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C OMPUTATIONAL F LUID D YNAMIC M ODEL OF A RTERIOVENOUS F ISTULA A NASTOMOSIS TO S TUDY THE E FFECTS OF V ESSEL S IZE AND P RESSURE G RADIENT ON THE P RESENCE OF C LINICAL S TEAL AND A T HRILL Nicole Varble BS 1, Dan Phillips Ph.D. 1, Risa Robinson Ph.D. 1, Karl Illig, MD 2, Ankur Chandra 2 1 Rochester Institute of Technology, Rochester, NY 2 University of Rochester, Rochester, NY Introduction Clinical steal, decreased or retrograde blood flow to the hand from the brachial artery, can occur after implementation of an arteriovenous fistula (AVF) anastomosis. Having the ability to predict the onset of steal has the potential to improve operating room procedures and treatment of steal. With the use of Computational Fluid Dynamics (CFD) software, an experimental model has been created which can predict the onset of retrograde flow in the distal brachial artery based on the outlet pressure of the AVF and the relationship of the AVF and distal brachial artery diameters. Objectives Part I: Discover a relationship between the outlet pressures and the onset of steal. The magnitude and direction of flow in the distal brachial artery relative to the inflow at the proximal brachial artery was monitored under several different AVF outlet pressure conditions. Ultimately, a pressure threshold at which retrograde flow occurs was found and quantified in terms of differential pressure between the two outlets. Part II: Discover a relationship between the ratio of the fistula and distal brachial artery diameter and the onset of steal. The magnitude and direction of flow in the distal brachial artery relative to the inflow at the proximal brachial artery was monitored under several different AVF sizes. The goal was to determine a threshold at which steal occurs based on the AVF diameter and develop a relationship between the ratio of the brachial artery and the AVF diameter. Methods -Assumptions Non- pulsatile flow Blood vessels are idealized as perfect cylinders Initial diameters were 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 and as found in current literature Working fluid is considered a Newtonian fluid with an average density, ρ = 1060 kg/m 3, and dynamic viscosity, µ = 0.005 Ns/m 2. -Mesh and Numerical Methods Quad elements were pave on the bifurcation (edge) and at the inflow and outflow faces. Tet/hybrid elements were used in the model volume. The model was tested for grid independence. A total of 153,024 elements were used. Scheme- simple, gradient- least squares cell based, pressure- standard, momentum- first order upwind. Residuals for mass conservation and momentum converged at 1e-6. Methods -Geometry and Boundary Conditions The geometry was created in Gambit (Ansys Inc.) and imported into the fluid dynamics solver, Fluent (Ansys Inc.). A small portion of the arm vasculature was modeled which focused on the bifurcation of the brachial artery and AVF. Geometric properties and boundary conditions include: Proximal Brachial Artery: Diameter = 4.4 mm, Length = 13 cm Distal Brachial Artery: Diameter = 4.4 mm, Length = 13 cm AVF: Diameter = 1.1 - 6.16 mm (typical 5.5 mm), Length = 10 cm Inlet Velocity of Brachial Artery = 570 mL/min Outlet Pressure of Brachial Artery = 67 mmHg Outlet Pressure of AVF = 47 - 67 mmHg All fluid entered the system at the proximal brachial artery and flowed either through the distal brachial artery or through the access vessel. Flow was pressure driven, but given an initial velocity. Results -Velocity Magnitude Plots Using velocity magnitude plots, areas of maximum velocity were identified (as shown red). This may give insight into locations of possible eddies and a resulting thrill. Results -Pressure Magnitude Plot The pressure magnitude plots gave insight to which vessel, the distal brachial artery or the AVF, acted as a low pressure vessel. Flow will preferentially travel through the low pressure vessel. -Velocity Vector Plots The differential pressure, dP, of the outlets (pressure outlet 1- pressure outlet 2 were varied until antegrade flow was observed. As shown in Figures 11 and 12 a dP of 20 mmHg resulted in retrograde flow, where a dP of 0 mmHg yielded antegrade flow. Areas of turbulence were also identified. -Prediction of Steal Compiling the results of 7 pressure differential situations and 7 vessel diameter ratios, thresholds were determined to be the following: Minimum pressure differential between P brachial and P fistula to ensure antegrade flow: dP > 10 mmHg Minimum ratio of fistula to brachial diameter to ensure antegrade flow: D fistula : D brachial > 0.80 -or- D brachial : D fistula > 1.25 Conclusions Part I: In all cases, the access acts as a low pressure vessel and flow preferentially travels through it. When the differential pressure between the outlet of the brachial artery and the outlet of the access is limited to 10 mmHg, antegrade flow can still be preserved in the distal brachial artery. Part II: In order to ensure that antegrade flow is achieved, the ratio of the diameter of the fistula to the diameter of the brachial artery must be greater than 0.80. Future Work Improvements such as the assumptions such as blood being non- Newtonian and the vessel walls being rigid can be eliminated. An investigation into the eddies and turbulent flow patterns at bifurcations can further enhance the understanding of the onset of retrograde flow in the brachial artery and examine the presence of a “thrill”. Meshed Bifurcation Antegrade Retrograde Figure 2: The 3D geometry created in Gambit Figure 3: Schematic of the modeled area Figure 1: The meshed edge (left) and the entire meshed geometry (right) Figure 5: Pressure magnitude plots [Pa] identify the low pressure vessel (blue). Figure 6: Velocity vector plots yield both the magnitude in m/s (high magnitude is red) and direction of flow (arrows). Results Conclusions Future Work Introduction Objectives Methods Model Results dP = 20 mmHg Low Pressure Vessel 9.76e+03 6.26e+03 dP = 0 mmHg Antegrade Flow 9.10e-01 8.36e-03 dP = 20 mmHg Retrograde Flow 1.43e+00 8.73e-03 Turbulent Regions Figure 4: An investigation of the effects of differential pressure (dP, figures to the left) and ratio of brachial diameter to fistula diameter (right), the location of the maximum flow [m/s] was identified through velocity magnitude plots. dP = 5 mmHg Maximum Flow 9.10e-01 0.00e+00 df = 6.16 mm db = 4.4 mm ratio: 1.4 1.17e+00 0.00e+00 df = 2.2 mm db = 4.4 mm ratio: 0.5 7.18e-01 0.00e+00 Brachial Artery AVF Wall, no slip Blood Flow Brachial Artery Access Vessel Inlet, v o Outlet, P 2 Outlet, P 1 df L2L1 L3 db Maximum Flow dP = 20 mmHg 1.41e+00 0.00e+00 Brachial Artery AVF

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