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CFD FINAL PROJECT MODELING THE ACCESS POINT ON THE BRACHIAL ARTERY Novemer 16, 2010 Nicole Varble

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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 Vein Hand Artery Vein Hand Figure 2: Native Circulation w/ AVF AVFAVF Area of Interest

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Problem Definition- Overview Brachial Artery Proximal Distal Vein Hand AVFAVF 1. Proximal Brachial Artery 2. Distal Brachial Artery 4. Antegrade Flow- Forward5. Retrograde Flow- Backwards Figure 3 Figure 4 Figure 5

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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

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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.

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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

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Project Definition- Boundary Conditions NameParameterValueUnitsConditionCitation Brachial DiameterDb4.4mm1,2[1] 0.0044m Access DiameterDa5.5mm1,2[2] 0.0055m Brachial Length InL113cm1,2[3] 0.13m Brachial Length OutL213cm1,2[3] 0.13m Access LengthL310cm1,2[4] 0.1m Inlet VelocityVo570mL/min1,2[5] 9.50E-06m 3 /s Brachial Pressure OutP167mmHg1[5] 8,930Pa Brachial Pressure OutP187mmHg2 11,600Pa Access Pressure OutP247mmHg1[5] 6,270Pa Access Pressure OutP267mmHg2 8,930Pa Table 1: Geometry and Boundary Conditions

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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

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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

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Mesh- Grid Independent Solution Percentage of Total Inflow in Distal Brachial Artery Number of Element Mesh 2 Mesh 3 Mesh 4 Ideal Mesh Figure 11: Analysis of grid independent solution. Knee of the curve (ideal mesh) is identified.

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Numerical Procedures Convergence Set to 1e-6, converged in every case Pressure- Velocity Coupling Scheme SIMPLE SIMPLEC PISO Coupled Gradient Green- Gause Cell Based Green- Gause Node Based Least Squares Cell Based Pressure Standard PRESTO! Linear Second Order Body Force Weighted Momentum First Order Upwind Second Order Upwind Power Law QUICK Third Order MUSCL Table 2: Numerical Procedures (choices highlighted in orange)

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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

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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 bifurcation Condition dP [mmHg] % of Flow in Distal Brach Retrograde?Location of V max Aim Normal20-33.30%yesinlet of access1 Hypertensive20-33.49%yesinlet of access2

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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

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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.

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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 mmHgdP = 8 mmHg dP = 5 mmHgdP = 0 mmHg Retrograde Flow Antegrade Flow

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Results- Prediction of Flow Retrograde Antegrade Figure 22: Relationship between differential pressure between distal brachial artery and access vessel and percent of total inflow in distal brachial artery

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Results- Summary Condition dP [mmHg] % of Flow in Distal Brach Retrograde?Location of V max Aim Normal20-33.30%yesinlet of access1 Hypertensive20-33.49%yesinlet of access2 10-2.20%yesinlet of access3 92.29%noinlet of access3 86.38%noinlet of access3 710.13%noinlet of access3 516.98%noprox brach3 031.74%noprox brach3 Figure 23: 2D schematic of modeled blood vessel geometry and boundary conditions Table 3: Summary of Results

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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)

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Questions?

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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.

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