# In-Vitro Simulation of the Blood Flow in an Axisymmetric Abdominal Aortic Aneurysm
## 1 Introduction  
An abdominal aortic aneurysm (AAA) is a localized irreversible dilatation of the abdominal segment of the aorta, often due to a weakening of the wall of the vessel. An AAA refers to a diameter increase of at least 50% compared to the normal arteria, which measures indicatively 2 cm. Thus, a segment of the abdominal aorta in which the diameter is equal or greater than 3.0 cm is generally considered an aortic aneurysm [1]. In developed countries, an AAA rupture represents an important cause of death with a mortality rate of approximatively 80-90% [2]; several risk factors are associated with the development of AAA including advanced age, male sex, Caucasian race, positive family history, smoking, presence of other large vessel aneurysms, and atherosclerosis [3; 4; 5; 6]. Despite the clinical importance of AAAs, the etiology and the involved pathogenesis remain still, in part, unclear; it is, then, evident how the identification of the factors that can influence the growth and progression of the aneurysm is fundamental for Public Health management. For asymptomatic patients, repair of the aneurysm is the most effective treatment to prevent rupture but considering the risks associated with surgery, AAA repair is recommended if the risk of rupture exceeds the risks associated with surgery, which typically occurs when the AAA diameter exceeds 5.5 cm [1]. Although AAA diameter is an important predictor of rupture, not all large AAAs break, it is then fundamental to look at this phenomenon in a more complex framework. To this aim, clinical, experimental, and numerical studies are being widely performed, focusing on the deep investigation of AAAs and the determination of possible risk factors, as well as on reproducing their hemodynamics. Usually, the local hemodynamics is quantified in terms of the distributions of wall pressure, wall shear stress (WSS), and wall shear stress gradient (WSSG). The peak WSS (PWSS) and the peak wall rupture risk (PWRR) have proved to be better predictors of rupture than the maximum AAA diameter ([7] and reference therein, [8]). The blood flow patterns associated with an AAA have been widely investigated via numerical methods [9; 10; 11]. The models may consider different levels of complexity. In [9], the authors investigated the flow field in an axisymmetric two-aneurysm model with rigid walls and assuming the blood as a Newtonian incompressible fluid in stationary conditions and in a range of Reynolds numbers \(10<Re<2265\); the flow was characterized in terms of the distributions of wall pressure, wall shear stress (WSS) and wall shear stress gradient (WSSG). In [10] the role of the shape and of the geometric features, as asymmetry and iliac bifurcation, are investigated; in [11] the correlation between blood flow and platelet deposition mechanisms in an axisymmetric aneurysm with rigid walls was investigated in the range \(300<Re<3600\), i.e., under both laminar and turbulent flow conditions. The numerical simulations performed using a computational fluid dynamics (CFD) package, were validated through digital particle image velocimetry (PIV) flow measurements that allowed correlating the flow pattern with the platelet deposition mechanism. As a matter of fact, intra-luminal thrombus (ILT) has been associated with an increased rupture risk as it impacts both the biochemical and the mechanical properties of the vessel's wall in correspondence of the aneurysm [12]. In [13], the authors found that both increased ILT thickness and percentage volume are associated with AAA rupture of small aneurysms with low wall stress. In this sense, ILT may represent _a surrogate marker_ of aortic wall degeneration and help in discerning high-risk aneurysms. By analyzing a large set of'small', 'large' ruptured, and non-ruptured AAAs, they were also able to show that early AAA rupture is not a result of elevated wall stresses but the result of compromised aortic wall strength. Similar findings were obtained by [PERSON] et al.