Particle Image Velocimetry–Validated, Computational Fluid Dynamics–Based Design to Reduce Shear Stress and Residence Time in Central Venous Hemodialysis Catheters

Abstract

As crucial factors in blood clot formation, shear stress distribution and low flow zones are assessed in different central venous catheter tip designs by using a combined numeric and experimental approach. Computational Fluid Dynamics was validated with Particle Image Velocimetry by comparing simulated and measured velocities and shear strains in three designs of the blood withdrawing arterial lumen: cylindrical and with tip (1) cut straight, (2) cut at an angle, or (3) cut straight with a sleeve entrance. After validation, four additional designs were studied: (4) with two side holes and tip cut straight or (5) at an angle, (6) concentric lumens, and (7) Ash Split–based. In these seven designs, shear stress (SS), blood residence time (RT), and Platelet Lysis Index, which combines the influence of shear stress magnitude and exposure time, were simulated. Concentric catheter was discarded due to highly elevated SS. Ash Split–based design had elevated RT values in the distal tip zone as major inflow occurs through the most proximal side holes, but this is compensated by low average SS. A straight-cut tip and possibly two side holes are preferred when aiming at minimal SS and RT. These data may lead to more patent catheters.

Central venous catheters are commonly used as a vascular access method for hemodialysis.¹ However, apart from several advantages, such as the ease of insertion and immediate access to the circulation, central venous catheter use is accompanied by a higher incidence of infection and thrombosis as compared with other means of vascular access such as grafts or fistulas.² Concerning thrombosis, stagnating blood zones in the catheter lumen and regions of elevated shear stress that induce platelet activation may promote the formation of a blood clot. Elevated shear stresses also give rise to damage to red blood cells. Significant levels of shear stress are mostly present in the blood-withdrawing (arterial) lumen of the catheter, more specifically, in the distal tip region. Although various catheter (tip) designs are marketed, presently, no proven advantage of one design over another exists. Nevertheless, changes in catheter tip design have been shown to cause alterations in local flow pattern and shear stress distributions.³ Further study of the local hemodynamics of different catheter designs might provide insight into how catheters can be optimized to reduce shear stress and stagnant zones, thus leading to possibly fewer thrombogenic catheters.

In this study, flow and shear stress distributions and blood residence time in different catheter designs are compared. For this analysis, a combined approach of Particle Image Velocimetry (PIV) and Computational Fluid Dynamics (CFD) is used. Computational Fluid Dynamics allows a time-efficient study of the hemodynamics of different catheter designs without the time-consuming effort of fabricating prototypes suitable for PIV measurements. However, validation of CFD results is necessary as mesh-independent shear stress fields, in contrast to flow fields, are difficult to achieve and are only obtained at very high (local) mesh density.⁴ For this purpose, PIV was chosen as a challenging approach to obtain both high resolution flow fields and shear stress distributions inside the lumens of different catheter models.

Consequently, this study is conducted in two parts. First, flow field and shear stress distribution in the blood-withdrawing lumen of three catheter models is assessed via PIV and CFD. Results of both approaches are compared to validate the numeric approach. Second, shear stress distributions and blood residence time in four additional (in total, seven) catheter designs are studied using CFD. Throughout the entire study, the distal end or tip of the blood-withdrawing (arterial) lumen is considered, as stagnant blood zones and highest shear stresses are expected there.³ Results are analyzed to assess which tip design is optimal to reduce shear stress levels and the presence of stagnating blood zones. Adoption of this information can lead to possibly less thrombogenic catheters.

Materials and Methods

Three Catheter Designs Studied by PIV and CFD

Three shotgun-type (or step-tip) catheters were studied by both PIV and CFD for flow and shear stress validation purposes. The arterial lumen, which withdraws blood from the vessel, has a round cross section with an internal diameter of 2.1 mm. The venous lumen, which returns cleansed blood to the circulation, is also cylindrical, with an internal diameter of 2.1 mm, but its tip extends 30 mm further in length. The three catheters differed only in the tip design of the arterial lumen. The distal end of catheter “Cut Straight” (Figure 1A) is cut orthogonally to its axis and has no “arterial” flow entrance other than the distal end-opening. This is the most simplistic catheter design and is considered as the reference catheter in the second part of this study. Catheter Cut Straight Sleeve (Figure 1B) also has a distal end that is cut at 90°, but it features a sleeve entrance (1.4 mm wide) at 3.1 mm distal from the arterial tip. Catheter Cut Angle (Figure 1C) has a distal end cut at an angle of 33° and only has one distal end-opening.

Figure 1.: Catheter designs studied. A = Cut Straight; B = Cut Straight Sleeve; C = Cut Angle; D = Cut Straight Hole; E = Concentric; F = Cut Angle Hole; F = Ash Split.

Four Additional Catheter Designs Studied by CFD Only

For the in-depth CFD study, four additional catheters were also simulated. Catheter Cut Straight Hole (Figure 1D) is a variant of catheter cut straight but with two symmetrically placed side holes (inner diameter = 1.2 mm) at 3.1-mm distal from the arterial tip. Catheter Concentric (Figure 1E) is a typical concentric catheter design. The inner venous lumen has an inner diameter of 2.1 mm. The surface area of the outer arterial lumen annulus is also identical to the arterial lumen surface area of the Cut Straight catheter, to make comparison to the shotgun-type catheters valid. Catheter Cut Angle Hole is analogously a variant of catheter Cut Angle, with two symmetrically placed side holes (inner diameter = 1.2 mm) at 3.1 mm distal from the arterial tip. The last catheter is based on the Ash Split design (Medcomp, Harleysville, PA, Figure 1F). It has a D-shaped lumen that changes to a circular lumen with a smaller cross section toward the tip (inner diameter = 1.8 mm). This catheter was scaled so the D-shaped lumen had the same surface area as the lumen in the reference catheter to allow comparison to other simulation results. It has four pairs of side holes (two pairs on top and bottom each alternating with two pairs on left and right of catheter lumen) extending the entire tip zone. Side holes most distal to the tip S1 have a diameter of 1.3 mm; the other side holes S2, S3, and S4 have a diameter of 0.9 mm. Side holes are positioned at 18.3 mm, 13.8 mm, 8.4 mm, and 3.2 mm, respectively, from the tip. The tip of the lumen is positioned under an angle of 3° to the horizontal axis.

The presented catheter designs are virtual designs. Nevertheless, they bear high resemblance to existing commercially available catheters, so results may be extrapolated to catheters of different manufacturers but with similar designs [e.g., Mahurkar, PermCath (Tyco Health Care, Mansfield, MA), Niagara, VasCath, OptiFlow (BARD Access Systems, Salt Lake City, UT), Duo-Flow and Split Cath (Medcomp, Harleysville, PA)]. Adoption of the results of this study may thus lead to better-performing catheters.

PIV Analysis

Catheter Prototypes

The three catheter prototypes were cast in an aluminum mold using a clear, homogeneous, transparent silicone (CF-2616, NuSil Silicone Technology, Carpinteria, CA) with a refractive index (RI) of 1.41. To make casting more feasible, experimental catheter models were scaled so the inner diameter of the lumen is 6 mm. Consequently, a geometric scaling factor α_L of 2.857 (= 6 mm/2.1 mm) was used for the entire in vitro setup.

Experimental Setup

In vivo, the tip of a central venous catheter is located in the superior vena cava (SVC), in the right atrium, or at the junction of both. Previous work has shown that this location has little or no influence on flow or shear stress distribution inside the catheter lumens.³ As such, in vitro, the catheter is placed in a duct representing the SVC. The following in vivo parameters were assumed: catheter flow rate is 300 mL/min, blood density (ρ) is 1060 kg/m³; blood viscosity (μ) is 3.5 mPa·s; SVC diameter (D) is 18 mm⁵; average blood velocity (v) in SVC during systolic inflow is 0.18 m/s,⁶ corresponding with a SVC blood flow rate of 2.7 L/min. According to the geometric scaling factor, the hydraulic diameter of the in vitro duct has to be 51.4 mm. However, to minimize optical distortion and diffraction of the PIV laser on a curved surface, a rectangular PMMA duct was used. Hydraulic diameter of a rectangular duct equals 4 times the cross-sectional surface area divided by the circumference. As such, cross section of the duct was chosen to be 40 × 72 mm, which complies with geometric similarity.

As a working fluid, 42 to 58 weight % water-glycerin mixture was used at 50°C to reduce fluid viscosity. The mixture provides a RI of 1.41, matching with the catheter model material (manufacturer's data). Mixture density (ρ) was measured 1150 kg/m³. Kinematic viscosity of the mixture was determined experimentally using an Ubbelohde capillary viscometer (ViscoSystem AVS, Schott-Geräte GmbH, Germany). In five measurements at 50°C, mixture kinematic viscosity (ν) was measured 2.961 × 10⁻⁶ m²/s (SD 2.8 × 10⁻⁹ m²/s). Consequently, a dynamic viscosity (μ = ν * ρ) of 3.405 mPa·s was obtained. Subsequently, dynamic similarity theory was used to determine the in vitro flow conditions in the scaled PIV model. According to dynamic similarity, Reynolds numbers (Re = ρ * D * v/μ) in the in vivo and in vitro situation must be identical for both the catheter flow (Re = 937) and the vein flow (Re = 981). From this, an in vitro duct flow rate of 9.7 L/min and an in vitro catheter prototype flow rate of 784 mL/min were obtained. Consequently, a velocity scale factor α_V of 0.314 and a shear rate scale factor α_γ (= α_V/α_L) of 0.11 was calculated. These values are used to scale the results of PIV measurements for comparison with CFD results.

An experimental setup (Figure 2) was constructed in which the catheter was mounted securely in the rectangular duct. Working fluid is kept at a constant 50°C and continuously circulated through the duct mimicking the SVC blood flow rate while another pump draws fluid via the arterial catheter lumen.

Figure 2.: Schematics of PIV set up.

Measurement Protocol

For the flow visualization through the catheter model, standard PIV was used. Figure 2 shows schematics of the PIV set up. As a light source for the measurements, we used a double-cavity Nd:YAG Solo PIV I (New Wave, Fremont, CA) laser with 532 nm wave length and 50 mJ of energy per pulse. An articulated mirror arm redirected the laser beam from the laser head to the light sheet optics. A 12-bit CCD camera (Sensicam QE, PCO, Kelheim) with the resolution of 1376 × 1040 pixels was used to record 100 pairs of images at 4-Hz frequency. A Nikorr Micro 60-mm 2.8 lens was attached to the camera. To calibrate the region of interest (ROI) to real units (mm) we used a black aluminum plate with white cross-markers precisely written on it by a laser at given distances. The master of the acquisition procedure was a synchronizer (ILA GmbH, Jülich, Germany), which controlled synchronized recording of the images to the emitted laser pulses in chosen frequency domain. The camera was orthogonally inclined to the laser light sheet optics, and both were fixed to the traverse unit, allowing the positioning along the axis parallel to the main flow (Figure 2).

Rhodamine-B–coated red fluorescent particles, microspheres of 10-μm diameter, were added to the working fluid. Fluorescent particles emitted the red light (λ emission = 580 to 620 nm) once they were illuminated with the green laser light (λ excitation = 532 nm) sheet. To avoid reflections at the wall of the catheter, we applied a red bandpass filter in front of the CCD chip. Through this filter, only red light (λ = 590 ± 20 nm) was visible for the camera.

The resolution is given by an interrogation window size for the adaptive correlation of 32 × 32 pixels,² with an overlap shift of 8 pixels. The light sheet thickness was about 0.7 mm, with a spatial gaussian distribution. As such, particles in the middle of the sheet are only just detectable, whereas particles out of the middle plane act as noise. The latter is filtered out due to subsequent correlation function and filter algorithms.

For three different catheters, we measured 3 ROI serially organized to the flow direction in 2 longitudinal central planes, normal and transverse (Figure 3). The combined ROIs in one plane covered approximately 13.7 × 32.8 mm² of the arterial catheter tip region.

Figure 3.: PIV measurement planes: Normal and transverse plane were measured by combining three subsequent ROIs in each plane.

For evaluation of the PIV images, we used the commercial VidPIV software package (ILA GmbH, Jülich, Germany) with iterative window deformation,⁷ B-Spline gray value interpolation,⁸ and phase correlation.⁹ In all ROIs, in-plane velocity magnitudes and shear strain values were computed. The evaluation results were computed from statistical average of 100 instantaneous flow field measurements for each ROI.

CFD Analysis

All catheter models were constructed in in vivo scale in the CAD package SolidWorks 2003 (SolidWorks Corporation, Concord, MA) and exported into the grid generation software Gambit 2.1 (Fluent Inc., Lebanon, NH) via the Parasolid data format. Catheter models were inserted concentrically in an in vivo–scale, straight, rigid cylinder representing the SVC. Fluent 6.2 was used as numeric solver.

Comparison with PIV

For comparison with PIV, blood was modeled as an incompressible, newtonian fluid. Velocity inlet value of the SVC was set at a constant 0.18 m/s (cfr. in vivo flow conditions – supra). Catheter lumen boundary faces were set at 300 mL/min, either entering or leaving the fluid domain. All walls in the model were set as rigid, impermeable, and with no slip at the wall surfaces. SVC outlet face was set as a pressure outlet to provide a zero reference pressure. A T-Grid mesh was used, which was locally refined to gain better resolution for the assessment of shear stress and to achieve grid independence. Resulting average number of grid cells in the tip volume was 1.5 million cells. Average skewness was 0.35 (range, 10⁻⁵ ∼ 0.83). In-plane velocities (Equation 1) and shear strain values (Equation 2) in the PIV measurement planes of the three catheters were computed and compared with the PIV results (u_i = i-component of velocity vector).

Quantitative comparison was performed by comparing numeric and experimental average velocity magnitudes and average (absolute values of) in-plane strain rates in the measurement planes.

Assessment of Shear Stress Levels and Blood Residence Time

In subsequent simulations to assess possible blood clotting risk in catheters, blood was modeled as a non-newtonian fluid, using the Quemada¹⁰ blood viscosity model (Equations 3–5). Hydrodynamic boundary conditions were unchanged.

Parameter k is function of the intrinsic viscosities k₀, characterizing the red blood cell aggregation at zero shear stress, k_∞, describing the orientation and deformation of red blood cells at important shear stress, and the shear rate γ.

With

Hematocrit H was set at 40%; plasma viscosity μ_p is 1.3 mPa·s. Boundary conditions are applied as mentioned above. Grid adaptations were applied to the same extent as was necessary for PIV comparison. Shear stress (SS) levels are calculated by Fluent as the multiplication of viscosity and strain rate. The latter is defined as (2D_ijD_ij)^1/2, with D_ijD_ij the inner product of the strain rate tensor

Blood residence time (RT) is modeled by solving Equation 6 (u_i = velocity x,y,z-components; x_i = x,y,z-coordinate, t = time value) in the arterial lumen of the catheter.

This equation is a specific form of the continuity equation for variable t. The value of t at the inlet faces is set at zero. No flux boundary conditions are imposed on all outflow surfaces. This results in a t-value throughout the arterial lumen domain that indicates at any location the time that has elapsed since the fluid in that location has entered the lumen (residence time).

As the flow inside the catheter lumen is proven to be three-dimensional,³ shear stress and blood residence time were evaluated in a constant tip volume of the arterial lumen of each catheter model. A tip volume of 0.075 mL was considered, e.g., corresponding to the distal 2.16 cm end of the arterial lumen in the Cut Straight reference catheter. Volume-averaged shear stress in this tip zone is calculated for all catheters. A shear stress threshold of 10 Pa for platelet activation was selected.¹¹ As such, also the percentage of the tip volume that is subjected to a shear stress of 10 Pa or more is calculated for each catheter. Concerning residence time, the average value of parameter t at the end of the tip volume is 0.015 second for each catheter, given the tip volume and the catheter blood flow rate. However, due to local stagnation of blood in the tip zone, the time since the blood has entered the arterial lumen can locally exceed 0.015 second. Consequently, the percentage of tip volume with RT >0.015 second and the percentage of tip volume with RT >0.030 second was evaluated for each catheter design. Extended residence time combined with elevated shear stress can lead to platelet activation and eventually blood clotting. As such, also the average shear stress in zones with RT ≤0.015 second and in zones with RT >0.015 second was calculated for each catheter design.

The choice of the 10-Pa shear stress threshold for platelet activation can be questioned as the range of shear stresses over which platelet adhesion and subsequent aggregation are observed is approximately 0.1 to 20 Pa.¹² Waniewski et al.¹³ used a two-level critical threshold of 2500 s⁻¹ (∼8.75 Pa) to 7500 s⁻¹ (∼26.5 Pa) to assess the conditions of thrombosis. As such, to reduce the sensitivity of the results and conclusions of this study to the choice of the shear stress threshold, the Platelet Lysis Index^14,15 (PLI, Equation 7) was added. Similar to the Hemolysis Index equation by Giersiepen,¹⁴ this experimentally fitted equation describes the lysis of a platelet, taking into account the combined effect of magnitude of shear stress (τ) and the exposure time (t).

This approach allows linking high shear stress to subsequent low flow zones via path lines. Although the equation is set up for platelet lysis, it can be used to assess possible platelet activation as the same determinants are applicable. As such, the index is used as a comparative tool in the quantitative assessment of the catheter tip designs rather than as a predictive tool of actual platelet activation.

For each inlet of a catheter, a minimum of 1000 path lines were computed by Fluent 6. Each path line takes 3000 steps of 10 μm to allow the path line to extend well past the disturbed flow in the tip zone and into the poiseuillian flow further downstream the catheter lumen. At every point, shear stress and velocity magnitude values are exported. The time value is computed as the distance between to subsequent points along a path line divided by the average velocity over the segment. PLI values of every step along a path line are summed up. Subsequently, for each catheter a weighted average of all path line PLI values is computed using the entrance velocity of a path line as weighing factor. As such, each path line contributes to the PLI according to the amount of catheter inflow they represent.

Influence of a Realistic SVC Flow

A realistic SVC velocity profile⁶ was imposed in one case (Cut Angle) to assess the influence of pulsatile flow and even backflow in the catheter surrounding vein. Figure 4 shows the velocity profile⁶ (period = 1 second) imposed at the vein inlet face. Average shear stress in the tip was monitored during the second cycle to avoid transitional flow effects.

Figure 4.: Realistic time-dependent superior vena cava average inlet velocity (m/s) and average SS (Pa) in catheter Cut Angle tip under these transient conditions.

Results

CFD Validation by PIV Measurements for Three Catheter Designs

Figure 5 shows in plane velocity magnitudes and strain rates in the normal and transverse plane of the three catheters studied. The range of velocity magnitude and shear strain is set equal for PIV and CFD. The inflow in Cut Straight catheter is homogeneous in both normal and transverse plane. Only very small zones of low velocity and flow separation are present just downstream the inlet and are both visible in PIV and CFD. Shear strains are highest near the inlet where the flow bends around the catheter entrance and near the border of the small recirculation zone and the large inflow. In case the inlet of the catheter is cut at an angle of 33° (Cut Angle), a large zone of low velocities is present close to the top of the arterial lumen. Maximal velocity values are higher as compared with the catheter Cut Straight as the effective inflow area is reduced. In the transverse plane, velocities are high near the wall and low in the center of the lumen. This illustrates how the major flow enters the lumen. The incoming flow bends to the bottom of the lumen and flows to the top along the side walls and comes back down more downstream in the center of the arterial lumen. This swirl motion during arterial inflow was already observed in previous work.³ As a result of the complex three-dimensional flow, high shear strains are present throughout the tip of the Cut Angle catheter. Adding a sleeve entrance to the straight cut catheter (Cut Straight Sleeve) results in low velocities in the most distal zone of the catheter's tip. Majority of the flow is now drawn into the lumen through the sleeve. A zone of low velocities is noticed near the wall just downstream the sleeve and a relatively large zone near the top of the lumen in the most distal zone extending to the center of the lumen. As such, high strain rate values are mostly present near the sleeve wall and at the bottom of the lumen.

Results show that PIV measurements and CFD simulations are in good qualitative agreement in all cases for both velocity magnitudes and shear strain values. Quantitative agreement is presented in Table 1.

Table 1: Quantitative Comparison of PIV and CFD Results of Average Velocity Magnitude and Average Absolute Value of Strain Rate in the Two PIV Measurement Planes of the Three Catheters Studied Using Both PIV and CFD (Cut Straight, Cut Angle, and Cut Straight Sleeve)

CFD Assessment of Shear Stress and Residence Time in the Tip of Seven Catheter Designs

The following parameters were assessed in the tip zone of the arterial lumen of each catheter: (1) tip volume average SS, (2) percentage of tip volume with SS >10 Pa, (3) percentage of tip volume with RT >0.015 second, (4) percentage of tip volume with RT >0.030 second, (5) average SS in zones with RT ≤0.015 second, (6) average SS in zones with RT >0.015 second, and (7) PLI. Also, flow division is reported in case of different flow entrances. Results are presented in Table 2. Catheter Cut Straight is set as the reference catheter as its design is no more than just a simple cylindrical lumen.

Table 2: Parameters Calculated in the Tip Zone of the Arterial Lumen of Each Catheter

Tip volume average SS in Cut Straight catheter attains 12.6 Pa. Cutting the inlet at an angle increases average SS with about 30%. Incorporation of side holes renders quasi-identical results irrespective of at which angle the inlet is cut and leads to about 14% to 17% higher SS as compared with the reference case. Adding a sleeve entrance does not significantly change tip average SS as compared with the reference catheter. A 3.6-fold average SS compared with the reference case is noticed when a concentric catheter design is used. Using an Ash Split design reduces average SS about 8%. Similar trends are noticed in the percentages of volume where SS attains 10 Pa or more.

The percentage of volume with an RT of more than 0.015 second is reduced when the end-opening is cut at an angle compared with a straight cut by about 17%. The amount of volume with an RT of more than double the average RT at the end of the tip zone, however, has strongly increased in this case, up to 2.6% of the tip volume compared with 0.1% in case of Cut Straight. Addition of side holes to catheter Cut Straight or Cut Angle both reduce the volume with RT >0.015 second by more than one third, compared with the reference case; adding a sleeve to the Cut Straight catheter, however, increases the volume with RT >0.015 second by about 17%, as well as again increasing the amount of volume with RT >0.030 second to 2.7%. Concentric Catheter has 13% more zones with RT >0.015s in its tip zone but 83-fold of volume with RT >0.030 second. The largest increase in percentage of volume with RT >0.015 second and >0.030 second was found in the Ash Split catheter tip, with a respective 3.6-fold and 314-fold of values compared with the reference catheter.

Looking at the SS levels in zones with different RT levels, SS is approximately 21 Pa in zones with RT larger than 0.015 second and approximately 11 Pa in zones with RT smaller than 0.015 second. In the case of Cut Angle, Cut Straight Hole, and Cut Angle Hole, the change in tip-averaged SS is due to a change in SS levels in zones with RT <0.015 second. In catheter Ash Split, the change in average SS is mostly due to the change in SS levels in zones with RT >0.015 second. In case of Concentric catheter, the rise of average SS level compared with the reference case is equally pronounced in both RT interval zones.

As for average shear stress and residence time parameters, the PLI is lowest for the reference catheter Cut Straight. Trends for PLI values do not always clearly follow the SS or RT values as both parameters are used to calculate the PLI. Catheter classification according to lowest PLI is Cut Straight < Cut Straight Hole < Cut Angle Hole < Ash Split–based < Cut Angle < Cut Straight Sleeve < Concentric.

Under transient SVC flow, average tip SS in catheter Cut Angle varied between minimally 15.3 and maximally 16.8 Pa, slightly past the period of maximal backflow during atrial contraction and of maximal forward flow during systole, respectively. The average SS during pulsatile SVC flow at the point of steady-state flow conditions (= 0.18 m/s inflow) is almost identical to the results of the steady-state case.

Discussion

CFD allows the most time-efficient assessment of flow and shear stress distribution in central venous catheters.¹⁶ Nevertheless, validation with PIV was found to be relevant and necessary as mesh independence for shear stress distribution was only achieved when using very high mesh densities. For the first time, flow inside a catheter lumen was assessed using PIV. This was highly successful due to maximal reduction of optical distortion by matching the RI of the fluid and catheter material and by using red fluorescent particles, while respecting dynamic similarity theory. As such, standard PIV was enhanced to allow the application to this small scale geometry. Very high resolution of velocity measurements was achieved, even to such a level that it was possible to accurately compute first order derivatives (shear strains). Quantitative agreement between PIV and CFD results are reported in Table 1. The inconsistency can be due to a slight translational displacement of the PIV laser sheet to the exact position of the normal and transverse plane in CFD, which causes obvious differences in maximal and overall velocity magnitude and consequently shear stress distribution. The relative errors for the average velocity values in the normal planes are below 15%. The errors in the transverse planes are larger, but this can be understood when looking at the flow field. The slow-flow zone downstream the end-opening (and sleeve) is located at the top of the lumen. As such, the measurement results are more prone to “vertical” shifts of the transverse plane (adding the risk of missing the slow flow zone when not measuring close enough to the top of the lumen) than to “lateral” shifts of the normal plane. To illustrate the sensitivity of the results to the exact positioning of the measurement planes, average velocity and strain rate values were computed for a slightly shifted plane for both normal and transverse planes. In the case of the Cut Straight Sleeve catheter, the relative error on velocity magnitude is reduced from 34.4% to 8%, with a plane shift of only 0.5 mm in the transverse plane. A slight rotational displacement of the PIV laser sheet is evident in the PIV results of the transverse plane of catheter Cut Angle (Figure 5), in which an asymmetrical flow was measured. The quantitative discrepancy between PIV and CFD may be further reduced by devising a procedure for a more accurate positioning of the PIV measurement planes in future work.

Figure 5.: CFD and PIV results of in-plane velocity and shear strain distribution defined according to Equation 2 in the normal (A) and transverse (B) plane through the arterial lumen tip of three catheter models (Cut Straight, Cut Angle, and Cut Straight Sleeve).

After validation of numeric results with PIV, a second goal of this work was to study possible thrombogenicity of different central venous catheter designs. The methodology used in this study solely concentrated on flow and shear stress parameters inside the catheter lumens. It did not include other major promoters of thrombus formation like interdialytic loss of locking solution, type of catheter material used, and catheter surface finishing.¹⁷ Also, within a range of elevated shear stresses (>3 Pa), platelet thrombus production also depends on vWF binding to platelet GpIb/IX/V and GpIIb-IIIa.¹²

Apart from high shear stresses, areas of flow stagnation or recirculation that are characterized by longer residence time may implicate platelet aggregation. Flow-induced platelet activation and aggregation has been shown in stenosed human coronary arteries¹⁸, where a volume average SS of approximately 46 Pa and an average transit time of approximately 0.004 second can be calculated (based on an average stenotic diameter of 1.1 mm, 5 mm in length, a peak diastolic blood flow rate of 73 mL/min, wall SS of average 70 Pa along the stenosis wall, and assuming a linear SS profile across the artery lumen). Given the comparable settings regarding SS and RT values, the results of this study are considered to be relevant and may prove to be of importance in order to minimize risk of blood clotting. In vitro validation, however, may be useful to ascertain the results of this numeric study.

Catheter Cut Straight was set as a reference model, as it represents the simplest tip design: a straight cylindrical tip. Blood inflow is highly homogeneous. The tip volume-averaged SS attains 12.6 Pa. Theoretically, the average SS in laminar flow through a cylinder under the simulated conditions is approximately 12.5 Pa (calculated with constant μ = 3.4 mPa·s). As such, little additional shear stress is induced by the catheter inflow design. Due to the homogeneous inflow, RT values larger than 0.030 second are virtually nonexistent. This indicates that almost no local recirculation or zones with low velocities exist in the catheter tip. As a consequence of the low SS and RT, PLI is lowest for this catheter.

Cutting the end-opening at an angle (Cut Angle) reduces the effective inflow area as blood is drawn into the arterial lumen as close as possible to the driving force (i.e., pump). This leads to relatively increased SS levels as compared with the reference catheter. The more complex three-dimensional inflow (see Results) gives a slightly better washout of blood residing near the wall (= zones with high RT), reducing the percentage of volume with RT >0.015 second. Nevertheless, washout is not complete near the inlet as a zone with a significant RT is present near the most distal end of the tip zone, significantly increasing the volume with RT >0.030 second, as compared with the reference case. The combination of elevated SS and RT causes the PLI to increase to a more than six fold value as compared with the Cut Straight catheter.

Adding side holes to the reference catheter (Cut Straight Hole) strongly reduced percentage of volume with RT >0.015 second, indicating that the side holes provide a more disturbed flow patterns near the wall and consequently a better washout near the wall. However, this is at the cost of a slightly increased SS level. Adding side holes to the angular cut catheter (Cut Angle Hole) disturbs the inflow pattern and reduces the size of the slow-flow zone near the distal tip of the lumen. Consequently, regions with RT >0.030 second have almost disappeared, whereas the larger effective inflow area decreases average shear stresses. Also, since side holes provide slightly more than 50% of the total blood inflow rate, the importance of the distal end-opening is reduced. So, quasi-identical results are obtained when adding side holes to the Cut Angle catheter as compared with the Cut Straight Hole catheter and PLI level for catheters with side holes is between the Cut Straight and Cut Angle designs.

Adding a sleeve to the reference design (Cut Straight Sleeve) causes low entrance velocities in the most distal tip zone as more than 80% of the flow enters through the sleeve. More zones with elevated RT are now present: an almost doubled percentage of volume with RT >0.015 second as compared with using side holes. RT >0.030 s zones are at the same level as in Cut Angle. Although average SS levels are maintained at the level of the reference catheter, PLI of Cut Straight Sleeve is strongly elevated, slightly higher than Cut Angle.

Although the inflow surface area of the Concentric catheter is identical to the reference catheter and inflow is homogeneous throughout the end opening, the higher SS levels in the Concentric catheter are a consequence of the annular design of the inflow surface. The latter has more inner wall surface, forcing the flow through the thin area between the two walls. Also because of the flow separation near the entrance, percentage of tip volume with RT >0.030 second is also highly elevated. Consequently, this catheter accounts for the highest PLI of all tip designs studied.

The Ash Split–based design has multiple side holes that give a more spread inflow pattern. This accounts for the lowest average SS levels of all catheters studied. However, as more than 80% of the incoming flow is drawn by the two most proximal pairs of side holes (S1 and S2), the most distal region of the tip is characterized by very low velocities. This observation can be extrapolated to every catheter design that uses multiple (sets of) side holes that are located longitudinally across the tip length (e.g., Tesio) as the most proximal holes receive the largest blood flow and increase the residence time in the low-flow distal tip region. This strongly increases local RT values, causing blood in about one third of the tip volume to be present in the tip zone for longer than twice the average RT of blood passing through the tip zone. For this catheter with a different trend in SS and RT levels, the PLI parameter allows us to assess how the combination of decreased SS and increased RT influences the classification of this design according to possible platelet activation. PLI of Ash Split type is between values of the tip designs with side holes and the Cut Angle design. So, although RT are the highest of all tips studied, the less than linear dependence of PLI on exposure time causes the PLI value to be far lower than the PLI of the Concentric catheter.

Concerning the influence of pulsatile SVC flow, as average SS in the catheter tip closely follows SVC flow rate, catheter classification according to thrombogenicity is not expected to change.

In conclusion, the Concentric catheter is discarded due to the highly elevated SS levels. This numeric study recommends using the reference catheter Cut Straight as a minimal risk to platelet activation. Catheters Cut Straight Hole and Cut Angle Hole render second-best results, showing that adding two (relatively large) side holes, symmetrically placed close to the tip, are not detrimental to the catheter performance. Catheter Cut Angle Hole (with end opening cut at an angle and with two lateral side holes close to the tip) may be preferred in practice because of ease of insertion as compared with the Cut Straight catheter. Catheters Cut Angle, Cut Sleeve, and an Ash Split–based design render suboptimal results.

Conclusions

As crucial factors in blood clot formation, shear stress distribution and low flow zones are assessed in different catheter tip designs using a combined numeric and experimental approach. Computational Fluid Dynamics was validated by using PIV. The chosen standard PIV was a successful method to measure velocity magnitudes in the small scale of a dialysis catheter model. Velocity and derived shear strain distributions in two orthogonal planes of three different catheter models compared qualitatively and quantitatively well with the numeric results.

After validation, four additional catheter designs were studied. In each of the seven catheters studied, six parameters concerning average shear stress (SS) levels and blood residence time (RT) values were assessed. Also Platelet Lysis Index, which combines the influence of shear stress level and exposure time, is studied. The Platelet Lysis Index proved to be a fast and comprehensive parameter to assess possible thrombogenicity of catheter tip designs and allowed comparison when shear stress and residence time values showed different trends. In conclusion, we state that the concentric catheter designs are not recommended due to elevated shear stress levels and residence time values, respectively. Ash Split–based design has elevated residence time values in the distal tip zone as major inflow occurs through the most proximal side holes, as can be expected with catheter designs with multiple side hole along its tip. Concerning possible platelet activation, the elevated residence times are compensated by low average shear stresses. Nevertheless, a cylindrical lumen, preferably Cut Straight or with the addition of only two lateral side holes close to the tip (Cut Straight Hole and Cut Angle Hole) are preferred designs when aiming at a combination of minimal shear stress levels and local residence time values. Transient flow in the SVC is not expected to influence this recommendation. In vitro validation, however, may be useful to ascertain the results of this numeric study.

Acknowledgments

Dr. Mareels was supported by a BOF grant (011D09503) from Ghent University, Belgium.