TRANSITIONAL FLOW AT THE VENOUS ANASTOMOSIS OF AN ARTERIOVENOUS GRAFT
UNDER STEADY FLOW CONDITIONS

**Francis Loth**^1^**, Nurullah Arslan**^2^, **Paul F. Fischer**^3^**,
Christopher D. Bertram**^4^**,**

**Seung E. Lee**^5^**, Thomas J. Royston**^6^**, Ruo-Hua Song**^7^**,
Hisham S. Bassiouny**^8^

> ^**1**^ Assistant Professor, Department of Mechanical Engineering, The
> University of Illinois at Chicago, Chicago, Illinois, floth@uic.edu
>
> **^2^** Assistant Professor, Department of Industrial Engineering,
> Fatih University Istanbul, Turkey,
> [narslan@yahoo.com](mailto:n_arslan@yahoo.com)
>
> **^3^** Research Scientist, Mathematics and Computer Science Division,
> Argonne National Laboratory, Argonne, Illinois, fischer@mcs.anl.gov
>
> **^4^** Associate Professor, Graduate School of Biomedical
> Engineering, University of New South Wales, Sydney, Australia,
> c.bertram@unsw.edu.au
>
> **^5^** MS student, Department of Mechanical Engineering, The
> University of Illinois at Chicago, Chicago, Illinois, <slee48@uic.edu>
>
> **^6^** Associate Professor, Department of Mechanical Engineering, The
> University of Illinois at Chicago, Chicago, Illinois, troyston@uic.edu
>
> **^7^** ?title, Department of Surgery, The University of Chicago,
> Chicago, Illinois, ?ename@surgery.bsd.uchicago.edu
>
> **^8^** Associate Professor, Department of Surgery, The University of
> Chicago, Chicago, Illinois, hbassiou@surgery.bsd.uchicago.edu

# Abstract

We present experimental and computational results that describe the
level, distribution, and importance of velocity fluctuations within the
venous anastomosis of an arteriovenous (AV) graft. The motivation of
this work is to better understand the importance of biomechanical forces
in the development of intimal hyperplasia within these grafts. Steady
flow in vitro studies (Re=1060 and 1820) were conducted within a graft
model that represents the venous anastomosis using laser Doppler
anemometry to measure velocity. Numerical simulations with the same
geometry and flow conditions were conducted employing the spectral
element technique. As flow enters the vein from the graft, the velocity
field exhibits flow separation and coherent structures that originate
from the separation shear layer. We also report results of a porcine
animal study in which the distribution and magnitude of vein wall
vibration on the venous anastomosis was measured at the time of graft
construction. Preliminary biology studies indicate an increased level of
activity of mitogen-activated protein kinases (MAPKs) and intimal
thickening at regions of increased vein wall vibration. These findings
implicate velocity fluctuations and the associated vein wall vibration
in the development of intimal hyperplasia in AV grafts. However, further
research is necessary in order to differentiate the vibration effect
from that of flow separation.

# INTRODUCTION

Individuals with end-stage renal disease would die within a few weeks or
months if not sustained by some form of dialysis therapy or a kidney
transplant. An AV graft (Figure 1) is constructed from an artery to a
vein to provide an access site for hemodialysis patients. By bypassing
the high resistance vessels (arterioles and capillaries), high flow
rates can be achieved that are necessary for efficient hemodialysis. A
synthetic graft material Polytetrafluoro-ethylene (PTFE) is often used
for these grafts. More than half of the AV grafts fail and require
surgical reconstruction within three years \[1\]. The majority of these
graft failures are caused by occlusive venous anastomotic intimal
hyperplasia (VAIH) which is a stenosis or narrowing of the vein
downstream of the graft. The use of AV grafts as hemodialysis access
grafts is expected to rise. Therefore, there is significant interest in
finding treatments that stop/reduce the development of VAIH in AV
grafts.

While the natural healing response after surgery causes some intimal
thickening, the biomechanical environment appears to be responsible for
occlusive VAIH. Biomechanical forces in the AV graft are unique, with
generally high wall shear stress (WSS) acting on the vein, a region of
flow separation, and pressure fluctuations that vibrate the vein wall
and surrounding tissue. Kanterman et al. have shown that hyperplastic
stenoses occur predominantly in the proximal venous segment (PVS),
downstream of the graft-to-vein junction \[1\]. This suggests the
possible involvement of disturbances to flow created in the
graft-to-vein junction and advected downstream. In an AV graft canine
animal model, Fillinger *et al*. \[2-5\] measured perivascular tissue
vibration and intimal thickening in AV graft venous anastomoses,
investigating in separate studies the results of varying both flow-rate
and geometric details. They found the highest tissue vibration and
intimal thickening to be correlated (r=0.92, p\<0.001). In the absence
of direct measurements of flow turbulence, they hypothesized that tissue
vibration was caused by turbulent flow, and that the degree of vibration
was correlated with the blood turbulence level. They concluded that a
high flow-rate, in a geometry tending to cause flow disturbances, led to
flow instability, deposition of vibration energy in the vessel wall,
venous intimal-medial thickening and the initiation of hyperplasia.

Extensive numerical and experimental investigations of the fluid
dynamics of distal end-to-side anastomoses associated with arterial
bypass grafts have been conducted, motivated by the fact that this
junction is a site of particularly high risk in intimal hyperplasia. A
further motivation is that the junction offers a situation providing a
complex mix of fluid dynamic phenomena and can potentially aid the quest
for causal linkages between disease localization and fluid dynamic
details for arteries in general. To date there has been only one
detailed set of investigations of the fluid dynamics of the
graft-to-vein anastomosis. Shu *et al*. \[6-8\] obtained the mean
velocity profiles and WSS inside realistic AV graft models. They
implicate the low and oscillating WSS near the stagnation point and
separation region in the development of a lesion downstream of the toe.
No measurements of turbulence levels were reported. The fluid mechanics
of the arterial and venous end-to-side anastomoses differ primarily
because of differences in flow rate. This produces a much higher
Reynolds number in the graft-to-vein junction than in the distal
arterial end-to-side anastomosis and implies a greater tendency to flow
instability and turbulence, as noted by Fillinger *et al.*

The goal of the present research is to investigate the hemodynamic
environment (turbulence and wall shear levels) and its possible
relationship to AV graft failure. Herein, we report evidence regarding
the level and importance of velocity fluctuations within the venous
anastomosis based on: 1) color Doppler ultrasound measurement in a human
AV graft; 2) experimental measurements of velocity within an in vitro
model; 3) wall shear stress (WSS) and velocity simulations using
computational fluid dynamics for the same geometry; 4) vein wall
vibrations measurements taken during an porcine animal study; and 5)
preliminary molecular biological studies regarding the distribution and
level of activity of mitogen-activated protein kinases (MAPKs) at
different regions of the venous anastomosis.

# METHODS

## In Vivo Measurements on Patients

Color Doppler ultrasound measurements (Acuson 128XP/10) were conducted
on two dialysis patients to determine AV graft-vein junction flow
conditions and vessel diameters. The measurements were conducted within
one month of graft construction. The PTFE AV graft connected the
brachial artery to the basilic vein near the patient's elbow. The
measured graft lumen diameter (D~g~) for one patient was 6.0 mm; in the
other patient it was 6.7 mm based on measurements taken from a B-scan
mode outline. In both patients, the PVS and DVS were of comparable
diameter and somewhat smaller than the graft. The angle of between the
graft and the vein was approximately 45° in one patient and less than
10° in the other patient. There is considerable variation in the
anastomotic geometry from patient to patient for surgical reasons.

After imaging the flow in color Doppler scan mode, a static Doppler
sample volume was deposited in the center of each vessel, spanning
approximately one third of the vessel diameter. A marker was aligned
with the vessel axis, and the angle between the Doppler line of sight
and the vessel axis was computed. Since the Doppler scan plane was
arranged to be that containing the axes of the vein and the graft at the
junction, this measured angle was the true angle between the Doppler
line of sight and the vessel axis. It was therefore possible to compute
true axial velocities.

The velocity trace for the graft showed much higher velocities than in
normal arteries, with a low pulsatility index since the sonograph trace
remained well above zero throughout the cycle (Figure 2a). For one
patient, the instantaneous mean of the sonograph trace was estimated to
be 1.5 and 1.0 m/s at the maximum and minimum of the cycle,
respectively. For the other patient, the corresponding numbers were 1.2
and 0.8 m/s. Measurements were also made in the PVS and DVS; however,
determination of the mean velocity was difficult because of the degree
of spectral broadening.

Reynolds numbers for the graft are difficult to estimate, since the
shape of the velocity profile is unknown and the sample volume did not
cover the whole vessel lumen. Based on the velocity measured in the
sample volume (V), and assuming normal blood viscosity (μ = 0.035
mPa-s). The above measurements lead to a systolic peak Reynolds number
of 2700 and a diastolic minimum of 1800 for one patient (Re~g~ =
ρVD~g~/μ, where ρ = blood density, 1.05 g/ml). For the other patient,
the corresponding values are 2400 and 1600. This is under the assumption
that that the velocity profile is flat. Under an assumption of a
parabolic flow profile, Reynolds numbers would be half as much. The true
*in vivo* Reynolds number therefore remains unknown although it is
expect to fall somewhere between values for parabolic and flat velocity
profiles. Thus, Reynolds numbers at diastole and systole are estimated
as 1100 and 1800, respectively. Blood flow entering from the distal vein
(DVS) was estimated to be 10% of the total blood flow however, clinical
experience is that the DVS often occludes due to thrombus.

## Flow Model Geometry

The anastomosis model used in this study was that previously used by
Loth *et al*. (1997) to investigate the hemodynamics in a distal
end-to-side arterial bypass anastomosis. This model geometry also
closely approximates the graft-vein junction of the AV graft. The model
was scaled up 7.6 times relative to the *in vivo* case. The model
material was a transparent elastomer (Sylgard 184, Dow Corning), and the
walls were thick enough that the model could be considered essentially
rigid. The graft‑to-vein diameter ratio was 1.6, with a graft lumen
diameter of 50.8 mm and a host vein diameter of 31.75 mm. The graft axis
intersected the host vein axis at an angle of 5°.

## In Vitro Measurements

### Flow System. A flow system was designed and constructed to provide the upscaled model with the proper inlet and outlet flow conditions. The fluid employed, a mixture of 42% water and 58% glycerin by weight, was chosen to match the index of refraction of the Sylgard model (n=1.41). This fluid had a refractive index of 1.41, a density of 1110 kg/m^3^, and a dynamic viscosity of 10 mPa-s as measured by a viscometer at 23°C Brookfield spindle-type (Model LVTDV-II) digital viscometer. A 1/3 HP split-phase centrifugal Teel pump \[Model 1V308\] provided the pressure head to drive the flow. Bucket and stopwatch was used to measure the total flow-rate. The ratio of the graft inlet flow-rate to the DVS inlet flow-rate was here chosen to be 90:10. The DVS inlet flow-rate was measured by an ultrasound transit‑time flowmeter (Transonic Systems Inc., Model T101). Since fluid viscosity depends sensitively on temperature, a heater/mixer in the downstream tank was used to keep the fluid temperature at 23±0.5°C during the experiments. The model was placed in a flow circuit under steady flow conditions such that flow entered the graft from a straight tube four meters long with an inner diameter of 50.8 mm. Two different steady flow rates were set up, all with the same inlet flow ratio between the graft and the DVS. The corresponding Reynolds numbers based on the graft flow-rate and graft diameter were 1060 and 1820.

### Laser Doppler anemometry measurements were taken at the midplane and outside the midplane for the velocity components parallel and perpendicular to the floor (u and v, respectively). For Reynolds number 1060, velocity profiles were measured at 13 axial locations at the midplane. Outside the midplane, velocity profiles were measured along five lines on the graft side at a distance 0.8D (D-vein diameter) from the hood-midplane intersection and 11 lines on the vein side 0.5D from the floor-midplane intersection. Since preliminary measurements revealed that the turbulent fluctuation amplitudes within the anastomotic region were comparable to or lower than those measured at the graft inlet. On this basis, detailed measurements for the higher Reynolds numbers were confined to the graft inlet, the furthest proximal axial location within the anastomosis, and the PVS. For Reynolds numbers 1820, velocity measurements were taken at six axial locations at the midplane and outside the midplane on the vein side 0.5D from the floor-midplane intersection. 

The LDA system is a two-color laser system (DANTEC Electronics
mirror-type F147/B073, Model 5500A, blue=488nm, green=514.5nm) capable
of measuring two components of velocity. A 350mW Argon-Ion laser
provided the laser output. The system consists of two Bragg cells, two
photomultipliers with receiving optics and two electronic counters. The
Bragg cells were included such that forward and reverse velocities could
be detected. Backward scattered light coming from the particles in this
sample volume is collected at the photomultiplier tube in which the
signal is filtered and amplified. The signal is then processed by an
electronic counter (DANTEC 50N10 signal processor) that determines the
Doppler shifted frequency. The diameter (d~m~) and length (l~m~) of the
blue beam ellipsoidal probe volume are 0.19 and 1.66 mm, respectively.
The particles used to scatter the laser light were 0.993μm diameter
polymer microspheres (Duke Scientific Corporation, Palo Alto, CA, Cat
No. 4009B). The concentration of particles in the water-glycerin mixture
(2.3×10^9^ particles/liter) was determined by the ratio of the total
volume of liquid in the system to the probe fringe volume such that on
average, only one particle would be in the probe volume at a given time.

The data acquisition program called SIZEware was used to record the
instantaneous velocity for steady flow. Five thousand validated samples
were recorded inside flow field and then the mean velocity was found by
taking the average of the samples for **u** and **v** component of the
velocity. Since the data rate was lower near the wall of the model,
elapsed time mode was used and data was taken for five minutes
(validated samples were 200-1000). The fluctuation velocities were found
by subtracting the mean velocity from the instantaneous velocities at
each time step and then averaged over the specified number of validated
samples to find the variables at each measurement location. The
calculations for mean velocities, fluctuation velocities and Reynolds
stress are defined in the following equations:

$\overline{u} = \frac{\sum_{i = 1}^{N}u_{i}}{N}$,
$\overline{v} = \frac{\sum_{i = 1}^{N}v_{i}}{N}$,
$\overline{u^{2}} = \frac{\sum_{i = 1}^{N}{(u_{i} - \overline{u})^{2}}}{N}$,
$\overline{v^{2}} = \frac{\sum_{i = 1}^{N}{(v_{i} - \overline{v})^{2}}}{N}$,
$u_{\text{rms}} = \sqrt{\overline{u^{2}}}$,
$v_{\text{rms}} = \sqrt{\overline{v^{2}}}$,
$\overline{u^{'}v^{'}} = \frac{\sum_{i = 1}^{N}{(u_{i} - \overline{u})(v_{i} - \overline{v})}}{N}$.

> u~i~ = instantaneous velocity component of i^th^ particle along x
> direction
>
> v~i~ = instantaneous velocity component of i^th^ particle along y
> direction
>
> $\overline{u^{'}}$ =mean velocity
>
> i = 1, 2, 3,........N
>
> N = number of spherical particles passing through the measurement
> volume

All data is presented as *in vivo* scale by converting the *in vitro*
measurements through dynamic similarity (Re~g~ = ρVD~g~/μ) where *in
vivo* values are: (D~g~= 6.7mm, ρ = 1.05 g/ml, μ = 3.5 mPa-s). Note that
the Reynolds number based on the vein diameter is different than that
based on the graft diameter by the ratio of the vessel diameters and
flow rates given as: Re~v~ = (D~v~/D~g~)(Q~v~/Q~g~) Re~g~ = (1.6/0.9)
Re~g~.

## Numerical Simulation

### Mesh Development. The mesh generation involves two main steps. First, axial images of the bifurcation were converted into 3D-lumen geometry in a rapid prototype file format. Second, that geometry was used to generate the vertices and connectivity of a CFD mesh. The Slygard model was imaged axially using a spiral computerized tomography (CT) scanner (high speed CTI GE) with an axial spacing of 1 mm (256x256, field of view 120x120mm). The calculated pixel size was 0.5x0.5 mm and a total of 250 axial images were acquired. A commercially available software package (Mimics, Materialise, Ann Arbor, MI) was used to view the images and obtain the 3D-lumen geometry. Using Mimics, edge detection by thresholding was used to determine the lumen contour for each image. After initial edge detection, images were further refined manually, pixel by pixel, to achieve the (operator-perceived) best description of the lumen geometry (Figure 3). Points along each contour were unevenly spaced. A FORTRAN code was written to reinterpolate these points to be equidistant along the contour (0.25mm) and to smooth the surface geometry. The 3D geometric data represented as contour information is then used to create the 3D mesh. Details of the 3D reconstruction technique are given by Yedavalli *et al.* (2001). The mesh was constructed using hexahedral cells with the topology shown in Figure 4. Details of the technique are given by Seung *et al.* (2000). 

### 

### Solution Technique. The solution technique used a spectral element code developed at Argonne National Laboratory that is designed specifically for simulation of transitional and turbulent flows in complex geometries. The code is based on the spectral element method, which represents velocity and pressure in terms of high-order polynomials within each of the computational mesh cells. The polynomials can be differentiated to compute derived quantities, such as WSS, and provide for accurate high Reynolds number solutions with minimal numerical dissipation or dispersion. This code has been applied to a number of unsteady flows, including turbulent convection in atmospheric models, Rayleigh-Taylor instabilities, forced convection in heat exchanger passages, and transitional boundary flows triggered by roughness elements.(Fischer get this ref ????) 

Flow rate is imposed at the graft and vein inlet (DVS) by specifying the
velocity distribution as fully developed steady flow. Stress free
boundary conditions were imposed at the PVS. Blood was approximated as a
Newtonian fluid and the venous anastomosis was assumed to be rigid.
Calculations were for ??? seconds...to remove startup effects. The
solution was be performed on the parallel computer system at the Argonne
National Laboratory (???). The software is designed to run on this
parallel architecture to maximize computational speed.

## In Vivo Study

### Animal Model. Male miniature swine (25-30 kg) fed normal pig chow were used for the study. Anesthesia was induced by intramuscular injection of ketamine hydrochloride (2.2 mg/kg), xylazine (2.2 mg/kg), telazol (4.4 mg/kg), and atropine (0.4 mg/kg) and was maintained with 1-2.5% isoflurane via endotracheal intubation. To reduce the incidence of graft thrombosis, all animals were given 80 mg of aspirin orally one day preoperatively and postoperatively for the duration of the time course selected. Heparin sulfate (100 IU/kg) was administered intravenously 5 minutes prior to implantation of the infrarenal aorta to external iliac vein AV grafts to minimize perioperative graft thrombosis. Animals were killed by a lethal intravascular injection of sodium pentobarbital under general anesthesia following intervention. Housing and handling of animals was comply with "Principles of Laboratory Animal Care" and "Guide for the Care and Use of Laboratory Animals" (NIH publication \# 80-23, revised 1985).

The aorta to external iliac vein graft implantation was performed as
follows. Using a retroperitoneal right flank incision the pareital
peritoneum is reflected off the iliopsoas muscle. The distal infrarenal
aorta and external iliac vein are dissected. The internal iliac vein is
ligated at its confluence to create a relatively generous proximal
outflow segment with no side branches such that the turbulent flow field
properties are not influenced by convergence or mixing of blood flow. A
4-7mm externally reinforced PTFE graft was anastomosed proximally to the
partially side clamped aorta in an end to side fashion using 6mm
prolene. The graft is positioned in the retroperitoneal space using a
loop configuration. The external iliac vein was subsequently controlled
with atraumatic clamps remote from the planned anastomotic site. A
longitudinal venotomy was created using a #11 knife along the
anterolateral aspect and extended to a length equal to 1.5 vein
diameters. The 7mm end of the graft was trimmed to the length of the
venotomy and anastomosed in an end-to-side fashion using 6/0 prolene
suture. The aortic and venous clamps are then released after flushing
any potential air or debris. A sketch of the constructed graft geometry
is shown in Figure 5.

Noncontacting measurements of radial vein surface motion (vibration
velocity) were made using laser Doppler vibrometry (LDV) on the AV graft
vein anastomosis of the porcine animal model at three locations
indicated in Figure 5. Similar measurements have been reported in the
literature (Royston) on a soft tissue phantom. The measured velocity
levels were several orders of magnitude larger than the threshold
sensitivity of the Polytec CLV-800 LDV (0.3 um/s). Vein wall vibration
velocity was recorded at a sample rate of 2048 Hz for 4 seconds using a
dynamic FFT signal analyzer (HP #35670). Due to the Nyquist criterion
and necessary signal conditioning, this yields accurate measurements of
vibratory motion up to 800 Hz with a frequency resolution of 0.25 Hz.

### 

### Molecular Biology. Frozen tissue was homogenized with a Polytron homogenizer PCU-2-110 (Kinematica) on ice in buffer A containing 20 mM Hepes (pH 7.4) 50 mM b-glycerophosphate, 2 mM EDTA, 1 mM DTT, 1mM Na3VO4, 1% Triton X-100, 10% Glycerol, 2 mM leupeptin, 400 mM PMSF, and 10 U/ml aprotinin. The homogenate was incubated on ice for 15 min, and centrifuged at 17000g for 30 min. The supernatant was harvested and protein concentration was measured by Lawry method.

Western blot analysis was performed to measure protein levels of ERK1/2
and JNK in the extracts of porcine grafts. The protein extracts (40
mg/lane) was heated at 950 C for 5 minutes in sample buffer (94 mM
phosphate buffer pH 7.0, 1% SDS, 2 M urea and 3% b-ME), then
electrophoresis on 10% SDS-PAGE under reducing condition. The gels were
then placed onto Immobilon-P sheets (Millipore, Bedford, MA) that were
previously wetted with a buffer containing 48 mM Tris, 39 mM glycine, pH
8.9. Blotting is performed on a horizontal semi-dry electroblot
apparatus (Phamacia-LKB, Piscataway, NJ) at 0.8-1 mA/cm^2^ for 45 min at
room temperature. The blots were blocked in PBS containing 0.3% Tween 20
(PBST) and 5% non-fat dry milk followed by incubation with the
monoclonal antibody against phosphorylated ERK1/2 or JNK1, and
polyclonal antibody against ERK1/2 or JNK1 (Santa Cruz Biochem., Santa
Cruz, CA). The blots were then washed and incubated with anti-mouse or
rabbit horseradish peroxidase-labeled IgG. Subsequently, the blots were
developed with the ECL Western Detection Reagent (Amersham) according to
the manufacturer's instruction. The blots were stripped in PBST (pH
2.5-2.8) for 1 hour; and were labeled with a monoclonal antibody againet
b-actin (Sigma); then developed as described above. Graphs of blots were
quantified and normalized to the levels of actin by scanning
densitometry (Bio-Rad 620 scanner, Richmond, CA) of graphs.

Immunocytochemistry were performed on frozen sections. The tissue was
embedded in OTC and frozen in Freon cooled in liquid nitrogen. Cross
sections (5-8 m thick) were cut in a cryostat at --20°C, and then
brought to room temperature at the time of staining. Sections were
washed in PBS, quenched with 3% hydrogen peroxide for 5 min, and blocked
with 10% normal goat serum in 1% BSA-PBST for 30 min. Sections were
incubated with various primary antibodies at 4°C overnight. After
washing with PBS, the sections were incubated with corresponding
biotinylated secondary antibodies for 30 min (Envision kit). The
antigen-antibody binding was detected by DAB substrate chromogen system
(HK153-5K from Biogenex). The slides were washed, counterstained with
hematoxylin for 60 second, dehydrated, and cover slipped. For a negative
control, the sections were incubated in PBS without the primary
antibody. Immunocytochemical staining and analyses was used to determine
the distribution of ERK1/2 in cross- sectional slices of the venous
anastomosis after 4 days and 4 weeks of graft implantation. Using the
Digital Light Microscope Facility (Zeiss Axioskop microscope, Zeiss
Axiocam camera with PhotoShop plug in and Power Macintosh 9600/300
computer), each cross section was scanned and saved for further
analysis. With the aid of Adobe PhotoShop and NIH image 1.62,
semi-quantitative measurement and analysis of the density (in pixels) of
the specific immunostains for the ERK1/2 in the intima for each quadrant
were detected employing a standard density scale ranging from 210-255
for densely stained areas with ERK1/2.

# RESULTS

**[Experimental Measurements.]{.underline}** Figure 6 shows velocity
vectors, turbulence fluctuation amplitudes and Reynolds stresses for
Re~g~ =1060. SI units are used except for the Reynolds stresses, where
dynes/cm^2^ follow the convention established in the hemolysis and
arterial wall disease literature. At *x* = --6.6*D*, flow enters the
model via the graft and DVS with a fully developed laminar (parabolic)
velocity profile (Figure 6a). The two streams enter the anastomosis
region and merge, accelerating as they move proximally due to the
reduction in cross‑sectional area. A small separation region downstream
of the toe is evidenced by a retrograde vector near the wall at X =
+0.4*D*. Turbulent fluctuations and Reynolds stresses are small except
near the toe side of the PVS starting at X=+2.0*D* (Figures 6b, 6c, and
6d). The maximum fluctuation amplitude (u~rms~ at *x* = +2.0*D*) is
0.24m/s which is \~25% of the local mean velocity.

The normally quoted threshold Re for transition in a pipe is at best
approximate, and is valid only for an extremely long and smooth straight
pipe. Turbulence can be tripped at lower Reynolds numbers, but cannot be
sustained below about 2300 (Chris, should we have a reference for
this?). The recirculating-flow rig used here was not designed with
special precautions against flow instability, since no such ideal
circumstances can be assumed in biological flows. At Re~g~ = 1820
(Figure 7), we observed a small but distinct degree of blunting of the
graft inlet profile, indicating the flow to be near transition. The
velocity profile at the downstream (proximal) end of the anastomosis is
not greatly different from that at Re~g~ = 1060, but the turbulent
fluctuation amplitude is considerably higher (0.375 m/s) although it is
lower as a percentage (\~15%) of the local mean velocity. The
fluctuation amplitude was nearly constant (3-5%) across the vessel just
before (-0.4D) and after (+0.4D) the entrance to the PVS. The separated
eddy just downstream of the toe penetrated further into the lumen at *x*
= --0.4*D*, but reattachment occurs before *x* = +1.2*D*. This
penetration distance was examined more carefully in separate experiments
and was found to be 0.4?? diameters measured from the hood side. Further
downstream, the profiles generally resembled those found at Re~g~ =
1060, except that at *x* = +3.6*D* the *u*-component profile had become
blunt and almost symmetrical. Turbulent fluctuations and Reynolds
stresses were elevated relative to those at Re~g~ = 1060, and reached
significant amplitudes closer to the toe, at *x* = +1.2*D*. The maximum
Reynolds stress was 1300 dynes/cm^2^, whereas the maximum at Re~g~ =
1060 was 250. At both Reynolds numbers, the primary *u~rms~* peak on the
toe side [itself]{.underline} splits into two as the maximum amplitude
decays proximally in the PVS.

The model was constructed to be symmetric about the plane of the
bifurcation such that velocity profiles are expected to be symmetric
about the centerline. Symmetry is evident in the profiles of velocity
shown in Figure 8. Secondary flow is more pronounced at the higher
Reynolds number as expected.

**[Numerical Simulations.]{.underline}**

The velocity results of the CFD simulations are shown in Figure 9 for
Reynolds number 1060 and 1820 in the plane of the bifurcation. Good
agreement is observed between these CFD and experimental results
(Figures 6 and 7) both for the profiles of velocity vectors and the
fluctuation amplitudes. As seen in the experimental results, the primary
peak of the u~rms~ profile splits into two as the maximum amplitude
decays in the PVS.

### 

The vorticity distribution at Re~g~ =1060 and 1820 in the plane of the
bifurcation is shown in Figure 10 at one instant of time during the
simulation. Flow is nearly laminar at the lower Reynolds number while
coherent structures can be observed moving downstream from the
separation point at the toe at the higher Reynolds number. These
structures are more clearly identified when using the λ~2~ criterion of
Jeong and Hussain \[?\] as shown in Figure 11. The color in these
figures represents the instantaneous 3D-pressure distribution on the
lumen surface and on the λ~2~ contours.

The time average wall shear stress (WSS) within and just before the PVS
portion of the venous anastomosis is shown in Figure 12 on the hood and
floor for Re~g~ =1060 and 1820. The results show WSS to be generally
high throughout the PVS as expected due to the large flow rate of these
AV grafts. A spike in the WSS is present at the toe due to the cusp in
the model geometry. Wall shear stress is directed upstream in the small
region of flow reversal although the plotted values are only the
magnitude of WSS. The length of the recirculation region is 0.7D and
0.8D for Re~g~ =1060 and 1820, respectively. The distribution of WSS
magnitude in the axial and circumferential directions are shown in
Figure 12c where the angle, theta, is measured from the floor of the
graft as indicated in the figure. At Re~g~ =1820, the instantaneous WSS
vectors acting on the lumen surface are of a complex pattern and not all
directed axially as shown in Figure 13.

### Animal Study

### Vibration Measurements.

Passive measurements of vein surface motion (radial vibration velocity)
were made using laser Doppler vibrometry (LDV) at regions A, B and C in
vivo. The smallest and largest levels of vein vibration were detected at
positions A and B, respectively as seen in Figure 16. Regional variation
in turbulence-induced vibration intensity was evaluated by computing the
root mean squared (RMS) value of the vibration velocity in the frequency
range 40-800 Hz. The low frequency range (\< 40 Hz) was excluded since
vein wall vibration in this frequency range is not related to turbulent
fluctuations of velocity and pressure. The difference in turbulence
intensity at these locations was 2 and 5 fold greater at position B when
compared to position C and A, respectively.

### Molecular Biology

ERK1/2 phosphorylation (pERK1/2) and its activity (Elk1 phosphorylation)
were measured at the different regions of the anastomotic vein segment
with high (region B) and low (region A) vibration intensity levels at 4
hours after creation of the anastomosis. The ERK1/2 activity was
determined by phosphorylation of the immediate downstream transcription
factor Elk-1 that is known to be involved in growth and differentiation.
Using densitometric analysis, we found a three-fold increase in pERK1/2
at this early time point at region B when compared to region A (Figure
15 center panel). This was associated with a corresponding increase in
the phosphorylation of the Elk1 implicating enhanced vein wall vibration
in the rapid activation of the putative mechanotransduction pathways
(Figure15, top panel).

At 4 hours ERK1/2 localized predominantly at regions of elevated
vibration intensity (region B) within the intimal and medial cells.
Densitometric analysis revealed at least a 3 fold increase in ERK1/2
immunostaining at region B when compared to normal control vein and
regions exposed to reduced vibration intensity (region A) (Figures 16 a,
b and c). This pattern of localization persisted at 4 weeks. Densely
stained regions occupied close to 37% of the intimal/medial area in
region B versus only 15% in region A. Additionally there was a relative
5-fold increase in the intima/media thickness in region (Figures 17 a
and b).

We conducted cellular immunolocalization studies in contiguous cross
sections, 5μm apart, representing the different anastomotic regions,
namely regions A, B, and the suture line (vein- prosthetic junction).
The sections were investigated at 4 hours and 4 weeks. At 4 hours there
was minimal T cell (anti CD4 antibody) and macrophages (anti CD11b/ Mac1
antibody) infiltration across the anastomotic regions. ERK1/2
immunostaining was increased, however, in region B within endothelial
(anti CD31 antibody) and medial VSMC (anti-actin antibody) (Figure 17).
At 4 weeks, a modest increase in T lymphocyte and macrophage
infiltration was observed across the anastomotic regions. Further ERK1/2
immunostaining revealed no evidence of colocalization zones of T-
lymphocytes and macrophage infiltration in immediately adjacent cross
sections.

# DISCUSSION

The results presented herein detail the nature of the flow field to be
expected within the venous anastomosis of a dialysis patient's
blood-access AV graft. We have examined a range of Reynolds numbers
spanning the physiological range indicated by our own *in vivo*
measurements. The flow field is complex and three-dimensional in nature,
with transition to turbulence as a prominent feature. In normal arterial
flows, pulsatility plays an important role, and a quasi-steady flow
assumption may not apply. AV graft flows are abnormal in this respect,
in that the elevated mean flow rate gives rise to a reduced pulsatility
index. The results under steady flow conditions are therefore useful for
several reasons. First, a low pulsatility index implies that the
unsteadiness is of reduced importance. Second, steady flow provides
insight into the causes of specific flow features, which may also exist
in pulsatile flow, and allows them to be specifically identified as
geometric phenomena rather than unsteady phenomena. Third, numerical
solutions of the Navier-Stokes equations require experimental
measurements for code validation. Such measurements are particularly
needed for transitional flows. These results provide data for code
validation of the 3D steady flow solution inside a mathematically
defined, but clinically realistic, venous anastomotic geometry. This is
a necessary step on the way to a pulsatile solution.

The dominate feature in these flows is the transitional nature of the
flow, however the secondary flow patterns found in the proximal vein
segment (the outflow) are at first sight surprising, in that the
predominant flows toward the floor are close to the lateral walls. To
aid terminology, it helps to consider the graft as though the plane of
the bifurcation is vertical and the floor is horizontal and at the
bottom, while emphasizing that any such convention is purely arbitrary.
Based on this convention, since the downward-directed stream from the
graft must turn to align with the horizontal vein axis, the opposite
pattern of secondary flow would be expected: the stream curvature would
then suggest that the predominant downward stream in the PVS be on the
anastomosis plane of symmetry, with compensating upward flows on the
lateral walls. In fact, the whole secondary flow pattern is dictated by
that set up when the inlet flow from the graft impinges on the
anastomosis hood and is deflected downward. This stream curvature causes
lateral downward flows, which persist when the same stream meets that
which has arrived from the DVS. This latter stream is laminar at all
flow‑rates investigated, and therefore predominantly has momentum near
the vein axis. This profile further aids the secondary flow pattern
noted already, of upward flow in the bifurcation plane in the PVS,
because the stream from the graft is able to deflect the lateral fluid
more readily than that on the vein axis. A third contributing factor to
this overall picture is the relatively flat profile of the inlet graft
flow at Re~g~ =1820; this flow has much lateral momentum already, which
is deflected by the hood to form strong downward-directed lateral
streams. On the other hand, a flat profile with boundary layers forms a
weaker Dean vortex flow than does a parabolic one, all other things
being equal, so flatness at the inlet from the graft has both
contributory and opposing effects. Once the two streams merge in the
PVS, the flow is undeveloped and consequently has a reduced tendency to
form the classical Dean secondary flow pattern; this counts as yet a
fourth contributing factor to the observed pattern of upward flow in the
bifurcation plane. The PVS secondary flow pattern is qualitatively
similar at both Reynolds numbers examined, but is strongest at Re~g~ =
1820.

In the absence of boundary layers altogether, a flat profile exhibits
higher axial velocity on the inside of a bend, owing to the
inward-directed pressure gradient. This well-known effect is manifested
in our results at the position *x* = +0.4*D*, where the axial profile at
both Reynolds numbers is skewed toward the toe side. By *x* = +1.2*D*,
the stream curvature is finished, and this skew is already being
abolished. This secondary flow profile is different than that reported
by previous research on arterial distal end-to-side anastomoses
\[??-??\]. In particular, these results differ from those reported by
Loth et al. \[?\] with the same geometry and much low Reynolds number
(Re=222). They reported the classic Dean flow pattern in the distal
outlet segment which is referred to as the proximal venous segment here.

The question that arises from the described research is that regarding
the relative importance of WSS and turbulence in the development of VAIH
and eventual failure of AV grafts. The localization of intimal
thickening has long been thought to be correlated with the low and
oscillating WSS. In a canine animal study, Loth et al. \[?\] has shown
that while a correlation is seen between intimal thickening and the
reciprocal of WSS, the degree of correlation is reduced by the influence
of material and injury. The intimal thickening values along the native
artery are generally lower than those along PTFE for a given level of
shear stress. Also, intimal thickening near the suture line was higher
than those away from the suture line for a given material and a given
wall shear stress level. Within the venous anastomosis of the AV graft,
WSS is near one order of magnitude greater than that found in the
arterial distal anastomosis \[?\]. Still, a region of flow separation is
present that is approximately one vein diameter in length for both
Reynolds number examined which much have a low WSS values at the
reattachment point. Another difference is the fluctuating WSS which
changes significantly is both magnitude and direction. Along with this
complex WSS pattern is a distribution of tissue vibration. High
vibration regions are located just downstream of the toe in the PVS
which coincides with the region of greater fluctuations. Further
downstream from that point, the vein wall vibration decreases, as do the
velocity fluctuations. Since the region of large vein wall vibration is
near the region of the flow separation, it is difficult to separate the
effect of WSS and tissue vibration.

Immunocytochemical qualitative and semi-quantitative analysis of ERK1/2
co-localization with T-lymphocytes, macrophages, endothelial and VSMCs
at the suture line region and at regions of the venous anastomosis where
varied levels of vein wall vibration prevail proximal and distal to the
suture line junction. Such studies were conducted at four hours and four
weeks after porcine AV graft implantation. The finding of these studies
indicate: a) ERK1/2 co-localizes predominately in the intima
(endothelial cells) and to a lesser degree in the medial VSMC, b) ERK1/2
immunostaining is greatly enhanced in regions of elevated vein wall
vibration when compared to regions of suture line injury or reduced vein
wall vibration. c) ERK1/2 immunostaining appears unrelated to
T-lymphocyte and macrophage infiltration. This is evident at the suture
region where significant mural injury and inflammation is present. d)
Intimal thickening is greater in regions of elevated vibration when
compared to regions reduced vibration or injury. This finding indicate
that biomechanical variables namely turbulence induced vein wall
vibration may play an important role in regulating MAPK activation in
the intimal endothelial cells of the venous wall. The contribution of
inflammation to ERK1/2 activation appears minimal in this experimental
model.

The preliminary biological studies give evidence that the tissue
proximal (downstream) of the toe within the PVS has begun to elicit the
complex cascade of intracellular signaling events that typically occur
in response to shear stress stimulation of endothelial cells and
vascular smooth muscle cells. This is shown by the increases in activity
of ERK1/2 after four hours and four weeks. We suspect that vibration
plays a more dominant role that WSS within in the AV graft because the
results from Fillinger et al. on the correlation between tissue
vibration and VAIH in a canine study. They also found a VAIH to be
correlated with Reynolds number. It seems unlikely that grafts with a
greater Reynolds numbers would also be associated with larger region of
low and oscillating WSS. Nonetheless, we plan to further investigate
both vein wall vibration and WSS within experimental AV grafts in
further detail to hopefully separate these two effects. This will be
achieved by careful simulation of animal specific geometry and
immunohistochemical analysis as shown in Figures 16 and 17.

-   Separation → velocity profile inflection point → Kelvin-Helmholtz
    instability → coherent structures break-up downstream to random
    turbulence high urms, etc. high Reynolds stress (same picture for
    the inflection point on the other side created by the
    coming-together of the two streams)

```{=html}
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```
-   *u*~rms~ peak at 1.2*D* (e.g. Rey = 1500) becomes inner part of
    split peak further downstream; out part is similar to that on the
    other side and on the lateral walls (caused by high-shear turbulent
    flow) --- (?)seen downstream only when developing b.l. is resolved
    by LDA

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```
-   discuss comparison with 80:20 --- where the predominant things are
    spreading of the inflow, and consequently low shear on the hood,
    then Dean in the DOS (check flow vis., and note diameter ratio) ---
    turbulence or not is secondary

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```
-   idea of inertia

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```
-   exercise and utility in respect of arterial bypass-graft downstream
    anastomosis

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```
-   Glagov re differences between arterial and venous i-h development.

```{=html}
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```
-   Fillinger et al. (1989) re Rey correlation with venous
    intimal-medial thickness at toe (note final point off the line, at
    Rey = 2530!).

```{=html}
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```
-   ultrasound was used instead of phase contrast MR velocity since
    turbulence can cause signal loss with MR (also for resolution);
    explain shortcomings of *in vivo* turbulence measurements.

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```
-   Laufer's profile

-   Compare frequencies for vibration, vitro rms, cfd rms ...

-   RMS at 1060 not rubulence

# CONCLUSIONS

We have presented evidence that the flow field within the venous
anastomosis of an AV graft is transitional for cases in which the
Reynolds number is near 2000. First, this was demonstrated by spectral
broadening of the velocity measurement on a human by Doppler ultrasound.
Second, large values of velocity fluctuations were measured within in
vitro that closely represents the in vivo geometry under steady flow
conditions that match that observed in vivo. Third, numerical
simulations on the same geometry and steady flow conditions revealed the
detailed pattern of coherent structures within the PVS and demonstrated
the large WSS values present at these Reynolds numbers. Finally, we
presented preliminary results that implicated vein wall vibration as
biomechanical stimulus for the activation of MAPKs in the vein wall.
Future work is needed to determine the precise relationship between AV
graft failure and fluid dynamics variables such as velocity fluctuations
and WSS as well as their relative importance.

# AKNOWLEDGEMENTS

Many thanks to Down Hodge for her help in acquiring the CT images of the
AV graft model, Professor Steven A. Jones for his insightful discussion,
Dr. Henry Tufo for ???, and Wojciech Kalata for his help on the image
processing. A portion of this work performed at Argonne National
Laboratory while a Faculty Research Participant. Program administered by
the Argonne Division of Educational Programs with funding provided by
the U.S. Department of Energy. This work was supported in part by W.L.
Gore and Associates.

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