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Biomedical Engineering

Combined In Silico and In Vitro Approach Predicts Low Wall Shear Stress Regions in a Hemofilter that Correlate with Thrombus Formation In Vivo

Buck, Amanda K. W.*†; Groszek, Joseph J.; Colvin, Daniel C.*; Keller, Sara B.§; Kensinger, Clark; Forbes, Rachel; Karp, Seth; Williams, Phillip; Roy, Shuvo; Fissell, William H.

Author Information
doi: 10.1097/MAT.0000000000000649
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Abstract

Chronic kidney failure is associated with significant burden on patient and payor alike. Renal transplant is superior to dialysis with respect to survival, cost, and overall burden of care; however, transplant is severely limited by scarcity of donor organs. Approximately 63% of prevalent patients with end-stage renal disease (ESRD) require hemodialysis as a life-extending therapy,1 even though transplantation offers a survival advantage over hemodialysis.2 This persistent unmet need for donor organs has stimulated interest in technology-based approaches for overcoming the scarcity problem in organ transplant.3–7

Our team is using a biohybrid approach, combining a high-efficiency, silicon-chip hemofilter as a glomerular analogue and a bioreactor of renal tubule cells to accomplish the metabolic, regulatory, and transport functions of the kidney.6 This paper describes our approach to an iterative design process that identifies and eliminates potentially thrombogenic flow fields in candidate devices.

First, computational fluid dynamics (CFD) was used to model the flow field through a hemofilter blood path and predict areas of thrombus formation. The CFD results were verified using magnetic resonance imaging (MRI) to measure pulsatile flow through the device in vitro to simulate physiologic conditions. After iterative in silico and in vitro improvements, prototype blood flow paths were machined from polycarbonate. Because the purpose of this study was to minimize flow-induced thrombogenicity, the prototypes were machined to the dimensions of the intact hemofilter but did not contain the silicon nanopore filters. The prototypes were implanted in large animals to test whether locations of in vivo thrombus formation agreed with CFD predictions. In this study, we used CFD to model unsteady flow in a blood conduit (device A), and noticed agreement between regions of low wall shear stress (WSS) and thrombus formation. The shape of the blood conduit was revised to minimize regions of low WSS (device B), and we observed clot-free flow in 30 day implant studies. To our knowledge, this is the first report of physiologically relevant blood flow simulations used to minimize thrombogenic potential of a hemofilter design for renal replacement therapy.

Methods

Blood Conduit Design and Manufacturing

Two primary design criteria were defined for the implanted hemofilter device. First, the cross-sectional shape of the blood path needed to transition from the round conduits of vasculature and vascular grafts to the rectangular duct flow of a parallel-plate hemofilter, and back to vasculature. Second, to facilitate surgical anastomosis to artery and vein of similar size, a hilum-like configuration was sought: inflow and outflow conduits antiparallel but within a few centimeters of each other. These conditions are then further constrained by the need to prevent thrombosis and avoid stagnant or recirculating flow. The initial design transformed the flow cross-section between 6 mm diameter pipes and a 7 mm wide rectangular duct in a simple “U” shape (device A, Figure 1). Wall shear stress is the stress imparted on the conduit wall by the tangentially flowing fluid. Given the relationship between WSS and thrombus formation,8–11 this parameter is used in design of blood-contacting devices. Consequently, the shape was revised in response to in silico and in vivo findings to include a helical inlet12 and a gradual outlet curve (device B, Figure 1) to reduce the size and duration of low WSS regions. All flow paths were designed in SolidWorks 2008 x64 Edition (Dassault Systèmes, Vélizy-Villacoublay, France), and physical prototypes were milled from biocompatible (ISO10993) LEXAN, Resin HPS6 (Sabic; Riyadh, Saudi Arabia). Pieces were vapor polished and thermally bonded to form the blood flow path (Hayes Manufacturing Services, Sunnyvale, CA).

Figure 1.
Figure 1.:
Orthogonal views of the computational geometry used in simulations for device A (A) and device B with 500 μm channel (B) are shown. Manufactured flow paths are shown (C and D).

Flow Measurement by MR

Device A was imaged using a 63 mm inner diameter quadrature radiofrequency (RF) volume coil inside a Varian 9.4T horizontal bore MRI scanner (Agilent Technologies, Santa Clara, CA). A computer-controlled Masterflex L/S pump driver with dual Easy-Load II pump heads (Cole-Parmer, Vernon Hills, IL) drove pulsatile blood flow through the device, using LabVIEW System Design Software (National Instruments, Austin, TX) to prescribe cyclic flow parameters over a period of 560 ms (Figure 2). A pneumatic pillow was used to trigger magnetic resonance (MR) image acquisition. To reduce the longitudinal magnetization relaxation time, a 2 ml dose of gadopentetate dimeglumine (Magnevist; Bayer HealthCare Pharmaceuticals, Inc., Wayne, NJ) was added to approximately 500 ml of citrated bovine blood (Lampire Biological Laboratories, Pipersville, PA) pumped through the device, improving the signal-to-noise ratio of the images.

Figure 2.
Figure 2.:
A: In vitro flow loop. B: Pump mass flow rate measured via PC-MR velocimetry (triangles) and interpolated (line). PC-MR, phase contrast magnetic resonance.

Phase contrast MR (PC-MR) data were acquired in the through-plane direction using a velocity-encoded spoiled gradient echo sequence for “axial” slices (i.e., bulk flow direction at the inlet and outlet was normal to the slice). Imaging parameters included the following: repetition time = 700 ms; field of view = 38.4 mm × 9.6 mm; slice thickness = 1 mm; voxel size = 0.15 × 0.15 × 1 mm3. The velocity encoding (VENC) parameter was 150 cm/s. To correct for background phase effects due to field inhomogeneity, two sets of images were collected for each VENC direction, with the polarity of the bipolar VENC gradients reversed between acquisitions. After the trigger signal, a series of images collected for 16 cine time points described the pulsatile flow at a temporal resolution of 35 ms.

After data acquisition, images and 2D phase maps were reconstructed using MATLAB (The Mathworks; Natick, MA) and ITK-SNAP (www.itksnap.org),13 and velocity maps were calculated after phase subtraction of the two acquisitions. Velocity encoding aliasing was addressed using a phase unwrapping algorithm.14 Through-plane MR velocity data were imported into tec360 (Tecplot, Inc.; Bellevue, WA) for comparison with simulation data.

In Vivo Experiments

All animal experiments were approved by Vanderbilt University’s Institutional Animal Care and Use Committee. Devices were implanted in twelve 25–30 kg, mixed breed, female class A dogs: five device A and seven device B (multiple channel heights; Table 1). The 2–3 cm long externally supported polytetrafluoroethylene (PTFE) grafts were attached by end-to-side anastomoses from aorta to device inlet and from inferior vena cava to device outlet. After blood flow was established, the device was secured to the psoas muscle adjacent to the inferior pole of the left kidney. Intravenous heparin (100 units/kg) was administered during the operation, with an additional 1,000 units administered when creating the arterial anastomosis. Postoperatively, the dogs received either Lovenox (0.5 mg/kg; Sonofi, Bridgewater, NJ) once each day or antiplatelet therapy with 1.5 mg/kg acetylsalicylic acid (ASA) per day (Table 1). Blood flow through the grafts was assessed weekly by Doppler ultrasound. Devices were explanted if flow was not detected, or at the end of planned experiment (24–31 days; Table 1).

Table 1.
Table 1.:
Long-Term Anticoagulation Strategies and Outcomes for In Vivo Experiments

Computational Fluid Dynamics Simulations

Model construction.

The computational geometry and grid were constructed using ICEM-CFD (ANSYS, Inc.; Canonsberg, PA), and laminar simulations were conducted in Fluent v. 15 (ANSYS, Inc.). Entrance and exit lengths were appended to the device geometry to ensure fully developed flow. The computational volume was discretized using tetrahedral elements and three layers of thin, rectangular prism elements at the near wall region to improve boundary layer and WSS estimations.

Grid independence was confirmed when an approximately 50% increase in element number between grids produced a relative error of maximum WSS less than 5% and a maximum velocity relative error at the outlet less than 3%. For all simulations, blood was considered a Newtonian fluid, which is reasonable for the scale of these devices,15,16 with a density of 1,053 kg/m3 and an absolute viscosity of 0.00368 kg/ms.

Simulation of in vitro experiment.

For simulation of the in vitro experiment, inlet boundary conditions were based on MR-measured velocities obtained near the inlet of the device. Cine velocimetry measurements were interpolated in MATLAB to produce a volumetric waveform describing blood flow (Figure 2). The median Reynolds number was 260, and the Womersley number was 3.1. Three cycles were concatenated, allowing investigation of temporal convergence. The volumetric flow rate was imposed as the inlet boundary condition of the simulation; the outlet was prescribed as having zero diffusion flux; and the geometry was considered a rigid boundary. Visualization of results was performed using Fluent and Tec360 (Tecplot, Inc.).

Comparisons were made between CFD-calculated, through-plane velocity maps and MR-measured velocity data. The CFD data were extracted from the inlet and outlet faces of the computational geometry. The MR data were acquired from the slice closest to the inlet/outlet of the device and positioned inside the device. Comparisons were made at five time points in the cycle at which the MR and exported CFD data aligned temporally; these included data at the initial time point and peak flow through the device.

Simulation of in vivo experiment.

For device A, representative, ultrasound-measured centerline velocity data were obtained in a graft immediately proximal to an implanted device. Discrete points from the measured velocity waveform were interpolated in MATLAB. The median Reynolds number was 600, and the Womersley number was 3.1. This waveform was used to approximate the flow rate17 and was imposed as the transient inlet boundary condition. The outlet was prescribed as having zero diffusion flux, and the geometry was considered a rigid boundary. Because resistance of the device is expected to change with geometry revisions, for device B, an inlet pressure waveform measured in dogs18 defined the inlet boundary condition; the outlet pressure was defined as 5 mm Hg, and rigid boundaries were assumed. The median Reynolds number/Womersley number pairs were 770/0.8, 1,330/1.2, 1,680/1.6, and 1,870/2.6 for the 500, 750, 1,000, and 2,000 μm channel width devices, respectively. The pulsatile simulation was performed over three cardiac cycles to verify temporal convergence.

Results

Simulated and Measured Flows In Vitro

We compared velocity maps to test agreement between simulations and experiment. Figures 3 and 4 show inlet and outlet velocity contours at approximately the same locations for the in vitro and in silico models. Both CFD and MR results indicate a parabolic inflow velocity profile over time and a skewed outlet velocity profile. The mean maximum axial velocity errors were 8.9% and 10.4% at the inlet and outlet planes, respectively. The velocity maps demonstrate qualitative agreement between CFD simulations and in vitro measurements.

Figure 3.
Figure 3.:
A: Through-plane velocity (m/s) comparison for PC-MRI measurements in vitro and CFD simulations at the flow rate at the beginning of the cycle. Contours at the inlet and outlet are presented, and positive/negative velocity values demonstrate relative direction of flow. B: Schematic showing approximate MR acquisition plane and orientation. CFD, computational fluid dynamics; PC-MRI, phase contrast magnetic resonance imaging.
Figure 4.
Figure 4.:
A: Through-plane velocity (m/s) comparison for PC-MRI measurements in vitro and CFD simulations at the peak flow rate. Contours at the inlet and outlet are presented, and positive/negative velocity values demonstrate relative direction of flow. B: Schematic showing approximate MR acquisition plane and orientation. CFD, computational fluid dynamics; PC-MRI, phase contrast magnetic resonance imaging.

Simulated Flows and Thrombus Formation In Vivo

Given the relationship between shear and thrombogenicity, simulated time-averaged WSS (TAWSS) maps were constructed. The CFD-simulated TAWSS demonstrates locally low WSS regions at the outer wall of the proximal curve and at the inner wall of the distal curve (Figure 5). Because of high WSS values during systolic acceleration, the TAWSS maps obscure regions of persistently low WSS. Mean WSS patterns averaged over the cardiac cycle excluding systolic acceleration demonstrate larger zones of low WSS (Figure 6). In device B, the zones of low TAWSS are smaller than those seen in device A, and the location of low TAWSS “foci” varies with channel height (Figure 7).

Figure 5.
Figure 5.:
For the simulation of in vivo conditions for device A, three views are shown of the TAWSS map (Pa) from CFD simulations. Gray arrows indicate inflow region of the device, and black arrows indicate regions of locally low TAWSS. CFD, computational fluid dynamics; TAWSS, time-averaged wall shear stress.
Figure 6.
Figure 6.:
For the simulation of in vivo conditions for device A, three views are shown of the mean WSS (in Pa) calculated for the portion of the cardiac cycle excluding systolic acceleration. Gray arrows indicate inflow region of the device, and black arrows indicate regions of locally low WSS. WSS, wall shear stress.
Figure 7.
Figure 7.:
For the simulation of in vivo conditions in device B, two views are shown of the TAWSS map (Pa) for CFD simulations for flow through device B with (A) 500 µm; (B) 750 µm; (C) 1,000 µm; and (D) 2,000 µm channel widths. Gray arrows indicate inflow region of the device, and black arrows indicate regions of locally low TAWSS. CFD, computational fluid dynamics; TAWSS, time-averaged wall shear stress.

In device A, clots developed in three of five implants; however, in device B, no clots were revealed upon explant (Table 1). Clots in two of the device A prototypes were identified as residing or originating at sites corresponding to regions of low TAWSS and low mean WSS (Figures 5 and 6) identified in the CFD simulations. Figure 8 shows an extracted clot with a platelet-dominated portion formed in the inner wall region of the distal curve. The location corresponds to CFD-simulated regions of low WSS, particularly over the nonsystolic acceleration portions of the cycle (Figure 6). This platelet-dominated, pale region likely marks the region of thrombus initiation.

Figure 8.
Figure 8.:
A: Device A: TAWSS map (left); explanted (middle); extracted clot demonstrating a platelet-dominated portion (right). The location of the platelet-dominated portion of the clot was the inner wall of the distal curve, which corresponds with a simulated area of low mean WSS. B: Device B: TAWSS map (left); explanted device B (right). TAWSS, time-averaged wall shear stress; WSS, wall shear stress.

In device B, no thrombi were observed in the experiments (Figure 7). Notably, although the simulated low TAWSS loci changed with channel height in device B, no clots developed in vivo, indicating the revised design performs well for the range of channel heights.

Discussion

Device hemodynamics influence coagulation, platelet activation, and eventual thrombosis (e.g., 8–11,19,20). The accurate prediction of flow fields is an essential step in design of blood-contacting devices.8–11,21–28 Zones of low WSS can accompany recirculation areas or separation regions, beyond which flow reattachment convects platelets toward the surface.11 The combination of slow flow and physical forcing of platelet-surface interaction is a powerful stimulus for clot formation.

Distributions of WSS are a function of geometry, blood flow rate, and pulsatility. Early investigations demonstrated the importance of studying hemodynamics in the context of physiologic conditions.29 Our implantable bioartificial kidney relies on cardiac perfusion for blood circulation. We hypothesized that simulating in vivo conditions when integrating CFD in the device design cycle would reduce thrombosis. The simulations based on physiologic flows agreed with in vivo observed thrombus location. Design modifications eliminating areas of low WSS also eliminated device thrombosis over a 30 day implant period. To our knowledge, this is the first investigation of hemodynamics in a cardiac pressure–driven hemofilter using physiologic flow conditions.

Shear loading experienced by platelets traversing intravascular devices causes long-term platelet activation.30 Although the fluid shear stresses in our device are below hemolysis thresholds,6 subhemolytic levels of shear may prime platelets for local or distant thrombosis. Lagrangian and Eulerian approaches for calculating platelet damage28,31,32 and platelet residence time calculations may improve future thrombogenicity assessments.33

Our study is limited by the techniques used. Because of constraints of MR measurement and registration with CFD-calculated values, the locations of the inlet and outlet comparison planes were not identical in the measured and simulated data sets. Additionally, use of human viscosity values to simulate flow of citrated bovine blood may have resulted in velocity estimation errors. In the absence of in vivo pressure data, use of the diffusion flux boundary condition also may have contributed to discrepancies between measured and simulated velocity fields. A laminar model was used for these simulations. The vast majority of physiologic flows are laminar, but notable exceptions include arteriovenous grafts,34 severe stenosis,35 valve disease,36 and mechanical heart valves.37 Although instantaneous peak flows may reach Reynolds numbers associated with transitional flow under steady state conditions, they do not necessarily produce instabilities in pulsatile flow. Trip et al.38 (2012) demonstrated that for oscillating flow in a pipe, laminar flow persisted at mean Reynolds numbers higher than those investigated in this study. Further, they found that in the transition region, transitional flow was independent of Womersley number, contrary to previous works (e.g., 39,40). It should be noted that the Trip et al.38 study examined pipe flow. Although the geometries we considered are more complicated than pipe flow, our devices do not have sudden expansions.

The simulations presented here estimate hemodynamic parameters at high spatiotemporal resolution. Inclusion of in vivo and in vitro experiments allows demonstration of phenomena that models cannot predict, such as the accumulation of blood components on membranes and how this may induce a sieving effect or formation of clotting precursors. This underscores the utility of a combined in silico and in vivo/in vitro experimental approach when designing intravascular devices.

Conclusion

This study employed a combination of in vivo, in vitro, and in silico approaches to identify potential fluid dynamics contributors to thrombogenicity in an implantable hemofilter design under realistic operating conditions and to guide future device iterations. The results demonstrate both the feasibility and the utility of such a combined approach in developing intravascular, bioartificial, organ-replacement devices.

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Keywords:

hemofilter; hemodynamics; thrombogenicity; bioartificial kidney

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