440,
170
(
3
), pp.
809
817
.
39.
Wang
,
J. H. C.
, and
Thampaty
,
B. P.
, 2006, “
An Introductory Review of Cell Mechanobiology
,”
Biomech. Model. Mechanobiol.
1617-7959,
5
, pp.
1
16
.
40.
Gupta
,
V.
, and
Grande-Allen
,
K. J.
, 2006, “
Effects of Static and Cyclic Loading in Regulating Extracellular Matrix Synthesis by Cardiovascular Cells
,”
Cardiovasc. Res.
0008-6363,
72
, pp.
375
383
.
41.
Chiquet
,
M.
,
Renedo
,
A. S.
,
Huber
,
F.
, and
Fluck
,
M.
, 2003, “
How Do Fibroblasts Translate Mechanical Signals Into Changes in Extracellular Matrix Production?
,”
Matrix Biol.
0945-053X,
22
, pp.
73
80
.
42.
Sluijter
,
J. P. G.
,
Smeets
,
M. B.
,
Velema
,
E.
,
Pasterkamp
,
G.
, and
de Kleijn
,
D. P. V.
, 2004, “
Increase in Collagen Turnover But Not in Collagen Fiber Content Is Associated With Flow-Induced Arterial Remodeling
,”
J. Vasc. Res.
1018-1172,
41
, pp.
546
555
.
43.
Mimata
,
C.
,
Kitaoka
,
M.
,
Nagahiro
,
S.
,
Iyama
,
K.
,
Hori
,
H.
,
Yoshioka
,
H.
, and
Ushio
,
Y.
, 1997, “
Differential Distribution and Expressions of Collagens in the Cerebral Aneurismal Wall
,”
Acta Neuropathol.
,
94
, pp.
197
206
. 0001-6322
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