## 4 Discussion
### Contact Forces and Load Transfer Mechanics  
Supporting oral tissues can withstand orthodontic forces up to a biological threshold, beyond which excessive uncontrolled forces lead to undesirable effects [42]. In the current simulation, the extrusion force generated on the molar was around 0.6 N (61 g), which lies within the range of optimum forces for orthodontic tooth movement [43]. Some studies suggested that forces up to 150 g are considered to be biologically acceptable for molar uprighting [44]. In general, molar uprighting forces should not be more than 1 N [45], and the moment produced should not exceed 1500 g-mm [46], which is in agreement with the present results.  
Another interesting finding throughout the molar uprighting simulation was the 0.71 mm progressive increase in the spring's short lever arm length over the course of treatment, which occurred without any wire sliding. This phenomenon can be explained by the spring's relaxation, force decay, and evolving contact force distribution during the uprighting process. We were able to analyze this change by considering the interplay between the molar buccal tube slot and the uprighting spring wire, a factor overlooked in previous studies [13; 16].  
At the beginning of the treatment simulation, the spring wire was highly deflected due to the initial bending moment generated by the prescribed rotation applied to the arm of the uprighting spring in order to anchor it to the anchorage wire. Due to the tilted inclination of the molar, the mesial contact was relatively concentrated at the upper corner, while the distal contact was more distributed along the lower inner wall of the buccal tube slot. The resultant distal force acted farther from the distal edge, reducing the effective lever arm length to approximately 3.25 mm, which was notably shorter than the full slot width of 4 mm. This resulted in an unbalanced force distribution with a larger mesial-upward contact force and a smaller distal-downward force, producing both a counterclockwise moment and an extrusion force on the molar.  
As uprighting progressed and the deformation of the wire diminished, the spring no longer remained curved but instead adopted a more oblique alignment within the buccal tube slot, making contact primarily at the upper mesial and lower distal corners. This shift allowed the mesial and distal contact forces to migrate toward the outermost edges of the 4 mm wide slot, increasing the effective lever arm length to approximately 3.96 mm by the end of the treatment. With this realignment, the spring transmitted lower and more symmetrically distributed forces to the molar, generating a substantially reduced counterclockwise moment and extrusion force by the end of the treatment simulation. These findings underscore the importance of accounting for evolving force contact points within brackets and buccal tubes during treatment, as they can significantly influence the applied force system, the resulting tooth movement, and ultimately, orthodontic treatment outcomes [36].  
The current 2D simulation possesses a challenge in real orthodontic clinical setup scenarios. As the second-order dimension is thoroughly assessed, the remaining first-order and third-order movements cannot be visualized. However, given the couple force system generated at the molar tube, the resulting second-order correction, including the mesio-distal molar tilt, should be, in general terms, independent of changes in other dimensions [13; 36]. Nevertheless, the current data must be interpreted with this 2D limitation in mind, until further analysis with 3D comprehensive modeling is carried out in the future.