Invasive diagnostic catheterizations are normally required to evaluate the pressure gradient in patient with Coarctation of the Aorta (CoA), allowing the assessment of vascular function and revealing the severity of the disease¹. The CoA cause an irreversible pressure loss post-CoA given by the energy dissipation, increasing the ventricular workload required to maintain a certain arterial pressure. Additionally, turbulent flows posterior to the CoA can generate an irreversible damage in the surrounding tissue under mechanical stresses fluctuation². Some method based on MRI to calculate the energy loss and turbulence^3,4 have been proposed. These methods uses finite differences, however, this technique cannot handle the smooth and complex boundaries of vessels in the cardiovascular system, and therefore induces important errors when the geometry is simplified⁵. In this work we proposed a method based on finite elements to obtain 3D quantitative maps of energy loss, kinetic energy, vorticity and helicity from 4D-flow data sets. We performed an in-vitro study that related the pressure gradient (PG), pulse wave velocity (PWV) and elastic modulus with the energy loss, vorticity and helicity parameters.We developed a finite element based computational framework to obtain the velocities gradient from 4D-flow in three orthogonal direction generating continuous 3D maps of energy loss, kinetic energy and turbulence parameters. The algorithm is based in a similar least-squares projection method previously published⁶. Using a MR Phillips Achieva 1.5T, the 4D-flow data was acquired in a realistic aortic phantom in normal conditions and with three different CoA 13, 11, 9 mm, one volunteer and one patient with repair CoA (Figure 1). Additionally, for the phantom with and without CoA we acquire 2D-flow (2D PC-MRI) in two position, the ascending and descending aorta in order to calculate the PWV between these two points (see figure 1A-B). The phantom model T-S-N-005 (Elastrat Sàrl, Geneva, Switzerland) is used with a pulsatile MR-compatible flow pump (Simutec, London, Ontario, Canada), and a catheterization unit to measure invasively pressures between the ascending and descending aorta in order to obtain the elastic modulus between these two points (see figure 1). A summary of the MR acquisition parameters is shown in table I. The process for creating the tetrahedral mesh from the 4D-flow images consist in: first, a generation of an angiography image, then a segmentation of the lumen of the aorta applying an intensity threshold separating the vessel of interest, and finally creating a tetrahedral mesh using the library iso2mesh in Matlab. The next step is to transfer the velocity field over each node of the tetrahedral mesh using a cubic interpolation. The finite element analysis was developed using the Python 
software, and for the visualization and analysis of the data we used the open source software Paraview. Result of PG, PWV and EM for the phatom data are shown in table II. We can see a reduction of the PWV if we increase the severity of the coarctation in the phantom, this is probably generated by the loss of kinetic energy of the flow that pass through the coarctation, affecting the pressure gradient between the ascending and descending aorta. Additionally, the elastic modulus decreased in the ascending aorta for small coarctations. In figure 2 we show the 3D result for vorticity, helicity density, energy loss and kinetic energy for the phantom data with and without CoA. There was an increment of turbulent flow (Vorticity and helicity density) for small CoA, that generated higher loss of energy in this location, affecting directly the pulse propagation along the vessel. The peak values of vorticity, helicity density, energy loss and kinetic energy for all cardiac phases were: 500/1500/1200/875 s^-1, ±60/±420/±150/±100 m/s², 20/200/70/46 μW and 34/240/118/60 μJ for the phantom without CoA and with CoA of 9 mm, 11 mm and 13 mm respectively. To show the applicability of our method we apply our algorithm in one patient with a repair CoA and one volunteer (Figure 3). The peak values obtained in the patient and volunteer data were: 1000/800 s^-1, ±190/±70 m/s², 120/74 μW and 120/110 μJ for vorticity, helicity density, energy loss and kinetic energy respectively.We have proposed a
 novel method that allowed us to obtain 3D maps of energy loss, kinetic energy and turbulence parameters derived from
 4D-flow data using finite elements, which has 
been validate in data obtained from an aortic phantom. From the validation process we can conclude that the 3D maps of energy loss together with the vorticity and helicity may allow assessing the severity of the CoA and the identification of the regions affected.