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Blood Flow Characteristics in a Femoral Artery Bypass Graft.

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Dev. Chem. Eng. Mineral Process., I I (1/2)t pp. 15-28, 2003.
Blood Flow Characteristics in a Femoral
Artery Bypass Graft
J.S. Cole* and J.K. Watterson
School of Aeronautical Engineering, The Queen s University of Belfast,
~ ~ r a n m i ~Road,
l i s Belfast BT9 5AG, Northern Ireland, UK
and M.J.G. O’Reilly
Vascular Surgical Unit, BeIfast City Hospital, BeIfast BT9 7AB,
Northern Ireland, UK
The development of disease at sites where a bypass grafr is attached to an artery is a
major cause of grafr failure. Localisation of this disease suggests that it may be
promoted by the local disturbedjlow field.
Computational Fluid Dynamics (CFD) simulations of the pulsatile, nonNewtonian flow of blood through a life-likefemoral artery bypass configuration have
been performed in order to further the understanding of bypass flows, and to identi&
aspects of the flow which encourage the progression of disease. It may then be
possible to develop more effective bypass systems.
The grafr/artery junction flow is characterised by extensive recirculation, flow
separation and reversal, complicated flow paths, elevated fluid particle residence
times, and an unusual wall shear stress distribution. It is believed that the occurrence
of disease is related to high particle residence times and the unnatural shear stresses
acting on the artery wall.
Introduction
Cardiovascular disease, which encompasses disease of the heart and circulatory
system, is the principal cause of death in the United Kingdom. In a typical year,
cardiovascular disease is responsible for more than 260,000 deaths [ 11. This
represents 41% of all deaths in the United Kingdom. The statistics for Northern
Ireland, in particular, are worse. Here, coronary heart disease is the main cause of
death, while stroke is the fourth most common cause of death and is the leading cause
of disability [2].
*Authorfor correspondence.
15
J.S.Cole, J.K. Watterson, and MJ.G. O’Reiily
The foremost underlying contributor to cardiovascular disease is atherosclerosis, a
degenerative disease of medium and large arteries. This disorder is characterised by
the patchy thickening of the artery wall due to the accumulation of fatty material. The
disease process occurs over a lifetime and results in the gradual narrowing of the
blood vessel. Severe atherosclerosis reduces the blood supply below the arterial
narrowing - a critical condition. An arterial bypass procedure is a common and well
established treatment for atherosclerotic vessels. This entails the surgical attachment
of a bypass graft from above the area of narrowing to a relatively disease-free vessel
below this site. A new route is created, enabling an adequate supply of blood to be
restored to the part of the artery beyond the blockage. The bypass graft may be of a
prosthetic material, or comprise a segment of vein harvested fiom the patient’s leg.
Unfortunately, the effectiveness of the bypass is compromised in the medium and
long term by the development of anastomotic intimal hyperplasia. This abnormal,
progressive thickening of the innermost layer of the artery wall is observed to occur
predominantly at the distal anastomosis of a bypass system, as depicted in Figure 1,
being especially prominent at the heel, toe and along the suture line where the graft is
fixed to the recipient vessel, and on the artery floor opposite the junction [3]. Intimal
hyperplasia causes the gradual narrowing of the vessel lumen, restricting the flow of
blood, and is a major factor responsible for bypass graft failure [4]. Eventually, the
graft may become totally occluded or a blood clot may form.
Mechanisms for intimal hyperplasia are unclear, but it is believed that many
interrelated issues are involved [4-61. These include a defect or injury to the
endothelium (the inner lining of the artery wall) at anastomotic sites, complicated
interactions between elements of the blood and the vessel wall, and the mismatch in
the mechanical properties of the graft and artery [7, 81. Significantly, the focal nature
of the intimal hyperplasia indicates that local haemodynamic factors may play a key
role in its development [9].
Modelling of arterial bypass flows presents a number of challenges. Consideration
must be given to the pulsatile nature of blood flow, the material properties of blood
including its shear-thinning nature, and the non-linear distensibility of the artery walls.
It is agreed [lo] that in a study of arterial blood flow, it is of primary importance to
employ a realistic geometry and appropriate flow parameters, and to account for flow
pulsatility. Wall compliance and non-Newtonian rheology are believed to have
secondary influences on the fluid dynamics in medium and large arteries.
The aim of this study is to obtain, via numerical modelling, a definitive description
of the pulsatile, non-Newtonian flow of blood through a realistic model of a human
femoral artery bypass graft. Correlations between aspects of the flow and the
localised development of intimal hyperplasia are sought. With such knowledge, it
may be possible subsequently to modify the design of bypass prostheses, or to adjust
the surgical technique, in such a way that the graWartery junction will be less
susceptible to disease.
Model Geometry
The model host artery, representative of a human femoral artery, has an internal
diameter of 8 mm and is assumed to be filly occluded. The bypass graft is a circular
16
Blood Flow Characteristics in a Femoral Artery Bypass Graji
host artery
blockage / occlusion
intimal hyperplasia
',,
' ~ ~
.,., ~ floor I far wall
blood
flow
-
proximal
side-to-end
anastomosis
bypass graft
distal
end-to-side
anastomosis
Figure 1. Schematic of arterial bypass system showing typical distribution of
anastomotic intimal hyperplasia.
Figure 2, Femoral artery bypass model.
17
J.S. Cole, J. K. Watterson,and M.J.
G. 0'Reiily
tube of internal diameter 6 mm, symbolising a synthetic graft. The graft is of length
14 cm and follows the arc of a circle, making an angle of 20" with the host artery at
both junctions. It is believed that, due to physical constraints, this is the smallest
angle at which the surgeon can suture the graft to the artery. The artery and graft
walls are assumed to be rigid. It is claimed that such an idealisation can be made
when only local flow patterns in short segments of large arteries are of interest [1 1,
121. These conditions prevail in the current study.
The filly structured grid, containing approximately 97,000 active cells, overlaying
the bypass geometry is presented in Figure 2. The host artery is continued 25 artery
diameters upstream from the proximal anastomosis. This extended inflow channel
would provide for the desired filly developed flow profiles on arrival at the
anastomosis, despite the condition of a time-dependent, uniform velocity profile
specified at the inlet boundary. The outlet boundary was placed at approximately 12
artery diameters downstream from the distal junction, at sufficient distance so as not to
affect the computed junction flow behaviour. It had previously been established that
grid independent solutions would result using this mesh. Additional computations for
Newtonian and non-Newtonian pulsatile flow were obtained on a finer mesh
consisting of approximately 250,000 active cells. Very similar flow fields were
achieved on the two meshes, and the agreement between predicted wall shear stress
distributions was generally better than 95%. Therefore, the original grid was
considered satisfactory.
Numerical Model and Flow Conditions
The density of the blood is 1050 kg m-3. A power law was employed to account for
the non-Newtonian, shear-thinning nature of blood:
Pen -
w-'
p,, is the effective viscosity,
is the magnitude of the local shear rate, and
the constants k = 0.042 kg m-' s"-* and n = 0.61. This relation is a good fit to the
dynamic viscosity curve for human blood with a haematocrit of 45% [ 131.
Blood flow through the femoral artery bypass has the attributes of threedimensional, time-dependent, incompressible, isothermal, laminar flow. The
governing equations for such a flow are:
where
v*u=o
au
p -+ p(u * v)u = -vp
at
Continuity equation
+ v .(p
, , &
vu)
Navier-Stokes equations
where u is the velocity vector, p is the density, t is the time, andp is the pressure.
18
Blood Flow Characteristics in a Femoral Artery Bypass Graji
time I s
Figure 3. Femoral artery volumeJlow pulse.
(SA - Acceleration phase; M - Maximum pow; SDI, SD2, SD3 Deceleration phase; D - Late cycle)
The commercial Computational Fluid Dynamics (CFD) flow solver FLUENT 4
[ 141, based on the finite volume method [ 151, was used to obtain a numerical solution
to the governing equations.
Flow simulations were conducted under representative physiological conditions.
A time-dependent velocity, calculated fiorn the femoral artery volume flow pulse [ 161
(see Figure 3), was applied at the inflow boundary. The mean flow rate of 2.25 ml s-',
analogous to a mean flow velocity of 4.48 cm s-', is comparable to measured femoral
artery bypass flow rates. The mean femoral artery Reynolds number, based on arterial
diameter and a reference blood viscosity of 0.0035 kg m-' s-', is 107. (The reference
viscosity is the blood viscosity at high shear rates when its behaviour approaches that
of a Newtonian fluid.) The maximum Reynolds number during the cycle is 830.
Assuming a typical heart rate of 75 beats per minute, the period of each cycle is 0.8 s.
FLUENT'S OUTLET condition was stipulated at the artery outflow boundary,
requiring that the gradients in the flow variables (except pressure) be zero in the flow
direction at this site. Such a condition is acceptable, the boundary having been
located sufficiently far downstream from the junction and the associated junction flow
disturbances. The no-slip condition was applied at all walls.
Each pulse cycle was divided into 320 time steps of size 2.5 ms. The computation
of 1.3 cycles was necessary in order to eradicate any start-up effects and achieve
repeatability between flow patterns computed in successive cycles. Extensive
validation of this numerical model has been accomplished [ 171.
19
J.S. Cole, J. K. Watterson, and M.J. G. 0 'Reilly
Figure 4.
Flow patterns at the downstream graftartery junction in the symmetry
plane at various times during the cycle. (Arrow length is directly
proportional tofluid speed)
20
Blood Flow Characteristics in a Femoral Artery Bypass Graft
4e. Late cycle (0).
Figure 4. Continued.
21
J.S. Cole, J.K. Watterson, and M.J. G. 0 'Reilly
Results
The flow patterns within the bypass system exhibited very complicated temporal and
spatial variations during the cardiac cycle. Since disease is much more likely to
develop at the downstream junction, this paper concentrates on reporting the flow
features at that site.
During the acceleration phase of the cardiac cycle, local flow disturbances are low
(see Figure 4a). The characteristic features of separation at the heel (H) and a
stagnation point (SP) on the artery floor opposite the junction are present. A zone of
low momentum, recirculating fluid (R) is contained between the junction and the
blockage in the artery. Separation does not yet arise at the toe (T) and the velocity
distribution across the channel downstream fiom the junction is symmetric.
At the maximum flow rate (see Figure 4b), the fluid exiting the graft tends to
continue across the channel and impacts on the far wall of the artery. Separation at the
toe is encouraged, the floor stagnation point drifts downstream, while the recirculation
(R) over the heel is enlarged.
The junction flow disturbances are greatly magnified throughout the deceleration
phase. The blood flow at the junction is increasingly driven across the vessel in the
direction of the far wall. The separation region (S) develops downstream from the toe
(see Figure 4c). The recirculatory motion (R), formerly located close to the heel,
becomes more elongated in shape and is drawn downstream to sit opposite the centre
of the junction. Some fluid particles depart this region, flowing past the heel and
upstream along the graft wall.
With further deceleration, the bypass flow is completely reversed and the stagnant
flow distal to the toe moves back towards the junction (see Figure 4d). The expansive
recirculation progresses towards the interface between the graft and artery.
The local flow patterns are less dramatic during the remainder of the cardiac cycle
when the flow returns to the primary direction and the flow velocities are much lower
than those occurring earlier (see Figure 4e).
The skewing of the flow within the bypass graft, and as the fluid turns through the
junction, generates secondary motions which are essential to the flow topology and
which influence the residence times of blood elements in the vicinity of the junction.
Secondary flow is particularly noticeable during the deceleration phase.
Figure 5 traces the development of the secondary motion in a cross-plane located
at one arterial diameter downstream from the toe. At the maximum flow rate, motion
across the vessel is apparent (see Figure 5a). Secondary flow grows over the
deceleration phase (see Figure 5b). The high momentum fluid in the symmetry plane
is increasingly deflected across the channel towards the far wall on returning from the
graft to the artery (see Figure 4c). In turn, the blood close to the side walls is
constrained to pass circumferentially in the opposite direction. It is thus demonstrated
that the fluid advances downstream along helical paths during this phase of the cardiac
cycle.
Secondary flow at this location subsequently becomes more influential (see Figure
5c). However, some of the fluid particles sweeping over the side walls are now
dragged upstream within the swelling separation region at the near wall, causing their
residence times in the vicinity of the junction to lengthen. At other times during the
cycle, motion in cross-flow planes is relatively weak.
22
Blood Flow Characteristics in a Femoral Artery Bypass Graji
Wall shear stress is a crucial variable associated with intimal thickening. Figure 6
plots the shear stress distribution along the far wall of the host artery at different times
during the cycle. The most notable spatial and temporal variations in the shearing
force occur opposite the junction. In this region, large shear stress magnitudes are
detected during the early part of the cycle as the powerful systolic flow issuing from
the bypass impacts on the artery floor. The negative shear stresses are related to the
zone of recirculating fluid confined between the mainstream and the occlusion with
fluid in this region passing upstream along the far wall of the vessel. Moreover, the
local shear stress alters sharply over a narrow section of the endothelium, of about
three artery diameters in length, where the flow divides about the floor stagnation
point. This gives rise to elevated spatial gradients of wall shear stress so that the
artery wall is subjected to a stretching action. During the later part of the cycle, wall
shear stress levels are low and show little variation along the wall due to the depressed
flow rate and associated more quiescent flow behaviour. Further downstream in the
artery, at all times, the wall shear stress attains a constant value as fully developed
flow is achieved. Between the junction and the occlusion, the shear stress is
continually very low due to the stagnant flow in that region.
Discussion
It is increasingly acknowledged that vascular biological processes are influenced by
the local haemodynamics. In vivo experiments have demonstrated that augmenting the
blood flow rate, and hence wall shear stress, inhibits the proliferation of intimal
thickening in PTFE grafts [18-201. The existence of flow disturbance at the
graft/artery junction has been highlighted [21]. In vitro and numerical studies have
confirmed that the junction flow patterns are strongly dependent on the local geometry
[22-251. Correlations have been made between the anastomotic regions susceptible to
disease and the features of flow separation, recirculation, elevated particle residence
times, and the unsteady wall shear stress distribution. It was shown that under
exercise conditions, the distal junction flow contained more vigorous axial and
secondary motions which amplified wail shear stress magnitudes and reduced the
areas affected by high particle residence times [26]. It is relevant that arteries
establish a diameter which, under normal flow conditions, results in a mean fluid
dynamic wall shear stress in the range 1-2 Pa [27]. lntimal thickening could be an
adaptive response of the live arteries to the disturbed flow conditions in an attempt to
restore a wall shear stress level within the normal range [20,28].
The current study has identified several important characteristics of the junction
haemodynamics including extensive recirculation (especially at the distal junction),
flow separation and reversal, complicated flow paths, elevated fluid particle residence
times, and an unusual unsteady floor shear stress distribution. Here, associations
between these aspects of the disturbed flow and the preferential sites for disease are
considered.
23
J.S. Cole, J. K. Watterson, and M.J.G. O'Reilly
ARTERY FLOOR
ARTERY FLOOR
5a. Maximum flaw (M).
5b. Deceleration (Sol).
ARTERY FLOOR
Sc. Deceleration
Figure 5.
Secondary jlow at one arterial diameter downstreamfrom the junction at
various times during the cycle.
24
Blood Flow Characteristics in a Femoral Artery Bypass Graft
It has been advocated that the intimal thickening at the heel, toe, and suture line arises
from injury to the vessel wall induced by the surgical procedure, and is promoted by
the compliance mismatch between the graft material and the artery [9]. The flow
conditions at the distal anastomosis may also favour the progression of intimal
hyperplasia at the heel and toe. In the vicinity of the heel, the flow within the
occluded segment of the artery exhibits a large, low momentum recirculation. The
residence times of blood elements in this region will be augmented, thus increasing the
likelihood of adhesion of platelets and leukocytes to the endothelium, and leading to
the stimulation of intimal thickening.
It is probable that intimal thickening at the toe of the anastomosis is promoted in
like manner. Fluid particle residence times are elevated when flow separation arises
just downstream from the toe during the flow deceleration phase, while the subsequent
migration of the vortical structure towards the grawartery interface is followed by
stagnation in the graft upstream from the toe, facilitating interaction between the blood
and the thrombogenic prosthetic surface of the graft. One way of alleviating the
problems at the toe may be to modify the design of the bypass in that region, with a
gentle expansion at the end of the graft in a fashion similar to that proposed by some
surgeons [29].
Haemodynamic events surely fulfil a more prominent role in the development of
intimal hyperplasia on the floor of the artery opposite to, and isolated fiom, the distal
anastomosis. Some have linked this intimal thickening to flow stagnation and low
shear stress on the floor [22]. However, this study has identified that the distal floor
stagnation point travels rapidly downstream. Moreover, strong flow alongside the
floor, in both the downstream and upstream directions, was demonstrated during the
early part of the cycle along with the related, relatively high wall shear stress levels.
This flow behaviour, and the lack of a concentrated low shear region, suggests that a
low shear mechanism for intimal thickening, involving the aggregation of platelets and
leukocytes, is unlikely at this location.
The spatial gradient of shear stress implies that the endothelial cells on the floor
are experiencing a stretching force, the magnitude of which varies over the cardiac
cycle. This cyclic, unnatural, sharp stretching of the endothelial cells, caused by the
changing spatial gradients of the wall shear stress, may promote intirnal hyperplasia,
possibly due to the activation of cellular reactions or through endothelial deformation
or injury [30,3 13.
Studies such as this one, which provide a detailed description of the junction flow
field, are important as attempts continue to determine which aspects of the
haemodynamics promote the progression of the disease. If these detrimental flow
conditions are identified, then efforts can be concentrated on modifying the bypass
flow field, possibly by improving bypass graft design, so that the anastomotic regions
will be less susceptible to disease. If successful, then the consequences for the patient,
in terms of a better quality of life, are obvious.
Finally, researchers have recently been attempting to improve the arterial blood
flow models. Non-invasive magnetic resonance imaging has been used to provide
vessel geometry data for specific patients [32]. The incorporation of such geometries
into the CFD models will permit an enhanced appreciation of the flow behaviour in
the human arterial system.
25
J.S. Cole, J.K. Watterson, andA4.J.G. O'Reilly
4
3
2.
k
L*3X;I
-1175
0
235
235
-2 r
-3 ;
-4 -5
-5
distance along artery I mrn
66. Maximumjlow (M).
6a. Acceleration (SA).
4.
<
A
.)
f
-3.
4-
-5.
4.
4.
3.
f
distance along artery I mm
2
V
c
3.
2-
:-
3 1
2-
.3.
-4.
-5
-5.
dmbnce along artery1 mm
dmbncs along amry I mm
6c. Deceleration (Sol).
r;
I -
6d. Deceleration (SD3).
1
dmbnce along amry I mrn
6e. Late cycle (0).
Figure 6. Shear stress distributions along the artery wall opposite thejunction at
various times during the cycle. Points opposite the Heel and Toe are
denoted by
26
* and
X
respective&.
Blood Flow Characteristics in a Femoral Artery Bypass Grap
Conclusions
A CFD simulation of pulsatile, non-Newtonian blood flow through a realistic model of
a femoral artery bypass graft has been performed. Significant temporal and spatial
variations in the gramartery junction flow field are predicted. Important features of
the junction flow include extensive recirculation, flow separation and reversal,
complicated three-dimensional flow paths, elevated fluid particle residence times, and
an unusual wall shear stress distribution. It is suggested that the progression of
disease at the gramartery junction is influenced by the local flow behaviour and that
graft performance will be enhanced by procedures which promote smoother flow
patterns and a less adverse shear stress distribution on the artery wall.
There is tremendous potential for the application of CFD to biological flow
systems, to the development of medical devices, and in other related industries.
Nomenclature
Non-Newtonian power law parameter,
measure of average viscosity (kg m-'s " - ~
Non-Newtonian power law parameter,
measure of deviation from Newtonian
fluid behaviour
Pressure
( Pa 1
Time
(s)
Velocity vector ( m s" )
Subscripts
eff effective
Greek letters
? shear rate
(s-'
. ,
p dynamic viscosity (kg m-' s-' )
p density
(kg
1
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