When incisors are retracted in sliding mechanics with direct skeletal anchorage, power arms have the effect of increasing the incisor torque expression. The present study showed that the use of power arms produced a deflection of the archwire (Fig. 6), so that its anterior portion is lifted in an apical direction and twisted in the third order of space. It was found that the longer the power arms, the more substantially the archwire could be deformed, and higher the incisor torque expression could be. Tominaga et al.  have also suggested that the anterior portion of the archwire is subjected to torsion caused by power arms, and consequently the torque is practically transmitted to the bracket on the incisor. The results obtained from this study suggested that when the conventional 0.019 × 0.025-in archwire is used, a power arm longer than 14 mm is required to achieve bodily movement of the central incisor because of the large bracket-archwire play. Such a long power arm would not be clinically applicable because it could cause patient discomfort. In addition, this length of power arm would require to place miniscrews in a very apical position, beyond the mucogingival junction, in the gingival mucosa, which is more prone to inflammation and where miniscrews stability is lower . Furthermore, especially due to manufacturing tolerances, the play between the archwire and bracket is larger than the theoretically ideal play [8, 9], which may exacerbate this problem in the clinical practice.
Besides patient discomfort, the longer the power arm, the more substantially the occlusal plane is rotated counter-clockwise as an undesirable side effect (Fig. 4). Above-mentioned results support the previous study suggesting that a retraction force height superior to the CR of the entire maxillary dentition will cause the counter-clockwise rotation of the occlusal plane . In the present analysis, the counter-clockwise rotation of the occlusal plane became minimal when the length of power arms was 8 mm (Fig. 4a). These results are in agreement with the finding that the CR of the FE model for the entire maxillary dentition, which was used in this study, was located at the level of 8.1 mm from the bracket slot. The counter-clockwise rotation of the maxillary occlusal plane and the resultant molar extrusion could cause clockwise rotation of the mandible, and consequently the facial profile would be worsened in the treatment of maxillary protrusion cases. This event would be particularly harmful in Class II dolichocephalic patients, where a clockwise rotation of the mandible further reduces the chin projection. Conversely, the utilization of power arms of approximately 8 mm would maintain the inclination of the occlusal plane during incisor retraction, and prevent unwanted clockwise mandibular rotation.
On the other hand, the dual-section archwire has shown some advantages as compared to the conventional 0.019 × 0.025-in archwire. The cross section of the anterior portion of the dual-section archwire is 0.021 × 0.025-in, which reduces the play between the archwire and brackets, thereby minimizing the loss of anterior torque control and increasing the torque expression in the bracket slots. As a result, the use of the dual-section archwire allows for achieving bodily movement of the incisors in combination with a shorter power arm than the 0.019 × 0.025-in archwire (Fig. 3). The present study indicates that the dual-section archwire could reduce power arm length to approximately 8 mm, which causes minimal counter-clockwise rotation of the maxillary occlusal plane, when bodily movement is required (Fig. 4).
Frictional resistance at the interface between the archwire and posterior brackets with the 0.019 × 0.025-in archwire was greater than that with the dual-section archwire up to the residual space of 1 mm, although there was no significant difference between them (Fig. 5). The values of frictional resistance ranged from 0.01 to 0.1 N, which were smaller than 5% of the retraction force of 2 N and seemed not to give great impact on tooth movement. This is because no external force was applied directly to the posterior brackets when a skeletal anchorage was employed.
The frictional resistance was found to be negligible in the present study. Nevertheless, a greater amount of frictional resistance could be generated in case of reciprocal retraction without using skeletal anchorage. Although the dual-section archwire is considered to have an advantage under such a situation, further investigations and clinical studies are needed to verify the biomechanical effectiveness of the dual-section archwire with respect to its feature to reduce the amount of friction in the posterior segment due to its undersized cross section.
Most of studies on the simulation of orthodontic tooth movement had been limited to analyses of the initial displacement [6, 10, 12]. It was therefore difficult to precisely predict overall tooth movement, since it reflects the archwire deformation including torsion within the brackets, which could change the force system during space closure, thereby exerting great influence on the torquing effect and the resultant incisor movement. The novel method employed in the present study enabled us to predict the long-term orthodontic tooth movement and to accurately determine the force system acting on each tooth in the course of treatment. As a result, biomechanical effects of the conventional 0.019 × 0.025-in and dual-dimension archwires on the anterior tooth movement could be successfully evaluated and compared. The null hypothesis was rejected; the dual-section archwires produced a more favorable biomechanical effect, compared to the conventional 0.019 × 0.025-in archwires, during en-masse retraction of anterior teeth with the use of direct skeletal anchorage.
One limitation of this study is its computational nature. These results should be confirmed by clinical trials.