## 4 Discussion
In particular, while CW and WS shapes showed relatively high velocities at ostium level, rapidly decreasing in the middle planes, CF and CS morphologies were characterized by an overall low velocity, especially for the CS case. Such condition may indicate a higher probability of blood stagnation and thus a major probability of thrombi formation. Furthermore, the CF and CS analyzed shapes present a high number of lobes (10 and 9 respectively) in respect to CW and WS (5 and 3). Recent study has demonstrated that there is a significant correlation between the number of lobes and the risk of thromboembolism events [29]. Reasonably, the formation of a small thrombus is higher than a big one. In this vein, in Figure 7, the volume representing the cells with extremely low velocity (<0.001 cm/s) was found to be higher in the cases of CW (Figure 8a) and WS (Figure 8c) inrespect to CF (Figure 8b) and CS (Figure 8d). Nevertheless, the volumes of CF and CS shapes appeared as composed of several small sub-volumes located in the lobes (Figure 8b-d). The few CFD studies available on this topic [13; 14] focused on the correlation between the flow simulation and the LAA morphologies only at a single instant of the cardiac cycle. Most of previous segmentation approaches were based on 3D rotational angiography [13; 30] or standard CT technique [14], thus focusing on a static model for their morphological analysis. With respect to the previous works, we analyzed all the phases of the cardiac cycle. The main finding of this work is that analysis of morphological and CFD results are consistent, since both image-based and computational strategies focus the attention on the CF and CS LAA shapes for stroke risk. On one hand, imaging elaboration highlighted a bigger ostium, which was already identified in the literature as a high risk factor for AF patients [31]. Moreover, a reduced motility for the CF and CS shapes in respect of CW and WS cases was found, as well as a higher number of lobes which may be representative of suitable sites for thrombi generation. On the other hand, CFD post-processing showed for CF and CS shapes relatively very low velocities in proximity of lobes, again supporting that these two morphologies could be more prone to develop thrombobolic events, as in accordance with clinical reports [24]. Our approach can be further improved. Obviously the clinical problem we are facing is very complex, as an interchangeable conditioning effect between the LA and the LAA shapes and both effects can be hypothesized and should be considered. Moreover, future developments will be focused on considering a larger number of patient-specific LAAs in order to fully investigate its wide anatomical variability and increase the statistical relevance of the study. However, the investigation on the correlation between ECG-gated CT volumetric datasets along the cardiac cycle and CFD analyses is novel, as similar studies only considered single-phase CT datasets. However, the assumption of rigid wall in the numerical simulations could be strong, especially when it was verified from imaging analysis that the motility of the LAAs is not negligible. More complex strategies will be adopted to overcome such limitations, in order to take into account for the wall movements. Figure 10: Variation of centerline and tortuosity indices at each phase of cardiac cycle for CW (**a**), CF (**b**), WS (**c**) and CS (**d**) shapes with respect to the systolic phase (30%).