Three‐dimensional quantification of vorticity and helicity from 3D cine PC‐MRI using finite‐element interpolations

Abstract

Purpose: We propose a 3D finite-element method for the quantification of vorticity and helicity density from 3D cine phase-contrast (PC) MRI. Methods: By using a 3D finite-element method, we seamlessly estimate velocity gradients in 3D. The robustness and convergence were analyzed using a combined Poiseuille and Lamb-Ossen equation. A computational fluid dynamics simulation was used to compared our method with others available in the literature. Additionally, we computed 3D maps for different 3D cine PC-MRI data sets: phantom without and with coarctation (18 healthy volunteers and 3 patients).Results: We found a good agreement between our method and both the analytical solution of the combined Poiseuille and Lamb-Ossen. The computational fluid dynamics results showed that our method outperforms current approaches to estimate vorticity and helicity values. In the in silico model, we observed that for a tetrahedral element of 2 mm of characteristic length, we underestimated the vorticity in less than 5% with respect to the analytical solution. In patients, we found higher values of helicity density in comparison to healthy volunteers, associated with vortices in the lumen of the vessels. Conclusions: We proposed a novel method that provides entire 3D vorticity and helicity density maps, avoiding the used of reformatted 2D planes from 3D cine PC-MRI. Magn Reson Med 79:541-553,

Primal and Mixed Finite Element Methods for Deformable Image Registration Problems

“…Traditionally, the transformation mapping has been the fundamental field sought in DIR applications, particularly in medical applications where the goal is to align the reference and target images [39]. However, recent applications of medical image quantification have highlighted the importance of guaranteeing certain accuracy and convergence when estimating stress tensor fields [38] and rotation tensor fields [37], due to their important connection to medical conditions. Further developments to improve the accuracy of the numerical solution, that are naturally developed within the finite-element framework adopted in this work, are the introduction of a-posteriori mesh refinement methods, where recent results in linear elasticity for mixed formulations with Neumann boundary conditions [16] can be extended to the case of DIR problems addressed here.…”

Comprehensive Assessment of Left Intraventricular Hemodynamics Using a Finite Element Method: An Application to Dilated Cardiomyopathy Patients

“…4D Flow allows a qualitative and quantitative analysis of several hemodynamic parameters. It has been applied extensively in the great vessels, particularly in the aorta [9][10][11] and in the left ventricle (LV) for assessing intraventricular flow in some cardiovascular diseases [12][13][14][15][16][17][18][19]. Previous studies have demonstrated that lower kinetic energy values in diastole are associated with the deterioration of ventricular filling, induced by morphological alteration commonly found in Fontan patients, mitral regurgitation, and LV dysfunction or remodeling [13][14][15].…”

“…In this work, we adapted a method for quantifying 4D Flow in the aorta [9][10][11]20]. We modified the methodology applied in the left ventricle to obtain several hemodynamic parameters from a single segmentation from a 4D Flow dataset and cine MRI.…”

“…To show the applicability of this approach, we performed a proof-of-concept study in which we applied the method in a small cohort of DCM patients to find which parameters were different from volunteers. We obtained three-dimensional hemodynamic parameters, including kinetic energy, vorticity, helicity density, viscous dissipation, and energy loss [9,13,[21][22][23][24][25].…”

Reconstructing haemodynamics quantities of interest from Doppler ultrasound imaging

“… Pressure and pressure drop ( 3‐7 ): this is particularly relevant, since it is one of the main indicators of the severity of stenoses and eventual arterial blockages. The direct measure of a pressure (or even a pressure drop) could be performed by implanting a catheter, hence in a rather invasive way. The vorticity ( 8‐11 ): this quantity is monitored especially in the heart cavity and around cardiac valves. A too large vorticity could induce, for instance, haemolysis. The wall shear stress (WSS) ( 12‐14 ): this is related to the mechanical stress that the blood exerts on the endothelial cells, of paramount importance in aneurysms and plaque formation.…”