Hemodynamic impingement and the initiation of intracranial side-wall aneurysms

Abstract

Objective

The natural history intracranial aneurysms (IA) remains poorly understood despite significant morbidity and mortality associated with IA rupture. Hemodynamic impingement resulting in elevations in wall shear stress and wall shear stress gradient (WSSG) has been shown to induce aneurysmal remodeling at arterial bifurcations. We investigate the hemodynamic environment specific to side-wall pre-aneurysmal vasculature. We hypothesize that fluid impingement and secondary flow patterns play a role in side-wall aneurysm initiation.

Methods

Eight side-wall internal carotid artery aneurysms from the Aneurisk repository were identified. Pre-aneurysmal vasculature was algorithmically reconstructed. Blood flow was simulated with computational fluid dynamic simulations. An indicator of isolated fluid impingement energy was developed by insetting the vessel surface and calculating the impinging component of the fluid dynamic pressure.

Results

Isolated fluid impingement was found to be elevated in the area of aneurysm initiation in 8/8 cases. The underlying fluid flow for each area of initiation was found to harbor secondary flow patterns known as Dean’s vortices, the result of changes in momentum imparted by bends in the internal carotid artery (ICA).

Conclusion

Isolated fluid impingement and secondary flow patterns may play a major role in the initiation of side-wall aneurysm initiation. We are unable to determine if this role is through direct or indirect mechanisms but hypothesize that elevations in isolated fluid impingement mark areas of cerebral vasculature that are at risk for aneurysm initiation. Thus, this indicator provides vascular locations to focus future study of side-wall aneurysm initiation.

Keywords

Intracranial aneurysm aneurysm initiation hemodynamics computational fluid dynamics

Introduction

Intracranial aneurysms (IAs) are pathological dilations in the cerebral vasculature. Despite significant morbidity and mortality associated with their existence and rupture, the natural history of these diseased vessels is poorly understood. The pathogenesis of IAs consists of three phases: initiation, growth, and rupture.¹ Aneurysm initiation is thought to occur as the result of a complex interplay between local hemodynamic forces and the ensuing cellular-level biological processes at the vessel wall. Vasculature that has been weakened by various acquired (e.g., cigarette smoking) and/or inherited (e.g., polycystic kidney disease) insults is known to increase risk,^2,3 and the cerebral vasculature, which lacks external elastic lamina, medial elastin, and supporting adventitial and perivascular tissues, is postulated to be intrinsically prone to the effects of these mechanical forces.⁴

Wall shear stress (WSS), the hemodynamic force exerted on the vessel wall by the local tangentially aligned fluid flow, has been studied extensively with regards to aneurysm pathophysiology. Elevations in this shearing force have been shown to induce endothelial damage,⁵ initiate aneurysmal remodeling histologically,^6,7 and correlate with aneurysm location on parent vessels both when studied retrospectively⁸ and after digital reconstruction.⁹ Additional hemodynamic factors such as wall shear stress gradient, gradient oscillatory number (GON),¹⁰ oscillatory shear index,¹¹ and aneurysm formation indicator¹² have also been derived and investigated with respect to initiation.^6–10 Combination studies incorporating computational fluid dynamics (CFD) with animal flow models have revealed that areas of high WSS and positive WSS gradient, resulting from impingement of fluid on the vessel wall, correlate with the induction of histologic aneurysmal vascular remodeling, specifically at animal intracranial arterial bifurcations.^6,7 However, the hemodynamic environment underlying the parent vasculature of side-wall aneurysms harbors no obvious fluid impingement, and while having been shown to positively correlate with local elevations in WSS, the parent vasculature has not been shown to be well correlated with local elevations in WSSG.⁹

Given the ubiquitous nature of WSS elevations within the carotid siphon, in conjunction with the documented lack of correlation between WSSG elevations and pre-side-wall-aneurysmal vasculature, we question whether side-wall aneurysm initiation is a hemodynamically distinct process from bifurcation initiation. As side-wall aneurysms tend to occur on the outer curvature of the toroidal internal carotid artery (ICA) bends, we hypothesize that fluid impingement—though not as obvious as impingement at bifurcation aneurysms—may directly or indirectly play a role in this process. In this paper, we study the hemodynamics of side-wall pre-aneurysmal vasculature. We hypothesize that fluid impingement and secondary flows, created by momentum changes imparted by the tortuous carotid siphon, play major roles in side-wall aneurysm initiation. Previously, wall pressure had been used to study fluid impingement forces at the vessel wall in the contexts of initiation,^6,13 growth, and rupture.¹⁴ In order to investigate the role of fluid impingement in the hemodynamic environment of side-wall aneurysms, we propose a method to isolate the fluid impingement energy with a novel hemodynamic indicator: the isolated impingement indicator (III). This metric quantitatively measures the fluid energy normal to the vessel surface at an offset distance from the wall, and thus the impingement energy. We use CFD simulations to observe the pre-aneurysmal hemodynamic environments of the parent vessels reconstructed from eight side-wall ICA aneurysms, and assess correlations between elevations in III and the site of aneurysm initiation.

Methods

Study population

An open-source repository of vascular imaging data, Aneurisk Repository,¹⁵ was analyzed and filtered. Criteria for selection included ICA location, side-wall type, lack of aneurysm-perforating vessels, lack of vessels on or near the aneurysm segment, and lack of multiplicity. Patient-specific stereolithographic geometries of the first six consecutive aneurysms, as well as two aneurysms that did not appear to occur on the positive curvature of the parent vessel, were chosen for the study and obtained from the Aneurisk Repository.

Modeling of arterial vasculature

The aneurysms associated with each model were digitally removed from the obtained geometries and parent vessels were subsequently reconstructed. Both actions were performed in Vascular Modeling Toolkit (VMTK) (Orobix) using the algorithm proposed by Ford et al.¹⁶ as adapted to VMTK.¹⁷ The reconstructed parent vessel surfaces were smoothed, clipped proximally between ICA segments C2 and C3, complemented with flow extensions at the inlets and outlets, and surface meshed in Meshmixer (Autodesk). Tetrahedral volume meshing was performed in Fluent (ANSYS). A sensitivity analysis for mesh density was performed on the first model. Mass flow rates at the outlets and velocity at two points internally offset from the vessel wall near the aneurysm region were probed. Convergence was found at mesh density of >2500 nodes/mm³. This resulted in models with 6–10 million cells. Three models were simulated at this mesh density, the first two consecutive as well as the first that did not appear to occur on a positive curvature, in order to observe the intricacies of the vascular hemodynamics. The solutions were also found to converge qualitatively at a lower mesh density of 300 nodes/mm³. Thus, for efficiency, the lower mesh densities were chosen to simulate all cases to observe the qualitative pattern of impingement only.

CFD studies

In order to study side-wall pre-aneurysmal hemodynamics and assess the utility of this proposed factor, CFD simulations were performed. Pulsatile blood flow simulations were performed in Fluent using the following parameters: Blood was approximated as an incompressible Newtonian fluid with laminar flow and three-dimensionally modeled by unsteady Navier-Stokes equations. Vessel walls were treated as rigid bodies and had “no slip” boundary conditions applied to them. The density and viscosity of blood were set as 1069 kg/m³ and 0.0035 kg/(m*s), respectively. The inflow aspect of the model was defined as a velocity inlet and the outflow aspects were defined as pressure outlets. As patient-specific blood flow information was not available for these patients, the inlet boundary condition was set to equal a previously derived volumetric flow rate waveform given by Castro et al.¹⁸ This flow rate was scaled to a cycle-averaged ICA WSS of 1.5 Pa.¹⁹ The pressure outlet boundary conditions were set equal to 0 Pa. A sensitivity analysis was performed to assess time-step size. Mass flow rates at the outlets and velocity at two points internally offset from the vessel wall near the aneurysm region were probed. Convergence of these parameters was found at 0.005 seconds/time-step for the one-second cardiac cycle. Thus, time-step size was set to 0.005 seconds, resulting in 200 time-steps for the one-second cardiac cycle. The simulations were run for two cardiac cycles, and the data from the second cardiac cycle are presented.

Derivation of a novel impingement force indicator: III

We propose a hemodynamic indicator of isolated fluid impingement energy on the vessel wall, III. The derivation of this indicator can be seen in Figure 1. Given the CFD simulation with “no-slip” boundary conditions, fluid velocity is by definition 0 at all surface nodes. As such, the surface nodes are offset internally a small distance along the vector normal to the vessel surface, in order to sample the hemodynamic environment a small distance off the wall (Figure 1, Step 1). The surface normal component of the fluid velocity is then obtained at these sample points by taking the projection of the velocity vector along the surface normal vector. The energy of the fluid is then obtained by calculating the dynamic pressure of the normal component of the fluid velocity (Figure 1, Step 2). Thus, this represents the energy of fluid that is pushing outward against the wall a small distance off the wall internally. Results were normalized for the lower mesh density simulations by dividing III by the average III of the inset surface.

Post-simulation analyses

CFD-Post (ANSYS) was used to analyze the results and create the III with the cycle-averaged velocity data. Offset distance was set to 10% of the inlet radius for each model; the qualitative pattern of the indicator was found to be preserved at 5%, 10%, 20%, and 30% offsets. Range was set to a minimum of 0 Pa in order to display only fluid impingement energy directed outward, normal with respect to the wall.

Results

The average age of the patients was 52.1 ± 18.4 years, all were female, and two were ruptured. The results of the blood flow simulations show common hemodynamic themes in the areas of aneurysm initiation on the pre-side-wall-aneurysmal vasculature. Cross-sections of time-averaged velocity contours (Figures 2 –4(d), first column) depict high-velocity axial fluid columns that deflect to the outside of the toroidal bends in the ICA, toward the areas of aneurysm initiation. These deflections are the result of changes in momentum imparted by the bends in the ICA. Cross-sections of time-averaged tangential velocity vectors (Figure 2 –4(d), second column) reveal the development of secondary flow patterns and show that the tangential vectors change direction from being directed at the vessel wall in line with the proximal toroidal ICA bend to being directed at the current toroidal ICA bend at the site of initiation. These vectors appear to exist in a common pattern at the initiation sites: a central column directed at the initiation site with two counter-rotating vortices created by the deflection of the central column by the wall. These patterns are known as Dean’s vortices, and are well known to be caused by centripetal forces acting on the fluid as the fluid courses through bends, as occurs in the ICA,²⁰ and have been shown to occur in pre-aneurysm vasculature in prior studies.¹²

The proposed indicator of fluid impingement, III, correlates with the site of aneurysm initiation in all eight of the pre-aneurysmal vessels (Figures 2 –4(a) and (b) and Figure 5). The indicator takes advantage of the commonality of the fluid deflection, subsequent impingement of the high-velocity fluid columns, and formation of Dean’s vortices at all sites of initiation. These results indicate that the sites of initiation are subject to an elevation in fluid energy directed normally against the wall. The cycle-averaged fluid impingement energy ranges between 10 Pa and 50 Pa with offsets between 10% and 30% of the inlet velocity when isolated with III. Surface pressure results (Figures 2 –4(c)) reveal that fluid impingement energy values, as measured by III, do not correlate directly with local elevations in surface pressure, highlighting the unreliability of surface pressure as a standalone metric of impingement energy in hemodynamic environments of side-wall pre-aneurysmal vasculature. We note the cases in Figure 4 and Figure 5(g) and (h) as illustrative cases to demonstrate aneurysms that do not appear to occur on the positive curvature of a toroidal bend, yet the location correlates with fluid impingement locations as measured by III (Figure 4 and Figure 5(g) and (h)).

Discussion

Mechanical forces and fluid flow directed perpendicularly toward the vessel wall, namely surface pressure and fluid impingement, have been studied in an attempt to elucidate IA pathophysiology both for side-wall and bifurcation aneurysms. In studying the hemodynamics at common branch points affected by cerebral aneurysms, Takeuchi and Karino concluded that the most important factor for the development of cerebral aneurysms is the magnitude of the approaching blood velocity at bifurcations and bends.¹³ This blood velocity magnitude determines the force exerted on the vessel wall upon impingement. Kulcsár et al. retrospectively analyzed a set of patients that had pre-aneurysmal parent vessel geometry data available and found that the relative surface pressure at the affected segments was elevated in all three models, two of which were bifurcations and one that was a side-wall case.⁸ In dogs with common carotid artery manipulation, Meng et al. histologically showed that well-defined impinging flow on arterial bifurcations produced aneurysm-like remodeling in high-WSS positive-WSSG regions; however, it was demonstrated that the impingement zone was histologically marked by constructive endothelial remodeling while the “acceleration zone,” a distal region of vasculature that formed as a result of fluid impingement forces, was marked by destructive endothelial remodeling.⁶ In a study of two parent vessels digitally reconstructed from side-wall aneurysmal vessels, Le et al. found the area of aneurysm initiation was subjected to a lower pressure compared with the adjacent parent artery.²¹ Furthermore, in a study of the rapid development of bifurcation artery aneurysms, Doenitz et al. found that wall pressure did not directly correlate with aneurysm location.²²

These studies display the apparent dichotomy that exists between aneurysm initiation sites and perpendicularly aligned wall forces. The strongest evidence is presented by Meng et al. in the aforementioned histologic findings at impingement sites of surgically created arterial bifurcations in dogs.⁶ However, there is a distinction between hemodynamic environments of bifurcation pre-aneurysm vasculature and side-wall pre-aneurysm vasculature. Direct impingement, stagnation, acceleration, and deceleration zones are not obviously identified in side-wall pre-aneurysmal vasculature. While the normal component of fluid velocity relative to the wall and the resulting impingement forces are dwarfed by axially aligned fluid flow in side-wall pre-aneurysm vasculature, bends in the ICA create changes in momentum that facilitate the development of secondary flow patterns and impart impingement forces on the vessel wall. In order to isolate these fluid impingement energies, we developed the hemodynamic indicator, III, a factor to account for outward fluid insult on vessel walls by the fluid in an attempt to further understand and predict side-wall aneurysm pathophysiology.

The potential importance of fluid impingement in side-wall aneurysm initiations and the utility of this indicator is demonstrated in the CFD simulation results in Figures 2 –4 and 5, in which local elevations in III correlated well with aneurysm ostium location in all eight cases. It is apparent from the cross-sectional contours (Figures 2 –4(d), first column) that the elevation in III is created by the impingement of the high-velocity fluid column on vessel walls at the sites of aneurysm initiation. This impingement itself is the result of the secondary flow created by the axially aligned high-velocity fluid column deflecting around the bends in the ICA. Additionally, the impingement of the fluid column on the wall facilitates the development of the well-known Dean’s vortices,²⁰ which appear to be common to all initiation sites (Figures 2 –4(d), second column). This Dean’s vortical pattern is responsible for the secondary flow-derived circumferential impingement column that is detected by the III indicator. This commonality at initiation sites fuels the utility of III’s predicative ability. Thus, we hypothesize that this secondary flow plays a role in side-wall aneurysm inception. Additionally, we find that local III elevations generally correlate with overall shape of the future ostium, a characteristic that other factors, such as WSS, WSSG, and GON, appear to lack.^8–10,16 We are unable to determine if this role is through a direct or indirect process. It is possible that the mechanism occurs as a result of elevations in circumferential WSS and WSSG, which are not immediately evident because of the large, axial-aligned forces. These forces have been proven to induce endothelial damage and cause histologic destructive remodeling.^5,6 Future studies may help delineate the relationships between these factors. However, given the positive correlations between III both to location and general ostium shape, we hypothesize that the cyclical insult by this local perpendicular force pushing out over the background surface pressure in conjunction with the resulting shear forces both culminate to increase the risk of aneurysm initiation on that vascular segment.

We point out that while positive correlations in our findings indicate a potential high sensitivity, local elevations elsewhere on the vasculature indicate a low specificity of III as a marker of initiation. This low specificity can be accounted for by the fact that aneurysm initiation results from an interplay of hemodynamic forces, wall characteristics, and systemic factors. As such, we hypothesize that III indicates vascular areas that are hemodynamically at risk for aneurysm initiation. Hence, another utility of this indicator lies in providing metrics to informatively localize areas of vasculature to focus on while studying aneurysm inception. We also postulate that hemodynamic impingement is a necessary factor of side-wall aneurysm initiation as it forms the basis or foundation for the inflow jet into the future aneurysm. Intra-aneurysmal flow created by the inflow jet is a major contributor to aneurysm growth and rupture. Thus, it’s likely that hemodynamic impingement is a necessary factor in the initiation of side-wall aneurysms, but is not sufficient alone for inception, explaining the high sensitivity and low specificity of this marker. The biological factors that may be required in the initiation process remain to be studied.

We also note the relatively low magnitude (cycle-average III of 10–40 Pa; systolic III of 30–70 Pa (not shown)) of the isolated III compared to the surface pressure acting on the vascular walls imposed by the systemic blood pressure (∼12,000 Pa). Takeuchi and Karino postulated that impinging dynamic pressure magnitudes are significant despite relatively low values due to incessant insult throughout the patient lifetime as well as high-momentum energy on the vessel wall, which results in increased wall shear forces, both of which affect endothelial cell function.¹³ Despite the incongruences between elevations in III (Figures 2 –4(a) and (b)) and elevations in surface pressure (Figures 2 –4(c)), the positive correlation between aneurysm initiation and elevation in III leads us to theorize that this force remains important and that III is a more robust marker of this isolated impingement in side-wall pre-aneurysmal vasculature.

Our study had several limitations. For the CFD simulations, which inherently work under many assumptions, the vessels’ walls were treated as rigid bodies, the blood was approximated as a Newtonian fluid, the quantitative flow waveform was derived from measurements on a healthy patient, and the pressures at the outflow boundary conditions were assumed to be zero. Additionally, it was assumed that the algorithmic reconstruction of the parent vessel was significantly similar to the geometry of the parent vessel of the patients prior to aneurysm initiation. Furthermore, the study utilized a preexisting, preformatted database of cerebral aneurysms on which the vasculature lacked visibility of ICA side branches such as the ophthalmic artery, anterior choroidal artery, and posterior communicating artery. Given that the proximity of these side branches to the aneurysms within our study were unknown, disturbed flow from these ICA branches were unaccounted for within our CFD simulations. However, prior studies have shown that small branching vessels do not significantly affect flow.²³

Conclusions

The results suggest that the hemodynamic environment adjacent to the vessel wall plays a role in the initiation of side-wall aneurysms. We find that the fluid energy directed in the surface normal direction, the result of the development of Dean’s vortical patterns created by the secondary flow as the fluid is deflected around bends in the ICA and measured by III, when elevated, is an indicator of vascular sites that are hemodynamically at risk of side-wall aneurysm initiation. This leads us to propose that secondary flow and the resulting impingement measured by III play a role in side-wall aneurysm initiation as a factor in the complex interplay that culminates in side-wall aneurysm formation. We postulate that the importance of the hemodynamic impingement lies in it being the precursor of the aneurysmal inflow jet, and propose a schema of side-wall aneurysm initiation in which four environments exist at the vessel wall with different outcomes: 1. Vessel wall damage AND impingement/inflow precursor MAY result in aneurysm initiation. 2. Vessel wall damage WITHOUT impingement/inflow precursor MAY NOT result in aneurysm initiation. 3. Impingement/inflow precursor WITHOUT vessel wall damage MAY NOT result in aneurysm initiation. 4. NEITHER vessel wall damage NOR impingement/inflow precursor MAY NOT result in aneurysm initiation. This schema provides a theory explaining the ubiquitous yet specific nature of hemodynamic impingement as it relates to aneurysm initiation. While the mechanism of initiation remains unclear, given the positive correlations and the correlating general shapes of the III elevations and the future aneurysm ostia in all cases in this study, we conclude that hemodynamic impingement plays a significant role in side-wall aneurysm initiation and III serves as a viable indicator of vessels at risk for side-wall aneurysm initiation. The biological factors that may result from this impingement energy and that may differentiate the side-wall initiation process from the bifurcation initiation process remain to be studied.

Footnotes

Acknowledgment

Portions of this work were presented in abstract/poster form at the Northeast Biomedical Engineering Conference, Newark, NJ, USA, April 2, 2017.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

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