## 4 Discussion  
In this study, we assessed the influence of the LAA morphology and hemodynamics on the stroke risk in patients affected by non-valvular AF condition. Regarding the morphological features, currently, there is a strong necessity to understand the anatomical properties of the LAA during the cardiac cycle. This effort arises from a twofold need: from one side, to stratify the risk of LAA thrombus formation in AF patients, and, on the other hand, to develop new percutaneous closure procedures. Previous studies have demonstrated the alterations in shape, size and contraction patterns of LAA in AF condition by using different imaging techniques [12; 21; 22; 23]. In the work presented here, the LAA morphological parameters were analysed along the entire cardiac cycle by using ECG-gated CT images, as several studies have assessed the correlation between image-based variables with increased risk of stroke in AF patients [24; 25; 26]. The processing of CT images in all the phases of the cardiac cycle allowed to highlight the main differences between patients in terms of motility of the respective LAA. Figure 4 allows qualitatively notifying the changes of all the LAAs along the cardiac cycle. The quantitative analysis of the LAA volume, ostium area, centerline length and tortuosity is shown in Figure 5, where it is possible to verify the considerable variability of the analyzed morphological parameters among different LAAs and within the cardiac cycle. Starting from the LAA volume analysis (Figure 5a), the CS shape resulted in being the biggest and with more variability, while the CW and the CF morphologies were small and characterised by low expansions during the cardiac cycle. For the ostium area quantification (Figure 5b), the trend was different and CF and CS cases showed a huger ostium than CW and WS shapes. This result may suggest that CF and CS morphologies presented low flow velocities, as a big ostium is usually related to blood stagnation and thus a higher risk of thrombi formation [27; 28]. On the other hand, the analysis of centerline variation (Figure 5c) along the cardiac cycle confirmed such scenario, where CF and CS shapes presented a low length as well as a low variability suggesting a reduced LAA motility. Finally, the tortuosity analysis (Figure 5d) showed that the CW morphology presented the highest value and the highest variability, which reflect the high curvature of the shape as appreciable in Figure 4. Centerline length and tortuosity trends of the LAAs for all the ten phases of the cardiac cycle (0-90%) are depicted in Figure 10, where values were calculated as percentage variation in respect to the 30% phase, i.e., when the atrial systole occurs. As we can see, the CF and CS shapes are characterised by a high value of tortuosity variation (about 30%) associated with a low centerline length variation (<10%). According to Equation (1), the combined effect of these two parameters produce a bending phenomenon, potentially suggesting an augmented risk of thrombus dislodgement and migration. The WS shape presented instead a slightly higher centerline and tortuosity values (Figure 10c) than the more critical CF and CS morphologies. This combined behaviour reduces the bending effect and potentially the risk of thrombus dislodgement. The CW shape resulted in being the less risky as centerline length variation were higher (Figure 10a), indicating a constant washout of the LAA during the cardiac cycle. The tortuosity variation for this model maintains a low value (<20%). The CFD analysis showed similar global velocity fields for the four studied cases (Figure 6). Locally, very low velocities were found in the LAAs in respect to the global scale (Figure 7). This trend is in line with previous CFD studies [11; 14]. Considerations of specific planes for each LAA (Figure 9a) allowed a shape-specific velocity analysis showing how differently the blood flow decreases from the ostium to the tip (Figure 9b).