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TECHNICAL PAPERS: Fluids/Heat/Transport

Local and Global Geometric Influence on Steady Flow in Distal Anastomoses of Peripheral Bypass Grafts

[+] Author and Article Information
S. Giordana, J. Peiró, D. J. Doorly, J. S. Crane, K. E. Lee, N. J. Cheshire, C. G. Caro

Department of Aeronautics, Department of Bioengineering and Regional Vascular Unit, St Mary’s Hospital,  Imperial College London, London U.K.

S. J. Sherwin1

Department of Aeronautics, Department of Bioengineering and Regional Vascular Unit, St Mary’s Hospital,  Imperial College London, London U.K.s.sherwin@imperial.ac.uk

1

Author for correspondence

J Biomech Eng 127(7), 1087-1098 (Jun 15, 2005) (12 pages) doi:10.1115/1.2073507 History: Received July 28, 2004; Revised June 15, 2005

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.

Copyright © 2005 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

(a) Definition of the angles between the graft and proximal host vessel (GPA), between the proximal and distal host vessel (PDA) and between the graft and distal host vessel (GDA). (b) Definition of planarity based upon the angle I formed by the graft and a reference plane that contains the anastomosis. (c) Example of a planar anastomosis.

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Figure 2

High-order computational meshes of the distal anastomosis for (a) study 1, (b) study 2, and (c) study 3. The letters G, P, and D denote the graft, the proximal and the distal part of the host vessel respectively. In all the computations presented, the graft is considered as an inflow and the proximal and distal host vessels are outflow vessels. Plots (d)–(f), indicate the graft path for the anastomoses shown in plots (a)–(c), respectively.

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Figure 3

(a) Distribution of the average diameter along the medial line of the blood vessels of study 1. (b) Medial lines and cross sections used to determine the average diameters; the arrows indicate the direction of the parameterisations of the medial lines, which start from the common point and end at the extremities.

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Figure 4

Two views of the shear stress map for study 1 with indicated salient values. The shear stress is nondimensionalised by the inflow wall shear stress at the same Reynolds number.

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Figure 5

(a) Isosurface of velocity V=1.2V¯; the arrow points at the skewed core velocity profile typical of curved tubes. (b) Isosurface of velocity V=0.6V¯. (c) Position of three inspection slices shown in (d)–(f). (d) Contours of nondimensional velocity magnitude V∕V¯ at station 1 and in-plane streamlines indicating the counter-rotating Dean vortices; the letters I and O indicate the inner and the outer walls with respect to the center of curvature. (e) and (f) Contours at stations 2 and 3 as indicated in (c) demonstrating the deceleration of the flow in the anastomosis.

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Figure 6

Trajectories of fluid particles: (a) Ring of particles distributed along a circle of 3∕4 the diameter of the graft. (b) Later evolution of the motion of the ring 3∕4 the diameter of the graft. (c) Evolution of a ring of particles of 1∕4 the diameter of the graft, at the same time intervals used for the larger ring in (a).

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Figure 7

Follow up study of the anastomosis in study 1. (a) Nondimensional wall shear stress magnitude distribution and (b) isosurface of velocity V=0.6V¯ one week post-operatively. (c) Reconstruction of the same anastomosis six weeks post-operatively. The proximal host vessel is occluded and the anastomosis tends to narrow around the faster fluid distal to the hood and at the floor.

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Figure 8

Three views of the shear stress magnitude map for study 2. The shear stress is nondimensionalized by the wall shear stress at the inflow at the same Reynolds number. The gray scale isocontours used in these plots are identical to Fig. 4.

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Figure 9

Isosurfaces of velocity for study 2. (a) The isosurface V=1.2V¯ highlights areas of slow fluid at the toe of the anastomosis. (b) The isosurface V=1.8V¯ shows the flow accelerating through the restriction in the graft. (c) A detail of the isosurface V=2.5V¯ shows high velocity gradients at the floor.

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Figure 10

Trajectories of fluid particles for study 2. (a) Ring of particles at 3∕4 of the diameter of the inflow to the graft. (b) Later evolution of the motion of the ring at 3∕4 of the diameter of the graft. (c) Evolution of a ring of particles at 1∕4 of the diameter of the graft at the same time instances used for the larger ring.

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Figure 11

Geometrical evolution of study 2. (a) Shear stress map three weeks post-operatively. (b) Shear stress map two months post-operatively. (c) Six months post-operatively. (d) Nine months post-operatively. This anastomosis occluded in the next three months.

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Figure 12

(a) Distribution of the average diameter along the medial line of the blood vessels for study 3. (b) Medial lines and cross sections used to determine the average diameters; the arrows indicate the direction of the parameterizations of the medial lines, which start from the common point and end at the extremities.

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Figure 13

Two views of the normalized shear stress map for study 3. Contour levels range are identical the the two previous figures.

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Figure 14

Isosurfaces of velocity for study 3. (a) The isosurface V=V¯. (b) Isosurface of velocity V=1.2V¯ which indicate high velocity gradients at the anastomosis floor.

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Figure 15

Trajectories of fluid particles for study 3. (a) Ring of particles at 3∕4 of the graft’s diameter. (b) Later evolution of the ring at 3∕4 of the graft’s diameter. (c) Ring of particles of at 1∕4 of the graft’s diameter. (d) Later evolution of the movement of the ring at 3∕4 of the graft’s diameter. The wider GPA and the perianastomotic graft stenosis cause the two rings to mix within the anastomosis. (e) Some particles belonging to the faster ring and marked with the + sign eventually exit the anastomosis via the proximal host vessel.

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Figure 16

Evolution of the anastomosis of study 3. (a) Nondimensional wall shear stress one week post-operatively. (b) Reconstruction of the same anastomosis two years and four months post-operatively. The proximal host vessel is almost completely occluded as its flow generates almost no signal in the MRI.

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