Nicole Varble
CFD Modeling Part II:
Relationship of Fistula and Distal Brachial Artery Diameter and Distal Brachial Flow
December 9, 2010
Figure 1: Model of the Brachial Artery with Arterial Venous Fistula with the ratio df:db = 0.75
Overview: The purpose of the following models is to create a relationship between the ratio of the
fistula and distal brachial artery diameter. Seven cases were run each altering the diameter of the
fistula. The magnitude and direction of flow in the distal brachial artery relative to the inflow at the
proximal brachial artery was monitored in each case. Ultimately, the goal was to create a rudimentary
experimental model which can predict the onset of retrograde flow in the distal brachial artery based on
the relationship of the fistula and distal brachial artery diameters.
Geometry: The geometry of the model was considered the variable parameter in the following cases.
The inlet and outlet of the brachial artery remained a constant size; however, the fistula size was
altered. Because the ratio of the outlet diameters is the important parameter, either the fistula or the
distal brachial artery could have been altered and arguably yield the same results.
Boundary Conditions: As described previously, a velocity flow inlet was placed at proximal brachial
artery at nominal conditions for all flow cases. Likewise, as shown before, pressure outlets were
prescribed at the fistula and distal brachial artery. In each of the subsequent cases, the flow and
pressure conditions were set to the nominal conditions.
Assumptions: The assumptions remained the same as previously stated and include: Non- puslitile flow,
blood vessels are idealized as perfect cylinders with sections of constant diameter, diameters are based
on the average size of blood vessels complied from the current literature, inlet and outlet pressures and
flows are based on average pressures and flows in the vessels and blood, the working fluid, is considered
a non-Newtonian fluid with an average density and dynamic viscosity as shown in Tables 1 and 3.
Mesh: The geometry was first created in Gambit and meshed using the same procedure as stated
previously. The edge of the bifurcation was meshed using a successive ratio of 1.016 and an interval
count of 10. The inlet and outlet faces were then meshed using a quad/pave scheme with an interval
count of 10. Finally, the volume was meshed using the default tet/hybrid mesh with an interval size of 1.
Once imported to Fluent, the mesh was adapted once and the final results were assumed to be a mesh
independent solution.
Results: For each of the following cases, the percentage of total flow that reached the distal brachial
artery was considered the extent to which retrograde flow was occurring. Positive flow is considered
flow from proximal to distal brachial artery (antegrade) and negative flow is considered distal to
proximal (retrograde). As shown in Table 1, it is evident that for all ratios of less than 0.80 retrograde
flow will occur. Therefore, this model suggests that to avoid the onset of retrograde flow, a ratio of the
diameter of the fistula to the diameter of the distal brachial artery must be above 0.08. The linear
relationship between the ratio of diameters and the parentage of flow that reaches the distal brachial
artery can be seen in Figure 2. 100% of flow is considered all the flow that initially enters the proximal
brachial artery.
Table 1: Summary of Results
Case
3
6
2
5
4
7
8
Diameter
of Fistula
(df)
mm
6.16
5.5
4.4
3.3
3
2.2
1.1
Diameter of
DIST Brach.
(db)
mm
4.4
4.4
4.4
4.4
4.4
4.4
4.4
Ratio
(df:db)
% total flow
in DIST Brach.
Flow Reversal?
1.4
1.25
1
0.75
0.682
0.5
0.25
-54.37%
-43.91%
-29.31%
-1.27%
9.02%
31.49%
61.26%
yes
yes
yes
yes
no
no
no
Percent of Inflow in Distal Brachial
Artery
80%
60%
Antegrade
40%
20%
0%
-20%
-40%
-60%
-80%
0.25
0.5
0.75
1
Retrograde
1.25
1.5
y = -1.0111x + 0.8036
R² = 0.9804
Dfistual:Dbrachial
Figure 2: Relationship of Fistula and Brachial Diameter to % Distal Brachial Flow
Conclusions: As with the relationship created previously in this project, a tool, much like that shown in
Figure 2, can be used by physicians in the operating room to analyze the risk of the occurrence of
retrograde flow before the fistula is put in place. By measuring the diameter of the existing brachial
artery distal to the site of the fistula/brachial bifurcation, the physician will have the ability to
appropriately size the fistula to deter the onset of steal. The model of course, needs to be confirmed
with a more complex CFD model and then experimentally in the operating room. Factors such as
pulsitile flow, elasticity of the vessel walls, and the hemodynamics of blood as a Newtonian and nonNewtonian fluid should all be considered before this model is considered valid. This is, however, the first
step in a long and insightful investigation of how the physical parameters surrounding an arterial venous
fistula directly affect the onset of steal.
Appendix A: The following appendix gives the pictorial representations of the geometries in fluent.
Three images are shown in order: The velocity vector plot, the velocity magnitude contour plot, and the
pressure contour plot.
Case3:
df = 6.16 mm
db = 4.4 mm
ratio: 1.4
flow reversal? yes
Case6:
df = 5.5 mm
db = 4.4 mm
ratio: 1.25
flow reversal? Yes
Case2:
df = 4.4 mm
db = 4.4 mm
ratio: 1
flow reversal? yes
Case5:
df = 3.3 mm
db = 4.4 mm
ratio: 0.75
flow reversal? Yes
Case4:
df = 3 mm
db = 4.4 mm
ratio: 0.682
flow reversal? No
Case7:
df = 2.2 mm
db = 4.4 mm
ratio: 0.5
flow reversal? No
Case8:
df = 2.2 mm
db = 4.4 mm
ratio: 0.5
flow reversal? No