## 4 Relationship Between LAA and Stroke
### Geometric Characteristics of Left Atrial Appendage  
The geometric features of the LAA can be described in terms of shape and dimensions. [PERSON] et al. [57] identified four distinct shapes for the LAA: cactus, chicken wing, windsock, and cauliflower. Dimensions involve the quantitative analysis of specific geometric parameters of the LAA, such as volume, surface area, orifice diameter, and the number of lobes. The shape and dimensions of the LAA can provide complementary insights; for instance, the cactus shape typically exhibits a smaller orifice diameter and shorter central length, while the cauliflower shape often features a greater number of lobes [13; 15; 58]. The shape of the LAA provides an intuitive geometric description. In 2012, [PERSON] et al. [13] proposed that the chicken-wing-shaped LAA is less likely to result in stroke or transient ischemic attack (TIA), while the cauliflower shape is most strongly associated with strokes. This concept has gained widespread acceptance in clinical practice, leading to the classification of the chicken wing as the \"safest\" LAA shape [59]. A growing body of evidence links the cauliflower-shaped LAA to a higher incidence of thrombus formation [6; 58; 60]. Additionally, a study conducted in 2015 [61] indicated that the windsock-shaped LAA, which has the largest average volume among the four types, is also more  
Figure 1: Components of [PERSON]’s triad for thrombogenesis in atrial fibrillation [55]. The upward arrow indicates an increase in the content of the corresponding substance. prone to strokes. However, other studies report no association between LAA shape and stroke risk [37, 62]. This inconsistency underscores the need for further investigation. Furthermore, many studies recognize the challenges in accurately categorizing LAA shapes into these four types [63, 64]; subtle features can be difficult to distinguish in clinical evaluations, particularly between cactus and windsock shapes [64]. Moreover, most studies have not definitively proven that thrombin in stroke events originate from the LAA, indicating the necessity for quantitative validation and confirmation. In contrast, LAA dimension offers a more quantitative description, providing greater objectivity and reproducibility than shape classifications. Several consistent findings have emerged: an increased LAA volume, more lobes, greater centerline length, and larger LA diameter or volume correlate with a higher risk of thrombosis [65, 66, 67, 63, 33, 6, 6]. These dimensional features are thought to promote blood stagnation within the LAA. However, there is some debate over the influence of certain parameters on thrombotic risk, such as the LAA orifice [62, 66]. [PERSON] et al. [15] suggested that this debate arises from differing definitions of the orifice. Additionally, aging and chronic AF can lead to remodeling of the LA. [PERSON] et al. [64] anatomically examined 200 cadaveric hearts and found that older adults often exhibit larger LAA volumes, longer lengths, and greater orifice areas. These age-related LAA changes potentially increase the amount of electrical activity and trigger atrial tachycardias. Furthermore, the relative position of the pulmonary veins to the LAA is also related to stroke risk; for instance, [PERSON] et al. [68] discovered that the higher starting points of the upper and lower edges of the LAA correlate with an increased risk of thromboembolism. Furthermore, [PERSON] et al. [37] found that the area of the left inferior pulmonary vein in the stroke group was significantly larger than in the non-stroke group. Compared to LAA shape, LAA dimension appears more suitable for guiding stroke risk stratification. [PERSON] et al. [63] compared traditional methods (classifying the chicken wing shape as low risk) with the LAA folding angle to identify patient stroke risk, demonstrating the advantages of dimensional analysis. Additionally, [PERSON] et al.