We consider the effect of geometrical configuration on the steady flow field of representative geometries from an in vivo anatomical data set of end-to-side distal anastomoses constructed as part of a peripheral bypass graft. Using a geometrical classification technique, we select the anastomoses of three representative patients according to the angle between the graft and proximal host vessels (GPA) and the planarity of the anastomotic configuration. The geometries considered include two surgically tunneled grafts with shallow GPAs which are relatively planar but have different lumen characteristics, one case exhibiting a local restriction at the perianastomotic graft and proximal host whilst the other case has a relatively uniform cross section. The third case is nonplanar and characterized by a wide GPA resulting from the graft being constructed superficially from an in situ vein. In all three models the same peripheral resistance was imposed at the computational outflows of the distal and proximal host vessels and this condition, combined with the effect of the anastomotic geometry, has been observed to reasonably reproduce the in vivo flow split. By analyzing the flow fields we demonstrate how the local and global geometric characteristics influences the distribution of wall shear stress and the steady transport of fluid particles. Specifically, in vessels that have a global geometric characteristic we observe that the wall shear stress depends on large scale geometrical factors, e.g., the curvature and planarity of blood vessels. In contrast, the wall shear stress distribution and local mixing is significantly influenced by morphology and location of restrictions, particular when there is a shallow GPA. A combination of local and global effects are also possible as demonstrated in our third study of an anastomosis with a larger GPA. These relatively simple observations highlight the need to distinguish between local and global geometric influences for a given reconstruction. We further present the geometrical evolution of the anastomoses over a series of follow-up studies and observe how the lumen progresses towards the faster bulk flow of the velocity in the original geometry. This mechanism is consistent with the luminal changes in recirculation regions that experience low wall shear stress. In the shallow GPA anastomoses the proximal part of the native host vessel occludes or stenoses earlier than in the case with wide GPA. A potential contribution to this behavior is suggested by the stronger mixing that characterizes anastomoses with large GPA.

1.
Ouriel
,
K.
, 2001, “
Peripheral Arterial Disease
,”
Lancet
0140-6736,
358
, pp.
1257
1264
.
2.
Leng
,
G. C.
,
Lee
,
A. J.
,
Fowkes
,
F. G.
,
Whiteman
,
M.
,
Dunbar
,
J.
, and
Housley
,
E.
,
et al.
, 1995, “
Incidence, Natural History and Cardiovascular Events in Symptomatic and Asymptomatic Peripheral Arterial Disease in the General Population
,”
Int. J. Epidemiol.
0300-5771,
25
, pp.
1172
1181
.
3.
Gelin
,
J.
,
Jivegard
,
L.
,
Taft
,
C.
,
Karlsson
,
J.
, and
Sullivan
,
M.
,
et al.
, 2001, “
Treatment Efficacy of Intermittent Claudication by Surgical Intervention, Supervised Physical Exercise Training Compared to no Treatment in Unselected Randomised Patients I: One Year Results of Functional and Physiological Improvements
,”
Eur. J. Vasc. Endovasc Surg.
1078-5884,
22
, pp.
107
113
.
4.
Taft
,
C.
,
Karlsson
,
J.
,
Gelin
,
J.
,
Jivegard
,
L.
,
Sandstrom
,
R.
, and
Arfvidsson
,
D.
,
et al.
, 2001, “
Treatment Efficacy of Intermittent Claudication by Invasive Therapy, Supervised Physical Exercise Training Compared to no Treatment in Unselected Randomised Patients II: One-Year Results of Health-Related Quality of Life
,”
Eur. J. Vasc. Endovasc Surg.
1078-5884,
22
, pp.
114
123
.
5.
Lemson
,
M. S.
,
Tordoir
,
J. H.
,
Daemen
,
M. J.
, and
Kitslaar
,
P. J.
, 2000, “
Intimal Hyperplasia in Vascular Grafts
,”
Eur. J. Vasc. Endovasc Surg.
1078-5884,
19
, pp.
336
350
.
6.
Watelet
,
J.
,
Soury
,
P.
,
Menard
,
J. F.
,
Plissonnier
,
D.
,
Peillon
,
C.
,
Lestrat
,
J. P.
, and
Testart
,
J.
, 1997, “
Femoropopliteal Bypass; In Situ or Reversed Vein Grafts? Ten Year Results of a Randomized Prospective Study
,”
Ann. Vasc. Surg.
0890-5096,
11
, pp.
510
519
.
7.
Varty
,
K.
,
Allen
,
K. E.
,
Bell
,
P. R. F.
, and
London
,
N. J. M.
, 1993, “
Infra-Inguinal Vein Graft Stenosis
,”
Br. J. Surg.
0007-1323,
80
, pp.
825
833
.
8.
Brain
,
A. J.
, and
Angelini
,
G. D.
, 1994, “
The Biology of Saphenous Vein Graft Occlusion: Etiology and Strategy for Prevention
,”
Curr. Opin. Cardiol.
0268-4705,
9
(
6
), pp.
641
649
.
9.
Cheshire
,
N. J.
, and
Wolfe
,
J. H.
, 1993, “
Infrainguinal Graft Surveillance: A Biased Overview
,”
Semin Vasc. Surg.
0895-7967,
6
(
2
), pp.
143
149
.
10.
Mills
,
J. L.
,
Fujitani
,
R. M.
, and
Taylor
,
S. M.
, 1993, “
The Characteristics and Anatomic Distribution of Lesions That Cause Reversed Vein Graft Failure: A Five Year Prospective Study
,”
J. Vasc. Surg.
0741-5214,
17
(
1
), pp.
195
206
.
11.
Watson
,
H. R.
,
Buth
,
J.
,
Schroeder
,
T. V.
,
Simms
,
M. H.
, and
Horrocks
,
M.
, 2000, “
Incidence of Stenoses in Femorodistal Bypass Vein Grafts in a Multicentre Study
,”
Eur. J. Vasc. Endovasc Surg.
1078-5884,
20
, pp.
67
61
.
12.
Cheshire
,
N. J.
,
Wolfe
,
J. H.
,
Barradas
,
M. A.
,
Chambler
,
A. W.
, and
Mikhailidis
,
D. P.
, 1996, “
Smoking and Plasma Fibrinogen, Lipoprotein (a) and Serotonin are Markers for Postoperative Infrainguinal Graft Stenosis
,”
Eur. J. Vasc. Endovasc Surg.
1078-5884,
11
(
4
), pp.
479
486
.
13.
Gentile
,
A. T.
,
Mills
,
J. L.
,
Gooden
,
M. A.
,
Westerband
,
A.
,
Cui
,
H.
,
Berman
,
S. S.
,
Hunter
,
G. C.
, and
Hughes
,
J. D.
, 1997, “
Identification of Predictors for Lower Extremity Vein Graft Stenosis
,”
Am. J. Surg.
0002-9610,
174
(
2
), pp.
218
221
.
14.
Davies
,
M. G.
,
Kim
,
J. H.
,
Klyachkin
,
M. L.
,
Barber
,
L.
,
Dalen
,
H.
,
Svendsen
,
E.
,
Carson
,
C. C.
, and
Hagen
,
P. O.
, 1994, “
Diabetes Mellitus and Experimental Vein Graft Structure and Function
,”
J. Vasc. Surg.
0741-5214,
19
(
6
), pp.
1031
1043
.
15.
Reddan
,
D. N.
,
Marcus
,
R. J.
,
Owen
,
W. F.
,
Szczech
,
L. A.
, and
Landwehr
,
D. M.
, 2001, “
Long-Term Outcomes of Revascularization for Peripheral Vascular Disease in End-Stage Renal Disease Patients
,”
Am. J. Kidney Dis.
0272-6386,
38
, pp.
57
63
.
16.
Caro
,
C. G.
,
Fitz-Gerald
,
J. M.
, and
Schroter
,
R. C.
, 1971, “
Atheroma and Arterial Wall Shear. Observation, Correlation and Proposal of a Shear Dependent Mass Transfer Mechanism for Atherogenesis
,”
Proc. R. Soc. London, Ser. B
0962-8452,
177
(
46
), pp.
109
159
.
17.
Asakura
,
T.
, and
Karino
,
T.
, 1990, “
Flow Patterns and Spatial Distribution of Atherosclerotic Lesions in Human Coronary Arteries
,”
Circ. Res.
0009-7330,
66
(
4
), pp.
1045
1066
.
18.
Ku
,
D. N.
, and
Giddens
,
D. P.
, 1983, “
Pulsatile Flow in a Model Carotid Bifurcation
,”
Arteriosclerosis (Dallas)
0276-5047,
3
(
1
), pp.
31
39
.
19.
Friedman
,
M. H.
,
Bargeron
,
C. B.
, and
Deters
,
O. J.
,
et al.
, 1987, “
Correlation Between Wall Shear Stress and Intimal Thickness at a Coronary Artery Branch
,”
Atherosclerosis (Berlin)
0170-0626,
68
(
1-2
), pp.
27
33
.
20.
Ojha
,
M.
,
Ethier
,
C. R.
,
Johnston
,
K. W.
, and
Cobbold
,
R. S.
, 1990, “
Steady and Pulsatile Flow Fields in an End-to-Side Arterial Anastomosis Model
,”
J. Vasc. Surg.
0741-5214,
12
(
6
), pp.
747
753
.
21.
Sottiurai
,
V. S.
,
Yao
,
J. S.
, and
Batson
,
R. C.
,
et al.
, 1989, “
Distal Anastomotic Intimal Hyperplasia: Histopathologic Character and Biogenesis
,”
Ann. Vasc. Surg.
0890-5096,
3
(
1
), pp.
26
33
.
22.
Bassiouny
,
H. S.
,
White
,
S.
, and
Glagov
,
S.
,
et al.
, 1992, “
Anastomotic Intimal Hperplasia: Mechanical Injury or Flow Induced
,”
J. Vasc. Surg.
0741-5214,
15
(
4
), pp.
708
717
.
23.
Lei
,
M.
,
Kleinstreuer
,
C.
, and
Archie
,
J. P.
, 1997, “
Hemodynamic Simulations and Computer-Aided Designs of Graft-Artery Junctions
,”
J. Biomech. Eng.
0148-0731,
119
(
3
), pp.
343
348
.
24.
Ojha
,
M.
, 1993, “
Spatial and Temporal Variations of Wall Shear Stress Within an End-to-Side Arterial Anastomosis Model
,”
J. Biomech.
0021-9290,
26
(
12
), pp.
1377
1388
.
25.
Malek
,
A. M.
,
Alper
,
S. L.
, and
Izumo
,
S.
, 1999, “
Hemodynamic Shear Stress and its Role in Atherosclerosis
,”
J. Am. Med. Assoc.
0098-7484,
282
, pp.
2035
2042
.
26.
Davies
,
P. F.
, 1995, “
Flow-Mediated Endothelial Mechanotransduction
,”
Physiol. Rev.
0031-9333,
75
(
3
), pp.
519
560
.
27.
Davies
,
P. F.
, 2000, “
Spatial Hemodynamics, the Endothelium and Focal Atherogenesis: A Cell Cycle Link?
,”
Circ. Res.
0009-7330,
86
(
2
), pp.
114
116
.
28.
Pedley
,
T. J.
, 1995, “
High Reynolds Number Flow in Tubes of Complex Geometry With Application to Wall Shear Stress in Arteries
,”
Symp. Soc. Exp. Biol.
0081-1386,
49
, pp.
219
241
.
29.
Caro
,
C. G.
,
Doorly
,
D. J.
, and
Tarnawski
,
M.
,
et al.
, 1996, “
Non-Planar Curvature and Branching of Arteries and Non-Planar Type Flow
,”
Proc. R. Soc. London, Ser. A
1364-5021,
452
, pp.
185
197
.
30.
Papaharilaou
,
Y.
,
Doorly
,
D. J.
, and
Sherwin
,
S. J.
, 2002, “
The Influence of Out-of-Plane Geometry on Pulsatile Flow Within a Distal End-to-Side Anastomosis
,”
J. Biomech.
0021-9290,
35
(
9
), pp.
1225
1239
.
31.
Sherwin
,
S. J.
,
Shah
,
O.
,
Doorly
,
D. J.
,
Peiró
,
J.
,
Papaharilaou
,
Y.
,
Watkins
,
N.
,
Caro
,
C. G.
, and
Dumoulin
,
C. L.
, 2000, “
The Influence of Out-of-Plane Geometry on the Flow Within a Distal End-to-Side Anastomosis
,”
J. Biomech. Eng.
0148-0731,
122
, pp.
1
10
.
32.
Schulman
,
M. L.
,
Badhey
,
M. R.
, and
Yatco
,
R.
, 1991, “
Superficial Femoral-Popliteal Veins and Reversed Saphenous Veins as Primary Femoropopliteal Bypass Grafts: A Randomized Comparative Study
,”
J. Vasc. Surg.
0741-5214,
6
, pp.
1
10
.
33.
Sottiurai
,
V. S.
, 1990, “
Biogenesis and Etiology of Distal Anastomotic Intimal Hyperplasia
,”
Int. Angiol
0392-9590,
9
, pp.
618
627
.
34.
Hughes
,
P. E.
, and
How
,
T. V.
, 1996, “
Effects of Geometry and Flow Division on Flow Structures in Models of the Distal End-to-Side Anastomosis
,”
J. Biomech.
0021-9290,
29
(
7
), pp.
855
872
.
35.
Ethier
,
C. R.
,
Steinman
,
D. A.
, and
Zhang
,
X.
,
et al.
, 1998, “
Flow Wavevorm Effects on End-to-Side Anastomotic Flow Patterns
,”
J. Biomech.
0021-9290,
31
(
7
), pp.
609
617
.
36.
Sherwin
,
S. J.
, and
Doorly
,
D. J.
, 2003, “
Vascular Grafts: Experiments and modelling
,” Vol.
34
of
Advances in fluid mechanics
,
WIT Press
.
37.
Lei
,
M.
,
Kleinstreuer
,
C.
, and
Archie
,
J. P.
, 1996, “
Geometric Design Improvements for Femoral Graft-Artery Junctions Mitigating Restenosis
,”
J. Biomech.
0021-9290,
29
, pp.
1605
1614
.
38.
Moore
,
J. A.
,
Steinman
,
D. A.
,
Prakash
,
S.
,
Johnston
,
K. W.
, and
Ethier
,
C. R.
, 1999, “
A Numerical Study of Blood Flow Patterns in Anatomically Realistic and Simplified End-to-Side Anastomoses
,”
J. Biomech. Eng.
0148-0731,
121
, pp.
265
272
.
39.
Giordana
,
S.
, 2004, “
Geometrical Reconstruction From Medical Images, Classification and Modelling of Arterial by-Pass Grafts
,” PhD thesis, Dept. of Aeronautics, Imperial College London.
40.
Giordana
,
S.
,
Sherwin
,
S. J.
,
Peiró
,
J.
,
Doorly
,
D. J.
,
Papaharilaou
,
Y.
,
Caro
,
C. G.
,
Watkins
,
N.
,
Cheshire
,
N.
,
Jackson
,
M.
,
Bicknall
,
C.
, and
Zervas
,
V.
, 2005, “
Automated Classification of Peripheral Distal by-Pass Geometries Reconstructed From Medical Data
,”
J. Biomech.
0021-9290,
38
, pp.
47
62
.
41.
Jackson
,
M.
,
Bicknell
,
C.
,
Zervas
,
V.
,
Cheshire
,
N. J. W.
,
Sherwin
,
S. J.
,
Giordana
,
S.
,
Peiró
,
J.
,
Papaharilaou
,
Y.
,
Doorly
,
D. J.
, and
Caro
,
C. G.
, 2003, “
Three-Dimensional Reconstruction of Autologous Vein Bypass Distal Anastomoses Imaged by Magnetic Resonance: Clinical and Research Applications
,”
J. Vasc. Surg.
0741-5214,
38
, pp.
621
625
.
42.
Crane
,
J. S.
,
Jackson
,
M. J.
,
Bicknell
,
C. D.
,
Giordana
,
S.
,
Peiró
,
J.
,
Doorly
,
D. J.
,
Sherwin
,
S. J.
,
Cheshire
,
N. J. W.
, and
Caro
,
C. G.
, 2003, “
In Vivo Geometric Features of Distal Vein Graft Anastomoses: Magnetic Resonance Surface Reconstruction in Different Graft Techniques
,” Manchester, May 7–9, Association of Surgeons of Great Britain and Ireland.
43.
Peiró
,
J.
,
Giordana
,
S.
,
Griffith
,
C.
, and
Sherwin
,
S. J.
, 2002, “
High-Order Algorithms for Vascular Flow Modelling
,”
Int. J. Numer. Methods Fluids
0271-2091,
40
, pp.
137
151
.
44.
Eck
,
M.
,
DeRose
,
T.
,
Duchamp
,
T.
,
Hoppe
,
H.
,
Lounsbery
,
M.
, and
Stuetzle
,
W.
, 1995, “
Multiresolution Analysis of Arbitrary Meshes
,” in
Computer Graphics Proceedings, SIGGRAPH95
, pp.
173
180
.
45.
Sherwin
,
S. J.
, and
Peiró
,
J.
, 2000, “
Mesh Generation in Curvilinear Domains Using High-Order Elements
,”
Int. J. Numer. Methods Fluids
0271-2091,
53
, pp.
207
223
.
46.
Sherwin
,
S. J.
, and
Karniadakis
,
G. E.
, 1995, “
A Triangular Spectral Element Method: Applications to the Incompressible Navier-Stokes Equations
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
123
, pp.
189
.
47.
Sherwin
,
S. J.
, and
Karniadakis
,
G. E.
, 1996, “
Tetrahedral hp Finite Elements: Algorithms and Flow Solutions
,”
J. Comput. Phys.
0021-9991,
124
, pp.
14
45
.
48.
Karniadakis
,
G. E.
,
Israeli
,
M.
, and
Orszag
,
S. A.
, 1991, “
High-Order Splitting Methods for the Incompressible Navier-Stokes Equations
,”
J. Comput. Phys.
0021-9991,
97
, pp.
414
443
.
49.
Caro
,
C. G.
,
Pedley
,
T. J.
,
Schroter
,
R. C.
, and
Seed
,
W. A.
, 1978,
The mechanics of the circulation
,
Oxford University Press
.
50.
Doorly
,
D. J.
,
Sherwin
,
S. J.
,
Franke
,
P. T.
, and
Peiró
,
J.
, 2002,
Vortical Flow Structure Identification and Flow Transport in Arteries
.
Computer Methods in Biomechanics and Biomedical Engineering
,
5
(
3
), pp.
261
275
.
51.
Dean
,
W.
, 1928, “
The Streamline Motion of Fluid in a Curved Pipe
,”
Philos. Mag.
0031-8086,
5
, pp.
673
695
.
52.
Coppola
,
G.
,
Sherwin
,
S. J.
, and
Peiró
,
J.
, 2001, “
Non-Linear Particle Tracking for High-Order Elements
,”
J. Comput. Phys.
0021-9991,
172
, pp.
356
380
.
53.
Leuprecht
,
A.
,
Perktold
,
K.
,
Prosi
,
M.
,
Berk
,
T.
,
Trubel
,
W.
, and
Schima
,
H.
, 2002, “
Numerical Study of Hemodynamics and Wall Mechanics in Distal End-to-Side Anastomoses of Bypass Grafts
,”
J. Biomech.
0021-9290,
35
, pp.
225
236
.
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