Particle Image Velocimetry data-based pressure determination in phantoms of diseased coronary arteries

The in vitro characterization of the local fluid dynamics in realistic phantoms of healthy and diseased coronary arteries is of paramount importance, because of the need for robust data to be used for validation purposes of computational hemodynamics models, having the latter being elevated to dignity of clinical tool for specific applications. In recent decades, Particle image velocimetry (PIV) has been widely applied not only as a method for computational validation but also for assessing the haemodynamic performance of implantable devices and predicting the outcome of surgical procedures. However, this technique currently adopted for the experimental measurement of the velocity vector field does not give any information about pressure, a physical parameter of considerable interest also in the clinical context. The aim of this thesis work is to identify and implement a procedure for estimating pressure from velocity data measured through Particle Image Velocimetry (PIV) in-vitro, in realistic phantoms of coronary arteries. Two-dimensional pressure fields were derived from PIV data. To compute the material derivative of velocity and subsequently the pressure gradient, a first method was developed based on the Navier-Stokes momentum equations. This method was integrated with the spectral decomposition algorithm of Wang et al. (Exp Fluids, 58:84, 2017) capable of deriving the pressure field from its gradients by means of a least-square reconstruction. In order to validate the algorithm for estimating the pressure from the velocity, the Poiseuille flow was initially taken as a case study. The latter was simulated by both CFD simulations and 2D discretization of the analytic solution in Matlab. For both cases, the estimated pressure drop was found to be similar to the theoretical one. Then, the algorithm was applied to experimental PIV data on a straight pipe. Again, the results were in line with the theoretical ones, with accuracy depending on the spatial resolution of PIV measurements. The method was subsequently applied to a contraction flow with a bluff body. This configuration was exploited as a benchmark for the identification of vortices (von Kármán vortex street) with local pressure minima moving in time. In this case, a second method was also tested, namely the Poisson equation for pressure. It was observed that for this type of flow the predominant and most error-prone component of the estimate was the time derivative, which was subsequently corrected by optimizing the acquisition frame-rate according to the literature. Finally, the PIV-based pressure estimation procedure was successfully applied to the following two cardiovascular realistic phantoms: a simplified stenosis and a silicone dummy of a coronary artery obtained from angiographic images. In conclusion, the identified and implemented approach for pressure calculation from in vitro velocity measurements was able to adequately estimate experimental pressure drops. In the future, a more robust pressure estimation could be attained using three-dimensional PIV data and not simply planar data, since 2D motion field analysis does not capture the complex flow within blood vessels, especially in the case of vessels of small size such as coronary arteries.