# In-Vitro Simulation of the Blood Flow in an Axisymmetric Abdominal Aortic Aneurysm
## 2 Materials and Methods
### Flow Measurements  
Flow measurements were performed in the symmetric vertical mid-plane of the model test section illuminated by a diode-pumped all-solid-state 5W green laser (\(\lambda=532\) nm). This laser emits a planar sheet of 1.5 mm thickness, and the distance of the test section from it was set so to obtain a uniform light distribution in the measuring section. The working fluid was seeded with a reflecting neutrally buoyant passive tracer (VESTOSINT@)2157 Evonik Corporation, Germany, average diameter \(d_{p}=56\ \upmu\)m, and density \(\rho_{p}=1016\) Kg/m\({}^{3}\)), and flow images were acquired by the acquisition system, i.e., a high-speed (up to 500 fps) and high-resolution (\(1280\times 1024\)) Mikrotron EoSens camera connected to a digital video recorder IO Industries DVR Express@Core (IO Industries, Ontario, Canada). In the first set of experiments (ID 1 to 6, see Table 1), the vertical dimension of the area framed by the camera was 20 cm and enclosed the aneurysm and a portion of healthy aorta \(\sim\)12 cm long upstream of the AAA (spatial resolution of 64 px/cm). A second set of experiments was performed with the same set of parameters but increasing the spatial resolution (ID 1' to 6', see Table 1). In this case, the vertical dimension was 12 cm with a portion of healthy aorta \(\sim\)3 cm long upstream of the AAA (spatial resolution of 96 px/cm). This set of experiments was aimed at improving the spatial resolution close to the AAA boundary to ensure a better evaluation of the WSS. The acquisition frame rate considered for each run is reported in Table 1. The maximum average displacements were on the order of 3 pixels and of 4 pixels for the first and second set of experiments, respectively. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**ID** & _pixel/cm_ & _fps_ & \(\mathbf{Q\ (\text{m}^{3}\text{s}^{-1})\times 10^{-3}}\) & \(\mathbf{W_{b}\ (\text{ms}^{-1})}\) & \(Re\) & \(\mathbf{W_{m}\ (\text{ms}^{-1})}\) \\ \hline
1-1′ & 64–96 & 100 & 0.006 & \(2.3\times 10^{-2}\) & 410 & \(4.56\times 10^{-2}\) \\
2-2′ & 64–96 & 100 & 0.009 & \(3.3\times 10^{-2}\) & 600 & \(6.68\times 10^{-2}\) \\
3-3′ & 64–96 & 150 & 0.016 & \(6.2\times 10^{-2}\) & 1100 & \(1.25\times 10^{-1}\) \\
4-4′ & 64–96 & 200 & 0.023 & \(8.9\times 10^{-2}\) & 1600 & \(1.73\times 10^{-1}\) \\
5-5′ & 64–96 & 250 & 0.028 & \(11.1\times 10^{-2}\) & 2000 & \(2.03\times 10^{-1}\) \\
6-6′ & 64–96 & 400 & 0.037 & \(14.7\times 10^{-2}\) & 2650 & \(2.38\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental parameters in the performed experiments: spatial resolution _pixel/cm_, image acquisition frame rate _fps_, flow rate \(Q\), bulk velocity \(W_{b}\), Reynolds number \(Re\), maximum longitudinal velocity in the healthy aorta \(W_{m}\). The acquired images were processed using hybrid Lagrangian particle tracking (HLPT). The tracking algorithm is based on the solution of the optical flow equation. It selects, within each image, areas where strong light intensity gradients exist [29]; such regions can be associated with tracer particles and can then be considered as good features to track in the sequence [24]. Once the features have been identified, the algorithm reconstructs the trajectories: the fluid motion is then described in a Lagrangian frame of reference, and the velocity of the particles is evaluated by calculating the displacement along the trajectory and the corresponding elapsed time. Image processing is achieved in three subsequent steps: 1) a pre-processing step aimed at removing the background and improving image contrast; 2) particle detection and temporal tracking via the solution of the optical flow equation to isolate particles and track them in consecutive frames; 3) post-processing to obtain the relevant flow parameters [30]. Pre-processing is carried out to improve the quality of acquired images; basically, it implies the removal of parts of the image, which are not significant for the flow analysis as the areas outside of the vessel walls.