# In-Vitro Simulation of the Blood Flow in an Axisymmetric Abdominal Aortic Aneurysm
## 2 Materials and Methods
### Flow Measurements
In this case, in fact, the glares due to the interaction between the laser sheet and the walls may interfere in the selection of good features by the processing algorithm. To properly border the domain, we employed a mask obtained by identifying the Cartesian coordinates of a large number of points belonging to the walls of the aneurysmal bulge and interpolating them by sixth-order polynomials. The definition of the boundaries plays a crucial role in the WSS calculation as it allows for the calculation of the unit tangent and normal vectors in correspondence of the wall (see the Appendix A). The particle detection algorithm, the core of the HLPT technique, is based on the solution of the optical flow equation [24]: a set of positions associated with the displacement vector predictor, for which the optimization problem is well-posed, is detected via the solution of the image intensity conservation equation. Those positions, also defined as features, are then associated with the centroid coordinates using two 1D Gaussian functions built around the integer position of the local maximum of the intensity value of each detected feature. The set of validated particle image locations and the displacement vector predictor, associated with the particle, given by the approximated solution of the optical flow equation, are, finally, used as input data for the tracking algorithm. The nearest neighbor principle is employed to identify the successive positions of each particle/feature and extract the displacement of the particle along its trajectory. Among all the possible candidates, the principle selects the one associated with the minimum Euclidean distance from the position determined with the displacement predictor. As the solution of the assignment problem is strengthened by using the displacement vector predictor, the proposed method does not suffer from the typical drawbacks of the classical nearest neighbor method, i.e., being erroneously influenced by fast-moving particles with respect to the mean inter-particle distance. An example of reconstructed trajectories for run 6 is reported in Figure 3. The adaptive Gaussian arithmetic average method described in [30] was employed to map randomly spaced Lagrangian data onto the regular grid. After reaching the constant flow condition, properly checked through the flowmeter, each experiment lasted on average 60 s; given the characteristic time scales of the flow ~0.05 s, we estimated such a duration suitable to provide enough data to ensure a robust statistical analysis. The instantaneous flow fields are then averaged, and the time average (\(U\), \(W\)) of both the horizontal and vertical velocity components are obtained; for all the performed measurements, we estimated fluctuations were increasing with Re of the order of (but less than) 10%. The post-processing of the velocity fields allows the calculation of all the quantities of interest for the description of the fluid motion; as it will be widely discussed in the next section, we will focus on stream function and WSS.