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  1,2  1,2  1,2  1,2  1,2  Brachial Pressure Out P1 1  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  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  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.  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.  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.  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.  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.  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.