## 4 Discussion
### Displacement Patterns  
All models demonstrated buccal inclination along the X-axis, consistent with previous findings on the limited root control of aligners [30; 31]. M0-25 VA and M2-25 VA minimized bucco-palatal tipping most effectively, while M0-NA showed the greatest tipping. All models showed distal rotation, with greater buccal displacement on the mesial side. As meso-palatal rotation is common in Class II cases [32; 33], this pattern may provide beneficial derotation as a secondary effect. Rotational control is particularly difficult in conical teeth such as premolars and canines [34; 35]. Although rotation was not directly targeted, consistent stopalatal rotation was observed across all models, suggesting that distalization with aligners--regardless of attachment presence--may contribute to improving Class II molar relationships. Distal tipping occurred in all models along the Y-axis. In M0 models, M0-NA had the most mesial root movement, indicating poor root control, while M0-DHA showed the most favorable movement pattern. This aligns with the assumption that double horizontal attachments offer improved root anchorage. [PERSON] et al. [36] showed that 2-3 mm of distalization is achievable with aligners, but attachments did not significantly affect the amount of movement. Notably, their study did not assess side effects like tipping or rotation. In our study, M2 models achieved more distalization than M0 models, supporting [PERSON] et al. [20], who found that longer trimlines improved third-order (root) control. Although our FEA simulation revealed consistent tipping across all configurations, [PERSON] et al. [37] reported variable tipping behavior in clinical cases, with first molars showing less and second molars showing more distal tipping than planned. This highlights how biomechanical interactions--such as force application height and anterior retraction phases--may differentially affect tipping expression across molars. Vertical (Z-axis) displacement was observed in all models, consistent with distal tipping. [PERSON] et al. [38] reported no vertical dimension loss in clinical cases, in contrast to our findings. However, a recent systematic review and meta-analysis by [PERSON] et al. [39] concluded that although clear aligners may produce slight molar intrusion, no clinically significant vertical skeletal changes were observed. This discrepancy highlights the influence of evaluation methods--such as lateral cephalometry versus FEA modeling--and the need for cautious interpretation in the absence of occlusal loading. Finally, trimline length influenced the homogeneity of surface displacement. Longer trimlines resulted in more consistent tooth surface movement, echoing findings by [PERSON] et al. [29]. M2-25 VA and M2-DHA showed the most balanced distribution, while M0-NA had the most uneven displacement. [PERSON] and [PERSON] [16] similarly found that horizontal attachments improved occluso-gingival control. The focus on the maxillary first molar reflects its pivotal role in orthodontic treatment and occlusion. As noted by [PERSON] [40], this tooth is critical for establishing normal occlusion and stabilizing the posterior arch. Serving as a primary anchorage unit, it influences the movement of adjacent teeth, particularly during distalization. Prior studies have emphasized the need for precise control of this tooth's position. [PERSON] and [PERSON] [34] addressed the challenges posed by its rotation, while [PERSON] et al. [2] highlighted its tendency for mesial drift, underscoring the importance of maintaining its position for treatment success. Similar to [PERSON] [40] three-dimensional evaluation of molar positioning, this study focused on the maxillary first molar in three dimensions. This approach offers a more comprehensive understanding of its movement and interaction with aligner mechanics, enabling more precise distalization.