## Abstract

In this paper, we present a comprehensive 3D CFD simulation utilizing ANSYS 19.2 Software to explore the intricate interplay between aneurysm size and bifurcation angles ($α°$) in the anterior communicating artery (ACoA) zone. We utilize 15 idealized models created through the simplification of patient-specific artery. Our investigation encompasses wall hemodynamics, flow structure, tissue mechanical parameters, and the assessment of rupture risk. The complex wall hemodynamics are studied in detail, revealing distinct flow recirculation patterns that exhibit a strong dependence on both aneurysm size and $α°$. These patterns shed light on the distribution of velocity and pressure within the ACoA, providing critical insights into the underlying flow dynamics. Moreover, our analysis highlights positions of maximum deformation and equivalent von Mises stress ($σ_{VM}$), offering a comprehensive view of the interplay between these parameters and aneurysm size or $α°$. These revelations not only contribute to the understanding of aneurysm biomechanics but also offer essential information for clinical decision-making and management strategies.

## Objective

The primary objective of this paper is to conduct a comprehensive 3D transient CFD simulation using ANSYS aimed at investigating the influence of aneurysm size and bifurcation angles $α°$ on various critical aspects of the anterior communicating artery (ACoA) zone. In particular, we focus on studying wall hemodynamics, flow structure, tissue mechanical parameters, and the risk of rupture, which are essential factors in understanding the behavior and potential hazards of aneurysms in this region. The study focuses on idealized benchmarks sizes adapted from MRI-based model of the ACoA with scalar aneurysms observed in 59-year-old women, as depicted in **Figure 1**. The MRI-based data shows an approximately elliptical scalar aneurysm with a major axis of 8.013 mm and a minor axis of 6.601 mm. The benchmark of the post-communicating artery length is approximately 12.241 mm.

The patient-specific models is constructed using the SimVascular software. The process begins by meticulously selecting relevant medical images that depict the examined area. Key points situated at the center of the artery and its primary branches are identified and interconnected to establish path lines. Subsequently, the artery undergoes segmentation based on these identified points. Finally, a three-dimensional (3D) model is generated using MRI data and a specialized modeling tool, as illustrated in **Figure 1a**.

The study encompasses 15 idealized bifurcation aneurysm models with elliptical scalar aneurysms, where the major axis $D$ varies as (8 mm, 6 mm, 4 mm), and the minor axis $d$ varies as 6.6 mm, 4.95 mm, and 3.3 mm, as shown in **Figure 2**. To maintain consistency, a constant major and minor axis ($D/d$) ratio of 1.212 is maintained for each aneurysm size. Moreover, the bifurcation angles $α$ vary from 25° to 135°, as illustrated in **Figure 2c**. The selected values for the aneurysms and the average aspect ratio are determined based on dimensions obtained from multiple MRI-based analyses of the anterior communicating artery (ACoA), as detailed in **Appendix A**. The aspect ratio considered is an average across three cases, varying from 1.191 for the "F-48-3.0546" case to 1.2252 for the "F-57-6.10152" case.

<figure><img src="image_1.png" /><figcaption>**Figure 1.** (a-d) the anterior communicating artery (ACoA) of 59 old woman with scalar aneurysm, and (e) the idealized bifurcation aneurysm models build on the MRI based case.</figcaption></figure>

<figure><img src="image_2.png" /><figcaption>**Figure 2.** (a) Idealized bifurcation aneurysm models with elliptical scalar aneurysms, (b) the aneurysm size with different major $D$ and minor $d$ axes values, and (c) The bifurcation angles $α$.</figcaption></figure>

## Numerical methods

### 1. Governing Equations:

$$ \nabla \cdot \vec{u} = 0 \qquad (1) $$

$$ \rho \left( \frac{\partial \vec{u}}{\partial t} + \vec{u} \cdot \nabla \vec{u} \right) = -\nabla p + \nabla \cdot \tau + \rho \vec{g} \qquad (2) $$

$$ \mu(\dot{\gamma}) = \mu_{\infty} + (\mu_0 - \mu_{\infty})[1 + (\lambda\dot{\gamma})^2]^{\frac{n-1}{2}} \qquad (3) $$

### 2. The boundary conditions:

<figure><img src="image_3.png" /><figcaption>**Figure 3.** The velocity profiles are applied at the artery inlet, while the pressure profiles are imposed at the artery outlets.</figcaption></figure>

### 3. Model validation:

<figure><img src="image_4.png" /><figcaption>**Figure 4.** Mesh independence study for (a) the CFD simulation and (b) the Mechanical simulation.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 5.** Time-step independence study for the CFD simulation.</figcaption></figure>

## Results

<figure><img src="image_6.png" /><figcaption>**Figure 6.** Blood flow maximum velocity variation during cardiac cycle phases (a) Early Diastole Phase, (b) Systolic Peak Phase, and (c) Late Deceleration Phase.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Figure 7.** Flow pattern map of the flow regimes due to the change of the aneurysm size and bifurcation angles $α$.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 8.** WSS variation within aneurysm during cardiac cycle phases for different bifurcation angles (a) 25°, (b) 50°, (c) 75°, (d) 100°, (e) 135°, alongside (f) maximum WSS value.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 9.** The maximum mechanical deformation within aneurysm.</figcaption></figure>

## Conclusion

In conclusion, this study aimed to comprehensively investigate the intricate interplay between aneurysm size and $α°$ within the ACoA zone. The primary objective was to examine various critical aspects of aneurysms, including wall hemodynamics, flow structure, tissue mechanical parameters, and rupture risk factors. The research employed a sophisticated 3D transient CFD simulation approach, utilizing 15 idealized models derived from the simplification of patient-specific anatomical models. A series of idealized bifurcation aneurysm models were meticulously studied, encompassing variations in both size and $α°$.

The analysis of flow structure revealed fascinating insights into the relationship between aneurysm size and the resulting flow patterns. Notably, the study identified three distinct recirculation patterns influenced by aneurysm size. Pattern 1 was characterized by recirculation onset at the aneurysm's neck, diverting flow towards the bifurcation. Pattern 2 exhibited an intermediate behavior, combining features of Patterns 1 and 3, while Pattern 3 displayed recirculation onset at the aneurysm's base, a consequence of its shorter neck size. Additionally, aneurysm outlet flow patterns were influenced by $α°$. Pattern A exhibited a low-velocity zone near the bifurcation, while Pattern B showcased transitional behavior, and Pattern C reflected a more stable flow. The simultaneous variations in size and $α°$ resulted in a rich tapestry of nine unique flow patterns, deepening our understanding of flow behavior within cerebral arteries.

The investigation into WSS underscored its strong correlation with both aneurysm size and $α°$. Larger aneurysms exhibited elevated WSS values, while variations in $α°$ had minor influence on WSS magnitude. Moreover, the study unveiled intriguing patterns in maximum wall pressure behavior across different cardiac cycle phases. Transitioning to deformation, it was found to be primarily influenced by size, with minor variations seen in select scenarios involving $α°$.

Furthermore, the analysis of the $σ_{VM}$ highlighted its dependence on aneurysm size, with only slight deviations due to $α°$ variations, especially in certain cases. These insights were complemented by an explanation of how stress propagation and deformation patterns varied in different aneurysm sizes, particularly in relation to stress concentration distribution.

## References

[1] A. G. Rahma and T. Abdelhamid, “Hemodynamic and fluid flow analysis of a cerebral aneurysm: a CFD simulation,” *SN Appl. Sci.*, vol. 5, no. 2, p. 62, Feb. 2023, doi: 10.1007/s42452-023-05276-0.

[2] A. G. Rahma and T. Abdelhamid, “Assessing the effects of stenosis and aneurysms on hemodynamic parameters: A numerical investigation,” in *2023 3rd International Conference on Electronic Engineering ({ICEEM})*, IEEE, Oct. 2023.

[3] T. Abdelhamid and A. G. Rahma, “The Ability of the CFD Approach to Investigate the Fluid and Wall Hemodynamics of Cerebral Stenosis and Aneurysm BT - Nature-Inspired Methods for Smart Healthcare Systems and Medical Data,” A. M. Anter, M. Elhoseny, and A. D. Thakare, Eds., Cham: Springer Nature Switzerland, 2024, pp. 227–248. doi: 10.1007/978-3-031-45952-8_12.