A modern technique for the treatment of cerebral aneurysms involves insertion of a flow diverter stent. Flow stagnation, produced by the fine mesh structure of the diverter, is thought to promote blood clotting in an aneurysm. However, apart from its effect on flow reduction, the insertion of the metal device poses the risk of occlusion of a parent artery. One strategy for avoiding the risk of arterial occlusion is the use of a device with a higher porosity. To aid the development of optimal stents in the view point of flow reduction maintaining a high porosity, we used lattice Boltzmann flow simulations and simulated annealing optimization to investigate the optimal placement of stent struts. We constructed four idealized aneurysm geometries that resulted in four different inflow characteristics and employed a stent model with 36 unconnected struts corresponding to the porosity of 80%. Assuming intracranial flow, steady flow simulation with Reynolds number of 200 was applied for each aneurysm. Optimization of strut position was performed to minimize the average velocity in an aneurysm while maintaining the porosity. As the results of optimization, we obtained nonuniformed structure as optimized stent for each aneurysm geometry. And all optimized stents were characterized by denser struts in the inflow area. The variety of inflow patterns that resulted from differing aneurysm geometries led to unique strut placements for each aneurysm type.

References

References
1.
Appanaboyina
,
S.
,
Mut
,
F.
,
Lohner
,
R.
,
Putman
,
C.
, and
Cebral
,
J.
,
2009
, “
Simulation of Intracranial Aneurysm Stenting: Techniques and Challenges
,”
Comput. Methods Appl. Mech. Eng.
,
198
(
45-46
), pp.
3567
3582
.10.1016/j.cma.2009.01.017
2.
Appanaboyina
,
S.
,
Mut
,
F.
,
Lohner
,
R.
,
Scrivano
,
E.
,
Miranda
,
C.
,
Lylyk
,
P.
,
Putman
,
C.
, and
Cebral
,
J.
,
2008
, “
Computational Modeling of Blood Flow in Side Arterial Branches After Stenting of Cerebral Aneurysms
,”
Int. J. Comput. Fluid Dyn.
,
22
(
10
), pp.
669
676
.10.1080/10618560802495255
3.
Augsburger
,
L.
,
Farhat
,
M.
,
Reymond
,
P.
,
Fonck
,
E.
,
Kulcsar
,
Z.
,
Stergiopulos
,
N.
, and
Rufenacht
,
D. A.
,
2009
, “
Effect of Flow Diverter Porosity on Intra-aneurysmal Blood Flow
,”
Klin. Neuroradiol.
,
19
(
3
), pp.
204
214
.10.1007/s00062-009-9005-0
4.
Anzai
,
H.
,
Ohta
,
M.
,
Falcone
,
J.-L.
, and
Chopard
,
B.
,
2012
, “
Optimization of Flow Diverters for Cerebral Aneurysms
,”
J. Comput. Sci.
,
3
(
1-2
), pp.
1
7
.10.1016/j.jocs.2011.12.006
5.
Hirabayashi
,
M.
,
Ohta
,
M.
,
Rufenacht
,
D. A.
, and
Chopard
,
B.
,
2003
, “
Characterization of Flow Reduction Properties in an Aneurysm due to a Stent
,”
Phy. Rev. E Stat. Nonlin. Soft Matter Phys.
,
68
(
2
), p.
021918
.10.1103/PhysRevE.68.021918
6.
Ionita
,
C. N.
,
Paciorek
,
A. M.
,
Hoffmann
,
K. R.
,
Bednarek
,
D. R.
,
Yamamoto
,
J.
,
Kolega
,
J.
,
Levy
,
E. I.
,
Hopkins
,
L. N.
,
Rudin
,
S.
, and
Mocco
,
J.
,
2008
, “
Asymmetric Vascular Stent: Feasibility Study of a New Low-Porosity Patch-Containing Stent
,”
Stroke
,
39
(
7
), pp.
2105
2113
.10.1161/STROKEAHA.107.503862
7.
Lieber
,
B. B.
,
Stancampiano
,
A. P.
, and
Wakhloo
,
A. K.
,
1997
, “
Alteration of Hemodynamics in Aneurysm Models by Stenting: Influence of Stent Porosity
,”
Ann. Biomed. Eng.
,
25
(
3
), pp.
460
469
.10.1007/BF02684187
8.
Srinivas
,
K.
,
Townsend
,
S.
,
Lee
,
C. J.
,
Nakayama
,
T.
,
Ohta
,
M.
,
Obayashi
,
S.
, and
Yamaguchi
,
T.
,
2010
, “
Two-Dimensional Optimization of a Stent for an Aneurysm
,”
ASME J. Med. Devices
4
(
2
), p.
021003
.10.1115/1.4001861
9.
Nakayama
,
T.
,
Jeong
,
S.
,
Srinivas
,
K.
, and
Ohta
,
M.
,
2010
, “
Development of Stent Strut Pattern for Cerebral Aneurysm
,” Proceedings of the 3rd ASME 2010 Joint US-European Fluids Engineering Summer Meeting and 8th International Conference on Nanochannels, Microchannels, and Minichannels, Paper No. FEDSM/ICNMM 2010-30592.
10.
Imai
,
Y.
,
Sato
,
K.
,
Ishikawa
,
T.
, and
Yamaguchi
,
T.
,
2008
, “
Inflow Into Saccular Cerebral Aneurysms at Arterial Bends
,”
Ann. Biomed. Eng.
,
36
(
9
), pp.
1489
1495
.10.1007/s10439-008-9522-z
11.
Hoi
,
Y. M.
,
Meng
,
H.
,
Woodward
,
S. H.
,
Bendok
,
B. R.
,
Hanel
,
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.
,
101
(
4
), pp.
676
681
.10.3171/jns.2004.101.4.0676
12.
Anzai
,
H.
,
Nakayama
,
T.
,
Takeshima
,
Y.
, and
Ohta
,
M.
,
2010
, “
The Effect of 3D Visualization on Optimal Design for Strut Position of Intracranial Stent
,” Proceedings of the 3rd ASME 2010 Joint US-European Fluids Engineering Summer Meeting and 8th International Conference on Nanochannels, Microchannels, and Minichannels, Paper No. FEDSM/ICNMM 2010-30591.
13.
Janiga
,
G.
,
Rossl
,
C.
,
Skalej
,
M.
, and
Thevenin
,
D.
,
2013
, “
Realistic Virtual Intracranial Stenting and Computational Fluid Dynamics for Treatment Analysis
,”
J. Biomech.
,
46
(
1
), pp.
7
12
.10.1016/j.jbiomech.2012.08.047
14.
Kim
,
M.
,
Taulbee
,
D. B.
,
Tremmel
,
M.
, and
Meng
,
H.
,
2008
, “
Comparison of Two Stents in Modifying Cerebral Aneurysm Hemodynamics
,”
Ann. Biomed. Eng.
,
36
(
5
), pp.
726
741
.10.1007/s10439-008-9449-4
15.
Tremmel
,
M.
,
Xiang
,
J.
,
Natarajan
,
S. K.
,
Hopkins
,
L. N.
,
Siddiqui
,
A. H.
,
Levy
,
E. I.
, and
Meng
,
H.
,
2010
, “
Alteration of Intra-Aneurysmal Hemodynamics for Flow Diversion Using Enterprise and Vision Stents
,”
World Neurosurg.
,
74
(
2-3
), pp.
306
315
.10.1016/j.wneu.2010.05.008
16.
Karino
,
T.
,
1986
, “
Microscopic Structure of Disturbed Flows in the Arterial and Venous Systems and Its Implication in the Localization of Vascular Diseases
,”
Int. Angiol.
,
5
(
4
), pp.
297
313
.
18.
Axner
,
L.
,
Hoekstra
,
A. G.
,
Jeays
,
A.
,
Lawford
,
P.
,
Hose
,
R.
, and
Sloot
,
P. M. A.
,
2009
, “
Simulations of Time Harmonic Blood Flow in the Mesenteric Artery: Comparing Finite Element and Lattice Boltzmann Methods
,”
Biomed. Eng. Online
,
8
, p. 23.10.1186/1475-925X-8-23
19.
Breuer
,
M.
,
Bernsdorf
,
J.
,
Zeiser
,
T.
, and
Durst
,
F.
,
2000
, “
Accurate Computations of the Laminar Flow Past a Square Cylinder Based on Two Different Methods: Lattice-Boltzmann and Finite-Volume
,”
Int. J. Heat Fluid Fl.
,
21
(
2
), pp.
186
196
.10.1016/S0142-727X(99)00081-8
20.
He
,
X.
,
Duckwiler
,
G.
, and
Valentino
,
D. J.
,
2009
, “
Lattice Boltzmann Simulation of Cerebral Artery Hemodynamics
,”
Comput. Fluids
,
38
(
4
), pp.
789
796
.10.1016/j.compfluid.2008.07.006
21.
Noble
,
D. R.
,
Georgiadis
,
J. G.
, and
Buckius
,
R. O.
,
1996
, “
Comparison of Accuracy and Performance for Lattice Boltzmann and Finite Difference Simulations of Steady Viscous Flow
,”
Int. J. Numer. Methods Fluid
,
23
(
1
), pp.
1
18
.10.1002/(SICI)1097-0363(19960715)23:1<1::AID-FLD404>3.0.CO;2-V
22.
Succi
,
S.
,
2001
,
The Lattice Boltzmann Equation, for Fluid Dynamics and Beyond
,
Oxford University Press, UK.
23.
Isoda
,
H.
,
Hirano
,
M.
,
Takeda
,
H.
,
Kosugi
,
T.
,
Alley
,
M. T.
,
Markl
,
M.
,
Pelc
,
N. J.
, and
Sakahara
,
H.
,
2006
, “
Visualization of Hemodynamics in a Silicon Aneurysm Model Using Time-Resolved, 3D, Phase-Contrast MRI
,”
ANJR. Am. J. Neuroradiol.
,
27
(
5
), pp.
1119
1122
.
24.
Johnson
,
D. S.
,
Aragon
,
C. R.
,
Mcgeoch
,
L. A.
, and
Schevon
,
C.
,
1991
, “
Optimization by Simulated Annealing—An Experimental Evaluation.2. Graph-Coloring and Number Partitioning
,”
Operations Res.
,
39
(
3
), pp.
378
406
.10.1287/opre.39.3.378
25.
Kirkpatrick
,
S.
,
1984
, “
Optimization by Simulated Annealing—Quantitative Studies
,”
J. Stat. Phys.
,
34
(
5-6
), pp.
975
986
.10.1007/BF01009452
26.
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
,”
Arteriosclerosis
,
5
(
3
), pp.
293
302
.10.1161/01.ATV.5.3.293
27.
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
28.
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
29.
Ram
,
D. J.
,
Sreenivas
,
T. H.
, and
Subramaniam
,
K. G.
,
1996
, “
Parallel Simulated Annealing Algorithms
,”
J. Parallel Distributed Comput.
,
37
(
2
), pp.
207
212
.10.1006/jpdc.1996.0121
30.
Liou
,
T. M.
,
Yi-Chen
,
L.
, and
Juan
,
W. C.
,
2007
, “
Numerical and Experimental Studies on Pulsatile Flow in Aneurysms Arising Laterally From a Curved Parent Vessel at Various Angles
,”
J. Biomech.
,
40
(
6
), pp.
1268
1275
.10.1016/j.jbiomech.2006.05.024
31.
Zeng
,
Z.
,
Durka
,
M. J.
,
Kallmes
,
D. F.
,
Ding
,
Y.
, and
Robertson
,
A. M.
,
2011
, “
Can Aspect Ratio Be Used to Categorize Intra-Aneurysmal Hemodynamics?—A Study of Elastase Induced Aneurysms in Rabbit
,”
J. Biomech.
,
44
(
16
), pp.
2809
2816
.10.1016/j.jbiomech.2011.08.002
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