Importance of flow division on transition to turbulence within an arteriovenous graft.

Abstract

Transitional blood flow in an arteriovenous graft under various conditions of flow division was examined through direct numerical simulation. This junction consists of an inlet vessel (prosthetic graft) connected to a host vessel (vein) at an acute angle (21.6 degrees ). Inlet Reynolds numbers, based on mean velocity and graft inlet diameter, ranged from 800 to 1400. Various flow divisions between the two ends of the host vessel (i.e., the proximal venous segment, PVS, and distal venous segment, DVS) were considered (PVS:DVS ratios of 100:0, 85:15, 70:30 and 115:(15)). The numerical technique employed the spectral element method which is a high-order discretization ideally suited to the simulation of transitional flows in complex domains. High velocity and pressure fluctuations were observed for the PVS:DVS=70:30 and 85:15 cases and absent from the 100:0 and 115:(15) cases; the results indicate the importance of flow division on the development of turbulence in this junction. Transition to turbulence was observed at Reynolds numbers as low as 1000 and 800 under flow divisions of 85:15 and 70:30, respectively, significantly lower than the critical value of 2100. The frequency spectra of velocity fluctuations indicated a significant intensity within the frequency range of approximately 300Hz downstream of the junction. An adverse pressure gradient developed in the PVS when graft inflow divided into opposite directions in the junction. This pressure gradient had a destabilizing effect on the flow and enhanced transition to turbulence in the PVS. These findings suggest that measurements of in vivo flow rates at the inlet and outlets are critical for the accurate prediction of arteriovenous hemodynamics. A potential clinical application of these results might be to close off the DVS during graft construction to ensure a 100:0 flow division.

Full text

Page 1

Journal of Biomechanics ] (]]]]) ]]]–]]]
Importance of flow division on transition to turbulence
within an arteriovenous graft
Sang-Wook Leea, David S. Smithb, Francis Lothb,c,?,
Paul F. Fischerd, Hisham S. Bassiounye
aImaging Research Laboratories, Robarts Research Institute, 100 Perth Drive, London, Ont., Canada N6A 5K8
bDepartment of Mechanical and Industrial Engineering, The University of Illinois at Chicago, 842 W. Taylor St., Chicago, IL 60607, USA
cDepartment of Bioengineering, The University of Illinois at Chicago, 851 S. Morgan St., Chicago, IL 60607, USA
dMathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439, USA
eDepartment of Surgery, The University of Chicago, 5841 S. Maryland Ave., Chicago, IL 60637, USA
Accepted 15 March 2006
Abstract
Transitional blood flow in an arteriovenous graft under various conditions of flow division was examined through direct
numerical simulation. This junction consists of an inlet vessel (prosthetic graft) connected to a host vessel (vein) at an acute angle
(21.61). Inlet Reynolds numbers, based on mean velocity and graft inlet diameter, ranged from 800 to 1400. Various flow divisions
between the two ends of the host vessel (i.e., the proximal venous segment, PVS, and distal venous segment, DVS) were considered
(PVS:DVS ratios of 100:0, 85:15, 70:30 and 115:(15)). The numerical technique employed the spectral element method which is a
high-order discretization ideally suited to the simulation of transitional flows in complex domains. High velocity and pressure
fluctuations were observed for the PVS:DVS ¼ 70:30 and 85:15 cases and absent from the 100:0 and 115:(15) cases; the results
indicate the importance of flow division on the development of turbulence in this junction. Transition to turbulence was observed at
Reynolds numbers as low as 1000 and 800 under flow divisions of 85:15 and 70:30, respectively, significantly lower than the critical
value of 2100. The frequency spectra of velocity fluctuations indicated a significant intensity within the frequency range of ?300Hz
downstream of the junction. An adverse pressure gradient developed in the PVS when graft inflow divided into opposite directions in
the junction. This pressure gradient had a destabilizing effect on the flow and enhanced transition to turbulence in the PVS. These
findings suggest that measurements of in vivo flow rates at the inlet and outlets are critical for the accurate prediction of
arteriovenous hemodynamics. A potential clinical application of these results might be to close off the DVS during graft
construction to ensure a 100:0 flow division.
r 2006 Elsevier Ltd. All rights reserved.
Keywords: Arteriovenous graft; Direct numerical simulation; Transition to turbulence; Flow division; Hemodynamics
1. Introduction
While much of the hemodynamics in a healthy human
body has low Reynolds number resulting in laminar
flow, relatively high Reynolds number flow is observed
at some specific locations, which can cause transition to
turbulence. For example, the peak Reynolds number in
the human aorta has been measured to be approxi-
mately 4000 (Ku, 1997). Surgical constructions such as
the arteriovenous (AV) graft, which consists of a
prosthetic graft material that is surgically attached
between an artery and a vein, also result in relatively
high Reynolds number flow (1000–3000, Fillinger et al.,
1990; Ram et al., 2003). Complex geometries such as a
severe stenosis can cause turbulent flow in the vascu-
lature as well (Hutchison and Karpinski, 1985). The
ARTICLE IN PRESS
www.elsevier.com/locate/jbiomech
www.JBiomech.com
0021-9290/$-see front matter r 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jbiomech.2006.03.024
?Corresponding author. Tel.: +13129963045;
fax: +13124130447.
E-mail address: floth@uic.edu (F. Loth).

Page 2

term turbulence refers to the motion of a fluid having
local velocities and pressures that fluctuate randomly.
AV grafts are constructed in a side-to-end fashion at
the arterial junction and an end-to-side manner at the
venous junction to provide an access point for
hemodialysis. By bypassing the high-resistance vessels,
these grafts provide high flow rates, which are necessary
for efficient dialysis. The sustained high flow rates make
the hemodynamics of the AV graft unique in the
vasculature with generally high wall shear stress (WSS)
acting on the vein, flow separation and recirculation,
and velocity and pressure fluctuations that vibrate the
vein wall and surrounding tissue. When coupled with the
complex geometries of the arterial and venous anasto-
mosis, blood flow can transition to a weakly turbulent
state that is often discerned by a palpable ‘‘thrill’’ or
audible ‘‘bruit’’ by a physician. The geometry examined
herein and the nomenclature employed are shown in
Fig. 1.
The prevalent cause of AV graft failure is occlusive
venous anastomotic intimal hyperplasia (VAIH), which
is manifest by a stenosis, or narrowing, of the vein
downstream of the graft (Kanterman et al., 1995). The
primary endpoint of AV graft failure is thrombosis
(Sirken et al., 2003). While the natural healing response
after surgery causes some degree of intimal thickening,
the biomechanical environment appears to be partly
responsible for progression of intimal thickening to
occlusive VAIH. Fillinger et al. (1990) have shown the
correlation of perivascular tissue vibration with VAIH
(r ¼ 0.92, po0.001) in a canine model and hypothesized
that the tissue vibration was caused by turbulent flow
because the Reynolds numbers were near the critical
value of 2100. These regions of high tissue vibration also
are regions of flow separation and recirculation, and
high and low WSS, which has been shown to play a
role in intimal thickening in arterial grafts (Loth et al.,
2002).
In order to better understand the biomechanical
environment within the venous anastomosis of an AV
graft, a numerical and in vivo experimental study were
performed in parallel using a canine animal model (Lee
et al., 2005). Measurements of vein-wall vibration
(VWV) during surgery were performed by using a laser
Doppler vibrometer and the results showed higher VWV
levels on the proximal venous segment (PVS) than on
the distal venous segment (DVS), which is similar to the
perivascular tissue vibration results reported by Fillinger
et al. (1990). The numerical study simulated the flow in
the same geometry under pulsatile flow conditions using
the flow waveforms acquired during surgery. The
simulation showed that while velocity and pressure
fluctuations were present, the flow remained laminar
throughout the cardiac cycle. These results were
unexpected because the in vivo VWV measurements
showed significant high-frequency vein-wall motion,
which could not have been due to the cardiac cycle
alone and was probably caused by transitional flow.
ARTICLE IN PRESS
Fig. 1. Nomenclature and spectral element mesh for the AV graft geometry (2640 hexahedral elements).
S.-W. Lee et al. / Journal of Biomechanics ] (]]]]) ]]]–]]]
2

Page 3

This led to an investigation of the potential sources of
transitional flow.
The computational fluid dynamics (CFD) simulation
(Lee et al., 2005) did not account for the non-Newtonian
nature of blood and the compliance of the vein wall. The
simulation based on a rigid-wall assumption seemed
reasonable since veins are known to have low compli-
ance at arterial pressures (less than 0.1%/mmHg for
canine femoral vein at 60mmHg, Brossollet, 1992) and
PTFE has even smaller compliance (0.01%/mmHg for
PTFE at 60–150mmHg). The assumption of a New-
tonian fluid seemed reasonable since blood exhibits a
Newtonian behavior at high rates of shear. However,
the effect of compliance and/or a non-Newtonian fluid
on flow stability is not well known.
Lee et al. (2005) accounted for flow pulsatility, which
for arterial flows has been shown to cause instability
after peak systole during the deceleration of the flow
(Mittal et al., 2003). However, since the mean compo-
nent dominates the flow profile in an AV graft and
pulsatility is small in comparison to the mean (Lee et al.,
2005; Shu et al., 1987), pulsatility alone was not
sufficient to cause the flow to become unstable.
Many experimental and computational studies for a
blood flow junction (end-to-side anastomosis) have been
performed and several have demonstrated flow distur-
bances. Ethier et al. (2000) described steady-flow
separation patterns in a 451 junction that resembles an
anastomosis with inlet Reynolds numbers in the range
250–1650 and zero flow in the DVS. Transition to
unsteadiness was observed experimentally at Re ¼ 1650
(Re—Reynolds number) by using the photochromic dye
tracer technique, but not at Re ¼ 1100. Loth et al.
(2003) reported significant levels of velocity fluctuations
in both experimental and computational studies for
Re ¼ 1820 in an AV graft geometry. However, they
found no evidence of velocity fluctuations at Reynolds
number 1060 with 11% flow entering the anastomosis
from the DVS. Crawshaw et al. (1980) investigated flow
disturbances in plastic models with inlet angles of 151
and 451 using flow visualization with a dye injection
technique. They showed that flow disturbances were
minimal when the inlet angle was low with the DVS
occluded. Hughes and How (1996) experimentally
visualized flow structures in models with different
anastomosis angles and flow divisions under steady
and pulsatile flow conditions. They too did not observe
any unsteadiness when the DVS was occluded. When
approximately one-third of the inlet flow passed up-
stream into the DVS, however, particles in the PVS were
observed to fluctuate radially at Re ¼ 630. Additionally,
experimental models of the AV graft flow loop have
been used to examine the local pressure drop with no
flow through the DVS (Jones et al., 2005; Van Tricht
et al., 2004). Van Tricht et al. (2004) cited flow
disturbances, which should be expected since the
Reynolds number was 2800. Jones et al. (2005) found
that their experimental data did not follow a sharp
transition from laminar to turbulent flow at Re ¼ 2000;
rather, the disturbed flow appeared to occur over a
range of Reynolds numbers. Thus, research suggests
that both flow division and Reynolds number determine
whether turbulence is present within the PVS. However,
the relative importance between flow division and
Reynolds number has not been established for AV
grafts. Therefore, the present study examines the
importance of flow division between the PVS and DVS
on the transitional nature of flow in the venous
anastomosis of an AV graft.
In order to capture the small-scale structures present
in a weakly turbulent flow of an AV graft, specialized
CFD techniques must be employed. Mittal et al. (2003)
simulated the pulsatile flow in a planar channel with a
one-sided semicircular constriction using direct numer-
ical simulation and large eddy simulation over a range
of Re from 750 to 2000. They reported complex flow
patterns downstream of the constriction and transition
to turbulent flow for Reynolds numbers higher than
?1000. The pressure and velocity fluctuations were
associated with the periodic formation of vortex
structures. Even though this geometric configuration
differs from the junction considered in our study, it
demonstrates that CFD can capture the complex
vortical structures as well as velocity and pressure
fluctuations provided specialized CFD techniques are
employed.
This paper presents numerical simulation results that
demonstrate the importance of flow division on transi-
tion to turbulence within the venous anastomosis of an
AV graft. Better understanding of the hemodynamic
forces within these grafts may be important in determin-
ing the underlying biomechanical cellular response, or
mechanotransduction, leading to graft failure. Validation
of the numerical approach used here has been reported
by Lee et al. (2006), who presented a detailed
comparison showing good agreement between experi-
ments and the present numerical simulations for
transitional flow within this same geometry.
2. Methods
2.1. Blood vessel junction geometry and computational
mesh
The blood vessel junction is the venous anastomosis
portion of an AV graft constructed in a canine model.
Details of the procedures for obtaining this geometry
have previously been reported (Lee et al., 2005).
Housing and handling of the animal were in compliance
with ‘‘Guide for the Care and Use of Animals’’
(National Academy of Sciences, copyright 1996).
ARTICLE IN PRESS
S.-W. Lee et al. / Journal of Biomechanics ] (]]]]) ]]]–]]]
3

Page 4

A perfusion fixed plastic cast of a canine venous
anastomosis was scanned by using a computerized
tomography (CT) scanner (GE Medical Systems, UK).
From these slice-based CT images, a three-dimensional
(3D) geometry was reconstructed with commercial
image-processing software (Mimics, Materialise, Bel-
gium). The prosthetic graft, DVS and PVS diameters
were 6, 6 and 6.5mm, respectively. This model geometry
was used to create a computational mesh. A 3D high-
quality computational mesh was created based on
isotemperature surfaces from heat-conduction-based
solutions, which guarantees orthogonality of elements
to the wall boundary with minimal deformation for
complex bifurcation geometries (Lee et al., 2000; Lee,
2002; Verma et al., 2005). The mesh comprised 2640
hexahedral elements and is shown in Fig. 1. For the
spectral element technique, this results in 2640?N3
nodes, where N is the polynomial order of the basis
function. The polynomial orders ranged from 9 to 14
and are shown for each case in Table 1.
2.2. Numerical techniques
The numerical solution considered the 3D unsteady
incompressible Navier–Stokes equations, given in non-
dimensional form by
qu
qtþ u ? ru ¼ ?rp þ1
Rer2u, (1)
r ? u ¼ 0,
where u ¼ ðu;v;wÞ and p are the non-dimensional
velocity and pressure, respectively. The equations are
non-dimensionalized by the characteristic length-scale d,
(2)
which is the graft inlet diameter, and the convective
time-scale, d/U0, where U0is the mean inflow velocity at
the graft inlet. The Reynolds number is Re ¼ U0d=n,
where n is the kinematic viscosity of fluid, which is the
ratio of dynamic viscosity to the density. A spectral
element method was employed, which is a high-order
weighted residual technique that has the advantage of
the tensor product efficiency of spectral methods with
the geometric flexibility of the finite element method.
This computational solution technique has been de-
scribed in detail in Fischer et al. (2002). Rigid walls and
Newtonian fluid assumptions were considered. The
venous anastomosis of an AV graft has been shown to
have high shear rates (Lee et al., 2005; Loth et al., 2003).
While blood is a non-Newtonian fluid, it acts much like
a Newtonian fluid at high rates of shear.
A fully developed (parabolic) velocity profile was
imposed on the graft inlet boundary. Although, the in
vivo flow waveform measured during the animal study
was pulsatile (Lee et al., 2005), the mean component of
flow was significantly greater than the pulsatile compo-
nent. Thus, steady inlet flow conditions were employed
in this study, which simplified the collection of statistics
and thus significantly reduced the computational ex-
pense. Note that the exact velocity distribution of the
flow entering the graft in vivo is unknown. However, a
known velocity profile is better than an arbitrary one. In
addition, a fully developed velocity profile has minimal
disturbances entering the anastomosis. For an occluded
DVS, a homogeneous Dirichlet condition (u ¼ 0) was
applied on the DVS boundary along with stress-free
conditions on the PVS outlet. When flow exited the
DVS, however, stress-free boundary conditions were
employed in both the PVS and DVS outlets with
additional treatments on each to obtain the desired flow
division. Further details of the boundary condition
treatment are given in Fischer et al. (2005) and Lee et al.
(2006).
The simulations were initiated at Re51 by assigning
the viscosity to 5000 times the normal value, and then
the Reynolds number was ramped up to the desired
value by exponentially decreasing the viscosity over one
to two flow-through times. No perturbations were
introduced into the flow field. The fluctuations naturally
occur due to the instability of the Navier–Stokes
equations.
Simulations were performed for Reynolds number
800, 1000, 1200 and 1400 with flow divisions of 100:0,
85:15, 70:30 and 115:(15). Here, (?) indicates that the
direction of DVS flow is negative and thus acts as an
inlet instead of an outlet. Animal measurements have
shown the flow in the DVS to be as high as 30% of the
graft inlet flow and to be either exiting or entering the
flow junction. A summary of all cases examined is
shown in Table 1. Initial transient results for approxi-
mately two flow-through times were discarded in the
ARTICLE IN PRESS
Table 1
Reynolds number, flow division and polynomial order of the basis
function in spectral element method for each case
Case
number
Re
Flow division (PVS:DVS)
% of graft flow
Polynomial
order
1
2
3
4
5
6
7
8
9
800
800
800
800
1000
1000
1000
1000
1200
1200
1200
1200
1400
1400
1400
1400
100:0
85:15
70:30
115:(15)
100:0
85:15
70:30
115:(15)
100:0
85:15
70:30
115:(15)
100:0
85:15
70:30
115:(15)
9
11
11
11
9
11
11
11
9
11
12
12
12
14
14
12
10
11
12
13
14
15
16
S.-W. Lee et al. / Journal of Biomechanics ] (]]]]) ]]]–]]]
4

Page 5

statistical analysis in order to ensure statistically
stationary results. Simulations have been conducted on
the Pittsburgh Supercomputing Center TCS1 and the
National Center for Supercomputing Applications
(NCSA) Xeon Linux Cluster with 1024 and 128 parallel
processors, respectively. Grid independence and a
comparison with experimental measurements were pre-
viously reported for the same geometry (Lee et al.,
2006).
3. Results
The overall flow patterns within the AV graft are
shown for four different flow configurations at Reynolds
number 1200 as time-averaged velocity vector plots at
the midplane in Fig. 2. The time-averaged axial velocity
distributions are given for various cross-sections in
Fig. 3 and demonstrate the complex nature of the flow
field. Typical contours of instantaneous transverse
ARTICLE IN PRESS
(a)
(b)
(c)
-3
(d)
-2 -1012345
2U0
2U0
2U0
2U0
x/d
Fig. 2. Time-averaged velocity vectors in the midplane for Re ¼ 1200: (a) PVS:DVS ¼ 100:0; (b) 85:15; (c) 70:30; (d) 115:(15). Note that (?) indicates
DVS flow direction is the same as PVS.
S.-W. Lee et al. / Journal of Biomechanics ] (]]]]) ]]]–]]]
5

Page 6

vorticity ozin Fig. 4 show the transitional nature of the
flow field under different flow conditions at Reynolds
number 1200. Similarly, typical contours of ozat the
midplane are shown at different Reynolds numbers for
the 70:30 flow division in Fig. 5.
An overview of the importance of flow division and
Reynolds number is given as cross-sectional views of the
root-mean-square (r.m.s.) of the axial velocity u0r.m.sin
the midplane and at the axial position of 3.33 graft
diameters downstream of the toe (Fig. 6). The axial
variation in the time-averaged pressure coefficient along
the floor of the vein is shown in Fig. 7 for Reynolds
number 1200 at flow division 100:0, 85:15, and 70:30.
Fig. 8 shows the time-averaged WSS magnitude
normalized by t0, which is the WSS of Poiseuille flow in a
straight pipe corresponding to the Reynolds number of
1200. Here, t0is computed as 32mQ=pd3, where Q is the
tw
jjhi,
flow rate in the pipe and d is the diameter of the straight
pipe. The r.m.s. of the WSS fluctuations t0r.m.sis shown
for the 70:30 case in Fig. 9 (values were not significant for
other flow divisions). The axial variation of the turbulent
kinetic energy (TKE) averaged over the cross-section is
shown in Fig. 10. Here, the TKE is defined as u0
The distribution of the TKE and Reynolds stress u0
normalized by U2
0, are shown at various cross-sections in
Fig. 11 for Reynolds number 1200 and flow division
70:30. Here, u0aand u0rare the velocity fluctuations in the
streamwise and radial direction, respectively.
iu0
?
i
au0
??=2.
r
?,
4. Discussions and conclusion
The results presented describe the flow environment
within an AV graft under various Reynolds numbers
ARTICLE IN PRESS
Fig. 3. The time-averaged axial velocity /uS, normalized by U0, at various locations for Re ¼ 1200: (a) PVS:DVS ¼ 100:0; (b) 85:15; (c) 70:30; (d)
115:(15). Note that (?) indicates DVS flow direction is the same as PVS. View is from PVS.
S.-W. Lee et al. / Journal of Biomechanics ] (]]]]) ]]]–]]]
6

Page 7

and flow conditions. As shown in Fig. 2, velocity profiles
are parabolic upon entry into the anastomosis and
become skewed toward the floor (similar to a jet near the
floor) within the PVS for each flow division. An
additional high velocity region was observed on the
hood side downstream of the toe of the graft for the flow
ratios 100:0 and 115:(15). This high velocity region does
not appear in the 70:30 and 85:15 cases since momentum
transfer is enhanced in these transitional flow cases such
that velocity peaks are reduced as flow moves through
the PVS and flow profiles become more uniform. While
the midplane gives an overview of the flow patterns, the
time-averaged axial velocity /uS at a cross-section
reveals the flow to be asymmetric and rather complex
(Fig. 3). High velocity (41m/s) was present near the
walls in the PVS, which indicates elevated WSS. The
axial velocity becomes nearly uniform without a distinct
high-velocity region as the flow convects downstream
for flow ratios of 85:15 and especially 70:30, which were
turbulent. In contrast, the regions of high axial velocity
remain distinct jets for the laminar cases 100:0 and
115:(15). The flow division 70:30 shows the largest
spatial variation of vorticity (Fig. 4c). Flow split 85:15
shows some fluctuations, while both 100:0 and 115:(15)
appear to be laminar. Time traces of axial velocity
fluctuations for the 70:30 case at Reynolds number 1200
revealed spectral broadening beyond the toe (x=d40:97)
with significant intensity within the frequency range
of 100–300Hz. The flow field becomes increasingly
complex with Reynolds number as well (Fig. 5), as
expected.
The flow remained laminar for the 100:0 and 115:(15)
cases (115:(15) cases are not shown in figure) for all
Reynolds numbers examined except Re ¼ 1400 (Fig. 6).
Transitional flow was observed at flow division 85:15
and 70:30 for all Reynolds numbers with the exception
of the 85:15 case at Reynolds number 800. Thus, the
flow field within this geometry can become transitional
at Reynolds numbers well below the critical value of
2100 provided that a portion of the inlet flow exits in the
DVS. While flow directed distally in the DVS is
unexpected because this segment (a section of vein)
normally carries blood back to the heart (i.e., same
direction as the PVS), it is still present in some cases for
a short period during systole and in other cases
throughout the cardiac cycle.
ARTICLE IN PRESS
Fig. 4. Typical contours of instantaneous transverse vorticity oz, normalized by U0/d, for Re ¼ 1200: (a) PVS:DVS ¼ 100:0; (b) 85:15; (c) 70:30; (d)
115:(15). Note that (?) indicates DVS flow direction is the same as PVS.
S.-W. Lee et al. / Journal of Biomechanics ] (]]]]) ]]]–]]]
7

Page 8

Differences in the transitional nature of the flow field
for changes in flow division in this geometry could be
caused by the pressure environment. The 100:0 case
shows a high-pressure region on the floor near and
downstream of the toe where the flow exiting the graft
impinges on the floor (Fig. 7). Otherwise, the general
trend is such that the pressure is higher in the graft and
decreases as flow exits the PVS, as is typically the case
with pressure driven flow in a constant diameter pipe. In
the 70:30 case, however, flow entering the anastomosis is
similar to a flow expansion since a greater cross-
sectional area is available to accommodate flow in the
two outlets (the PVS and DVS). This causes a lower
average velocity, and hence pressure rises in the PVS as
per the Bernoulli equation. Thus, flow entering the PVS
enters an unfavorable pressure gradient and is less stable
than that of the 100:0 case. This is similar to the lack of
stability of a flow in a diffuser as a result of an adverse
pressure gradient (Sano and Asako, 1993; Spencer et al.,
1995). This same trend in the distribution of the time-
averaged pressure coefficient was present at other
Reynolds numbers examined. In addition, previous
research (Forliti et al., 2005; Strykowski and Niccum,
1991) has shown that countercurrent jets, which create a
shear layer, have increased turbulence for counter-
current flows compared with concurrent flows. While
jet configurations are different from that of an AV graft,
similarities are present. DVS flow into the anastomosis
is similar to concurrent flow where laminar flow
conditions were obtained. DVS flow directed outward
appears similar to that of countercurrent flow particu-
larly at the midplane (see Fig. 2c, x/d ¼ 0) where
transition to turbulence occurs. These phenomena
underscore the importance of flow in a secondary
branch on the presence of turbulence.
The WSS distribution is quite complicated, with a
focal point of high WSS (4100dyn/cm2) occurring on
the floor of the vein near and downstream of the toe
(Fig. 8). The WSS distributions are similar for x/do2.0
for all flow divisions, while beyond this point the WSS is
greater for cases with increased PVS flow (i.e., 100:0 and
115:(15)). This variation in WSS distribution is con-
sistent with the skewed velocity profiles shown at the
midplane in Fig. 2. It is interesting to note that the WSS
distribution is nearly uniform within the PVS (x/d42)
for the transitional flow case in contrast to those cases
ARTICLE IN PRESS
Fig. 5. Typical contours of instantaneous transverse vorticity oz, normalized by U0/d, for various Reynolds numbers with PVS:DVS ¼ 70:30
condition: (a) Re ¼ 800; (b) 1000; (c) 1200; (d) 1400.
S.-W. Lee et al. / Journal of Biomechanics ] (]]]]) ]]]–]]]
8

Page 9

under laminar flow conditions. The r.m.s. of the WSS
fluctuations t0r.m.sfor the 70:30 case (Fig. 9) is complex.
Interestingly, maximum and minimum values of t0r.m.s
are located in regions of low and high WSS, respectively,
for the 70:30 case. While the biological importance of
this parameter is unknown at present, the plot shows
that some regions of relatively low WSS have significant
variation about that mean value.
The trend in axial variation of the TKE averaged over
the cross-section (Fig. 10) is similar to that described
previously in that turbulence is greater for higher
Reynolds numbers and for flow divisions with greater
DVS flow. The peak in TKE occurs farther downstream
in the PVS for the 85:15 case (x=d ? 5:0) than the 70:30
case (x=d ? 3:0). This is also true in the DVS, but the
difference is less. Reynolds number 1400 shows the peak
TKE to occur slightly upstream of the peak at lower
Reynolds numbers for both flow divisions. This is
similar to that found by Mittal et al. (2003) for turbulent
flow through a constricted channel flow. Also, interest-
ing is that while the TKE is greater within the PVS for
70:30 (Re ¼ 1200) than that at 85:15 (Re ¼ 1400), the
local Reynolds number within the PVS is actually lower
for the 70:30 case (RePVS¼ 1200?0.7 ¼ 840) compared
with that for 85:15 (RePVS¼ 1400?0.85 ¼ 1190) or
even for 100:0 (RePVS¼ 1400). This result demonstrates
ARTICLE IN PRESS
Fig. 6. The distribution of u0r.m.sat axial location, x/d ¼ 3.33, and in z-plane for Re ¼ 800, 1000, 1200 and 1400 and flow division values of 100:0,
85:15 and 70:30 (Note: 115:(15) case is similar to the 100:0 case).
S.-W. Lee et al. / Journal of Biomechanics ] (]]]]) ]]]–]]]
9

Page 10

the
Reynolds number on the transitional nature of these
flows. The maximum TKE and Reynolds stress at
Reynolds number 1200 and flow division 70:30 (Fig. 11)
are shown to be crescent shaped in the region where
high-velocity gradients were observed (x/d ¼ 3.13). The
importanceofflow divisioncompared with
TKE diffuses rapidly to the entire cross-section, how-
ever, and becomes uniformly distributed further down-
stream.
It is important to note that these results are for
steady-state conditions, a Newtonian fluid, rigid walls
and undisturbed flow entering the model. While the AV
graft flow waveform has a dominant steady component,
the pulsatile nature of the flow may still have an impact
on flow transition. Moreover, while one might expect
the non-Newtonian effects to be small for flows with
high shear rates such as that in an AV graft, the
importance of shear thinning fluids on transition to
turbulence has not been well documented and probably
warrants further study. Also, vein walls are less
compliant than arteries at arterial pressure. The
amplitude of in vivo VWV was reported to be less than
0.3% of the vein diameter in a canine AV graft model
(Lee et al., 2005). However, even a small amount of
compliance may play a role in the flow stability through
fluid–structure interaction; thus, compliance effects
should be further examined. Finally, flow entering the
graft in vivo is never perfectly parabolic and can even
contain disturbances depending on the geometry of the
ARTICLE IN PRESS
-3-2-1012345
-1.5
-1
-0.5
0
0.5
1
1.5
Cp
100:0
85:15
70:30
x/d
Fig. 7. The time-averaged pressure coefficient Cp¼ 2 p ? p0
the floor of vein at Re ¼ 1200.
??=rU2
0on
Fig. 8. The time-averaged WSS magnitude
ized by t0, on the vein wall at Re ¼ 1200: (a) PVS:DVS ¼ 100:0; (b)
70:30; (c) 115:(15).
tw
jjhi distribution, normal-
Fig. 9. The r.m.s. of WSS fluctuations t0r.m.sdistribution, normalized
by t0, on the vein wall for Re ¼ 1200 with PVS:DVS ¼ 70:30.
-3-2-101
x/d
2345
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Re= 1200, 85:15
Re= 1200, 70:30
Re = 1400, 100:0
Re= 1400, 85:15
Re = 1400, 70:30
k/U02
Fig. 10. Comparison of the TKE, normalized by U2
direction (values are computed by averaging over cross-sectional area
at each axial station).
0, along the axial
S.-W. Lee et al. / Journal of Biomechanics ] (]]]]) ]]]–]]]
10

Page 11

anastomosis (Lee et al., 2005). Unnikrishnan et al.
(2005) showed that the venous needle jet during
hemodialysis triggers turbulence downstream of the
needle and its effect can persist up to when flow enters
the venous anastomosis. Thus, the results presented
herein provide only a guide as to the importance of flow
division on the transitional nature of the flow in the
present graft geometry. Further research is required to
account for the effects of the assumptions listed above
both individually and together.
The importance of flow division described herein may
have been the cause of the discrepancy observed by Lee
at al. (2005) in that turbulence was not produced when
matching the in vivo pulsatile flow conditions. The
present study has shown that slight changes in DVS flow
conditions can cause transition to occur. Thus, measure-
ment accuracy of DVS flowrate in vivo is important.
Slight errors in the DVS flowrate measured by Lee et al.,
but within the published accuracy of the measurement
system, might account for the lack of transitional flow
observed.
High turbulence and/or high temporal gradients in
shear stress have long been implicated to stimulate
endothelial cell proliferation and vascular wall remodel-
ing. Davies et al. (1986) demonstrated that turbulent
fluctuating shear stress, rather than WSS magnitude
alone, significantly influences the endothelial cell turn-
over by in vitro experiment. White et al. (2001) and Ojha
(1994) also showed that temporal gradients in shear
stress, rather than spatial gradients, may induce
endothelial cell proliferation using a sudden expansion
flow chamber model and 301 anastomotic model,
respectively. More specifically, Loth et al. (2003)
reported that the region of high VWV is located at
elevated levels of mitogen activated protein kinases and
Fillinger et al. (1990) showed the perivascular tissue-
vibration, which appeared to be caused by turbulent
flow, is correlated with VAIH. Thus, a reduction of
turbulence intensity may prevent the development of
VAIH, and a detailed understanding of turbulence
characteristics in the AV graft will help identify the
turbulence source.
In conclusion, while the present CFD simulations
were made under assumptions that do not match
perfectly the in vivo environment, the overall impor-
tance of flow division on transition to turbulence in vivo
is expected to follow the same trend presented here.
Thus, the physiological significance of the present
finding is that distal flow within the DVS may promote
intimal hyperplasia that would lead to AV graft failure.
A potential clinical application of these results might be
to simply close off the DVS of the venous anastomosis
during graft construction to ensure a 100:0 flow division.
Acknowledgments
This work was supported by the Whitaker Founda-
tion (RG-01-0198); National Institutes of Health, RO1
Research Project Grant (2RO1HL55296-04A2); the
Mathematical, Information,
Sciences Division subprogram of the Office of Advanced
Scientific Computing Research, Office of Science, US
Department of Energy, under Contract W-31-109-Eng-38;
andComputational
ARTICLE IN PRESS
Fig. 11. (a) TKE and (b) Reynolds stress u0
au0
r
??, normalized by U2
0, for Re ¼ 1200 with PVS:DVS ¼ 70:30.
S.-W. Lee et al. / Journal of Biomechanics ] (]]]]) ]]]–]]]
11

Page 12

the NSF Pittsburgh Supercomputing Center; and the
National Center for Supercomputing Applications.
References
Brossollet, L.J., 1992. Effects of cryopreservation on the biaxial
mechanical properties of canine saphenous veins. Ph.D. Thesis,
Georgia Institute of Technology, Atlanta.
Crawshaw, H.M., Quist, W.C., Serallach, E., Valeri, C.R., LoGerfo,
F.W., 1980. Flow disturbance at the distal end-to-side anastomosis:
effect of patency of the proximal outflow segment and angle of
anastomosis. Archives of Surgery 115, 1280–1284.
Davies, P.F., Remuzzi, A., Gordon, E.J., Dewey Jr., C.F., Gimbrone
Jr., M.A., 1986. Turbulent fluid shear stress induces vascular
endothelial cell turnover in vitro. Proceedings of the National
Academy of Sciences of the United States of America 83,
2114–2117.
Ethier, C.R., Prakash, S., Steinman, D.A., Leask, R.L., Couch, G.G.,
Ojha, M., 2000. Steady flow separation patterns in a 45-degree
junction. Journal of Fluid Mechanics 411, 1–38.
Fillinger, M.F., Reinitz, E.R., Schwartz, R.A., Resetarits, D.E.,
Paskanik, A.M., Bruch, D., Bredenberg, C.E., 1990. Graft
geometry and venous intimal-medial hyperplasia in arteriovenous
loop grafts. Journal of Vascular Surgery 11, 556–566.
Fischer, P.F., Kruse, G.W., Loth, F., 2002. Spectral element methods
for transitional flows in complex geometries. Journal on Scientific
Computing 17, 81–98.
Fischer, P.F., Loth, F., Lee, S.W., Smith, D.S., Tufo, H.M.,
Bassiouny, H.S., 2005. Parallel simulation of high Reynolds
number vascular flows. In: Proceedings of the Parallel CFD,
University of Maryland, MD.
Forliti, D.J., Tang, B.A., Strykowski, P.J., 2005. An experimental
investigation of planar countercurrent turbulent shear layers.
Journal of Fluid Mechanics 530, 241–264.
Hutchison, K., Karpinski, E., 1985. In vivo demonstration of flow
recirculation and turbulence downstream of graded stenoses in
canine arteries. Journal of Biomechanics 18, 285–296.
Hughes, P.E., How, T.V., 1996. Effects of geometry and flow division
on flow structures in models of the distal end-to-side anastomosis.
Journal of Biomechanics 29, 855–872.
Jones, S.A., Jin, S., Kantak, A., Bell, D.A., Paulson, W.D., 2005.
Mathematical model for pressure losses in the hemodialysis graft
vascular circuit. Journal of Biomechanical Engineering 127, 60–66.
Kanterman, R.Y., Vesely, T.M., Pilgram, T.K., Guy, B.W., Windus,
D.W., Picus, D., 1995. Dialysis access grafts: anatomic location
of venous stenosis and results of angioplasty. Radiology 195,
135–139.
Ku, D.N., 1997. Blood flow in arteries. Annual Review of Fluid
Mechanics 29, 399–434.
Lee, S.E., Piersol, N., Loth, F., Fischer, P.F., Leaf, G., Smith, B.,
Yedavalli, R., Yardimci, A., Alperin, N., Schwartz, L., 2000.
Automated mesh generation of an arterial bifurcation based upon
in vivo MR images. In: Proceedings of the World Congress on
Medical Physics and Bioengineering, Chicago, IL.
Lee, S.E., 2002. Solution method for transitional flow in a vascular
bifurcation based on in vivo medical images. M.S. Thesis,
University of Illinois at Chicago, Chicago.
Lee, S.-W., Fischer, P.F., Loth, F., Royston, T.J., Grogan, J.K.,
Bassiouny, H.S., 2005. Flow induced vein wall vibration in an
arteriovenous graft. Journal of Fluids and Structures 20, 837–852.
Lee, S.-W., Smith, D.S., Loth, F., Fischer, P.F., Bassiouny, H.S., 2006.
Experimental and numerical simulation of transitional flow in a
blood vessel junction. Numerical Heat Transfer, in press.
Loth, F., Jones, S.A., Zarins, C.K., Giddens, D.P., Nassar, R.F.,
Glagov, S., Bassiouny, H.S., 2002. Relative contribution of wall
shear stress and injury in experimental intimal thickening at PTFE
end-to-side arterial anastomoses. Journal of Biomechanical En-
gineering 124, 44–51.
Loth, F., Fischer, P.F., Arslan, N., Bertram, C.D., Lee, S.E., Royston,
T.J., Shaalan, W.E., Bassiouny, H.S., 2003. Transitional flow at the
venous anastomosis of an arteriovenous graft: potential activation
of the ERK1/2 mechanotransduction pathway. Journal of Biome-
chanical Engineering 125, 49–61.
Mittal, S.P., Simmons, S.P., Najjar, F., 2003. Numerical study of
pulsatile flow in a constricted channel. Journal of Fluid Mechanics
485, 337–378.
Ojha, M., 1994. Wall shear stress temporal gradient and anastomotic
intimal hyperplasia. Circulation Research 74, 1227–1231.
Ram, S.J., Magnasco, A., Jones, S.A., Barz, A., Zsom, L., Swamy, S.,
Paulson, W.D., 2003. In vivo validation of glucose pump test for
measurement of hemodialysis access flow. American Journal of
Kidney Diseases 42, 752–760.
Sano, M., Asako, Y., 1993. Fluid flow and heat transfer in a
periodically diverging-converging turbulent duct flow. The Japan
Society of Mechanical Engineers International Journal 36,
207–213.
Shu, M.C., Noon, G.P., Hwang, N.H., 1987. Flow profiles and wall
shear stress distribution at a hemodialysis venous anastomosis:
preliminary study. Biorheology 24, 723–735.
Sirken, G.R., Shah, C., Raja, R., 2003. Slow-flow venous pressure for
detection of arteriovenous graft malfunction. Kidney International
63, 1894–1898.
Spencer, E.A., Heitor, M.V., Castro, I.P., 1995. Intercomparison of
measurements and computations of flow through a contraction and
a diffuser. Flow Measurement and Instrumentation 6, 3–14.
Strykowski, P.J., Niccum, D.L., 1991. The stability of countercurrent
mixing layers in circular jets. Journal of Fluid Mechanics 227,
309–343.
Unnikrishnan, S., Huynh, T.N., Brott, B.C., Ito, Y., Cheng, C.H.,
Shih, A.M., Allon, M., Anayiotos, A.S., 2005. Turbulent flow
evaluation of the venous needle during hemodialysis. Journal of
Biomechanical Engineering 127, 1141–1146.
Van Tricht, I., De Wachter, D., Tordoir, J., Verdonck, P., 2004.
Hemodynamics in a compliant hydraulic in vitro model of straight
vs. tapered PTFE arteriovenous graft. Journal of Surgical Research
116, 297–304.
Verma, C.S., Fischer, P.F., Lee, S.E., Loth, F., 2005. In: Proceedings
of the 14th International Meshing Roundtable, San Diego, CA.
White, C.R., Haidekker, M., Bao, X., Frangos, J.A., 2001. Temporal
gradients in shear, but not spatial gradients, stimulate endothelial
cell proliferation. Circulation 103, 2508–2513.
ARTICLE IN PRESS
S.-W. Lee et al. / Journal of Biomechanics ] (]]]]) ]]]–]]]
12