The vortices that form during left ventricular (LV) filling are critical determinants of directed blood flow during ejection. One of the first works was developed by Won et al in 1995¹ providing the first characterization of vortex flows in the LV using 3D magnetic resonance velocity mapping, analyzing the size, angular velocity and kinetic energy, in normal subject. Also studies based on CFD and echocardiography reveal that the vortices in the LV have a specific geometry and anatomical locations and any alteration of these characteristics affect directly the efficiency and ventricle workload^2-5. Recently, using magnetic resonance imaging the lambda2-method for the characterization of the vortices in the LV revealed another features as shape, location and orientation of LV vortex⁶. However, all these studies consist in a qualitative characterization of vortex flow in the LV. One notable exception is the work developed by Wong et al 2009⁷, in this work they make use of 2D planes in short axis to calculate the vorticity using a finite-different formulation. Nevertheless, they omit all information out of plane that can be relevant to characterize any vortex flow. Additionally, is known that the finite-difference methods cannot handle the smooth and complex boundaries, inducing important errors when the geometry is simplified⁸. Therefore, a quantitative characterization of vortex flow as turbulence (vorticity and helicity) and energy (kinetic energy and energy loss) may offer a novel index of LV dysfunction. In this work we propose a novel method based on a finite-element method to obtain a 3D quantitative maps of vorticity, helicity density, kinetic energy, and energy loss in the LV derived from 4D-flow data sets.We developed a finite-element based computational framework to obtain the velocity gradient in three orthogonal direction generating continuous 3D maps of vorticity, helicity density, kinetic energy, and energy loss in the LV. The algorithm was based in a similar least-squares projection method previously published⁹. Using a MR Phillips Achieva 1.5T, we acquired 4D-Flow data of whole heart and M2D-SSFP of short axis cover the entire ventricle, from fourth healthy volunteers (one female and three male 31±3 years) without any know cardiac abnormality. A summary of the MR acquisition parameters is shown in the Table I. We integrated a chan-vese active contour algorithm, manual refinement of the segmentation and contour smoothing, in Matlab (The MathWorks, Natick, MA, USA) to generate a tridimensional segmentation of the M2D-SSFP images. This process allowed us to extract the geometry of LV for each cardiac phase. The tetrahedral finite element mesh was created from the M2D-SSFP segmentation using the iso2mesh library for Matlab (Figure 1). Using the transformation matrix generated with the DICOM header information, we aligned both data sets including the tetrahedral mesh in reference to the volunteer position. Thereafter, we were able to transfer each velocity value from 4D-Flow images to each node of the tetrahedral mesh for each cardiac phase (Figure 2). The finite-element analysis and visualization was developed in Python and Paraview software (Kitware Inc., NY, USA) respectively. Result of LV end systolic volume, end diastolic volume, stroke volume, cardiac output, ejection fraction and cardiac frequency for each volunteer were: 40/73/61/71 ml, 116/157/140/180 ml, 76/84/79/109 ml, 4.3/4.5/5.2/4.9 L/min, 65/54/56/61% and 57/54/66/45 bpm for volunteer 1/2/3/4 respectively. Ventricular volume characteristics are normal for all volunteers. In figure 3 we show the result of 3D vorticity and helicity density maps in a middle systolic and diastolic phases, for the LV of volunteer Nº1. In the same figure we also show the ranges of vorticity and helicity density for all volunteers. In figure 3 we observe the vortex rings around the mitral valve and aortic valve, in both systole and diastolic phases, showing an increment of vorticity and helicity values in the diastolic phase. In figure 4 we show the kinetic energy and energy loss for the same cardiac phases and volunteer showed in figure 3, the range for these parameters are shown in the bottom part of the figure. There was a greater energy loss in diastole compared to systole, probably given by the turbulent flows presented in this part of the cardiac cycle. Additionally, higher values of kinetic energy are visualized in the systolic phase.We have proposed a
novel method that allowed us to obtain 3D maps of vorticity, helicity density, energy loss and kinetic energy in the left ventricle from 4D-flow MRI data using a finite-elements method. This new approach offers novel index for the assessment of LV dysfunction. We are currently working on validating this method in more volunteers and patients.