Computational fluid dynamics evaluation of flow reversal treatment of giant basilar tip aneurysm

Abstract

Therapeutic parent artery flow reversal is a treatment option for giant, partially thrombosed basilar tip aneurysms. The effectiveness of this treatment has been variable and not yet studied by applying computational fluid dynamics. Computed tomography images and blood flow velocities acquired with transcranial Doppler ultrasonography were obtained prior to and after bilateral endovascular vertebral artery occlusion for a giant basilar tip aneurysm. Patient-specific geometries and velocity waveforms were used in computational fluid dynamics simulations in order to determine the velocity and wall shear stress changes induced by treatment. Therapeutic parent artery flow reversal lead to a dramatic increase in aneurysm inflow and wall shear stress (30 to 170 Pa) resulting in an increase in intra-aneurysmal circulation. The enlargement of the circulated area within the aneurysm led to a re-normalization of the wall shear stress and the aneurysm remained stable for more than 8 years thereafter. Therapeutic parent artery flow reversal can lead to unintended, potentially harmful changes in aneurysm inflow which can be quantified and possibly predicted by applying computational fluid dynamics.

Introduction

Treating an intracranial aneurysm basically aims at its exclusion from the circulation. Surgically, the clip will obliterate the aneurysm neck, whereas endovascular treatment reduces inflow into the aneurysm as much as possible, ideally to the point of flow cessation.¹

Certain aneurysms, however, are difficult or risky to treat with standard surgical or endovascular procedures and require a different approach. Hence, in some aneurysms, cessation of flow can be achieved by therapeutic artery occlusion.^2,3 This can be performed using either of two different principles: (1) obliteration of the artery carrying the aneurysm (parent artery sacrifice) or (2) obliteration of proximal vessel(s) in order to induce flow reversal in the aneurysm parent artery. The latter principle is most often applied in large, partially thrombosed, untreated or failed basilar tip aneurysms that exert a tumour effect on surrounding brain tissue.⁴ The notion is that this redirection of flow reduces haemodynamic stress and inflow into the basilar tip aneurysm and thereby promotes intra-aneurysmal thrombosis and eventually shrinkage. However, intra-aneurysmal thrombosis upon flow reversal may occur in a delayed fashion, and increases in aneurysmal inflow have been observed.⁴ It would therefore be beneficial to better understand the haemodynamic effects induced by parent artery flow reversal. To this end, computational fluid dynamics (CFD) may be used. CFD can visualize haemodynamic stress and inflow into the aneurysm as well as identify areas with low flow or shear promoting thrombus formation.⁵

In this work, we present the CFD analysis of a giant basilar tip aneurysm treated with bilateral endovascular vertebral artery occlusion.

Case report

Case

A 55-year-old woman presented with intense, gradually increasing headaches. Cerebral computed tomography (CT) imaging disclosed a 20 × 15 × 18 mm large basilar tip aneurysm. Most of the aneurysm was thrombosed and compressed the brain stem. The circulated area within the aneurysm measured 4 × 9 mm. Neither CT nor a lumbar puncture could reveal signs of haemorrhage but the abrupt onset of headache was interpreted as presenting a warning leak. She underwent an uneventful bilateral vertebral artery balloon occlusion test and thereafter went on to endovascular coil occlusion of both vertebral arteries proximal to the branching of the posterior inferior cerebellar artery. The post-procedural course was uneventful and her headaches resolved. Two weeks later, she was readmitted due to recurring headache. No haemorrhage had occurred and the outer circumference of the aneurysm was unchanged. However, the circulated area within the aneurysm had increased significantly. Treatment with 75 mg of acetylsalicylic acid was halted and the aneurysm remained unchanged thereafter. Her headaches resolved after a few days.

This study has been approved by the internal Hospital board as part of the quality study “Computational fluid dynamics applied to cerebral aneurysms” approval number 2012/14013. The patient received written and oral information and consented to participate in the study.

Geometric model

Patient-specific images of the basilar tip aneurysm and the surrounding vasculature were obtained using computed tomography angiography at two separate dates. The first image was obtained prior to treatment, and the second image when she was readmitted after therapeutic vessel occlusion. The Vascular Modeling Toolkit⁶ was used to perform image segmentation to extract the vessel geometries and create computational meshes of approximately 8 million tetrahedral cells. Figure 1 shows four perspectives of the geometry selected for computation, which consists of the basilar artery (BA), the right P1 segment, and the superior cerebellar artery (SCA), the latter displaying an early branching and being larger than usual. There was no P1 segment of the left posterior cerebral artery. As computational flow extensions, straight pipes were added to the ends of the two SCA branches, the right P1 segment, and the BA. The segmentation process includes only the circulated part of the aneurysm, which differs significantly between the two geometries. In the geometry after treatment, the second SCA branch is missing due to poor image quality.

Figure 1.

Aneurysm geometry at baseline and in the chronic phase after therapeutic bilateral vertebral artery occlusion. BA: basilar artery, PCA: posterior cerebral artery, SCA: superior cerebellar artery.

Mechanical model and boundary conditions

As our model we used the standard Navier–Stokes equations. Blood was considered to be a Newtonian incompressible fluid, with mass density and viscosity set to 1060 kg/m3 and 0.0036 Pa s, respectively. Vessel walls were considered rigid with no-slip boundary conditions applied, including the thrombosed part of the aneurysm. For the outlets at the SCA branches, traction-free conditions were applied in all simulations. For the inlets and outlets at the BA and P1 segment, we applied Womersley profiles fitted to transient midpoint velocity curves. The velocity curves were obtained using transcranial Doppler ultrasound measurements,⁷ with one set of measurements obtained prior to treatment and one set taken when the patient was readmitted 2 weeks after treatment. We ran simulations of three situations: “Baseline” combines the geometry and blood flow velocities measured prior to treatment with flow reversal; “Early phase flow reversal” combines the geometry prior to treatment with early post-procedural blood flow velocities; “Chronic phase flow reversal” combines post-procedural geometry at readmission with post-procedural blood flow velocities.

Numerical methods

To compute the solution to the Navier–Stokes equations we use the CFD solver package cbcflow (https://bitbucket.org/simula_cbc/cbcflow/), which is an evolution of a solver previously validated and employed in haemodynamics studies.⁸ Cbcflow is implemented on top of the FEniCS finite element library.⁹ The solver is based on an Incremental Pressure Correction Scheme with a second-order time discretization¹⁰ and a P1-P1 finite element discretization. For the final computations we used a fine mesh with 8 M tetrahedral cells and small timesteps (0.5 × 10⁻⁴ s) to ensure a convergent solution in both time and space.

Baseline

Simulations of the situation prior to treatment indicate flow with a low velocity in the circulated area within the largely thrombosed aneurysm. Figure 2 (left part) shows streamlines in a snapshot of the flow at peak systole. Most of the blood flowing from the BA to the right P1 does not enter the aneurysm. Figure 3 (left part) shows the wall shear stress (WSS) at the same time. The maximum WSS in the aneurysm was <3 Pa for the entire heart cycle, except at the edge between the aneurysm and the P1 where it briefly surpassed 30 Pa at peak systole. The peak velocity was 1.4 m/s in the P1 segment.

Figure 2.

Streamlines at peak systole in baseline (left), early phase after flow reversal (middle), and chronic phase (right).

Figure 3.

Wall shear stress at peak systole in baseline (left), early phase after flow reversal (middle), and chronic phase (right).

Early phase after treatment with flow reversal

Simulations of the reversed P1 and basilar flow in the geometry prior to treatment disclosed a high-velocity jet with direct impact on the aneurysm wall close to the assumed edge of the thrombosed area. Figure 2 (middle part) shows streamlines in a snapshot of this flow at peak systole. At the site where this jet hit the wall there was a high-pressure spot and high WSS in the surrounding area (Figure 3, middle part). The maximum WSS in the aneurysm was above 40 Pa for the entire heart cycle, and surpassed 170 Pa at peak systole where the jet hits the aneurysm wall. The peak velocity at the core of the jet was 3 m/s, whereas the velocity inside the aneurysm was up to 1.3 m/s in the flow swirling around the dome. Figure 4 shows a slice of the flow pattern revealing circulation zones to the sides of the jet.

Figure 4.

LIC rendering of a slice of the flow pattern where the jet hits the aneurysm wall at peak systole in early phase flow reversal.

Chronic phase after treatment with flow reversal

Two weeks after treatment, the circulated area within the mostly thrombosed aneurysm had enlarged. The outer curvature of the aneurysm remained unchanged. Figure 2 (right part) shows streamlines of the flow in the aneurysm with the new shape at peak systole. The jet now hit the aneurysm wall at a smaller angle and the bulk of the flow was redirected around the aneurysm dome. Figure 3 (right part) shows the WSS. The maximum WSS in the aneurysm is <30 Pa most of the heart cycle, but still surpasses 75 Pa at peak systole where the jet hits the aneurysm wall.

Discussion

The core finding of the present study was that BA flow reversal caused an unintended change on intra-aneurysmal haemodynamics. The consequence of the altered inflow was a dramatic increase in aneurysm inflow and WSS (from 30 Pa to 170 Pa).

Therapeutic vertebral or BA occlusion in the treatment of selected, complex aneurysms has been practised for more than half a century.¹¹ Even though the therapeutic armamentarium has increased largely since then, there remain large or giant basilar tip aneurysms that are very difficult to treat and will have a higher risk of surgical or endovascular treatment as compared with therapeutic vessel occlusion with flow reversal. Left untreated the prognosis of giant aneurysms is poor, with up to 80% of individuals being dead or severely disabled within 5 years.^12,13 Hence, therapeutic vessel sacrifice with flow reversal in the BA may represent the safest treatment for some giant basilar tip aneurysms. The effectiveness of the treatment in terms of obtaining intra-aneurysmal flow cessation may, however, be questioned. Hence, Steinberg et al.⁴ obtained complete thrombosis of basilar tip aneurysms upon clipping of the BA in only a fraction of their patients. Furthermore, one of their patients experienced a dramatic enlargement of a basilar tip aneurysm after basilar clipping. Possibly, this observation was caused by a mechanism similar to what happened with our patient, in whom flow reversal lead to an increase of the circulated area within the aneurysm.

The effect of parent artery flow reversal on aneurysmal behaviour is hence variable, and it would be beneficial to identify predictors of the possibility to obtain complete thrombosis in a given aneurysm upon treatment. In general, the chance of intra-aneurysmal thrombosis is larger, the closer the site of therapeutic vessel occlusion is to the aneurysm.³ Since the site of occlusion in our patient was relatively remote to the aneurysm (coiling of both vertebral arteries), there is a possibility that the observed increase in intra-aneurysmal flow upon therapeutic vessel occlusion would have been less if we had clip-occluded the BA instead. The increased intra-aneurysmal circulation after flow reversal was not caused by growth of the aneurysm per se but by dissolution of an area that earlier was thrombosed. Most probably this happened due to the combined effect of the new, very focused jet into the aneurysm and the fact that the patient was administered acetylsalicylic acid consecutive to coiling of the vertebral arteries.

In the early phase following therapeutic flow reversal, flow simulation revealed the unusually high measured velocity of 3 m/s which resulted in a bundled jet from the P1 segment angled towards the aneurysm in such a way that the jet struck directly into the ostium of the aneurysm. As a result, the flow reversal induced a dramatic change in WSS, where the maximal WSS increased from 30 Pa near the aneurysm neck to 170 Pa where the jet hit the aneurysm wall – a WSS level 4.5 times higher than previously reported as indicative of increased risk of rupture.^14,15 Yet, the jet did not rupture the aneurysm but washed out an earlier thrombosed region in the aneurysm. It thereby created a new geometry with calmer flow, a steadier vortex and lower (but still high) WSS which preserved the aneurysm unchanged for more than 8 years. In other words, our aneurysm showed growth at normal WSS prior to treatment whereas it remained stable at elevated WSS after treatment. There obviously is a need for further studies in order to establish the range of “safe” values for WSS with respect to the risk of aneurysm rupture or enlargement.

In our simulations we applied boundary conditions based on a posteriori known velocity measurements. To apply CFD as a tool in decision-making prior to choice of treatment, a priori estimates of velocities must be made instead. A more conservative estimate of velocity magnitude would make our simulation results from early phase flow reversal less dramatic, but would still reveal how the angles of the vessels led the reversed flow into the aneurysm.

CFD could hence have predicted that therapeutic vertebral artery occlusion could cause a potentially harmful jet into the aneurysm. With this knowledge, treatment could have been modified. CFD thus carries the potential to identify aneurysms not suitable for therapeutic artery occlusion, and represents a valuable clinical tool. However, this is merely a single observation and for the development of risk estimates, multiple, larger studies are needed.

Limitations

In this study we assumed blood to be a Newtonian incompressible fluid. This has recently been shown to be an adequate simplification, since Newtonian and common non-Newtonian models correlate strongly in terms of most WSS-based indicators.⁸ Furthermore, we assumed the vessel walls to be rigid, an assumption that is based on the fact that the wavelength of the wall deformation is much larger than localized vessel segments as in this study. Therefore, the wall deformation is largely in synchrony and has little effect on the main flow.¹⁶ With the unusually high post-procedural velocities, complex transitional flow could be expected as recently reported;¹⁷ however, we found it sufficient to assume laminar flow for this study because we mainly cared about the main characteristics of the jet.

Note that the use of velocity measurements as boundary conditions on BA and posterior cerebral artery (PCA) forces the remaining flow volume to pass through the SCA. With one SCA branch missing in the second geometry, the SCA velocity becomes approximately doubled. However, as this is downstream of the aneurysm, we do not expect the flow to be affected significantly in areas of interest, particularly in light of the angle and high velocity of the jet into the aneurysm. A related error is the lack of a number of smaller arteries which would absorb more of the flow and further reduce the SCA velocity in both early and chronic phase.

This aneurysm was classified as a basilar tip aneurysm based on its anatomical position; however, this classification can be misleading, as the neck reaches below where the missing left P1 segment would have been located in a normal anatomy. In that respect, it was similar to a sidewall aneurysm as well. In particular, the flow pattern at baseline shared more characteristics with flow passing a sidewall aneurysm than flow entering a textbook basilar tip aneurysm. After treatment, the flow pattern had changed to an intermediate between sidewall and bifurcation aneurysm.

Conclusion

Therapeutic parent artery flow reversal can lead to unintended, potentially harmful changes in aneurysm inflow which can be quantified and possibly predicted applying CFD.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The work of Martin Sandve Alnæs and Kent-Andre Mardal has been supported by the Research Council of Norway through grant no. 209951 and a Center of Excellence grant awarded to the Center for Biomedical Computing at Simula Research Laboratory.

Declaration of conflicting interests

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