## 4 Discussion
They only had a sample size of 10 patients and were using an older generation of Invisalign(r). When evaluating the vertical dimension, we reported a mean difference of 0.7 \(\pm\) 1.3 mm, whereas [PERSON] et al. [7] reported a mean difference of 0.71 \(\pm\) 0.87 mm. Despite using an older generation of Invisalign(r) the differences were negligible. Regarding the transverse dimension, we reported an upper intercanine width accuracy of 97.9%, a lower intercanine width accuracy of 97.6%, an upper intermalor width accuracy of 97.6%, and a lower intermalor width accuracy of 97.7%, whereas [PERSON] et al. [10] reported 72.2%, 82.3%, 63.5%, and 79.8%, respectively. They mentioned that ClinCheck(r) overestimates bodily movement and that what is achieved is mostly dental tipping rather than actual bodily movement. Another paper by [PERSON] et al. [9] showed an upper intercanine width accuracy of 67.8% from cervical margin to cervical margin and 88.7% from cusp tip to cusp tip. They also showed a lower intercanine arch width of 61% and 100%, an upper intermalor width of 52.9% and 100%, and a lower intermalor width of 70.7% and 100%, respectively. They concluded that ClinCheck(r) predictions overly anticipated bodily movements, while the observed was more of a dental tipping than it was a bodily movement. They believed predictions tended to worsen the more posterior you go. It is possible that the conflicting results are due to the updated aligner material SmartTrack (LE30) or updated SmartForce features of GS compared to the previous studies. However, it should be noted that multiple potential factors, such as the patient's age, the initial malocclusion, the treatment plan design, and patient compliance, can influence the accuracy of tooth movement, and it is insufficient to determine the clinical significance based on accuracy alone. Further studies are needed that use the difference between predicted and achieved values as the evaluation indicator and control for confounding factors. There was also a reduced sample size in the previous studies. With respect to arch length, we reported a mean difference of 1.01 \(\pm\) 1.55 mm for upper crowding and a mean difference of 1.66 \(\pm\) 2.51 mm for lower crowding; however, [PERSON] et al. [7] reported a mean difference of 3.8 mm in the upper arch and a 5 mm difference in the lower arch. They concluded that moderate-to-severe crowding could be resolved by protruding the anterior teeth. The previous study did not consider posterior teeth, which could explain why we had conflicting results. It is important to note that the method used by Invisalign(r) and [PERSON] et al. to quantify the accuracy of pretreatment and post-treatment orthodontic movements has been criticized for not considering the geometric and biomechanical rules that govern tooth movement [22]. In a recent paper, [PERSON] et al. argued that the concept of \"accuracy\" in orthodontic treatment is complex and cannot be reduced to a simple comparison between planned and achieved tooth movements [23]. They argued that the precision of tooth movement may be influenced by a range of factors, including the initial tooth position, the type of malocclusion, and the orthodontic appliances used. Therefore, it is important to reevaluate the data obtained with the ClinCheck(r) models and consider the limitations of this method for accurately quantifying the accuracy of Invisalign(r) treatment. [PERSON] et al. [20] discussed the limitations of the method used by Invisalign(r) for evaluating the accuracy of pre- and post-orthodontic movements. The authors argue that the method lacks clear geometric and biomechanical rules for defining how teeth move in space, and therefore cannot provide a true measure of accuracy. They suggest that alternative methods, such as 3D imaging and finite element analysis, may provide more accurate and comprehensive data for evaluating orthodontic treatment outcomes. The authors also call for more standardized methods for evaluating orthodontic treatment outcomes to ensure consistent and reliable data.