CFD FINAL PROJECT
MODELING THE ACCESS POINT ON
THE BRACHIAL ARTERY
Novemer 16, 2010
Nicole Varble
Problem Definition- Overview

Problem- Patients on hemodialysis
need an access point





Native vessels become overstressed
Solution- Create an access vessel
between an artery and vein in the
arm

High flow
Low Pressure
Can be punctured repeatedly
Resulting Problem- Adequate flow
does not reach the hand


Artery
Blood flow is redirected through
access vessel
Hand is deprived of nutrients
Hand
Vein
Figure 1: Native Circulation
Area of Interest
Artery
Vein
A
V
F
Figure 2: Native Circulation w/ AVF
Hand
Problem Definition- Overview
1. Proximal Brachial Artery
2. Distal Brachial Artery
Proximal
Brachial Artery
A
V
F
Distal
Hand
Vein
Figure 3
4. Antegrade Flow- Forward
5. Retrograde Flow- Backwards
Hand
Hand
Figure 4
Figure 5
Project Definition- Overview



Goal: Gain insight to the flow patterns at the intersection of native artery
and access vessel
Interests comes from my thesis work
Model of the entire arm’s vasculature



Native circulation (NC), NC with access, NC with access and DRIL (a corrective
procedure)
For this project only interested in what happens at the intersection point
Little research on the topic
Brachial Artery
Access Vessel
Area of Interest
Figure 6: Brachialcephalic ateriovenous fistula
D.J. Minion, E. Moore, E. Endean, and K. (Lexington, "Revision Using Distal Inflow: A Novel Approach to Dialysis- associated Steal Syndrome," Annals of Vascular Surgery, vol. 19,
2005, pp. 625- 628.
Project Definition- Aims



Aim 1: Create the geometry based on the average blood vessel
diameter, length and boundary conditions. Analyze the entrance to
the access vessel and the magnitude and direction of flow to the
hand.
Aim 2: Change the boundary conditions to that of a hypertensive
patient (elevated blood pressure). Determine flow conditions at the
access changed.
Aim 3: If backwards flow does not occur in ‘Aim 1,’ determine the
boundary conditions at the outlet for which backwards flow occurs.
If backwards flow does occur, determine a threshold at which this
does occur and quantify in terms of differential pressure between
the two outlets.
Project Definition- Assumptions

Assumptions:





Non- puslitile flow
Blood vessels are idealized a
perfect cylinders with sections of
constant diameter
Diameters are based on the
average size of blood vessels
complied from 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.
Figure 7: 2D schematic of brachial artery
and access vessel
Project Definition- Boundary Conditions
Table 1: Geometry and Boundary Conditions
Name
Brachial Diameter
Parameter Value
Db
4.4
0.0044
Da
5.5
0.0055
L1
13
0.13
L2
13
0.13
L3
10
0.1
Vo
570
9.50E-06
Units
mm
m
mm
m
cm
m
cm
m
cm
m
mL/min
m3/s
Condition
1,2
Citation
[1]
1,2
[2]
1,2
[3]
1,2
[3]
1,2
[4]
1,2
[5]
Brachial Pressure Out
P1
1
[5]
Brachial Pressure Out
P1
Access Pressure Out
P2
Access Pressure Out
P2
mmHg
Pa
mmHg
Pa
mmHg
Pa
mmHg
Pa
Access Diameter
Brachial Length In
Brachial Length Out
Access Length
Inlet Velocity
67
8,930
87
11,600
47
6,270
67
8,930
2
1
2
[5]
Project Definition- Geometry and
Boundary Conditions

One velocity inlet
(constant)


Proximal brachial artery
Two pressure outlets
Distal brachial artery
 Access vessel

Figure 8: 3D geometry created in Gambit

Pressure Difference
dP = P1- P2
 Velocity inlet fixed
 Only P2 changed

Figure 9: Specified Boundary Condition, one
inlet velocity and two outlet pressures
Mesh

Edge meshed
Successive ratio = 1.016
 Interval count = 10


Faces meshed
Quad/pave
 Interval count = 10


Volume meshed
Default Tet/hybrid
 Interval size = 1

Figures 9 and 10: Close up image on bifurcation
and mesh geometry, the originally meshed
(yellow) and originally meshed faces (green)
labeled
Mesh- Grid Independent Solution

Percentage of Total Inflow in Distal Brachial Artery
Number of Element
Percent of Total Flow in Distal Brachial
Artery

70.00%
60.00%
50.00%
Mesh 2
Mesh 4
Mesh 3
40.00%
30.00%
Ideal Mesh
20.00%
10.00%
0.00%
0
100000
200000
300000
400000
Number of Elements
500000
600000
Figure 11: Analysis of grid independent solution. Knee of the curve
(ideal mesh) is identified.
Numerical Procedures

Convergence Set to 1e-6, converged in every case
Table 2: Numerical Procedures (choices highlighted in orange)
Pressure- Velocity Coupling
SIMPLE
SIMPLEC
Scheme
PISO
Coupled
Green- Gause Cell Based
Green- Gause Node Based
Gradient
Least Squares Cell Based
Standard
PRESTO!
Linear
Pressure
Second Order
Body Force Weighted
First Order Upwind
Second Order Upwind
Power Law
Momentum
QUICK
Third Order MUSCL
Results

Analyzed

Aim 1 and 2


Nature of flow in normal and hypertensive cases
Aim 1, 2 and 3
Point of maximum flow
 Pressure throughout control volume to identify the low pressure
vessel
 Direction and Magnitude of flow in the distal brachial artery


Outcome

Identify what at what pressure difference retrograde
(backwards) flow occurs
Results- Normal and Hypertensive Case



Possible turbulent regions found at bifurcation
Flow reversal immediately present
When changed to the hypertensive case, only a slight increase in in
velocity magnitude, no other change (pressure difference??)
Turbulent
Region
Turbulent
Region
Flow Reversal
Figure 12: Velocity vector plot at normal flow conditions. Note flow reversal in
the distal portion of the brachial artery and turbulent regions at the bifurcation
Condition
Normal
Hypertensive
dP
[mmHg]
20
20
% of Flow in
Distal Brach
-33.30%
-33.49%
Retrograde?
Location of Vmax
Aim
yes
yes
inlet of access
inlet of access
1
2
Results- Velocity Magnitude
Figures 13 and 14: Velocity Magnitude contour plot. Iso-surface was created along
constant z-axis. Maximum velocity occurring just beyond bifurcation in the access
vessel and in the proximal brachial artery for dP = to 20 and 5 mmHg respectively
Results- Static Pressure


Contour plot of static pressure on a constant z- surface.
Low pressure vessels are where flow will preferentially travel
Figures 15, 16 and 17: Contour plot of static pressure on a constant z- surface. The
low pressure vessels where flow will preferentially flow are label.
Results- Direction of Flow
Retrograde Flow
Retrograde Flow
dP = 20 mmHg
Antegrade Flow
dP = 8 mmHg
Antegrade Flow
dP = 5 mmHg
Figures 18- 21: Velocity vector plots on a constant z- surface. Flow reversal occurs at
dP of 20 mmHg and 8 mmHg and forward flow occurs at 5 mmHg and 0 mmHg.
dP = 0 mmHg
Results- Prediction of Flow
Percent of Inflow in Distal Brachial
Artery
40.00%
30.00%
Antegrade
20.00%
10.00%
y = -0.0329x + 0.3233
R² = 0.9986
0.00%
0
2
4
6
8
10
12
14
16
18
20
-10.00%
-20.00%
Retrograde
-30.00%
-40.00%
dP (mmHg)
Figure 22: Relationship between differential pressure between distal brachial artery
and access vessel and percent of total inflow in distal brachial artery
Results- Summary
Table 3: Summary of Results
Condition
Normal
Hypertensive
dP
[mmHg]
20
20
10
9
8
7
5
0
% of Flow in
Distal Brach
-33.30%
-33.49%
-2.20%
2.29%
6.38%
10.13%
16.98%
31.74%
Retrograde?
Location of Vmax
Aim
yes
yes
yes
no
no
no
no
no
inlet of access
inlet of access
inlet of access
inlet of access
inlet of access
inlet of access
prox brach
prox brach
1
2
3
3
3
3
3
3
Figure 23: 2D schematic of modeled blood vessel
geometry and boundary conditions
Conclusions






Maximum velocity occurs just beyond bifurcation or in
proximal brachial artery
All cases, access vessel acts as a low pressure vessel (flow
preferentially travels through it)
When differential pressure between outlets is limited to 10
mmHg flow is antegrade
CFD model predicts when retrograde flow in distal brachial
artery will occur based on differential pressure
Experimental verification needed
Potentially physicians can use this relationship or something
similar to eliminate need for corrective procedures (DRIL)
Questions?
References






[1]
A. Peretz, D.F. Leotta, J.H. Sullivan, C.a. Trenga, F.N. Sands, M.R. Aulet, M. Paun, E.a. Gill, and J.D.
Kaufman, "Flow mediated dilation of the brachial artery: an investigation of methods requiring further
standardization.," BMC cardiovascular disorders, vol. 7, 2007, p. 11.
[2]
J. Zanow, U. Krueger, P. Reddemann, and H. Scholz, "Experimental study of hemodynamics in
procedures to treat access-related ischemia," Journal of Vascular Surgery, 2008, pp. 1559-1565.
[3]
V. Patnaik, G. Kalsey, and S. Rajan, "Branching Pattern of Brachial Artery-A Morphological Study,"
J. Anat. Soc. India, vol. 51, 2002, pp. 176-186.
[4]
W.S. Gradman, C. Pozrikidis, L. Angeles, and S. Diego, "Analysis of Options for Mitigating
Hemodialysis Access-Related Ischemic Steal Phenomena," Annals of Vascular Surgery, vol. 18, 2004, pp. 5965.
[5]
K.A. Illig, S. Surowiec, C.K. Shortell, M.G. Davies, J.M. Rhodes, R.M. Green, and N. York,
"Hemodynamics of Distal Revascularization- Interval Ligation," Annals of Vascular Surgery, vol. 19, 2005,
pp. 199-207.
[6]
C.L. Wixon, J.D. Hughes, and J.L. Mills, "Understanding Strategies for the Treatment of Ischemic
Steal Syndrome after Hemodialysis Access," Elsevier Science, 2000, pp. 301-310.