CFD FINAL PROJECT MODELING THE ACCESS POINT ON THE BRACHIAL ARTERYNovemer 16, 2010Nicole 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 Blood flow is redirected through

access vessel Hand is deprived of nutrients

Artery

Figure 1: Native Circulation

VeinHand

Artery

VeinHand

Figure 2: Native Circulation w/ AVF

AVF

Area of Interest

Problem Definition- Overview

Brachial ArteryProximal Distal

VeinHand

AVF

Hand

Hand

1. Proximal Brachial Artery2. Distal Brachial Artery

4. Antegrade Flow- Forward

5. Retrograde Flow- Backwards

Figure 3

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

Area of Interest

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.

Figure 6: Brachialcephalic ateriovenous fistula

Brachial Artery

Access Vessel

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

Name Parameter Value Units Condition CitationBrachial Diameter Db 4.4 mm 1,2 [1]

0.0044 mAccess Diameter Da 5.5 mm 1,2 [2]

0.0055 mBrachial Length In L1 13 cm 1,2 [3]

0.13 mBrachial Length Out L2 13 cm 1,2 [3]

0.13 mAccess Length L3 10 cm 1,2 [4]

0.1 mInlet Velocity Vo 570 mL/min 1,2 [5]

9.50E-06 m3/sBrachial Pressure Out P1 67 mmHg 1 [5]

8,930 PaBrachial Pressure Out P1 87 mmHg 2

11,600 PaAccess Pressure Out P2 47 mmHg 1 [5]

6,270 PaAccess Pressure Out P2 67 mmHg 2

8,930 Pa

Table 1: Geometry and Boundary Conditions

Project Definition- Geometry and Boundary Conditions One velocity inlet

(constant) Proximal brachial artery

Two pressure outlets Distal brachial artery Access vessel

Pressure Difference dP = P1- P2 Velocity inlet fixed Only P2 changed

Figure 8: 3D geometry created in Gambit

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

0 100000 200000 300000 400000 500000 6000000.00%

10.00%20.00%30.00%40.00%50.00%60.00%70.00%

Chart Title

Number of Elements

Perc

ent

of T

otal

Flo

w in

D

ista

l Bra

chia

l Art

ery

Mesh 2 Mesh 3Mesh 4

Ideal Mesh

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

casePressure- Velocity Coupling

Scheme

SIMPLESIMPLECPISOCoupled

Gradient

Green- Gause Cell BasedGreen- Gause Node BasedLeast Squares Cell Based

Pressure

StandardPRESTO!LinearSecond OrderBody Force Weighted

Momentum

First Order UpwindSecond Order UpwindPower LawQUICKThird Order MUSCL

Table 2: Numerical Procedures (choices highlighted in orange)

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

Flow Reversal

Turbulent Region

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 bifurcationCondition dP

[mmHg]

% of Flow in Distal

Brach

Retrograde?

Location of Vmax

Aim

Normal 20 -33.30% yes inlet of access

1

Hypertensive

20 -33.49% yes inlet of access

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

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 = 20 mmHg dP = 8 mmHg

dP = 5 mmHg dP = 0 mmHg

Retrograde Flow Retrograde Flow

Antegrade Flow Antegrade Flow

Results- Prediction of Flow

0 2 4 6 8 10 12 14 16 18 20

-40.00%-30.00%-20.00%-10.00%

0.00%10.00%20.00%30.00%40.00%

f(x) = − 0.388469148046101 ln(x) + 0.847474770532635R² = 0.978033718139826f(x) = − 0.0329244907414238 x + 0.32327998607156

R² = 0.998573029078687

dP (mmHg)

Perc

ent

of In

flow

in D

ista

l Br

achi

al A

rter

y

Retrograde

Antegrade

Figure 22: Relationship between differential pressure between distal brachial artery and access vessel and percent of total inflow

in distal brachial artery

Results- SummaryCondition dP

[mmHg]

% of Flow in Distal

Brach

Retrograde?

Location of Vmax

Aim

Normal 20 -33.30% yes inlet of access

1

Hypertensive

20 -33.49% yes inlet of access

2

10 -2.20% yes inlet of access

3

9 2.29% no inlet of access

3

8 6.38% no inlet of access

3

7 10.13% no inlet of access

3

5 16.98% no prox brach 30 31.74% no prox brach 3

Figure 23: 2D schematic of modeled blood vessel geometry and boundary

conditions

Table 3: Summary of Results

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. 59-65.

[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.