## 4 Discussion
### Forces and Moments from Planned Lingual Bodily Movement  
In general, TC-85 exerted the lowest force and moment magnitudes for any given tooth and activation level compared to ATMOS or Zendura FLX. When the activation was increased from 0.25 mm to 0.50 mm, the force levels stayed relatively constant with TC-85, whereas with ATMOS and Zendura FLX, the force levels increased substantially. For example, on the maxillary left central incisor, the lingual force exerted by TC-85 with 0.25 mm activation was 0.99 N, within the range of optimal force for orthodontic tooth movement (0.50-1.00 N) [20]; with 0.50 mm activation, the force level increased by 65% to 1.53 N. With ATMOS and Zendura FLX, the lingual force levels with 0.25 mm activation were 3.82 N and 3.00 N, respectively, which increased by 2-2.7 times with 0.50 mm activation. Based on these findings, 0.50 mm activation with conventional thermoplastic materials may not be recommended in the clinical setting due to the generation of excessively high force levels, which is associated with increased pain response and root resorption [20]. If greater activation is desired per stage, then DPA may induce a safer, more physiological force system. This finding is in agreement with another in vitro study comparing extrusion forces produced by clear aligners fabricated using TFM and DPA, which reported that the forces produced by TC-85 fell within ideal ranges, whereas the TFM group produced forces up to 20 times higher [11]. In CAT, it should be the goal of the clinician to design precise and accurate force systems that avoid unintended movement of teeth. Although the present study was planned for only the lingual bodily movement of the maxillary left central incisor, it was evident that a more complex system of forces and moments was produced on the tooth, such as unplanned mesiodistal and occlusogingival forces and crown angulation and rotational moments. For example, a 0.25 mm lingual activation using thermofermed aligners generated not only lingual forces but also extrusive forces of similar magnitudes. Interestingly, these extrusive forces were contrary to previous studies, which reported intrusive forces with the bodily movement of incisors [21; 22]. When the lingual activation was increased to 0.50 mm, the vertical forces became intrusive, and the magnitudes of the intrusive forces were even greater than those of the lingual forces. On the other hand, the occlusogingival forces generated by TC-85 were minimal at both activation levels. To quantitively assess the directional control of the applied force system, angular deviation and off-axis force magnitudes were calculated at the maxillary left central incisor. TC-85 consistently delivered force vectors which were more closely aligned with the intended lingual direction at the center of resistance, with the smallest angular deviation and minimal off-axis force, particularly at the higher activation level. In contrast, thermofermed aligners produced larger directional deviations and greater off-axis loading. These findings suggest that TC-85 may provide a more predictable force system with fewer unwanted force components. Clinically, the minimization of unwanted forces means more accurate and efficient tooth movement, potentially reducing the need for redundant movements or additional aligner stages to correct side effects. The observed lower and more consistent force application with DPA can be attributed to the unique thermo-mechanical properties of TC-85, particularly its elastic modulus and shape memory effect [14]. Compared to conventional thermoplastics such as PET-G or TPU, the lower elastic modulus of TC-85 allows for aligners with a lower force-deflection rate, generating less initial force for a given amount of activation and contributing to better adaptation to the dentition. Moreover, unlike conventional thermoplastics, which exhibit limited elastic recovery upon excessive activation, shape memory polymers like TC-85 are designed to actively return to a pre-determined shape upon thermal activation.