The geometries of the pediatric CVLs were reconstructed from high-resolution imaging. The tips of the devices (ranging from 30 to 50 mm in length) were scanned using microfocus computed tomography (micro-CT) (Med-X Alpha; Nikon Metrology, Tring, UK). During the scanning procedure, the tip was attached to a carbon fibre plate and secured in place with parafilm B (Bemis, Neenah, WI, USA) to ensure stability during image acquisition. Images were obtained with optimised factors of an x-ray energy of 100 kVp, current of 100 µA, exposure time of 500 ms, with an optimised number of projections for each examination and 4 frames per projection using a Tungsten target. Voxel sizes ranged between 15.29 and 26.22 µm, with each acquisition taking approximately 40 min.

Following calibration, the images acquired with micro-CT (TIFF format) were post-processed to derive geometrical measurements using the commercially available segmentation software Simpleware ScanIP (Synopsys Inc., Mountain View, CA, USA). Geometrical information and dimensions were used to build CAD models of the CVLs by means of SolidWorks 2018 (Dassault Systèmes, Vélizy-Villacoublay, France). Models resembling the four pediatric CVLs included in this study are shown in Figure 1.

The CFD models were created in Ansys DesignModeler (Ansys Inc., Canonsburg, PA, USA). CFD analyses of CVLs were carried out on two main configurations: 1. an idealised geometry of superior vena cava (SVC) was used to isolate the CVLs performance; 2. an anatomical representation of SVC allowed to investigate the interaction CVL-vein and to evaluate possible differences in the CVL performance. More details of the CFD configurations are here presented. 1.

Idealised model: CVLs were coaxially placed inside a straight rigid cylinder with diameter comparable to the SVC of the different patient groups: 6 mm, 8.5 mm, 15 mm and 18 mm (Figure 2A). The length of each SVC-CVL model was chosen to ensure a fully developed velocity profile.

All the models were meshed in Ansys Meshing module and Ansys Fluent Release 19.0 using polyhedral elements. Local refinement of the mesh was applied to the proximity of the CVL and at the wall of the anatomical models (Figure 2B). A sensitivity analysis was carried out for each model to ensure mesh independent results in terms of velocity, pressure and wall shear stress. The final numbers of cells ranged between 1 million and 10 million. More details are provided in Supplementary Appendix A1.

A flat velocity profile at the inlet of the SVC (T1 in the ideal model, Figure 2A) and of the IVC in the anatomical model to match physiological flow rates for each patient group (18). At the venous and arterial lumens of each CVL (respectively V1 and A2 in Figure 2A), two identical but opposite velocity profiles were applied. Each CVL was tested with three velocity conditions closely mimicking the continuous blood flow rates used in routine clinical practice (Table 1) to investigate their performance at different working condition. A reference pressure equal to zero was set at the outlet of the SVC cylinder in the idealised geometry (T2, Figure 2A), and at the level of the tricuspid valve in the anatomical one. Walls were assumed to be rigid, and a no-slip condition was applied with steady state simulations carried out under the assumption of laminar flow.

The blood was modelled as an incompressible Newtonian fluid with a constant viscosity µ of 0.0035 Pa·s and density ρ of 1060 kg/m³. The assumption of Newtonian blood was considered reasonable in light of preliminary simulations showing a constant viscosity throughout the volume of interest. For each CVL, a set of simulations with varying input parameters were performed in Ansys Workbench Release 19.0. Navier-Stokes equations were resolved within ANSYS Fluent using a pressure-based solver with SIMPLE scheme for pressure velocity coupling, and Least Squares Cell Based, Second Order and Second Order Upwind for gradient, pressure and momentum, respectively. Simulations were considered completed when the scaled residual sum of continuity and velocity decreased by more than 10–5. Simulations ran in a workstation with Intel® Xeon® W-2275 CPU (3.30 GHz) processor and 64.0 GB of RAM.

For each simulation, velocity fields were assessed inside the CVL lumen, at the tip of the CVL and in the region of side-holes. In order to identify the presence of asymmetric and skewed jets through the openings of the CVL and compare the different designs, the ratio between the average and the maximum velocity at the CVL tip and side-holes were computed for both lumens of each CVL model. High velocity ratio indicates the presence of a flat velocity profile as described by Cavazzuti et al. in 2020 (19), whilst values close to zero are representative of asymmetric and skewed jets. Reynold numbers were computed at each opening to validate the assumption of laminar flow. Split flow proportions were computed dividing the flow rate through each CVL opening by the total flow rate inside the lumen. Blood residence time (RT) was evaluated in both tips of the CVLs, specifically inside the side-holes. A pathlines-based approach was used. Pathlines were coloured by particle properties, specifically time, and plotted in all the areas of interest. The maximum value of blood residence time was exported for every side-hole. This step was conducted solely on simulations run at intermediate flow rate. In accordance to previous CFD studies (8, 11), shear stress levels—levels of the frictional (tangential) force of the flowing blood - were evaluated on the volume of arterial tip of the CVL where blood is withdrawn. Here, shear stress values were computed according to:τ¯¯=μγ˙where µ is the viscosity of blood and γ˙ is the strain rate, γ˙=12D¯¯:D¯¯, with D¯¯ defined as D¯¯=(∂uj∂xi+∂ui∂xj) (8, 20).

To compare different designs, average values of shear stress were assessed together with the percentage of elements subjected to a level of stress higher than 10 Pa according to Mareels et al. (8).

Values of Platelet Lysis Index (PLI), indicator of platelet activation, were computed as it follows, using a pathlines-based method for each model (8):PLI=3.66⋅10−6t0.77τ3.075where t is the exposure time and τ the magnitude of shear stress.

For anatomical models, maximum velocities were measured in planes along the SVC, with and without CVL. On the same planes presence of secondary flows was investigated. Lastly, wall shear stress (WSS) was considered prior and after CVL insertion. A schematic of the evaluated parameters is provided in Supplementary Appendix A2.

The velocity profiles of the venous and arterial lumens are shown in Figure 3 where regions of low velocity are visualised within all arterial lumens of the CVLs.

The average to maximum velocity ratio measured in the side-holes were consistently lower compared to the tip in all models, and for both the venous and the arterial configuration. The outlets of the arterial configurations showed a skewed jet-like behaviour. The venous tips were characterized by a flatter velocity profile, with values ranging from 0.398 to 0.591 for every model, except for the Pediatric Split Cath. This same trend was observed in the arterial tip of the CVLs (Supplementary Appendix A3).

In all models, Reynolds numbers were below the threshold of 2,000, confirming the laminar nature of the flow analysed in all different configurations (Supplementary Appendix A4).

Split flow proportion between the distal tip and the side-holes are shown in Figure 4. In all models, the flow conditions vary between the venous and arterial lumens. The tip of the CVL plays a significant role when the blood is carried to the body (i.e., venous lumen). In the case of Tesio and Split Cath III, the flow repartition was almost equal between the tip and the side-holes. The Hemo-Cath was characterized by the highest percentage of blood through the tip for the 3 tested conditions (89.4%, 90.7% and 91.7%), whilst the Pediatric Split Cath showed the opposite behaviour with the highest side-holes flow rate (77.2%, 76.4% and 74.5%). The increase in the velocity imposed at the inlet reflected in an increase in the flow rate flowing through the tip for each CVL except for the Tesio (Tesio: 48.5%, 42.8% and 43.3%; Hemo-Cath: 89.4%, 90.7% and 91.7%; Pediatric Split Cath: 23.1%, 23.8% and 25.7%; Split Cath III: 48.8%, 50.3% and 51.6%). In the arterial configuration, the side-holes played a predominant role accounting for more than 90% of the overall flow rate in all models. In the case of Tesio, a flow loss through the tip was recorded in arterial configuration. This was compensated by an increase of flow through the side-holes. The percentage of flow loss seemed to reduce with the 3 tested conditions: 29.8%, 18.6% and 13.1%.

Values of residence times are reported in Table 2. The highest values of RT were found in the Tesio model, consistent with large areas of stagnation—an area with zero or nearly zero velocity—present inside the lumen. For this model, all side-holes except one showed a residence time above 0.030 s. Low values of residence time were recorded in the Hemo-Cath and in the Pediatric Split Cath models.

Values of average shear stress, percentage of shear stress above 10 Pa and PLI are reported in Table 3. The Hemo-Cath was associated with the highest percentage of shear stress above the threshold, whilst the Tesio with the lowest percentage. Overall, for each CVL shear stress values increased with the imposed inlet flow rate.

Peaks of shear stress were consistently recorded close to the proximal side-holes (Figure 5) in the arterial configuration. The Tesio model displayed the lowest values of PLI; the Pediatric Split Cath displayed the highest PLI.

When CVLs were placed in the anatomical SVC, the cross section of the vessel was reduced, causing an expected increase in the blood velocity within the SVC, as shown in Figure 6. Areas of high velocity non-symmetrically distributed were noted around the CVL. The highest increases of velocity were recorded in the Tesio and in the Hemo-Cath models: 34% and 28% difference in the maximum velocity respectively, and 15% and 13% in the average velocity, respectively. With the smaller CVLs (Tesio and Hemo-Cath), a pair of small asymmetric eddies appeared in the SVC close to the wall of the device (Figure 6B). Large eddies were found in the SVC cross-section.

After insertion of the CVL, WSS increased in all four models along the SVC wall, where the presence of the CVL altered the normal distribution. The highest WSSs were found in the smallest anatomical model. The Pediatric Split Cath recorded the highest increase in WSS, going from an initial value of 0.34 Pa to a final one of 1.48 Pa after CVL insertion.

Regarding the CVL performance, small differences were found in the levels of shear stress above the 10 Pa threshold for the bigger models (Pediatric Split Cath and Split Cath III), as shown in Figure 7. On the contrary, smaller CVL models recorded a higher percentage of shear stress above 10 Pa in the anatomical model. This difference is more evident in the Tesio 6.5 F CVL in which values were more than doubled at low flow rates.