# In-Vitro Simulation of the Blood Flow in an Axisymmetric Abdominal Aortic Aneurysm
## 1 Introduction
[14]; in this case, the authors numerically simulated the blood flow in ruptured AAAs to correlate local hemodynamic factors with rupture location. Nevertheless, it has to be noticed that numerical study may lack of an experimental validation; to this aim, in vitro modeling [15; 16; 17] have been very useful in the characterization of the complexity implicit in cardiovascular models. In this context, [PERSON] et al. [18] performed flow measurements using 2D particle image velocimetry (PIV) in a rigid and symmetric model of an AAA under pulsatile flow conditions. They investigated the flow pattern and the WSS and WSSG distributions changing the geometric parameters systematically. [PERSON] et al. [19] studied both steady and periodic flows in an axisymmetric model of a fusiform aneurysm using both computational fluid dynamics (CFD) and 2D PIV measurements in the range \(100<Re<700\). In [20], the authors considered a rigid diseased phantom emulating the pulsatile flow in an AAA with aorto-iliac bifurcation and stenosis and measured the flow using 2D PIV. They investigated the vorticity field evolution, the vortex core trajectory, and the hemodynamics characteristics. A now widely diffused approach consists in investigating the blood flow by combining experimental and CFD models built on patient-specific anatomical data acquired by medical imaging. [PERSON] et al. [21] used computed tomography to build a silicone model of a patient-specific AAA. The authors measured the 3D velocity field using particle tracking velocimetry (PTV) and performed CFD simulations of the flow within the entire abdominal aorta under averaged steady physiological flow conditions and with identical boundary conditions. [PERSON] et al. [22] studied both steady and periodic flows in an axisymmetric model of a fusiform aneurism using both numerical simulations and laboratory experiments. In the in-vitro model, the velocity field was measured using 2D PIV, while simulations were conducted using CFD. [PERSON] et al. [23] used CFD on models created by 3D reconstruction of in vivo acquired computed tomography images and investigated the correlation between geometric parameters, WSS, ILT, and AAA possible rupture. In the present study, we show the results of an in vitro measurement campaign performed in a laboratory model of the abdominal aortic segment affected by an axisymmetric AAA. We considered a simplified model of the vessel with rigid walls and symmetric shape and performed the experiments in steady flow conditions, varying the Reynolds number in the range \(410<Re<2650\). A characterization of the flow patterns, as well as 2D measurements of the velocity field, were obtained through image analysis; in particular we used hybrid Lagrangian particle tracking (HLPT), a technique that provides both the Lagrangian (fluid particles trajectories) and the Eulerian (instantaneous and time-averaged velocity field on a regular grid) descriptions of the flow field [24]. Once the flow field is obtained, the distribution of the WSS is computed as a function of \(Re\) both in the healthy aortic portion and within the aneurism. Remarkably, particle tracking techniques compared to PIV algorithms allow a larger spatial resolution (being able to detect regions very close to the walls) and an increased dynamic range. These two features make the employment of HLPT in this context particularly suited for the computation of WSS. The general aim of this work is to build an in vitro physiological model, which, gaining insights from the distinctive features of the advanced image analysis technique employed for image processing, is suitable to investigate the correlation of the local hemodynamic characteristics (velocity and vorticity distributions, pressure and WSS fields, and, eventually, turbulence) with both the AAA progression and the rupture location.