Implantable blood-contacting devices typically contain steps at connections between different components. However, these connections are invariably the areas susceptible to thrombosis. Consequently, patients often require anticoagulation therapy when using these devices. However, anticoagulation introduces the potential for hemorrhage complications without eliminating the risk of thromboembolism.1 Therefore, the geometries of step transitions deserve consideration,2 and optimization of thrombogenic performance is a necessary step in the design of blood contacting devices and implants.
Computational models of thrombus formation have typically focused on continuous, steady state flow; however, there are studies demonstrating the potential benefits of pulsatile flow. For example, a continuous-flow blood pump study revealed stagnation zones with low shear stress adjacent to the stenotic area, which were not present with pulsatile flow conditions.3 These results indicate that steady state flow may accelerate occlusion of arterial conduits in patients with preexisting stenoses and may lead to thrombosis with continuous flow devices in patients who have peripheral vascular disease. Furthermore, pulsatility has been linked to improvements in organ function with acute and chronic diseases, reduced inflammation, suppressed complement activation and cytokine production, and has been quantified by several metrics, such as energy equivalent pressure, pulse power index, and pulsatility index (PI).4,5
An interdependence of three quantities is important with respect to thrombosis, namely the state of blood coagulability, the properties of the material in contact with the blood, and the amount of flow stasis.6 It is well established that under steady flow conditions,1 platelets are activated by high shear stresses, and2 coagulation proceeds more rapidly in low shear stress areas; the proximity of both regions to each other could result in a synergistic production of platelets, fibrin, and thrombi.7–9
At low wall shear rates, platelets adhere to surfaces and thrombosis will occur. Hubbell and McIntire10 observed temporary adhesions of single platelets with a polyurethane surface at wall shear rates of 500 seconds−1, whereas clumping of 2–15 platelets was observed at wall shear rates of 100 seconds−1. Additionally, Affeld et al. 11 performed stagnation point experiments and found that platelets are deposited at defined shear rates between 10 and 20 seconds−1. Finally, polyurethane materials were found to thrombose at physiological temperatures and wall shear rates of <10 seconds−1.12–15 Hence, the published work in the literature strongly suggests that there is a safe range of blood shear rates to be maintained within medical implants and artificial organs.16–19
This study quantifies the effects of blood flow pulsatility on the fluid shear stress distribution around artificial transitions in the blood flow path for the purpose of understanding the effects of flow pulsatility on thrombus formation. We hypothesize that blood flow pulsatility will directly alter persistent stagnation regions by decreasing exposure time to low wall shear stress or shear rate. In addition, pulsating flow may improve washout of particles at the sites of low shear stress or shear rate. Blood flow stagnation will be considered using computational fluid dynamics (CFD) studies and flow visualization experiments. We anticipate that considerations for pulsating blood flow will ultimately help minimize life-long anticoagulation requirements, decrease device-related complications, and increase patient survival rates.
Methods and Materials
A sudden change in the blood flow path was modeled with a step change in wall geometry with both expanding and contracting conduits, as shown in Figure 1. Wall shear stresses were determined by CFD simulations under steady and pulsatile flow conditions, using the ADINA system (v.8.1; ADINA R&D, Inc., Watertown, MA). To save computational time and resource requirements, a 2-D axisymmetric model was used with no-slip boundary conditions applied at the wall, and a zero-gradient condition applied to the axis of symmetry. Non-Newtonian behavior of blood was approximated using the well-known relation developed by Walburn and Schneck.20 In the present simulations, hematocrit was set at 45% and total protein minus albumin was set at 2.7 g/dl.
Blood flow pulsatility was modeled by using a transient fluid model with half-sine wave velocity waveforms of varying amplitudes and a constant 60 beats per minute frequency. PI is defined as:
Here, a pulsatility index of zero simply means a steady flow condition.
Appropriate element size and time step was determined by preliminary grid refinement tests to ensure shear stress accuracy of <1% yielding 0.0125 mm element size for ±0.5 mm steps, and 0.0025 mm element size for ±0.1 mm steps, which resulted in, on average, 27,000 four-node quadrilateral fluid elements. The time step was set at 0.005 seconds. Two cycles were simulated and the results from the second cycle analyzed to ensure the solution was free from the transient effects because of the initial conditions. Mean wall shear stress differences between the two cycles, excluding the initial time step, were <1%. Comparisons were made with previous computational and experimental results published by Williams and Baker21 and in vitro blood loop experiments2 to validate our computational model.
Parametric studies were performed for 5-mm diameter tubes with four-step heights (±0.1 mm and ±0.5 mm), three pulsatility indices (0, 1.57, and 2.5), and three mean inlet velocities (5, 25, and 45 cm/s), representing flow in medium-sized arteries; 36 conditions in all. For each case, the resultant shear stress along the wall (as depicted in Figure 1) was analyzed over time and quantified using the metric of persistent stagnation, as defined below.
Using the Walburn and Schneck blood viscosity model20 and a wall shear rate threshold for thrombosis of 10 seconds−1,12–15 we then established a wall shear stress threshold for thrombus deposition of 0.1 Pa. Because of the low near-wall velocities, platelets and other cells in these low shear rate areas will stay relatively stationary and have long enough exposure times to initiate thrombosis. Therefore, areas with wall shear stress <0.1 Pa are considered to be practically stagnant and this threshold is considered to be time independent for the purposes of this study.
Regression analysis was performed using Minitab (v.13; Minitab, State College, PA) to determine the significance (p value) for each factor.
Definition of Persistent Stagnation
The stagnation index (SI) was defined as the percentage of time each element along the wall has shear stress below the 0.1 Pa threshold. Persistent stagnation length (PSL) is defined as the total length along the wall that maintains contact with stagnant flow throughout the cardiac cycle. PSL can identify areas with a high potential to initiate thrombus deposition and was used as a metric for comparison between different flow conditions. Specifically, the sum of corner and reattachment point stagnation lengths for expanding (negative) steps and the sum of corner and separation point stagnation lengths for contracting (positive) steps were included in the PSL.
Visualization of Particle “Washout”
Simulated particles were injected in the recirculation vortex of a −0.5-mm step. Eighteen particles were injected every 5 seconds and followed up for 20 seconds with varying amounts of pulsatility to demonstrate washout differences. For comparison, experimental flow visualization of neutrally buoyant Amberlite particles (Amberlite IRA-900; Alfa Aesar, Ward Hill, MA) was performed at a flow rate of 0.35 L/min with both continuous and pulsatile flow conditions.
Figure 2 displays wall shear stresses (WSS) for an expanding step of −0.5 mm, through a cycle with varying pulsatility. With steady flow (Figure 2A), there exist two regions with WSS persistently below the 0.1 Pa threshold: one at the corner and the other at the reattachment point. In Figure 2, B and C, the darkest contours represent areas with WSS below the threshold. With pulsatility, the low-WSS region at the reattachment point is observed to wander along the wall throughout the cycle, and stagnation is no longer persistent. The corresponding SI along the wall is shown in Figure 3. Persistent stagnation (SI = 100%) at the reattachment point is eliminated with any degree of pulsatility, whereas corner stagnation is persistent but reduced in size with pulsatility. For comparison, SI for a contracting step (+0.1 mm) is shown in Figure 4. With steady flow, there exist two separate regions with WSS below threshold similar to the case with an expanding step. One difference is that the second region occurs at the separation point with a contracting step rather than at the reattachment point with an expanding step resulting from differences in the geometry. The effect of flow pulsatility on the corner stagnation region is similar to that of the expanding step case, i.e., PSL is reduced with increased pulsatility. One major difference between the contracting and expanding step configurations is that persistent stagnation at the flow separation point is not eliminated unless the degree of pulsatility is relatively high (PI = 2.5 in this case), although the SI is significantly reduced with flow pulsatility.
Figure 5 demonstrates a summary of the effect of varying flow pulsatility on the PSL at different step heights with a mean velocity of 5 cm/s. The vertical axis represents total persistent stagnation length. The horizontal axis represents the step heights. The data show that (i) increased flow pulsatility reduces total PSL, whereas (ii) increased step height (both contracting and expanding) increases the total PSL. (iii) PSL is found to be less with contracting steps, whereas (iv) flow pulsatility was more effective at reducing PSL with large step heights than with small ones.
Concentrating on the total persistent stagnation downstream from a −0.5-mm step in Figure 5, (i) a reduction in stagnation is demonstrated with increasing pulsatility. PSL is reduced from 0.86 mm for PI = 0 to 0.68 mm for PI = 1.5 and to 0.43 mm for PI = 2.5. Overall, the mean persistent stagnation length is reduced from 0.25 mm for PI = 0 to 0.09 mm for PI = 2.5, considering all step heights and mean velocities (p = 0.002). Additionally, Figure 5 displays (ii) a reduction in PSL with smaller step heights. With PI = 1.5, PSL is reduced from 0.66 mm with a −0.5-mm step, to 0.10 mm with a −0.1-mm step. Overall, the mean PSL is reduced from 0.40 mm with a −0.5-mm step to 0.05 mm with a −0.1-mm step, considering all mean velocities and pulsatility conditions. Furthermore, (iii) PSL is found to be less with contracting steps in comparison with expanding steps with the same magnitude (p < 0.001): the persistent stagnation length is 0.40 mm for all −0.5 mm steps, but is only 0.12 mm for +0.5 mm steps. Finally, (iv) interaction between step height and pulsatility is also observed (p = 0.001) and indicates that the effect of pulsatility on reducing stagnation is more pronounced with larger steps.
Figure 6 demonstrates the decrease in persistent stagnation length observed with pulsatile flow for one step height (+0.1 mm), over the range of velocities evaluated in our study. In Figure 6, increased pulsatility leads to a reduction in mean persistent stagnation length from 0.05 mm for PI = 0 to 0.03 mm for PI = 2.5 even with a +0.1-mm contracting step.
Figure 7 demonstrates the decrease in persistent stagnation length with changes in blood flow velocity for a −0.1-mm step height; the reduction in PSL with velocity occurring over the range of pulsatility evaluated in our study. Mean persistent stagnation length in Figure 7 is reduced from 0.11 mm with 5 cm/s inlet velocity to 0.02 mm with 45 cm/sec inlet velocity (p = 0.001). It should be noted that the most significant reduction in PSL occurs at the low end of velocity from 5 to 25 cm/sec and pulsatility from 0 to 1.57.
Finally, washout of particles from the recirculation vortex with pulsatile flow is demonstrated in Figure 8. This simulation closely matches the experimental results displayed in Figure 8, A and B. After 20 simulated cycles, particles accumulate within the continuous vortex with steady flow (Figure 8C), whereas exchange of particles occurs with pulsatility demonstrating the washout effect (Figure 8D).
This study focused on quantifying the effects of blood flow pulsatility on the flow disturbances near a step-wall transition for the purpose of better understanding flow-related risks of thrombosis. The results strongly suggest that pulsatile flow significantly reduces persistent stagnation length, and therefore, it should significantly reduce the risk of thrombosis on steps compared with steady flow conditions.
Analysis of the wall shear stresses under steady state conditions in Figure 2A reveals separate regions of stagnation at the corner and reattachment point. Platelets would likely cover these surfaces leading to fibrin formation, trapped blood cells, and thrombus formation. In Figure, 2B and C, pulsatility causes the darkest contours at the flow reattachment point to wander along the wall throughout the cycle and the vortex eventually grows larger than the size of our model, only to be replaced by a new vortex in the next cycle. Platelets would be expected to temporarily adhere to the surfaces with the darkest contours, but it would also be expected to break free from the wall with higher shear stresses before an organized fibrin structure is formed.22 Therefore, areas that may temporarily be susceptible to thrombus deposition would be washed clean during the rest of the cardiac cycle.
The washout effect associated with the vortex shedding would likely encourage the exchange of activated platelets or proteins and offers a significant improvement compared with the potential entrapment of activated elements within the continuous recirculation vortex formed with steady flow. This phenomenon is visually demonstrated in Figure 8 in which flow visualization of experimental particles and simulations of injected particles in the recirculation vortex both result in washout of particles with pulsatile flow conditions.
Analysis of the results from the parametric studies reveals several findings. The amount of persistent stagnation is notably reduced with pulsatility (Figure 5). This pattern is more pronounced with expanding steps, most likely due to the larger recirculation vortex that forms. Even a small amount of pulsatility eliminates persistent stagnation at the reattachment point and significantly reduces the length of wall continuously exposed to low shear stresses (Figure 3). Conversely, contracting steps tend to have smaller recirculation vortices, and persistent stagnation at the separation point tends to merge with stagnation at the corner even with some amount of pulsatility (Figure 4). The amount of persistent stagnation is reduced with smaller step heights (Figure 5), whereas expanding steps are expected to produce more thrombosis than contracting steps. This finding is supported by experimental in vitro blood loop evidence.2 The increased PSL with expanding steps implies that device step transitions may be biased toward contracting steps rather than expanding steps. Also, increased pulsatility is observed to reduce persistent stagnation even with small contracting steps (Figure 6); even with small recirculation vortices and stagnation concentrated near the corner, the effects of pulsatility are still evident. Finally, higher inlet velocity is found to reduce persistent stagnation with a −0.1-mm step height (Figure 7), suggesting that higher velocities will indeed decrease the amount of persistent stagnation.
The most drastic reduction of persistent stagnation occurs between a PI of 0 and 1.5 (Figure 7). This level of pulsatility is lower than the maximum PI of 2.5 observed in the ascending aorta and compares favorably with the mean PI of 1.4 observed in human arteries.23,24 Similarly, the most drastic decreases in persistent stagnation occur at the low end of flow velocity in the range of 5 to 25 cm/s, with only incremental reductions thereafter. In comparison, human arteries 1–20 mm in diameter have a mean velocity range of 10–35 cm/sec, representing arteries as large as the aorta to as small as the radial artery.25–29 Hence, the range of conditions corresponding to the maximum effect of pulsating flow closely matches the physiologic range of PI and flow velocity in human circulation.
In this study, our CFD model was validated by comparing shear stress distributions to the location of thrombus deposits formed under steady flow conditions2 and we used a flow-dependent thrombosis threshold established through ex vivo studies on polyurethane surfaces.12–15 Patient coagulation characteristics, properties such as hematocrit and protein levels, anticoagulation regimen, and the type of material on the surface may all affect the actual threshold for thrombosis. Different thresholds for thrombosis will in turn affect the amount of surface area susceptible to thrombosis; however, the results will still be applicable qualitatively if not quantitatively due to the fact that blood flow patterns are independent of the threshold for thrombosis. Further studies are required to determine whether a steady-flow thrombosis threshold is consistent with a pulsatile flow thrombosis threshold and to determine the exact amount of risk for surfaces exposed to intermittent stagnation. For instance, a section of wall that is below a steady-state thrombosis threshold 100% of the time will likely lead to deposits; however, the amount of time a section of wall may be exposed to low shear stress and still be washed clean during the rest of the cycle remains to be determined. Nevertheless, this study clearly indicates that regardless of the thrombosis and persistent stagnation thresholds, the relative degree of surface area at risk for initiating thrombus formation is decreased by higher pulsatility, smaller steps, and higher velocities.
Stagnant or near stagnant regions in a blood flow path were determined to asses the effect of pulsating flow on the potential for thrombosis. The results show that PSL is reduced by increasing pulsatility index as well as decreasing step height and increasing mean velocity. There are also significant differences regarding the effect of pulsating flow on stagnant regions between contracting and expanding steps such that the risk of thrombosis associated with interconnects in medical devices may change with flow direction. Additionally, the most dramatic reduction in PSL is observed with pulsatility and mean velocities occurring in the human arterial circulation. Future studies performed under in vivo conditions would be extremely valuable to improve our understanding of the contribution of pulsatility to the thrombosis mechanism and to evaluate new devices without the use of expensive and potentially dangerous clinical trials.
Supported by NU Enhance funding 2008 and, in part, by NIH/NHLBI grant 2 R44 HL 78049-03.
The authors thank Robert T.V. Kung for providing experimental flow visualization pictures of suspended particles with continuous and pulsatile flow conditions.
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