## 1 Introduction  
A cerebral aneurysm is a lesion that presents as a focal bulging in blood vessels and is typically located in a region of the brain known as the circle of Willis [1]. The prevalence of this condition is about 3% among individuals without underlying health conditions [2]. The most severe outcome of these lesions is rupture, leading to subarachnoid hemorrhage (SAH) [3, 4], which is associated with a mortality rate that exceeds 40% [5]. The serious consequences that a cerebral aneurysm may produce, along with the high-complexity treatments the patient can receive, such as neurosurgery, necessitate the development of a method to predict the rupture risk of cerebral aneurysms. This would allow better decisions to be made regarding whether or not the patient needs complex treatment. Currently, such a method does not exist, but it is known that the interaction between blood flow and artery walls is the key factor involved in aneurysms' formation, as well as their development and rupture [6]. It is thought that wall shear stress (WSS) is one of the most important hemodynamic factors to study, as zones with high WSS levels are more prone to aneurysm formation [7, 8, 9], while zones with low WSS have been related to the development and rupture of existing lesions. Low stress levels have been found at sites where ruptures have been produced at the aneurysm dome [10, 11], although high WSS levels combined with other factors can also lead to rupture [12]. Newtonian fluid provides a good approximation for blood flow in large arteries. However, inside the aneurysm, this approximation is incorrect because of the presence of flow regions with lower velocities, in which non-Newtonian properties of viscosity become important. In such cases, blood flow must be simulated using a non-Newtonian model [12]. Once an aneurysm has been initiated, different outcomes can occur: rupture at an early stage, an increase in size, and then, rupture or stability over time [13]. The size of an aneurysm does not evolve at a constant rate [14]. There are periods where it does not change, other periods where it can grow, and different growth rates between ruptured and unruptured aneurysms [15]. It has been shown that aneurysm growth can lead to significant morphological changes from at least 23 weeks [16]. Although it may be intuitive to think that an aneurysm will rupture when it is large, small aneurysms also suffer from ruptures [17], which suggests that size is not the only risk factor. In addition to health conditions, such as hypertension or trauma, the aneurysm wall is thinner than that of the parent artery [18], and contrary to what may be thought, when the aneurysm grows, its wall thickness does not necessarily decrease [19], because it is a living structure that can repair itself. The rupture risk increases to 0.5% per annum for aneurysms with diameters greater than 10 mm [3]. The width of the aneurysm neck and the size ratio of the aneurysm have been reported to affect the rupture risk [16]. Other risk factors are the presence of atherosclerotic plaque, smoking, and hypertension [3]. In several studies, hemodynamic parameters have been modified to reflect different health conditions that might affect the rupture risk of an aneurysm, and a few studies have modified geometrical factors. [PERSON] et al. [20] showed that when an aneurysm grows and its wall thickness decreases, the rupture risk increases due to a reduction in the WSS and an increment in the von Mises stress at the aneurysm. Even at a constant wall thickness, the maximum von Mises stress still increases. [PERSON] et al. [21] studied spherical aneurysm geometries using structural simulations. Initially, aneurysms showed a reduction in the maximum von Mises stress, but this then increased along with the aneurysm size, leading to a higher rupture risk. Other works have used cylindrical/spherical membranes subjected to 1D enlargement to model the development of an aneurysm, and the mechanical response has been attributed to collagen and elastin [22].