Numerical study on the impact of central venous catheter placement on blood flow in the cavo-atrial junction

Abstract

An in silico study is performed to investigate fluid dynamic effects of central venous catheter (CVC) placement within patient-specific cavo-atrial junctions. Prior studies show the CVC infusing a liquid, but this study focuses on the placement without any liquid emerging from the CVC. A 7 or 15-French double-lumen CVC is placed virtually in two patient-specific models; the CVC tip location is altered to understand its effect on the venous flow field. Results show that the CVC impact is trivial on flow in the superior vena cava when the catheter-to-vein ratio ranges from 0.15 to 0.33. Results further demonstrate that when the CVC tip is directly in the right atrium, flow vortices in the right atrium result in elevated wall shear stress near the tip-hole. A recirculation region characterizes a spatially variable flow field inside the CVC side hole. Furthermore, flow stagnation is present near the internal side hole corners but an elevated wall shear stress near the curvature of the side hole’s exit. These results suggest that optimal CVC tip location is within the superior vena cava, so as to lower the potential for platelet activation due to elevated shear stresses and that CVC geometry and location depth in the central vein significantly influences the local CVC fluid dynamics. A thrombosis model also shows thrombus formation at the side-hole and tip-hole. After modifying the catheter design, the hemodynamics change, which alter thrombus formation. Future studies are warranted to study CVC design and placement location in an effort to minimize CVC-induced thrombosis incidence.

Introduction

In-dwelling central venous catheters (CVCs) are widely used as a means of therapeutic drug delivery and monitoring in an array of clinical settings, including acute and long-term management. CVCs are typically inserted in the large veins of the neck (jugular vein), shoulder (subclavian vein), or thigh (femoral vein) and advanced into the superior vena cava-right atrial junction or right atrium (distal tip). CVCs provide a critical means to deliver potentially lifesaving therapies; however, their use can be compromised by serious complications – including catheter-related thrombosis (CRT) and bloodstream infections, both of which can be fatal. Published CVC-related thrombotic complication rates vary between 14-18% with only 5% being symptomatic events.⁴⁰ CRT can present as an occluded or dysfunctional CVC or a more serious complication such as venous thromboembolism (VTE).^5,41 Occluded or dysfunctional CVCs present as intraluminal clots blocking CVC lumens, mural thromboses attached to CVCs and vessel walls, or fibrin sheaths attached to CVCs.^20,42 These thrombotic complications can embolize to the lungs - resulting in temporary or permanent derangement of effort tolerance and quality of life and long-term need for anticoagulation (with associated bleeding risks).

Due to the fluid mechanic alterations imposed by CVC insertion in the central veins, and the well-accepted influence that hemodynamics has on thrombosis, there is significant motivation to understand CRT development from a fluid mechanics perspective.^16,19 Published work has focused on in silico CVC-related thrombosis investigations with computational fluid dynamics (CFD) and thrombosis model-based studies.^3,9,18,24,25 Previous studies have focused on the flow in and around CVCs in hemodialysis and general central venous applications.^22,24,25 Computational findings have detailed that CVC insertion can increase local fluid velocity and pressure drop by up to 57%.²⁵ For example, it has been demonstrated that CVC insertion substantially increases the area of the central veins with a wall shear stress (WSS) higher than 10 dynes/cm² and also subjects the CVC surface to the magnitude of shear stress, inducing potential for blood damage and platelet activation.²⁵ CVC placement and CVC side/tip holes’ geometries also greatly affect local flow profiles and shear stress distributions.^22–25 Further, numerical models of flow around CVCs have shown that CVC tip and side holes (if present) geometry can greatly influence the local fluid mechanics and shear stress distributions, generally resulting in flow stagnation inside of the side holes, high shear stresses at side hole rims, and recirculation/flow vortices immediately distal to the tip.¹⁸ Stagnation and recirculation allow stasis and/or aggregation of blood cells and proteins. In contrast, areas of high shear stress can promote platelet activation and thrombin production, accelerating CVC-induced thrombosis.¹⁸ Numerical studies paired with in vivo work have shown that fibrin formation was also associated with regions of high shear stress on CVCs after placement, such as on side-hole rims. In contrast, fibrin plaque formation was favored in regions of low shear stress, such as inside the side holes.¹⁸

Further, there is evidence that CVC insertion in the central veins greatly decreases flow rotationality and helicity, thereby increasing thrombosis risk, but that when the CVC tip is in the right atrium (RA), the overall flow field’s vorticity is increased.^22,25 These findings demonstrate that the location of the CVC tip is critically important due to its effects on local and global flow characteristics. Typically, CVC placement is such that the CVC tip should sit in the junction between the superior vena cava (SVC) or inferior vena cava (IVC) and RA, depending on the device’s insertion location. Tip placement in the cavo-atrial junction allows for increased washing at higher flow rates to decrease overall cellular and protein adhesion to the device, which can accelerate thrombus formation. However, the fluid mechanic characteristics presented, in Peng et al.²⁴ and Oliviera et al.²², leaves open questions about what tip location can lower thrombotic risk for patients with CVCs with respect to the local and global fluid mechanics in the central veins, cavo-atrial junction, and right atrium. As a final important note, previous work has emphasized the importance of a realistic RA model; however, many studies use a basic cylindrical SVC model, especially when focusing on the catheter design.^6,20

In the literature, several thrombosis models have been developed, mainly inspired by the comprehensive continuum model introduced by Sorensen et al.^31,32 These models typically used scalar transport equations to simulate the platelet deposition and activation. Taylor et al.³⁶ used adenosine diphosphate (ADP) as the only platelet agonist considered but introduced aggregation intensity to incorporate thrombus deposition and breakdown, validated by magnetic resonance imaging measurements in a cylindrical backward-facing step channel.⁴⁶ Wu et al. included more species and good agreements were observed in the in-vitro measurements in an injured blood vessel and micro-channels with small crevices.⁴³ Rojano et al. extended the model further by incorporating fibrin formation, increasing the total number of biochemical species to 17.²⁸ Although these models have been applied to various blood-contacting devices such as a rotary blood pump and an artificial lung hollow fiber bundle, no studies have been conducted on a catheter.

The present study focuses on patient-specific models for anatomical relevance and a CVC model with an ovular side hole while altering the CVC tip location to sharpen understanding of CVC-induced thrombosis risk. This study aims to develop a computational framework to explore the impact of CVC placement in the cavo-atrial junction. To validate the numerical model, the simulated flow fields were compared with the particle image velocimetry (PIV) measurement in the idealized SVC. A thrombosis model was also incorporated to demonstrate the role of hemodynamics and potential modifications to lower the thrombus formation induced by the catheter.

Materials & Methods

Magnetic Resonance Angiogram Data and Computational Model Reconstruction

Two patient-specific central vein models were reconstructed from cardiac MRI (CMR) datasets acquired using commercial 3 Tesla scanners (General Electric, Waukesha, WI, USA): CMR datasets were attained from a pre-existing institutional registry of fully HIPAA de-identified images acquired at Weill Cornell Medicine (New York, NY) for which registry design has been previously reported.¹⁴ Institutional review board (IRB) approval for use of HIPAA de-identified retrospective CMR data was attained from the Weill Cornell IRB. Patient specific 3D models were derived from magnetic resonance angiography (MRA), which was performed using a conventional gradient echo pulse sequence, for which typical voxel size was 0.8203×0.8203×1 mm³. MRA acquisition frequency was once in one cardiac cycle at the end of diastole, so the central vein models were assumed rigid based on the available reconstructions. Segmentations were performed using Slicer (Version 5.2.1), as demonstrated in Figure 1a. Each exported geometry included the RA, the complete SVC, the IVC hepatic segment, and the outlet (i.e., the tricuspid valve to the right ventricle), as shown in Figure 1b. Images of respiratory compensated 4D flow acquisition in a sagittal-oblique orientation were used to extract the evolution of blood flow in the central vein (Figure 1c). The voxel size was 1.406×1.406×0.9 mm³, and the temporal resolution was 20 time-frames per cardiac cycle. An in-house Python script (in the supplementary material) was programmed to extract the velocity information from 4D flow images, and the velocity vector on one slice of the flow field at one time instance is shown in Figure 1d. The central vein reconstructed at the previous step was used as a mask to preserve velocity vectors in the central vein only (Figure 1e). The 4D flow field in a central vein model obtained at this step is provided as supplemental material.

Figure 1:

Workflow of central vein reconstruction from MRA and extraction of the velocity field from 4D flow MRI. (a): One slice of an MRA image and the segmentation of the RA. (b): Reconstructed RA based on 3D segmentation. (c): One slice of a 4D flow image. (d): One slice of 4D flow MRI after converting pixel values into velocity magnitudes in each direction. (e): Velocity field in a central vein. The red cuboid represents the position of 4D flow acquisition. (d): Velocity field in the central vein using reconstructed RA as a mask to filter 4D flow.

After the reconstructions of two patient-specific models (Figure 2a and Figure 2b in two views), a double-lumen CVC (Teleflex^® Arrow) was segmented from images acquired on a micro computed tomography scanner (GE v|tome|x L300 multi-scale nano/micro CT system) with a 7 French (2.33 mm) diameter, and one side hole and one tip hole (Figure 2c). The inner lumen connected to the side-hole was crescent-like, whereas the inner lumen of the tip hole was a straight cylinder (Figure 2d).

Figure 2:

Numerical models of central veins with virtual CVC insertion. (a): Mode A and Model B in View 1. (b): Model A and Model B in View 2. (c): CVC reconstructed from microCT. Outer diameter: 2.33 mm (7 French); Tip hole diameter: 0.75mm; and dimensions of the side hole: 3.58 mm×1.61 mm. (d): Zoomed-in view of the side-hole with the crescent-like lumen.

To explore the optimal depth of CVC insertion, the device was placed virtually at five locations 1 cm apart in each model, denoted by their location in the model name (i.e., “Model_A_10” for Model A, 10 mm insertion depth) (Figure 3a and Figure 3b). Due to the presence of the side hole, the catheter was non-axisymmetric about axis Z and was oriented in four directions 90° apart to investigate this geometry’s effect on the flow. Forty-two simulations were performed that included 40 numerical simulations derived from each patient-specific model with the CVC (i.e., 2 models × 5 depths × 4 orientations) and two without the CVC. To mimic ideal conditions, the catheter was fixed in the center of the vein only, without contacting the SVC lumen during simulations, though it may touch the lumen in practice. A 15 French CVC was also introduced as shown in Figure 1S in the supplementary material, to explore the effects of the CVC size. The 15 French was scaled up from the 7 French CVC.

Figure 3:

(a): Model A with virtual CVC insertion at five depths 10 mm apart. The straight arrow denotes the position of the side hole. (b): Model B with virtual CVC insertion at five depths 10 mm apart. In each model, it includes four sub-models (denoted by “×4”) based on the orientation, such as Model A_0_0, Model A_0_90, Model A_0_180 and Model A_0_270.

Numerical Modeling

In this study, blood was assumed to be an incompressible Non-Newtonian fluid with a density of 1,050 kg/m³, and the kinematic viscosity was modeled using the Cross-Power equation⁴⁷:

$$\nu ={\nu }_{\infty }+\frac{({\nu }_0-{\nu }_{\infty })}{1+{(m\dot{\gamma })}^j}$$ (1)

where ν₀ is 754 cSt at low shear rates (≤ 0.1 s⁻¹); ν₀ is 3.5 cSt at high shear rates (≥ 100 s⁻¹); m is 2.433 s; j is 1.229; and $\dot{\gamma }$ is the shear rate in s⁻¹. Mesh generations were performed using cfMesh implemented in OpenFOAM (Version 7). The grid numbers in the model with and without the CVC were approximately 2 million and 1 million, respectively (Figure 4a). Local refinements were applied to regions surrounding the device’s side and tip holes (green and red triangles). Based on the average flow rate and the effective SVC diameter ($(D_{eff}=2\sqrt{\frac{Are{a}_{cross-section}}{\pi }})$), Reynolds numbers in Models A and B were 990 and 1,340, respectively, so the flow inside the model was assumed to be laminar.

Figure 4:

Numerical simulation of flow around the CVC. (a): CFD mesh generation with refined regions near the tip hole and the side hole as regions of interest. Green triangle: side hole. Red triangle: tip hole. (b): Flow rate profiles in the SVC and IVC in both models. Dots denote 20 data points extracted from 4D MRI. Solid lines are the interpolated flow profiles.

Patient-specific velocity profiles were imposed at the SVC and IVC (Figure 4b) and were derived from 4D MRA measurements using an in-house Python script (in the supplementary material). The temporal resolution of 4D flow acquisition was 20 time-frames per cardiac cycle, and trigonometric interpolation was used to up-sample the periodic profile to 2,000 time-frames per cardiac cycle (Table S2 for detailed information in the supplementary material). The unsteady flow simulations were performed by merging the controls of the hybrid pressure-implicit with the splitting of operators (PISO) and the semi-implicit method for pressure-linked equations (SIMPLE), pimpleFoam solver in OpenFoam.¹ Furthermore, the pimpleFoam solver was customized to read the point-wise velocity profile at each time step. A no-slip boundary condition was applied to surfaces such as the lumens and outer walls of the CVC and the venous walls. The inletOutlet condition in OpenFOAM was imposed at the outlet because it switches between zeroGradient in the forward flow direction and fixedValue in the backward flow direction. The fixedValue was set as zero flow rate to mimic the unidirectional behavior of the tricuspid valve. The zeroGradient boundary conditions were applied to the pressures at both SVC and IVC, and the fixedValue boundary condition was set at the outlet.

A mesh convergence test was conducted by refining the numerical model progressively with a ratio of about 1.3 (described by Eq. 2).⁷

$$r\approx {\left(\frac{N_{medium}}{N_{coarse}}\right)}^{1/3}\approx {\left(\frac{N_{fine}}{N_{medium}}\right)}^{1/3}$$ (2)

where N is the number of grids in each mesh. All meshes were simulated under the constant flow rates in SVC and IVC, and the velocity and scalar shear stress convergences were monitored at the regions of interest (in the supplementary material). To examine the temporal convergence, the same criterion was monitored, the result was stabilized in the fourth cycle (Table S3 for detailed information in the supplementary material). The results presented hereafter are based on the fourth cycle.^22,35

The thrombosis model in this study was based on Rojano et al.’s work that could simulate the thrombus formation in-vitro experiments conducted by Yang et al. and Taylor et al.^28,37,46 The biochemical species and reactions were governed by scalar transport equations in the form written:

$$\frac{\partial C_i}{\partial t}+(u\cdot \nabla )C_i=\nabla \cdot (D_i\nabla C_i)+S_i$$ (3)

where C_i is the volume concentration of i^th species; D_i is the diffusivity; and S_i is the source term due to reactions. The thrombus was considered as a porous media, and its presence impeded the blood flow according to its concentration. The influence of the deposited platelets and fibrin was represented by the additional Brinkman’s term in the momentum equation:

$$\rho \left(\frac{\partial u}{\partial t}+u\cdot \nabla u\right)=-\nabla p+\mu {\nabla }^{2}u-\frac{C}{1-\varphi }u$$ (4)

where $\rho$ is the density; $\mu$ is the dynamic viscosity; u is the velocity; C is the hindrance function; and $\varphi$ is the volume fraction of thrombus. Details of the equations and the values of the parameters are available in the work published by Rojano et al.²⁹ The duration of the thrombosis simulation in this study was 15 minutes, encompassing more than one thousand cardiac cycles. To accelerate computations, a dual-time-step strategy was used in the thrombosis simulation.^28,48 A larger time step (dt = 0.01 s) was used for the thrombosis model, while the blood flow was simulated using a smaller time step ($\mathit{dt}=0.1\mu s$) for numerical stability. This approach was based on the observation that the influence of the thrombus growth on the surrounding blood in one time step (dt = 0.01 s) was trivial. Time-averaged flow profiles were imposed at the boundaries when the thrombosis model was used. In addition, the flow was simulated using the steady-state solver, serving as the initial condition of the thrombosis simulation to ensure the validity of the dual-time-step strategy. For the thrombosis simulation, the computational time was about one week on eight core Intel Xeon CPU Gold 6354 @ 3.00 GHz.

Experimental Validation

Figure 5 shows the schematic drawing of the flow loop that included an idealized SVC channel and a catheter with a side-hole and a tapered tip, mimicking the blood flow around the inserted catheter. The inner diameter of the channel and the outer diameter of the catheter were 16 mm and 5.28 mm, respectively, and thus the corresponding CVR was 0.33. The flow was driven by a pulsatile pump, and the flow rate was monitored by an ultrasound flow probe (Transonic systems, Ithaca, NY). The flow field was measured by a two-dimensional particle image velocimetry (PIV) system, consisting of a double-cavity pulsed Nd:YAG laser (Terra PIV; Continuum, San Jose, CA), a highspeed charge-coupled device (CCD) Phantom camera (AMETEK Inc, Berwyn, PA), and a laser pulse synchronizer (TSI Inc., Shoreview, MN). The laser pulse delay (delta T) was varied from 200 to 400 µs to capture 200 image pairs for each spatial and temporal position.

Figure 5:

Schematic drawing of the flow loop for the numerical model validation using PIV. (a): Flow loop driven by pulsatile pump and PIV system. Black dot: acceleration. Red dot: peak. Yellow dot: deceleration. (b) Image acquisitions at three positions. I: Tip, II: Side-hole, and III: velocity profile for numerical model. (c): Numerical model of the flow loop using the measurements at III as boundary condition. Red arrow: dominant flow direction.

To match the refractive index of the acrylic model and the viscosity of blood, the water-glycerin-sodium iodide analog ($\rho =1.71g/\mathit{ml}$, $\upsilon =3.52\mathit{cSt}$) was used and seeded with $10\mu m$ hollow glass microspheres (Potters Industries, Malvern, PA), similar to previous studies ^11,26. Image pairs were acquired at three instants (i.e., acceleration, peak and deceleration in Figure 5a) and two regions of interest (i.e., the tip and the side-hole in Figure 5b). The post-processing was conducted using Insight 4G™ software, including manual masks, background image subtraction, cross-correlation, 50% overlap of a final interrogation window of 16×16 pixels. The final velocity maps were processed using Python scripts based on NumPy, SciPy, and Matplotlib libraries.

The numerical model of the flow loop was meshed using the methodology akin to that used in the patient-specific model (Figure 5c). With the Reynolds number at the peak of about 1,800, the flow was assumed to be laminar. The velocity profiles at the inlet of the numerical model were extracted from the PIV measurements, and trigonometric interpolation was used to augment the temporal resolution to 2,000 time-frames per cycle. Similarly, the numerical results were based on the fourth cycle.

Results

Comparison between PIV and CFD in the simplified SVC

Figure 6 depicts the comparisons of velocity profiles between the PIV (red line) and CFD (green line) results around the side-hole and the tip at three instants (Figure 5a). Throughout the selected moments, the flow profile in the channel between the SVC and CVC region was predominantly parabolic except the side-hole and the wake of the tip. Although the flow rates at deceleration (Figure 6b) and acceleration (Figure 6c) were close, the opposite pressure gradients resulted in the discrepancy in the velocity profiles. In the side-hole and the wake of the tip, the recirculation was also more intense during the deceleration. These features measured by the PIV were all observed in the CFD results as well, demonstrating the capability of the numerical model in predicting the blood flow at the Reynolds number below 1,800. In addition, quantitative comparisons were also analyzed using the global relative comparison error, E, defined as:⁷

$$E(\%)=\frac{1}{n}\sum _{i=1}^n\left|\frac{{|u_{2D}|}_{PIV,i}-{|u_{2D}|}_{CFD,i}}{{|u_{2D}|}_{PIV}}\right|\times 100$$ (5)

where $|u_{\mathit{2D}}{|}_{\mathit{PIV},i}$ is the velocity magnitude at each spatial location of the PIV flow map, $|u_{\mathit{2D}}{|}_{\mathit{CFD},i}$ is the prediction at the corresponding position, and $|{\overline{u}}_{\mathrm{2D}}{|}_{\mathit{PIV}}$ is the average velocity magnitude measured with PIV on the plane. The comparison error is summarized in Table 1, and the relative errors at the side-hole and the tip were close to each other within 1.5%. The highest error (7.56 %) and the lowest error (4.4 %) occurred near the tip at the deceleration and the side-hole at the peak, respectively. The highest error (7.56%) occurred near the tip during deceleration, while the lowest error (4.4%) was observed at the side-hole during the peak.

Figure 6:

Comparison of the velocity profiles obtained from PIV (red line) and CFD (green line) results at the side-hole (left) and the tip (right). (a): Peak. (b): Deceleration. (c): Acceleration

Table 1:

Global relative comparison error between CFD and PIV at peak, deceleration and acceleration.

	Spatial
Temporal	Side-hole	Tip
Peak	4.40%	5.76%
Deceleration	6.50%	7.50%
Acceleration	4.90%	4.76%

Impacts of the insertion on the central vein model

Figure 7 shows the time-averaged internal flow fields with and without the CVC located at different locations. In Model A, the effective diameter of SVC was 14.3 mm, so the 15 French CVC (5 mm) occupied 12% of the cross-sectional area of SVC at a catheter-to-vessel ratio (CVR) of 0.35 (CVR for 7 French CVC was 0.16). The effective diameter of SVC in Model B was 15.3 mm, and the corresponding CVR was 0.33 (CVR for 7 Fr CVC was 0.15). The minor reduction from SVC resulted in inconspicuous differences between Model A and Model A_0 as well as Model B and Model B_0. In addition, the insertion depth played an insignificant role in the flow inside the RA, as demonstrated in Models A_0 versus A_40 and Models B_0 versus B_40 (Figure 7). The simulation results showed that the orientation of the side hole along the CVC’s long axis also had negligible effects on the flow in RA, owing to its relatively small dimensions to SVC and the entire central vein model. As anticipated, similar observations were found in the models with a 7 French CVC (Figure 7).

Figure 7:

Velocity fields in Models A (a) and B (b) at different depths.

Figure 8 shows the time-averaged WSS contours on the SVC without the CVC (left), with the CVC at the minimum depth (middle) and the maximum depth (right) in both models. The area-averaged WSS value in all models was below 1 Pa set as the upper limit of these contours. The comparison between Model A and Model A_0 demonstrated that the insertion increased the level of WSS surrounding the CVC indicated by the double-sided arrow (Figure 5a). As a result, the area averaged WSS elevated from 0.66 Pa to 0.79 Pa (7 Fr) or 0.83 Pa (15 Fr). In the models with the 15 Fr CVC, the WSS level in the lower third became higher after a deeper insertion (e.g., placing the tip in the RA), leading to a higher area-averaged WSS of 0.95 Pa, as shown in Model A_40 (Figure 8a). Regardless of the difference between the two models, the same trend was observed in Model B, evidenced by the area-averaged WSS values from 0.44 Pa to 0.62 Pa (Figure 8b). However, in the models with the 7 Fr CVC, the elevation of the WSS level inducted by the deeper insertion was negligible.

Figure 8:

WSS distributions on the SVC in Model A (a) Model B (b). Double ended arrow indicates the depth of the CVC insertion in the SVC. The area-averaged WSS value is labeled in each model.

Impacts of insertion on CVC tip-hole

Figure 9 shows the time-averaged velocity contours surrounding the tip-hole in the coronal plane and an isoline of 0.01 m/s highlighted in grey to indicate the low flow region. When the tip was located inside the SVC in Models A_0, A_10, B_0, and B_10, the primary flow direction was along the long axis of CVC, and the low flow region appeared in the wake of the tip (Figure 9). With a deeper insertion, the CVC tip entered the RA region dominated by the clockwise vortex that redirected the flow surrounding the tip from the axial direction along the CVC to the transverse direction, as demonstrated in Model B_30. As a result, the low flow region shifted to the lateral side of the CVC tip (white arrow denoted “Low”) rather than immediately distal to it in the previously discussed model depths. In addition, this lateral region also experienced low velocity gradients. Meanwhile, a region with a high velocity gradient appeared near the CVC tip (white arrow denoted “High”), promoting the potential of platelet activation. Note that this study only concerned the flow around the CVC, and no flow was perfused through the lumens of the device. Although the fields varied in the corresponding model with the 15 French CVC, the wider CVC did not change the patterns fundamentally (Figure 2S in the supplementary material).

Figure 9:

Velocity magnitude contours near the CVC tip on the coronal plane and WSS distribution on the tip in Model A (a) and Model B (b) with an isoline of 0.01 m/s in grey for models with a 7 French CVC. High arrow: Region under high velocity gradient. Low arrow: Region under low velocity gradient

Table 2 displays the areas of low WSS (≤ 0.1 Pa on the CVC tip of both models. When the CVC tip was placed within the SVC, its WSS and shear stress level in both models were in the desired range, owing to the smooth flow field (Figure 9). For other models (i.e., Model A_30, Model A_40, Model B_30, and Model B_40), the adverse flow direction change (Figure 9) induced a low WSS region behind the tip (Arrow in Figure 9b – Model B_30). At the same time, the transverse flow direction could elevate the shear stress level at the CVC tip in Model B_30. Its peak shear stress at the tip was around 10 Pa. Note that the region inside the tip-hole was excluded from the calculation in Table 2 since the WSS level was always low because of the zero flow rate in the lumen. Otherwise, its value would dominate the area of low WSS. Due to the smaller diameter of the 7 French CVC, the area of low WSS was smaller than that of the corresponding 15 French CVC.

Table 2:

Areas of low WSS (≤ 0.1 Pa) on the CVC tip of each model.

	7 Fr	15 Fr
Model	Area(mm2)	Area(mm2)
ModelA_0	0.0	0.0
Model A_10	0.0	0.9
Model A_20	0.3	5.4
Model A_30	0.4	0.8
Model A_40	0.1	0.8
Model B_0	0.0	0.0
Model B_10	0.0	0.0
Model B_20	0.0	4.7
Model B_30	0.2	8.7
Model B_40	1.5	10.6

Impacts of insertion on CVC side-hole

Based on the simulations, the flow in proximity to the side-hole varied in different orientations at each depth (Figures 3S and 4S in the supplementary material). Since the SVC is not a perfectly cylindrical vessel with adequate length for a fully developed flow, the variations among different orientations persisted at all depths. However, all the flow fields in the side-hole region shared a similar pattern, and it was close to the lid-driven cavity flow characterized by a vortex (indicated by the arrow), as shown in Figure 10a. All vectors have the same length for ease of displaying the velocity vector of low magnitude, and the color map differentiates the magnitudes. The recirculation persisted in the side-hole region, though its region varied with the flow in the SVC. Based on numerical simulations, the high shear stress (≥ 10 Pa) region appeared at the rim in Model A_40_0 (Figure 10b). In the region inside the side-hole, the low WSS (≤ 0.1 Pa) dominated, as shown in Figure 10c. The corners and the lumen were vulnerable to flow stagnation, where flow recirculation could occur.

Figure 10:

Flow field, shear stress and WSS near the side hole of Model A_40_0 with a 7 French CVC. (a): Velocity vector distribution on the plane perpendicular to the side hole at the maximum (left) and minimum (right). Vortex indicated by an arrow. (b): Shear stress contours on the surface of the side-hole in the top view. (c): Low WSS (≤ 0.1 Pa) region inside the side hole.

Thrombosis

Figure 11 illustrates the thrombus formation on both 7 Fr and 15 Fr CVCs at three depths, within 1 cm from the desired depth, in both models after a 15-minute simulation. When the CVC was inserted 1 cm shallower than the cavo-atrial junction (Figure 11a and Figure 11d), the flow stagnation led to thrombus formation in the side-hole and the tip-hole. Due to the relative high velocity at the opening of the side-hole (Figure 10), the thrombus growth was limited (Figure 11a and Figure 11d). In contrast, the slow-flow region in the wake of the tip facilitated the growth, and the thrombus partially covered the tip (Figure 11a and Figure 11d). At the desired insertion depth near the cavo-atrial junction, the influence of the deeper insertion on the thrombus in the side-hole was almost negligible (Figure 11b and Figure 11e). The flow near the CVC tip was redirected by the atrial flow (Figure 9), and the thrombus was observed on the lateral side in Model A (Figure 11b). However, the thrombus was entirely confined within the tip-hole in Model B (Figure 11e), due to a stronger velocity gradient as shown earlier in Figure 9. When the CVC was inserted 1 cm below the cavo-atrial junction in Model A (Figure 11c), the thrombus in the side-hole still remained largely unchanged, though the stronger velocity gradient suppressed the growth of the thrombus in the tip-hole beyond the opening. In Model B (Figure 11f), thrombus formation occurred on the lateral side of the tip, influenced by the atrial flow in the transverse direction.

Figure 11:

Thrombi formed on 7 Fr and 15 Fr CVCs at three depths in Models A and B after 15 minutes. (a): Model A_0. (b): Model A_10. (c): Model A_20. (d): Model B_10. (e): Model B_20. (f): Model B_30. Left: 7 Fr. Right 15 Fr.

According to the simulations, the thrombus beyond the tip-hole was related to the recirculation in the wake of the tip, and thus the profile was modified to reduce the cross-sectional area at the tip. For the side-hole, its lumen was streamlined to remove the corners prone to thrombus formation. Figure 12 shows the thrombus formation on the original and modified 7 Fr catheter in Model A_10 at the desired insertion depth after 15 minutes. The reduction of the cross-sectional area at the tip induced a smaller thrombus as expected, though this modification was not able to avoid the growth beyond the tip-hole (Figure 12 a&b). Due to the reduction of the flow stagnation region in the side-hole, the thrombus could only be initiated in the deep lumen, and its further expansion towards the catheter tip was inhibited by the velocity gradient. Compared with the original design, the thrombus in the side-hole had a smaller blood contacting surface (i.e. the thrombus did not cover the opening of the side-hole completely in Figure 12 b&d).

Figure 12:

Thrombus formation on the 7 Fr CVC in Model A_10 before (Upper) and after (Lower) the modifications. (a): Thrombus in the tip-hole of the original CVC. (b): Thrombus in the side-hole of the original CVC. (c): Thrombus in the tip-hole of the modified CVC. (d): Thrombus in the side-hole of the modified CVC.

Discussion

In the present study, a double-lumen CVC was placed virtually into two patient-specific models to understand the impacts of the insertion depth and CVC size on the blood flow in the central vein and CVC itself. Two models were reconstructed from MRA, and patient-specific flow profiles were applied to the boundaries. CVR is an important factor that quantifies the in-dwelling space occupied by the catheter based on the CVC diameter. The blood-contacting catheter can decrease blood flow, leading to potential blood flow stagnation.⁴ Meanwhile, a high shear rate in the viscous boundary layer can promote platelet activation.²³ Clinically, a 7-French catheter is most commonly used for adults ¹². Therefore, a catheter of the same size was selected, and the CVRs with respect to the corresponding SVC diameter were approximately 0.15. Clinical studies suggested that the correlation between the thrombosis risk and the CVR < 0.33 was insignificant.^30,33 As a result, a 15-French catheter was also introduced to push the CVR to the recommended limit. The comparisons between models with and without CVC indicated that the presence of the CVC would not significantly influence the internal flow in the central vein within the recommended CVR range (Figure 7). This can be explained by the relatively small diameter of the 7 French or 15 French CVC to the 1.5–2 cm SVCs in both subjects at CVR of about 0.15 or 0.33, respectively. For instance, the percent reduction in area at CVR of 0.33 is 11%.

Ideally, the catheter should stay in the center of the SVC, especially the tip, to minimize physical contact with the vein and mural thrombosis, as modeled in this study.^15,34 The CVC tip should stay near the cavo-atrial junction (i.e., the lower third of the SVC and the upper RA) beyond the pericardial reflection. The presence of the CVC elevated the area-averaged WSS level, as demonstrated in Figure 8. The magnitude of the increment was less than 0.5 Pa. In a similar study on the WSS level on the SVC, the relativity between the thrombosis occurrence in the clinical data and the WSS was not found.²⁵ Therefore, the changes in the WSS distributions on the SVC induced by the CVC insertion may have limited effects on thrombus formation.

The flow field surrounding the CVC tip and the WSS level was substantially affected by its location, as shown in Figure 9 and Table 2. The isoline at 0.01 m/s is illustrated to indicate the low flow velocity region, where flow stagnation could occur, potentially leading to blood clots ^21,27,39. In the tubular SVC, its streamlined shape ensured smooth flow except for the flow stagnation in the tip-hole. Based on other studies on the recirculation region in the backward-facing step tube, this stagnation and recirculation may stimulate thrombus formation.^38,46,47 However, this issue can be mitigated by device luminal flushing and anticoagulation medication.¹⁷ After a deeper insertion of the CVC into the RA, the flow field around the tip was influenced by the RA vortex and induced a drastic change in the flow direction from axial to transverse (e.g., Model B_30 in Figure 9). The CVC is primarily designed for a tubular flow in blood vessels along its thin body, and the transverse flow direction exacerbates its disturbance. This adverse change resulted in a low WSS region on the lateral side of the tip in Model B_30, leading to a higher thrombosis potential. The larger CVC size deteriorated it further, as shown in Table 2, and the bigger low WSS region may facilitate platelet adhesion. In addition, the high shear stress on the rim of the tip hole could enable platelet activation, facilitating the formation of a “white clot” (fibrin and platelet-rich) generally acknowledged as mechanically stronger and harder to remove.^8,13 In terms of hemodynamics, the tip of the catheter should stay in the SVC to minimize these adverse effects.

Simulations showed that the flow field at the side hole was affected by both insertion depth and orientation because the flow inside the entire SVC was not fully developed. Similar to the lid-driven flow, the fluid flowing across the opening generated recirculation inside the hole in Figure 10a. However, the geometry of the side-hole channel was more irregular with a crescent-like cross-section, and flow stagnation occurred at the corners and lumen in Figure 10c, leading to potential thrombus formation.^10,18 Compared with the tubular tip-hole lumen, the flushing in the side-hole lumen will be less effective in removing the thrombus inside due to the geometry of the lumen and the side hole itself, especially at the corners. As shown in Figure 10b, the rim of the side-hole was vulnerable to high shear stress when the CVC was deeply inserted into the RA due to the relatively sharp curvature.^4,23 Therefore, even with the recommended ovular side hole geometry, results show that the design of the side-hole must be further optimized to eliminate flow stagnation inside the channel and minimize the shear stress at the rim when no fluid is administered through the channel.

To obtain more intuitive estimations, thrombus formation was predicted on the CVC when the insertion depth was around cavo-atrial junction (within 1 cm) in both models. The thrombosis model was validated by in vitro tests in the backward-facing step tube, which had the similar range of flow rate and characteristic recirculation to the current study.^29,38,46 As expected, flow stagnations and recirculation contributed to thrombus formation in the side-hole and tip-hole (Figure 11). The side-hole mostly resided in the tubular SVC, and its thrombus was less susceptible to insertion depth. The velocity gradient at the opening of the side-hole constrained the growth (Figure 10), and the thrombus remained in the side-hole after 15 minutes (Figure 11). The tip was notably influenced by the flow in the RA, and thus its thrombus varied with insertion depth. When the tip was above the junction, the thrombus grew in the wake beyond the tip-hole in both models (Figure 11 a&c). However, the thrombus at the tip became more patient-specific when the CVC was inserted deeper. For the insertion depth at the junction, the thrombus at the tip in Model A was observed in the wake and the lateral side (Figure 11), while that in Model B was confined in the tip hole (Figure 11). After the tip was inserted 1 cm below the junction, the thrombus was not observed on the rim of the tip-hole in both models, due to the high velocity gradient (Figure 9). However, the thrombus formation occurred on the lateral side of the tip in Model B only (Figure 11). The discrepancies between these two models attributed to the anatomical and physiological differences, highlighting the importance of adopting a more patient-specific model over a simplified tube in understanding hemodynamics. The thrombi on the CVC identified regions for potential modification to enhance the CVC design. As depicted in Figure 12, the corners in the side-hole were removed, and the profile of the tip was streamlined further, leading to smaller thrombi. Therefore, the change of hemodynamics induced by the modification of the catheter design can play an important role in the development of thrombus, and the computational platform in this study will facilitate the optimization of the catheter design to minimize the thrombus formation in future studies. Several limitations should be noted. Because of the difficulties in reconstructing its dynamic motion, the RA was assumed rigid in this and other studies.^4,22 As a remedy, the simulation results were time-averaged. Regardless, the dominant vortex in the clockwise direction in the simulation was consistent with the 4D MRI measurement shown in the supplementary material. Secondly, more subjects should be selected to improve the generality of the patient-specific results. Thirdly, the CVC was placed in the center of the SVC in this study, though it could touch the lumen of the central veins. The contacting site can vary, depending on several factors such as the anatomy, catheter model, and insertion port. Among the very few patient-specific studies on the CVC, the catheter tip was either excluded or placed in the center.^20,25 When additional patient-specific data are available, more realistic models will be analyzed in future studies. Lastly, the thrombosis model was implemented under constant flow conditions, due to the dual-time-step strategy. For the numerical stability and the ease of experimental validation, all thrombosis models were developed or used at a constant flow rate.^{32,38,44,45,47} Given the relatively long time span of thrombus formation, its simulation is computationally expensive. There are basically two methods to reduce the burden, either removing the Brinkman term from the momentum equation or applying a dual-time-step approach. The former is at the expense of ignoring the impact of thrombus on the blood flow, and the latter was only applicable to constant flow rates.^2,29

Conclusion

This study numerically analyzed the flows in two patient-specific central vein models without CVC and with CVC at various insertion depths and side-hole orientations. This is the first numerical study to investigate the effects of a CVC under zero flow rate through the CVC and show the significant effects of RA flow on the CVC tip WSS distribution. The findings reveal that the CVC impact on the internal flow in the central vein is trivial at a CVR of < 0.33. The simulations suggest that the tip of the CVC should remain in the tubular SVC instead of the RA, as in the RA the effects of the fluid mechanics and vortex can increase the thrombosis potential. From a hemodynamic perspective, a smaller CVC size is more favorable because of a lower WSS elevation on the SVC and a smaller area for platelet adhesion. The thrombosis simulations also suggested the optimization of the side-hole by removing the corners, and streamlining the tip could reduce the thrombus as well.

Supplementary Material

Figure S1

Figure 1S: Numerical models of central veins with virtual CVC insertion. (a): A 15 French CVC. Outer diameter: 5 mm (15 French); Tip hole diameter: 1.68 mm; and dimensions of the side hole: 8.16 mm×4.22 mm. (b): Zoomed-in view of the side-hole with the crescent-like lumen. (c): Model A with virtual CVC insertion at five depths 10 mm apart. Straight arrow denotes position of the side hole. (d): Model B with virtual CVC insertion at five depths 10 mm apart. In each model shown in (c) and (d), it includes four sub-models (denoted by “×4”) based on the orientation such as Model A_0_0, Model A_0_90, Model A_0_180 and Model A_0_270.

Figure S2

Figure 2S: Velocity magnitude contours near the CVC tip on the coronal plane and WSS distribution on the tip in Model A (a) and Model B (b) with an isoline of 0.01 m/s in grey for models with a 15 French CVC. High arrow: Region under high velocity gradient. Low arrow: Region under low velocity gradient

Figure S3

Figure 3S: Velocity magnitude contours on the longitudinal plane perpendicular to the side-hole of a 7 French CVC in four orientations (a) at two depths for Model A (b) and Model B (c). The orientations of the cutting plane are 0° (red), 90° (green), 180° (blue) and 270° (yellow).

Figure S4

Figure 4S: Velocity magnitude contours on the longitudinal plane perpendicular to the side-hole of a 15 French CVC in four orientations (a) at two depths for Model A (b) and Model B (c). The orientations of the cutting plane are 0° (red), 90° (green), 180° (blue) and 270° (yellow).

Figure S5

Figure 5S: (a) A series of CFD meshes. (I): 4.7×105 (II): 9.5×105 (III): 1.9×106, and (IV): 4.7×106. (b): Probe line and probe spheres at the tip-hole (red) and side-hole (green)