# In-Vitro Simulation of the Blood Flow in an Axisymmetric Abdominal Aortic Aneurysm
## 2 Materials and Methods  
### Design of the Experimental Model  
Figure 1 shows a scheme of the experimental facility: the hydraulic loop is fed by a tank located on top of the test section. The tank is equipped with an overflow device that separates the fluid exceeding a defined level, thus ensuring a constant flow rate within the circuit. From the bottom of this tank, the fluid enters a handcrafted Pyrex tube characterized by a circular constant section of diameter \(d=1.8\) cm, modeling the healthy aorta, followed by an axisymmetric bulge, modeling the AAA (vessel model); the total length of the pipe is 140 cm.  
The AAA geometry is shown in Figure 2: we considered an axisymmetric aneurysm with a dilatation ratio \(D/d=1.66\) and elongation ratio \(L_{a}/d=3.66\), where \(D=3\) cm and \(L_{a}=6.6\)cm are the maximum diameter and the length of the aneurysm, respectively. Given the considered aspect ratio, we assumed that the used geometry is representative of fusiform aneurysms at a consolidated stage of the disease (i.e., increase in diameter \(>\)50%).  
The test section consists of a portion of the tube in correspondence of the AAA enclosed in a rectangular transparent Plexiglas box 10 L \(\times\) 10 W \(\times\) 25 H cm\({}^{3}\) in order to reduce distortion. The box was filled with distilled water in which the refractive index is close to that of Plexiglas. Furthermore, the use of distilled water allows for overcoming the formation of air bubbles that may form when tap water is used. As the model aorta is made of glass, it cannot account for vessel compliance; however, it is widely accepted [22; 25] that this assumption does not change the general flow characteristics. In fact, including compliance in the model only implies a slight modification in the magnitude of shear  
Figure 1: Experimental set-up.  
Figure 2: Geometry of the aneurysm model.  
stresses [25; 26; 27; 28]. Also, wall rigidity can be related to vessel stiffening, which then makes it possible to model further diseases related to the presence of an aneurysm.  
The working fluid is water; thus, we assumed the blood to follow in a Newtonian behavior; this assumption is compatible with the phenomena studied in this context as the vessel diameter is greater than 1 mm [18]. To fulfill geometric similarity, we considered a physiological shape of the bulge model with a 1:1 scale. As for dynamical similarity, the Reynolds number \(Re=Wb\ D/v\) (where \(W_{b}\) is the bulk velocity \(W_{b}=4\ Q/(\pi D)^{2}\), \(Q\) the flow rate and \(v\) the kinematic viscosity of the fluid) was varied in the range \(410<Re<2650\). This range was selected according to the values corresponding to the different phases of the cardiac systole-diastole cycle; since experiments were run in steady flow conditions, the flow pattern was investigated in correspondence of the minimum, average, and peak values of \(Re\) typically observed [18]. Several experiments were performed by varying \(Q\) and for the same \(Q\) by varying the dimension of the framed area. The flow rate was tuned by an adjustable tap, and a flowmeter downstream of the test section, right before water was discharged into the outflow tank, allowed for its measure. For each experiment, the flow rate value measured by means of the flowmeter was compared with the corresponding value obtained by integrating over the cross section the velocity profile in the healthy aorta reconstructed with the image analysis algorithm described in Section 2.2. A fine agreement between the two values was recovered. The values of the main experimental parameters for each run are reported in Table 1.