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Introduction
Early stent-graft designs were ill-prepared to face the hemodynamic forces generated by aortic blood flow and pressure. Long-term results were marred by high rates of migration,¹ component separation,² and structural failure.³ Current designs have proven to be more stable.² Though more rigorous pre-clinical testing has helped to assess the likelihood of each known failure mode before devices are implanted in patients, there is still no consensus as to the test conditions, because the hemodynamic environment of the endovascular stent-graft remains poorly understood.

Previously published data on fluid dynamics in aortic stent-grafts have used steady state flow conditions and hypothetical geometries to model the hemodyanamic load.^4,5 These studies helped to identify key determinants of displacement force, such as inlet diameter, blood pressure and limb angulation. Despite the simplicity of the models, clinical studies have shown that the same factors correlate with rates of stent-graft migration.⁵

Nevertheless, steady state modeling of the summated forces within simple constructs cannot provide an accurate representation of clinical conditions. The repetitive fluctuation of flow, pressure and force during the cardiac cycle is far more destabilizing. Cyclical stress and strain degrade not only stent-graft attachment, but also stent-graft structure. Persistent flexing of the metal stents generates stress that can cause stent fracture, and the movement of the metal stents along the graft fabric can cause holes in the stent fabric.³ Our group has used cine-flouroscopy to observe both pulsatile displacement of the graft and pulsatile diameter change of stent-grafts.⁶ We also used computational methods to model the effects of pulsatile pressure and flow at various points throughout the cardiac cycle, and various points on the surfaces of realistic geometries (derived from CT data in real stent-grafts) under realistic conditions of external (sac) pressure.⁶ In addition, we used cine-fluoroscopy to make direct observations of the cyclical strain (pulsatile micro-movement) exhibited by stent-grafts at various stages after clinical implantation. Both types of data are helpful in designing better stent-grafts and pre-clinical tests.

Computational Fluid Dynamics (CFD)
Methods. The fluid flow equations (Navier-Stokes) can be solved by analytic mathematical means only with simplified hypothetical models. It is only possible to determine internal hemodynamic effects, such as wall shear stress and local pressure, using numerical methods. Computational Fluid Dynamics (CFD) is a method for generating the numerical solutions to these equations at discrete points over a three-dimensional surface. The three-dimensional computational grid can be generated using either hypothetical stent-graft models or 3-dimensional imaging of real stent-grafts in clinical use. In either case, the validity of the CFD simulation depends on the accuracy of the chosen boundary conditions, including the viscosity and shear properties, the inlet and outlet flow velocities, the inlet and outlet blood pressures, and the pressure on the outside of the graft.

Previously published simulations of the hemodynamic forces through the stent-graft have used both analytical and numerical techniques, but none of these simulations modeled internal fluid motion. Most only calculated the hemodynamic force due to steady state flow, usually a mean peak inlet flow velocity. Furthermore, all these simulations used simplified models of the stent-graft geometry, incorporating only inlet and outlet diameters.^4,5,7,8 The models were generally composed of bifurcated tubes with geometrical stent-graft characteristics with proximal and branch components lying in a single plane. Limb angulation was limited to curvature in the same plane as the rest of the graft.^4,7 The sole exception was an analysis of a single patient-specific geometry.⁸

We have used both hypothetical (Figure 1) and patient-specific (Figure 2) geometries, for the 3-dimensional computational grids in our CFD simulations.⁶ In the hypothetical geometries, the different elements of graft design were varied to isolate factors such as diameter and angulation, and assess their effects on the displacing forces within various parts of the stent-graft. Our patient-specific models were derived from the arterial phase of high-resolution contrast-enhanced CT scans. Each 3-dimensional arrangement of contrast-enhanced voxels within a CT representation of luminal anatomy was converted to a surface mesh of interconnected triangles using an automated algorithm. A series of CT scans were selected to cover a range of possible stent-graft orientations. In addition, the different regions of the graft, the proximal trunk, the bifurcation and the iliac branches, were modeled separately to identify their contribution to the forces on the stent-graft.

In any CFD analysis of pressure-generated forces, the pressure on the outside of the stent-graft (sac pressure) is as important as the pressure on the inside of the stent-graft (systemic arterial blood pressure.) The transmural pressure gradient is what matters, not the absolute pressure. Most previous CFD models have assumed this outside pressure to be zero. In the absence of patient-specific data on sac pressure, published data were used on the mean pressure in each of four clinical circumstances, relating to endoleak status and aneurysm diameter change.⁹

In general, both blood pressure and blood flow generate forces on a stent-graft. Forces imposed by the walls of the stent-graft change the velocity of flowing blood: the higher the rate of flow, the higher the force. Since the combined cross-sectional area of stent-graft limbs are less than that of the trunk, the flows are higher. Therefore, the flow-related forces play more of a role in the limbs than in the trunk. Minor flow-related variations notwithstanding, blood pressure acts fairly uniformly on all the inner surfaces of the stent-graft, except at the inlet and the outlet. If the inlet and the outlet have different areas or orientations, the effect is an imbalance of pressure-generated forces, resulting in the creation of a net displacement force on the stent-graft.

Findings. CFD studies, using hypothetical stent-graft geometries at peak flow rates demonstrated that displacement forces generated by blood pressure were significant.^4–8 The calculated peak forces were often greater than pull-out forces demonstrated in cadaveric studies of stent-graft attachment.¹⁰ Steady state studies also showed that forces on the graft increased with increasing blood pressure, increasing inlet area and limb curvature. These models did not incorporate real geometry and could not predict the effect of out-of-the-plane curvature of the graft. Nevertheless, the predicted effects of the changing inlet diameter, pressure and angulation on displacement forces correlated with the observed effects on the migration rate.⁵

One study used various input flow profiles, which affected the velocity profiles at different points in the graft but not the total distal force generated.⁸ Blood pressure-generated forces were still observed to dominate over the blood flow forces. When a real geometry was incorporated into the model, forces were generated in all three directions, but the net overall force only increased 26%. An additional result was the bending or twisting moment on the graft that might increase the risk of graft displacement.

CFD studies confirmed that pressure-generated forces were far greater than flow-generated forces within both patient-specific and hypothetical geometries.⁶ For example, doubling the inlet blood pressure nearly doubled the total peak displacement force on the stent-graft, while doubling the blood flow produced only a 6% increase on the total peak displacement force. The blood pressure forces are dependent on both the inlet blood pressure and the inlet and outlet diameters and orientations. Large changes in diameter or graft orientation produced large displacement forces, and other factors being equal, larger grafts, or graft segments, generated larger pressure-derived forces. Accordingly, the stent-graft models with the largest curvature and change in area generated the greatest displacement forces.

In modeling the different segments of the stent-graft, the bifurcation (Figure 3) was the site of greatest overall diameter change. Therefore, the bifurcation made the largest contribution of displacement force. The tubular proximal component and limbs generated negligible displacement forces. The magnitude of the force depended on the absolute diameter of the stent-graft and the relative sizes of the trunk and graft limbs.
None of the real geometries contained areas of tapering within the trunk, but this was a feature of some hypothetical geometries (Figure 1). Because the trunk generally has a large cross-sectional area, a tapered trunk can make a significant contribution to the overall displacement force.

Implications for stent-graft design. It has been common practice to significantly oversize the main body of the stent-graft to ensure apposition and attachment. CFD studies suggested that oversizing may ultimately affect displacement force and migration risk. Immediately following surgery, the proximal stent of an oversized stent-graft is restricted by the diameter of the native abdominal aortic neck, but in time the neck dilates until it is limited by the diameter of the graft component of stent-graft. Therefore, the degree of oversizing, and not the preoperative aortic neck diameter, determines the ultimate inlet diameter. Since inlet diameter is a principle determinant of displacement force and migration potential, the larger the stent-graft, the higher the risk of migration. There is some support in the literature for the idea that greatly oversizing the stent-graft may increase the risk of migration, although the true explanation for this clinical observation may lie elsewhere.¹¹

Our CFD findings suggested that the relative lengths of the trunk and the limbs may influence force distribution and migration risk. Short, stiff limbs are capable of transmitting force from the bifurcation of the stent-graft, where most force is applied, to the bifurcation of the aorta, unlike long, floppy limbs. So all the displacement force on the bifurcation has to be borne by the proximal attachment between the trunk of the graft and the neck of the infrarenal aorta. Consequently, stent-grafts with short, stiff limbs are probably less prone to proximal stent migration than stent-grafts with long, floppy limbs.

Another strategy for stabilizing the proximal attachment is to create a modular junction within the trunk of the stent-graft (Figure 4). Deprived of support from above, the bifurcation must sit like a rider in a saddle. If it is low and stable enough to do so, the migration risk is low because the proximal stent-graft is protected from the high pressure-generated forces that act at the bifurcation. A modular junction within the trunk also creates an opportunity to have multiple variably tapered trunks in combination with a bifurcated component of one universal size. Although a taper in the trunk does reduce the displacement force acting at the bifurcation, it also contributes to pressure-generated forces on the trunk, which might increase migration risk.

CFD findings suggested that stent-graft specific variations in the sac pressure may affect migration risk. High sac pressures lower the pressure gradient over the graft wall and reduce migration forces.⁶ These CFD findings mirror the findings of an in-vitro study that verified the role of sac pressure in migration prevention on a simplified model.¹³ Clinical studies have shown that some stent-graft designs are associated with higher residual sac pressure, low rates of aneurysm shrinkage and high rates of aneurysm dilatation, even in the absence of endoleak.¹² This lack of change in the natural history of the aneurysm has prompted manufacturers to reduce the porosity of the offending stent-grafts. However, it is probable that, if effective, these changes will have the paradoxical effect of increasing migration rates, because lower sac pressure increases both the displacement force and the migration rate.

Stent-Graft Movement
Methods. We have been able to directly observe pulsatile motion of a stainless steel-based Zenith stent-graft using cine-fluoroscopy at 30 frames- per- second. We measured the systolic-to-diastolic variation in the diameter and position of endovascular stent-grafts perioperatively as well as at 1, 6, 12, and 24 months after to implantation.⁶

Findings. The pulsatile movement of the endovascular stent-graft was observed at all points of follow-up. Two modes of movement were noted: pulsatile displacement of the graft and pulsatile graft diameter change. Pulsatile displacement, the movement of the entire stent-graft, persisted through all points of follow-up. As a rule, the distal ends of the branches were the least mobile segments of the stent-graft. This probably reflects the relative immobility of the iliac bifurcation. The resulting disparity in movement caused repetitive bending of the graft. The extent of pulsatile displacement varied greatly between patients; the stent-grafts of some patients barely moved while others moved up to 6 mm every pulse cycle.

The pulsatile diameter change of the stent-graft varied according to the location of the stent within the stent-graft, surrounding arteries and the time from implantation. At the time of operation, the intra-aneurysmal stent displayed the greatest pulsatile diameter change. However, by 6 months, the pulsatile diameter change of the intra-aneurysmal stent was greatly reduced. The diameter change of the suprarenal stent also declined over a longer time-course.

Implications for current stent-graft design. The parameters for pre-clinical testing of stent-graft durability have no basis in clinical reality. For example, current finite-element analysis (FEA) models and accelerated fatigue test assume a 5% pulsatile diameter change for 5 years. Our study has shown that for the Zenith stent-graft, the pulsatile diameter change is not as significant or persistent. However, the current standards for pre-clinical testing cannot be abandoned completely, because they can be correlated with observed clinical fracture rates. However, more realistic tests may show ways in which stent and stent-graft designs of the future can retain durability while minimizing delivery profile.

Conclusion
Most improvements in the durability of endovascular stent-grafts occurred when the sources of late failure were identified in clinical use. Unfortunately, the inherent delays in this process put many patients at risk. More predictive pre-clinical testing of new designs relies upon a better understanding of the hemodynamic environment, better modeling of cyclical stress and strain, and more realistic accelerated durability testing. This information can also be valuable in the design phase of the development process. For example, the findings of Computational Fluid Dynamics suggest ways to minimize the forces on a stent-graft by changing stent-graft geometry, while the findings of cine-fluoroscopy provide a better understanding of the interaction between a prosthesis and the hemodynamic environment of clinical use.