# Branching and nonbranching intracranial aneurysms in the presence of a persistent stapedial artery and an aberrant internal carotid artery assessed with computational hemodynamics: illustrative case

Céline Salaud, Tristan Martin, Gilles El Hage, Michel W Bojanowski

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## To cite this version:

Céline Salaud, Tristan Martin, Gilles El Hage, Michel W Bojanowski. Branching and nonbranching intracranial aneurysms in the presence of a persistent stapedial artery and an aberrant internal carotid artery assessed with computational hemodynamics: illustrative case. Journal of Neurosurgery: Case Lessons, 2024, 8 (19), 10.3171/case24421. hal-05078636

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Branching and nonbranching intracranial aneurysms in the presence of a persistent stapedial artery and an aberrant internal carotid artery assessed with computational hemodynamics: illustrative case

Céline Salaud, MD, PhD,¹,² Tristan Martin, BSc(Hons),¹ Gilles El Hage, MD,¹ and Michel W. Bojanowski, MD¹

¹Division of Neurosurgery, University of Montreal Hospital Center, Montreal, Quebec, Canada; and ²Division of Neurosurgery, Nantes University Hospital Center, Saint-Herblain, France

**BACKGROUND** The mechanisms underlying the initiation and progression of bifurcation versus lateral wall aneurysms are not well understood. Computational fluid dynamics (CFD) can improve the understanding of these mechanisms and can consequently help identify patients at higher risk for developing aneurysms and monitor them more closely.

**OBSERVATIONS** A 36-year-old man presented with a ruptured anterior communicating artery aneurysm, which was successfully treated with microsurgical clipping. Imaging also revealed a persistent stapedial artery with an elongated and tortuous posterior communicating artery (PCoMA). Fourteen years later, he was readmitted for a ruptured aneurysm on a PCoMA loop. CFD helped identify considerable collateral circulation due to the aberrant internal carotid artery (ICA). High flow rates trigger both types of aneurysms, but nuances exist in the hemodynamic mechanisms that drive their growth.

**LESSONS** Berry aneurysms and lateral wall aneurysms initially start due to a high flow rate, a common underlying cause. However, the formation of true sidewall aneurysms is primarily characterized by locally increased wall shear stress, while the development of berry aneurysms is mainly linked to high local blood pressure at arterial bifurcations. An aberrant ICA can lead to supraphysiological compensatory flow in the anterior and posterior circulation, increasing the risk of intracranial aneurysm formation at both branching and nonbranching sites, underscoring the need for lifelong monitoring.

https://thejns.org/doi/abs/10.3171/CASE24421

**KEYWORDS** sidewall aneurysm; berry aneurysm; ICA agenesis; persistent stapedial artery; computational fluid dynamic

We present a case involving a persistent stapedial artery (PSA) associated with an aberrant internal carotid artery (ICA) in a patient who experienced two separate episodes of subarachnoid hemorrhage due to ruptured intracranial aneurysms occurring at branching and nonbranching sites of the circle of Willis. The first hemorrhage was due to the rupture of a berry aneurysm on the anterior communicating artery (ACoMA), which occurred in his 30s, while the second hemorrhage was attributable to the rupture of a very rare lateral wall aneurysm on the trunk of the posterior communicating artery (PCoMA) 14 years later. To our knowledge, this is the first report of intracranial aneurysms occurring at branching and nonbranching sites associated with both a PSA and an aberrant ICA.

Our analysis suggests that both berry aneurysms and sidewall aneurysms might initially share a common causal trigger, although the pathophysiological mechanisms involved in their growth, development, and rupture could differ. Furthermore, it underscores the importance of long-term monitoring for such patients, given the inherent risk factor of ICA agenesis present since birth.

## Illustrative Case

### History and Examination

A 35-year-old man presented with a subarachnoid hemorrhage characterized as World Federation of Neurosurgical Societies (WFNS) grade I and Fisher grade 4, resulting from the rupture of a berry AComA

**ABBREVIATIONS** ACA = anterior cerebral artery; AComA = anterior communicating artery; APA = ascending pharyngeal artery; CCA = common carotid artery; CFD = computational fluid dynamics; CTA = computed tomography angiography; ICA = internal carotid artery; MCA = middle cerebral artery; PCoMA = posterior communicating artery; PSA = persistent stapedial artery; WFNS = World Federation of Neurosurgical Societies; WSS = wall shear stress.

**INCLUDE WHEN CITING** Published November 4, 2024; DOI: 10.3171/CASE24421.

**SUBMITTED** June 29, 2024. **ACCEPTED** August 7, 2024.

© 2024 The authors, CC BY-NC-ND 4.0 (http://creativecommons.org/licenses/by-nc-nd/4.0/)
aneurysm. The lesion was associated with right hypoplasia of the A1 segment of the anterior cerebral artery (ACA), as evidenced by a left A1/right A1 radius ratio greater than 2¹ based on computed tomography angiography (CTA). Apart from medically managed hypertension, the patient had no other known risk factors for intracranial aneurysms, such as a familial history of cerebral aneurysms or personal history of smoking.

The angiogram revealed an aberrant right ICA characterized by an agenesis of its cervical segment, while its petrous segment, albeit of small caliber, was vascularized by the inferior tympanic branch of the ascending pharyngeal artery (APA; Fig. 1A). The middle meningeal artery arose from a PSA. CTA revealed the PSA entering the skull through a small persistent duct in place of the carotid canal (Fig. 1C), with a hypoplastic petrous ICA and the lower tympanic artery coursing through an enlarged inferior tympanic canal.

Interestingly, the right PComA was elongated and tortuous, forming two loops, and contributed to the vascularization of the supraclinoid ICA and middle cerebral artery (MCA) territory (Fig. 1B). However, the right ACA was mainly supplied by the left ICA via significant blood flow through the AComA.

## Treatment and Postoperative Course

Following surgical clipping of the AComA aneurysm, the patient had an excellent outcome. Four years later, the patient experienced a recurrent episode of subarachnoid hemorrhage characterized as WFNS grade I and Fisher grade 4, along with mild hydrocephalus. This occurrence was attributed to the rupture of a 6-mm sidewall aneurysm located on the caudal loop of the tortuous right PComA, previously identified on routine angiography (Fig. 1B).

The significant risks of occluding the PComA or its perforators during endovascular treatment of the aneurysm prompted microsurgical clipping via open surgery, during which a temporary external ventricular catheter was inserted to manage hydrocephalus. Postoperative angiography revealed successful exclusion of the aneurysm from the cerebral circulation (Fig. 1D). The surgery was uneventful, and the patient was discharged after 2 weeks with excellent evolution thereafter.

## Computational Hemodynamics

Computational fluid dynamics (CFD) allowed us to assess the hemodynamic factors influencing the pathogenesis of intracranial

aneurysms in this patient. We generated precomputational modeling and meshing of the circle of Willis using SimVascular's segmentation pipeline² (v2023-05) with postoperative CTA as input. While digital removal of cerebral aneurysms serves as a validated method for simulating cerebrovascular hemodynamics before aneurysm formation,³⁻⁶ we benefited by integrating CTA of postoperative clip reconstruction of the parent artery. This combined methodology, alongside established techniques validated for digital aneurysm removal, preserving the vessel radius about the parent artery spline-fitted centerline,³⁻⁶ allowed exclusion of the aneurysms from the cerebral circulation by using the microsurgical clips placed tangentially to the parent arteries to bound the healthy and pathological vessel walls.

Using these techniques, the tortuosity index of the right PComA was computationally confirmed to be significantly elevated with a value of 2.50, which we determined as the ratio between the total length of the vessel with the Euclidian distance between its endpoints. The true vessel length was notably determined by fitting a parametrized 8-degree polynomial in every axis:

$$g(t) = \left\langle \sum_{i=1}^{\theta} a_i t^i, \sum_{i=1}^{\theta} b_i t^i, \sum_{i=1}^{\theta} c_i t^i \right\rangle$$

to the points selected in SimVascular.

For CFD simulation, we modeled blood flow as an incompressible Newtonian fluid,⁷ setting the dynamic viscosity to η₀ = 0.0004 Pa·sec and the blood density to 1060 kg/m³. The ICAs and vertebral arteries perfused the circle of Willis over a cardiac cycle according to validated standard waveforms provided by SimVascular² (Fig. 2), without flow compensation in the patent vessels given the patient's age.⁸ However, the time-varying flow rate of the aberrant right ICA was appropriately scaled down by a factor of 20 to account for its vascularization by the APA, whose flow rate has been measured in previous hemodynamic studies.⁹ While this approximation is based on the literature, it is important to acknowledge that such a significant reduction is an assumption affecting hemodynamic results. Outflows in the P2 segments of the posterior cerebral arteries, the M1 segments of the MCAs, and the A2 segments of the ACAs were modeled as Poiseuille flow p = QR using 10,000 dynes·sec/cm⁵ resistors.¹⁰

CFD helped reveal significant compensatory flow in the patent left ICA evidenced by increased velocity and blood pressure in order

<figure><img src="image_3.png" /><figcaption>FIG. 1. A: External carotid artery injection angiogram revealing an inferior tympanic branch of the APA, which supplies the aberrant ICA through intratympanic anastomoses. The middle meningeal artery (MMA) arises from the PSA. B: Vertebral artery injection angiogram showing retrograde flow in a tortuous and elongated right PComA with a true PComA aneurysm. C: CT angiogram objectifying the persistent duct through which the PSA entered the skull in place of the carotid canal. D: Postoperative angiogram revealing successful exclusion of the PComA aneurysm from the cerebral circulation.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>**FIG. 2.** Patent ICA (**left**) and vertebral artery (**right**) flow rate waveforms (mm³/sec) throughout a cardiac cycle. Because of the anomalous vascularization by the APA, the flow rate of the aberrant ICA was proportionally scaled down by a factor of 20 for accurate CFD simulation.</figcaption></figure>

to accommodate for the hypoplastic right ICA and the A1 segment (Fig. 3). In fact, the peak flow velocity in the dominant A1 segment of the ACA was approximately 3 times the physiological value¹¹ in order to maintain appropriate bilateral perfusion of the distal ACA territories, at the cost of locally elevating blood pressure at the AComA-ACA bifurcation where the aneurysm eventually developed.

On the other hand, the right MCA and the hypoplastic supraclinoid ICA mainly received their vascular supply from the posterior circulation through retrograde flow in the right PComA, given the negligible contribution from the aberrant ICA. Despite its small caliber, the right PComA accommodated substantial flow from the posterior circulation, approximately corresponding to between 1 and 2 times the reference value for > 70% ipsilateral carotid stenosis.¹² Such a high compensatory flow rate likely contributed to the development of the PComA's significant tortuosity. This morphological evolution consequently caused blood to shear the length of the inferior wall of the caudal loop where the aneurysm eventually developed, evidenced by locally elevated wall shear stress (WSS; Fig. 4).

## Patient Informed Consent

The necessary patient informed consent was obtained in this study.

## Discussion

### Observations

To our knowledge, we describe the first case of ruptured intracranial aneurysms occurring at branching and nonbranching sites of

the circle of Willis in the presence of an anomalous trajectory of the ICA accompanied by a PSA. An embryonic developmental anomaly resulted in a PSA, which, Steffen speculated, might apply traction on the developing ICA, thereby resulting in the absence of its cervical segment,¹² as evidenced by the agenesis of the carotid foramen at the skull base. Lasjaunias and colleagues argued that the aberrant ICA can be supplied by the APA via intratympanic anastomoses through Jacobson's canal, serving as a limited collateral arterial pathway to the brain.¹³,¹⁴ However, this route was inadequate in our patient, requiring contralateral compensation via the circle of Willis, as validated by our CFD simulations. Notably, the right A2 segment of the ACA received supply from the left ICA via the AComA, while the right MCA and the right hypoplastic supraclinoid ICA were supplied by the posterior circulation from retrograde blood flow in the ipsilateral PComA. This case shows that the same initial hemodynamic conditions in a patient can trigger the initial structural changes required for the formation of two different types of intracranial aneurysms on drastically different time frames.

This considerable collateral circulation caused supraphysiological flow velocity on both the AComA and the PComA, as evidenced by our patient-specific CFD. Hence, lifelong monitoring for patients with a PSA and an aberrant ICA is warranted due to these pathological hemodynamic flow patterns.

Due to the right PComA's length, such a high flow rate in this artery likely exceeded the artery's elasticity, contributing to its tortuosity. In fact, it is well known from computational,¹⁵ in vitro,¹⁶ and in vivo¹⁷ experimentation that hypertension and increased flow in an initially linear artery can lead to mechanical instability and arterial buckling.¹⁸⁻²¹ Consequently, these factors contribute to endothelial cell injury and vessel wall remodeling,²²,²³ ultimately resulting in tortuosity.²¹ Our results agree with previous Doppler ultrasonographic assessments demonstrating that ICA occlusion is associated with such a compensatory increase in flow velocity in the ipsilateral PComA, possibly leading to the formation of a true sidewall aneurysm.²⁴

Yet, the tortuosity of the PComA likely developed gradually over a significant period. While a high flow rate appears to have been necessary for the formation of the true PComA aneurysm in this patient, it alone was not sufficient. Specifically, its pathogenesis first required a high-velocity profile to elongate the PComA, leading to arterial buckling. Second, high velocity in such a tortuous PComA caused blood flow to rapidly accelerate within a vessel loop, thereby shearing the length of the inferior wall of the caudal loop, as evidenced in our case by locally increased WSS where the aneurysm eventually developed.

<figure><img src="image_5.png" /><figcaption>**FIG. 3.** Flow velocity (cm/sec) and relative blood pressure (barye) at peak systole. The flow and pressure fields show increased velocity and relative blood pressure in the patent left ICA such that both A2 segments are perfused by the dominant left A1 (white arrow on the velocity graph, **left**), at the cost of locally elevating blood pressure at the AComA-ACA bifurcation where the aneurysm eventually developed (white arrow on the pressure graph, **right**). L = left; R = right.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**FIG. 4.** WSS (barye) in the right PComA at peak systole. In the coronal slice of the PComA, the velocity profile at the caudal loop exhibits a skew toward the outer curvature, resulting in increased WSS (white arrow) at the site where the sidewall aneurysm eventually developed. PCA = posterior cerebral artery.</figcaption></figure>

In our study, the supraphysiological flow rate in the A1 segment of the ACA was a sufficient condition for the formation of the AComA aneurysm. This could explain why the AComA aneurysm developed 14 years prior to the PComA aneurysm, particularly considering that the supraphysiological flow velocity was approximately 3 times the normal value in the A1 segment, compared to 2 times the reference value previously studied in ipsilateral PComAs associated with > 70% carotid stenosis.¹² While our CFD analysis provides valuable insights into the hemodynamic factors influencing aneurysm formation, it is essential to recognize the limitations imposed by the assumptions of flow, viscosity, and pressure. These assumptions, based on the relevant literature, can introduce variability in WSS and WSS gradient.

Occlusion and agenesis of the ICA are known risk factors for the formation of intracranial aneurysms,²⁵⁻²⁹ and notably for the development of extremely rare nonbranching aneurysms of the ipsilateral PComA.²⁴,³⁰⁻³⁴ The hypothesis that both berry aneurysms and sidewall aneurysms could initially share a common etiological trigger has been

previously examined in animal models.³⁵,³⁶ In their study, Kondo et al. ligated the left common carotid artery (CCA) as well as the posterior branches of the renal arteries to induce renovascular hypertension in 35 Sprague-Dawley rats.³⁵ They reported a significant incidence of intracranial aneurysms occurring at branching and nonbranching sites, with the latter solely manifesting on the sidewalls of vessel curvatures, as in our case. To compensate for the occluded CCA, the ipsilateral posterior circulation served as a crucial collateral pathway in most subjects,³⁵ as it did in the case presented herein. This increased flow rate mostly likely led to the observed dilation and tortuosity of the P1 segment,²¹,³⁵ similarly to our CFD simulations, indicating that the patient's tortuous PComA could be a result of increased collateral circulation. These findings are further supported by the presence of dilated vessels of the posterior circulation in patients with ICA agenesis.³⁷,³⁸

While berry and saccular aneurysms occurring in the presence of ICA occlusion or agenesis can initially share a high flow rate as a

<figure><img src="image_7.png" /><figcaption>**FIG. 5.** Flow fields and velocity profiles depicted to illustrate the formation and progression of sidewall and berry aneurysms. Sidewall aneurysms are characterized by high inflow jets shearing and dissecting the vessel wall, resulting in elevated WSS gradients at the distal boundary. Conversely, the formation and progression of berry aneurysms are associated with high inflow jets colliding perpendicularly with arterial bifurcations and subsequently the developing aneurysm dome. Upon impact, the jet disperses, leading to localized high WSS divergence on the aneurysm sac.</figcaption></figure>
common causal trigger in the same patient, our hemodynamic study suggests that different hemodynamic mechanisms subsequently drive their distinct morphological evolution on different time frames. Once the structural changes in the vessel wall are initiated, the progression and rupture of sidewall aneurysms have been shown to be dependent on the blood flow coursing parallel to the vessel lumen, exerting shear forces on the boundary of the aneurysm sac³⁹,⁴⁰ (Fig. 5). This results in a significant WSS gradient at the aneurysm boundary,⁴⁰ which is particularly elevated at high inflow angles, leading to significant shear jets at the distal boundary.³⁹ Mathematically, the gradient corresponds to the instantaneous rate of change of a vector field and is oriented toward areas of higher WSS (Fig. 5). Shearing and dissection of the vessel wall can thereby create an aneurysm sac characterized by a large ostium with no neck. This evolution is distinct from that of saccular aneurysms occurring at bifurcations, whose progression and rupture are dependent on blood flow entering the aneurysm sac and colliding perpendicularly with the aneurysm dome, whereby the inflow jet exerts localized elevated blood pressure on the aneurysm wall, as shown in our CFD study⁴¹ (Fig. 5). Thereafter, the jet breaks apart, yielding a localized area of high WSS⁴¹ and significant posi- tive WSS divergence on the aneurysm dome, after which blood flow follows the aneurysm sac toward its ostium. Mathematically, positive WSS divergence indicates that the WSS vector field spreads outward from the point where the blood flow jet collides perpendicularly with the aneurysm dome (Fig. 5). This effect has the potential to create a larger aneurysm sac with a well-defined neck.

## Lessons

Berry aneurysms and lateral wall aneurysms could initially exhibit a high flow rate as a shared etiological trigger. While the formation of the true sidewall aneurysm was subsequently characterized by locally elevated WSS in a significantly tortuous parent artery, the develop- ment of the berry aneurysm was associated with high local blood pressure at the bifurcation. Our analysis of this case underscores the importance of lifelong monitoring for patients, as the risk associated with agenesis of the ICA is present from birth and persists even after aneurysm repair.

## Acknowledgments

We used ChatGPT 3.5 to correct grammar and syntax.

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## Disclosures

The authors report no conflict of interest concerning the materials or methods used in this study or the findings specified in this paper.

## Author Contributions

Conception and design: Bojanowski, Salaud, Martin. Acquisition of data: Bojanowski, Salaud, Martin. Analysis and interpretation of data: all authors. Drafting the article: Salaud, Martin. Critically revising the article: Bojanowski, Salaud, Martin. Reviewed submitted version of manuscript: Bojanowski, Salaud, Martin. Approved the final version of the manuscript on behalf of all authors: Administrative/technical/material support: Bojanowski. Study supervision: Bojanowski.

## Correspondence

Michel W. Bojanowski: Centre hospitalier de l'Université de Montréal, Montreal, Quebec, Canada. michel.w.bojanowski.med@ssss.gouv.qc.ca.