A computational fluid dynamic study of stent graft remodeling after endovascular repair of thoracic aortic dissections

Article Outline

• Abstract
• Patients and methods
  • Governing equations
  • Boundary conditions
  • Drag force calculations
  • Stent graft model
  • Patient-derived models
• Results
  • Drag forces and cardiac cycle
  • Drag forces and stent graft geometry
  • Stent graft remodeling in aortic dissections
• Discussion
• Conclusion
• Author contributions
• References
• Copyright

Objectives

Significant stent graft remodeling commonly occurs after endovascular repair of thoracic aortic dissections because of continuing expansion of the true lumen. A suboptimal proximal landing zone, minimal oversizing, and lack of a healthy distal attachment site are unique factors affecting long-term stent graft stability. We used computational fluid dynamic techniques to analyze the biomechanical factors associated with stent graft remodeling in these patients.

Patients and Methods

A series of computational fluid dynamic models were constructed to investigate the biomechanical factors affecting the drag force on a thoracic stent graft. The resultant drag force as a net change of fluid momentum was calculated on the basis of varying three-dimensional geometry and deployment positions. A series of 12 patients with type B aortic dissections treated by thoracic stent graft and followed up for more than 12 months were then studied. Computed tomography transaxial images of each patient shortly after stent graft deployment and on subsequent follow-up were used to generate three-dimensional geometric models that were then fitted with a surface mesh. Computational fluid dynamic simulations were then performed on each stent graft model according to its geometric parameters to determine the actual change in drag force experienced by the stent graft as it remodels over time.

Results

The drag force on the stent graft model increases linearly with its internal diameter and becomes highest when the deployment position is closer to the proximal arch. Aortic curvature is not a significant factor. Serial computed tomography scans of patients showed an increase in mean inlet area from 1030 mm² to 1140 mm², and mean outlet area from 586 mm² to 884 mm² (increase of 11% and 58%, respectively; P = .05, .01). These increases are associated with a change in resultant drag force on the stent graft from 21.0 N to 24.8 N (mean increase, 19.5%; range, 0%-63.2%; P = .002). There is a positive relationship between increase in drag force and increase in stent-graft area.

Conclusion

The drag force on thoracic stent grafts is high. A significant change in stent-graft diameter occurs after endovascular repair for type B dissections, which is associated with an increase in hemodynamic drag force. These stent grafts may be subjected to a higher risk of distal migration, and continuing surveillance is mandatory.

Endovascular stent grafts placed in the aorta are subjected to significant displacement forces generated by high blood flow. Previous in vivo and computational studies¹, ² on abdominal aortic stent grafts have demonstrated that these forces are higher with a larger graft inlet diameter and can result in distal migration of abdominal stent grafts. Very few studies so far have been done on the hemodynamic forces of thoracic stent grafts.

Thoracic stent grafts are often of a larger diameter and are strategically placed near the aortic arch where there is a substantial element of transverse flow. There are also considerable variations in the length of the stent graft, its deployment position relative to the arch, and the curvature of the aorta. Thoracic stent grafts are predisposed to considerable remodeling after deployment because of the inherent large volume of the grafts. Remodeling is most evident in patients in whom the stent grafts are placed for aortic dissections, in which the changes in true lumen diameter (and therefore stent-graft diameter) can be substantial as the false lumen regresses. Stent grafts deployed in these situations therefore exist in a dynamic state of continuous geometric alterations, and changes in distraction forces can occur, which may affect long-term durability of the repair.

We aimed to (1) study, using computational fluid dynamics (CFD), the forces acting on thoracic stent grafts and their relationship to geometry and flow, and (2) determine the changes in resultant drag forces associated with stent-graft remodeling using three-dimensional (3D) flow models constructed from serial CT scan data in actual patients with stent grafts placed for aortic dissections.

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Patients and methods 

To perform computational simulation of pulsatile blood flow for a stent graft in the thoracic aorta, three major components are required: (1) geometry, which defines the 3D shape of the stent graft; (2) governing equations, which elucidate the fundamental fluid principles analytically; and (3) boundary conditions, which describe the characteristics of the pulsatile blood flow. The drag force on a stent graft can then be calculated by applying the fundamental principles of fluid mechanics.

Governing equations 

Blood flow in large arteries is typically sufficiently fast to justify the assumption that the blood behaves as a Newtonian fluid.³ The governing principles of the motion of a 3D fluid are the conservation laws of mass and momentum. More precisely, they are the continuity equation

and the Navier-Stokes equations for an incompressible fluid where u_i (i = 1, 2, 3) are the components of the velocity vector, p is the pressure, and ρ is the fluid density. The summation convention is employed.

Boundary conditions 

The governing equations are allowed to march forward in time with an established routine and appropriate boundary conditions. The rheological properties are assumed to be in ranges that permit blood to be treated as an incompressible, homogeneous, and Newtonian fluid. This is a reasonable assumption in larger arteries such as the thoracic aorta. With this working assumption, the shear stress in the blood is proportional to the velocity gradient in the blood. The dynamic viscosity of blood, μ, is taken to be 0.0035 Ns/m², and 1050 kg/m³ is the assumed blood density.⁴

Physiologically representative pulsatile velocity waveform and pressure waveform are applied at the inlet and outlet respectively (Fig 1). These velocity profile waveforms are verified in actual patients at the completion of thoracic endograft procedures by taking real-time pressure and waveform readings with a pressure transducer connected to a large-caliber catheter (VOTT; Cook Medical, Bloomington, Ind) placed at the inlet and pulled back at 2-cm intervals. The waveforms used in the simulations are in agreement and have also been verified by various in vivo experimental data.⁵, ⁶

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• Fig 1. 

  Blood flow waveform (a) and blood pressure waveform (b). The period is one second per cycle. Peak flow occurred at 0.25 seconds and peak pressure at 0.3 seconds.

The hemodynamic effects of blood plasma only were considered, and the particle effects on the simulation are deemed negligible so as to avoid an excessively high computational workload. In large blood vessels, the fluid flow is treated as laminar for moderate Reynolds numbers.⁶, ⁷

To attain a periodic state in a time-dependent calculation in CFD simulations,⁸, ⁹ a steady-state solution at the maximum flow rate is obtained first. Data and output from the fifth cycle are taken as the time-periodic solution. The domain wall boundaries are assumed to be rigid, and the no-slip boundary condition is applied at all vessel walls.

Drag force calculations 

Drag force was calculated from direct integration of the pressure and wall shear stress distributions on both surfaces of the stent-graft wall:

where F = drag force, P = pressure acting on the stent graft, τ = shear stress acting on the stent graft, and C.S. = control surface.

The drag force exerted by the blood flow on the stent-graft wall is mainly generated by two sources: the net change or efflux in fluid momentum and the friction on the graft wall. The net change in fluid momentum contributes the majority of a drag force on the stent graft.¹, ⁷ The net drag force acting on a stent graft induced mainly by the change of momentum in blood flow can be calculated by the momentum theorem from classical fluid mechanics.¹⁰ This theorem states that the total forces acting on a control volume containing fluid will be computed from the net rate of momentum efflux from the control volume, plus the time rate of change of momentum within the control volume. In our study, the latter made only a minor contribution to the total amount of drag force on the blood vessel; thus, the net drag force is effectively given by the net efflux term.

Stent graft model 

A stent-graft template was first defined on the basis of contrast-enhanced transaxial thoracic CT scan images of a patient. A cubic spline curve was fitted through the luminal cross sections, and the centerline was determined and used as a subsequent template for generating stent graft models of varying parameters. To limit the complexity, we assumed this initial model was non-tapering and without out-of-plane bending. Each model is generated as a smooth circular tube surface with the software Rhinoceros (Robert McNeel & Associates, Seattle, Wash) (Fig 2).

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• Fig 2. 

  a, Geometric parameters defining the stent graft model. b, Surface mesh elements created for the fluid domain. d, Diameter of the stent graft; θ, position of deployment of stent graft in clockwise direction from aortic valve; D, diameter of curvature of the aortic arch.

A stent-graft model in the form of the mesh elements was then generated, and the IGES format geometry files were then imported into a program ICEM CFX (Ansys Inc, Canonsburg, Pa) for surface mesh generation. A large number of elements and mesh smoothing are required to generate a sufficiently smooth surface and avoid sharp corners. Simulations of CFD are then performed on each stent-graft model according to its geometric parameters, and the governing equations and the boundary conditions. To solve these equations, we used the computational fluid dynamics code CFX, which is a finite volume method solver. Repeated calculations with finer meshes revealed the mesh independence of the results. More than 700,000 elements were created in the fluid domain for each model to achieve mesh independence.

Three geometric parameters were specified and studied in these idealized stent-graft models (Fig 2): the lumen (or stent graft) diameter, d; the starting position of the stent graft on the aorta, θ; and the diameter of curvature of the aortic arch, D. The starting position is defined by the proximal end of the graft and ranges from 0 to 180 degrees. The diameter of curvature of the aortic arch is the maximum horizontal distance between the centroids of the cross sections at the aortic arch. A standard stent graft length of 150 mm was used.

The relationship of the drag force with variations in the stent graft geometry was studied by applying the CFD simulations to different parameters of d (graft diameter), θ (graft position), and D (arch curvature). The graft diameter d studied ranged from 26 to 42 mm, graft position θ from 90 to 180 degrees, and arch curvature D from 70 to 130 mm. With each parameter being varied, the other two were fixed at their average values, assuming a constant value of d = 34 mm, θ = 90 degrees, and D = 100 mm.

Patient-derived models 

Twelve patients with uncomplicated Stanford type B dissections treated by primary endovascular thoracic aortic stent grafting and who were followed up for at least 12 months were then chosen for this study. Of the 12 patients, 11 were men and one was a woman, with a mean age of 56 years (range, 31-78 years). Two were treated for acute dissection, seven were in the subacute (less than 1-month) stage, and three were at a more chronic stage with aneurysmal changes. The stent grafts used were Zenith TX2 proximal endograft components (Cook Medical, Bloomington, Ind). The landing zones were all close to the left subclavian artery origin. The landing zone aortic diameter averaged 32.8 mm (range, 28-38 mm), and the graft diameter averaged 37 mm (range, 34-42 mm), with a mean oversizing of 12.8% (range, 5%-31%). The average graft length was 153 mm. Contrast CT scans were routinely performed postoperatively and every 3 to 6 months thereafter.

For each patient, the geometry of the stent graft in the thoracic aorta was defined on the basis of CT transaxial DICOM images. The earliest postoperative scan and the latest scan images (a and b) were used for this analysis; the mean interval between the two scans was 16.3 months (range, 12-27 months). The CT scans gave a resolution of 512 by 512 pixels, with a pixel size of 0.625 mm and a slice thickness of 1.25 mm. The boundaries of the stent graft were readily segmented for the entire set of CT images. The software program SURFdriver (Moody and Lozanoff, Alberta, Calif), a surface reconstruction application, was used to segment the stent graft semiautomatically and then the polygon models were reconstructed by the rendering engine. The polygon models were used as input to the Rhinoceros software program (Robert McNeel & Associates, Seattle, Wash) and lofted into 3D nonuniform rational B-spline surfaces. The stent graft models in the form of the mesh elements were then generated. The IGES format geometry files of the stent graft model were produced and then input into ICEM CFX (Ansys Inc, Canonsburg, Pa) for surface mesh generation. Then, CFD simulation was performed on each stent graft model according to its geometric parameters, and the governing equations and the boundary conditions as described previously (Fig 3). Changes in stent graft inlet and outlet diameters were measured. Because axial sections of stent grafts are seldom circular, we expressed the stent graft size in terms of inlet (A1) and outlet (A2) cross-sectional areas. Comparisons were made by using the two-tailed paired samples t test. The changes in drag force (Fb/Fa) were correlated to the changes in inlet and outlet areas (A1b/A1a and A2b/A2a) by using the Pearson correlation with two-tailed significance.

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• Fig 3. 

  Patient-derived CFX model of fluid dynamics velocity and vector plot in a thoracic stent graft before (left) and after (right) remodeling.

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Results 

Drag forces and cardiac cycle 

The derived drag forces are generally related to the pressure changes in the cardiac cycle. A time-dependent plot of drag forces in a representative stent graft model (d = 34 mm and D = 100 mm) is shown in Fig 4.

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• Fig 4. 

  Relationship between the drag force acting on the stent graft and the cardiac cycle.

Drag forces and stent graft geometry 

On the simple geometry CFD simulation models, the drag forces in the transverse and vertical directions increased with the internal diameter of the graft (Fig 5, a). The resultant force on the thoracic stent graft is significantly larger than that experienced by its abdominal counterpart, and measured 10.3 N when the graft diameter was 26 mm and increased to 26.8 N with a graft diameter of 42 mm. The frictional force exerted on the blood vessel by the fluid contributes 0.036 N, which is less than 0.5% of the total drag force. Forces due to shear stress or friction thus appear to be negligible.

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• Fig 5. 

  Relationship between the drag force due to net momentum change and the internal diameter of the thoracic stent graft (d) (a), the deployment position of the thoracic stent graft (θ) (b), and the diameter of curvature of the aortic arch (D) (c).

The relationship of the stent-graft landing position to the drag forces is shown in Fig 5, b. The force is greatest at the 90-degree position (top of the arch) and decreases significantly when the proximal landing zone is in the descending aorta (17.3 N at 90 degrees, 2.3 N at 180 degrees).

There is a slight decrease in drag force when the curvature of the thoracic aorta increases. The rate of change of the drag force in relation to the diameter of curvature of the aortic arch however is small (Fig 5, c). There is only an 8% reduction in resultant forces when the diameter changes from 70 to 130 mm.

Stent graft remodeling in aortic dissections 

Serial CT scans of patients showed that, after endovascular stent-graft placement for aortic dissections, there was a general increase in both inlet and outlet graft areas (Table, Fig 6, a and b). An increase in mean inlet area was observed in eight patients; the area changed from 1030 ± 228 mm² to 1140 ± 279 mm² (increase of 11%; P = .05). There was a more marked (58%) increase in the mean distal outlet area, which was evident in all but one patient, with a resultant change of 586 ± 180 mm² to 884 ± 367 mm² (P = .01; Table). The general shape of the stent grafts remains conical with a larger inlet area, although the inlet:outlet area ratio decreased from a mean of 1.93 (range, 0.94-3.59) to 1.50 (range, 0.76-3.26). In three patients the outlet diameter of the graft had exceeded the inlet area. There was no relationship with the timing of the dissection and the remodeling changes.

Table. Geometric and computational fluid dynamic data of 12 patients with thoracic aortic endografts

1, Initial postoperative scan measurements; 2, follow-up scan measurements; N, Newtons.

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• Fig 6. 

  Changes in the inlet area (a), the outlet area (b), and the drag force of the thoracic stent grafts (c).

A general trend of increasing drag force with larger-diameter stent grafts was observed.

In association with graft expansion, the CFD models showed an increase in resultant drag force on the stent graft in all but one patient (Fig 6, c). The mean drag force increased from 21.0 ± 3.5 N to 24.8 ± 3.4 N (mean increase, 19.5%; range, –4% to 63.2%; P = .002). There is a positive relationship between increase in drag force and increase in stent-graft outlet area (P < .05, Pearson correlation).

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Discussion 

Stent grafts placed in the thoracic aorta near the arch are subjected to considerable pressure and flow, but no previous study has addressed the hemodynamic forces acting on thoracic aortic stent grafts. To date, CFD studies on aortic stent grafts have been performed on only bifurcated abdominal graft models. In a simplified, non-pulsatile, steady-state uniform flow CFD model, Liffman et al¹ have demonstrated that forces on abdominal stent grafts are related to graft inlet diameter in the order of 3 to 5 N for small grafts and 7 to 9 N for larger grafts. A recent study using 3D non–steady-state CFD analysis on CT-defined models by the Stanford group² showed similar force magnitudes; the study also verified that pressure-related forces were much larger than flow-related forces in abdominal stent grafts, and that blood pressure, inlet graft diameter, and angulation were the determining factors. These studies also confirmed that forces on abdominal grafts act mainly on the bifurcation and thus implied that tube-shaped thoracic grafts should be more stable.

We used actual 3D, pulsatile flow mechanics to produce a more realistic CFD model. The pressure and velocity waves were verified by using in vivo arterial pressure measurements. This CFD model has been tested on a simulated abdominal bifurcated graft environment, and the outcome was in agreement with previous findings. We have demonstrated that the drag forces acting on the thoracic stent grafts were of a significantly higher magnitude than the abdominal counterparts, averaging 10 N for the smallest diameter grafts and reaching 26 N for grafts with a 42-mm diameter at the aortic arch. These forces were in an almost linear relationship with the diameter of the graft; a large-diameter graft is subjected to a higher displacement force. We have also shown that drag forces on thoracic stent grafts arise primarily from shifts in fluid momentum as a result of pressure and flow changes. Shear stress, the frictional forces between blood and the luminal surface, was two orders smaller. The effect of contact surface (and therefore the length) of the graft appears to be negligible.

The deployment position of the stent graft also has a significant bearing on resultant drag forces. A 34-mm graft deployed at the top of the arch experiences forces of 17 N compared with only 2 N when it is deployed at 180 degrees. Stent grafts that are placed in a proximal position must experience an additional transverse displacement force. This force may explain the significant increase in the resultant distraction forces of thoracic stent grafts placed in the curved part of the arch compared with a significantly smaller force on the straight part of the descending thoracic aorta.

Drag forces are counteracted by fixation forces from the stent graft, mainly frictional forces from the stents, and hooks and barbs at the proximal end. In bench top experiments, a force of 10 to 25 N is required to displace an abdominal endograft with suprarenal fixation,⁸, ¹¹ and more than 30 N is required for fenestrated grafts.¹¹ In vivo experiences also suggested that graft diameter is a significant determinant of migration.¹² There is no study on in vitro displacement forces of thoracic stent grafts. The drag force computations in this study in horizontal and vertical directions are the forces acting on the stent graft in isolation, and are only an estimation of one of many factors that may lead to stent graft migration in real life. Only an unknown portion of the total drag force estimated in our computations will be parallel to the attachment site. An additional counterbalancing force by stent graft contact and fixation hooks exists to oppose these drag forces on the graft.¹³ The choice of the length of thoracic stent grafts is more flexible, and a longer distal landing zone is often used, which may account for greater stability. The addition of a series of bare metal stents in the distal aorta as advocated by some centers may also help to maintain the position of the stent graft.

Although device migration is a known complication of thoracic stent grafts, there is very little long-term data on thoracic endograft migration. The Gore TAG registry on thoracic aneurysms reported a total migration rate of 10% at 2 years.¹⁴ The Cook Zenith TX2 trial registered a device migration rate of 2.8% at 12 months.¹⁵ A study using the computer centerline of flow measurements in 194 patients recorded migration in 6.7% of thoracic devices.¹⁶ These studies were performed on stent grafts for thoracic aneurysms; data on aortic dissections are lacking at this point in time.

Type B aortic dissection is now increasingly being treated by endovascular repair in which a short- to medium-length stent graft is used to cover the primary entry tear. Because of the anatomic proximity of the primary tear to the major branches of the arch, the proximal landing zone is often short and on less healthy tissue. Liberal oversizing at the top is not advisable for fear of iatrogenic dissections; it also reduces the proximal fixation force even more. The distal landing is typically in the diseased true lumen of a dissected aorta, with the majority of the stent grafts held against the dissection flap rather than a healthy aortic segment. After successful exclusion of the false lumen, there is a progressive dilatation of the true lumen with time attributable to realignment of the blood flow. A continuing, gradual expansion of the stent graft is usually observed on follow-up. Patients with aortic dissections are usually younger (the mean age of patients in our study was 56 years), and their aortas are more compliant and prone to dilation in future. The drag force on the stent graft may change with time and may not reach a steady state until many months after graft implantation.

We have shown that substantial remodeling of the stent graft existed in patients with aortic dissections. Progressive dilatation of both the proximal and distal lumens occurred, but was more marked for the latter. As the false lumen thromboses and regresses, the true lumen will gradually expand, whereas the proximal portion of the stent graft is constrained by a healthy aorta at the landing zone, resulting in a shape change of the graft from a more conical configuration to a more cylindrical appearance. Associated with these changes was an increase in hemodynamic drag forces, amounting to almost 20%, and in some of the cases exceeding 60%. These changes must be related to the remodeling of the stent graft configuration. Existing in a dynamic state, these thoracic stent grafts are at the highest risk of subsequent migration. Paradoxically excessive oversizing of a stent graft will result in further distal dilatation and a more significant rise in drag forces with time. Stent grafts composed of Gianturco Z-stent elements may also exhibit a gradual decrease in radial expansion force as the stent increases in diameter.

This study is subjected to the standard limitations of CFD analysis, and several assumptions were made to limit the complexity of the model calculations. In the initial geometry model, the stent grafts were built as cylindrical tubes without 3D twists and the inlet was axis symmetrical. The stent graft is viewed as a rigid, non-pulsatile tube, but in reality pulsations have been observed in stent graft elements. In a recent study¹⁷ using dynamic CT angiography, changes in thoracic stent graft diameter of up to 5 mm with aortic pulsatility were reported. In aortic dissection there are more propensities for movement, because the dissection flap moves with pressure. The experience of treating aortic dissection with stent grafts is still relatively new, and only time will tell whether these grafts will be less durable than other thoracic repairs.

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Conclusion 

Using 3D pulsatile flow CFD techniques, we have shown that the drag force on a thoracic stent graft is high, and that it is dependent on the graft diameter and the deployment position. In aortic dissections, consideration must be given to drag force changes, because significant graft diameter remodeling was evident.

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Author contributions 

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