## 4 Discussion  
We developed a method to characterize the left intraventricular hemodynamics in the LV from 4D Flow MRI using a finite element method, applied in a cohort of DCM patients. This approach estimates vorticity, helicity density, viscous dissipation, energy loss, and kinetic energy fields from a single segmentation. The hemodynamics results indicated that velocity magnitude, vorticity magnitude, viscous dissipation, energy loss, and kinetic energy revealed statistical differences between volunteers and patients, particularly at peak systole and e-wave. Some of the parameters reported in this study have been reported before. Nevertheless, those parameters have been obtained from different methodologies in different cohorts of patients. In our case, we calculated several parameters from a single segmentation at once from only one 4D flow dataset, which is difficult to determine with other methods. Some other methods are based on a finite difference approach, as in [PERSON] et al. [33]. However, it is well known that finite difference cannot effectively handle complex geometries, such as those found in the cardiovascular system. Neither can impose boundary conditions on irregular surfaces directly but they are both sensitive to noise. [PERSON] et al. showed that this approach suffers from a loss of accuracy in estimating hemodynamic parameters due to the omission of out-of-plane velocity information [34]. On the other hand, [PERSON] et al. demonstrated the convergence and robustness of the finite element method in cardiovascular flow [9; 10]. Further, they also showed that the finite element method is both stable and accurate in the presence of noise. Although DCM mainly affects the systolic function, we evaluated the hemodynamic parameters at systole and diastole, as several papers have shown that diastolic function is also affected by this disease. For instance, [PERSON] et al. and [PERSON] et al. reported that diastolic wall-motion abnormalities are prevalent in pediatric DCM. Their presence is associated with diastolic ventricular dysfunction and adverse outcomes [35; 36]. Some papers have assessed diastolic function in DCM patients using 4D Flow data [37; 38]. They have described alterations in the flow components related to velocity, vorticity, and kinetic energy in a different cohort of patients, consistent with our results [21; 22; 23; 24; 25]. As we showed in this study, intraventricular flow in DCM patients was altered compared to healthy volunteers at diastole. In addition, it is interesting to observe that, while end-diastolic volume was significantly larger in patients than healthy subjects, the maximum hemodynamic values for e-wave and end-diastole were smaller in patients than in volunteers. For instance, we found that in the normal LV, kinetic energy values were high. The highest kinetic energy values were observed during early diastole and regionally distributed near basal LV regions. In contrast, early- and end-diastole kinetic energy was lower than normal in a heterogeneous group of DCM patients and decreased with the LV volume. As we found in our results, this decrease of kinetic energy throughout diastole is associated with viscous dissipation and energy loss. That agrees with a previous study, where comparisons of inflow characteristics in healthy subjects and DCM patients showed more differences at e-wave between the two groups [36; 37; 38; 39; 40; 41]. These ventricular diastolic function aspects can be influenced by dynamic load and contractility; these may vary within the spectrum of normal conditions. Furthermore, large ventricles lead to weak suction pumps and have high wall tension, which has been previously suggested to cause energy waste and alter vortex ring dynamics [22; 23]. These results indicate that, despite the complex nature of ventricular finding factors, clinically useful information regarding left ventricular diastolic function is associated with distinct mitral flow velocity patterns.