# Three-Dimensional Force Characterizations in Maximly Molar Distalization: A Finite Element Study
## 3 Results  
The reaction forces on the canine and molar following implantation of each MSD are shown in Figure 3a,b, respectively. The extrusion force on the canine along the vertical direction (Z) induced by the JVB was 0.15 N (15%) less than the ones induced by the CM3D or CM3D Clear, which was 0.98 N. The force magnitude on the canine along the mesial direction (negative Y) was 0.90 N (74%) less than the ones induced by the CM3D or CM3D Clear, which were 1.23 N and 1.33 N, respectively. Of note, the force on the canine along the mesial direction induced by the JVB showed an opposite direction compared with the CM3D and CM3D Clear. The force on the canine along the buccal direction (X) showed relatively small values and minimal differences between all the MSDs. On the molar, the extrusion force in the Z direction induced by the JVB was 0.45 N (90%) more than the ones induced by other CM3 Ds, which were 0.05 N. The force along the distal direction (Y direction) induced by the JVB was 1.13 N (207%) higher than the one induced by the CM3D and 1.36 N (424%) higher than the one by the CM3D Clear, respectively. The magnitude of the CM3D and CM3D Clear along the distal direction was 0.55 N and 0.33 N, respectively. The differences between the JVB and the other two CM3 Ds were less than 0.33 N. In summary, the JVB induced higher force on the molar along the vertical and distal directions compared with the other two MSDs. All MSDs induced minimal force on the  
Figure 2: Three-dimensional model of maxilla and mandible with JVB located between the maxillary molar (UL7) and canine (UL3). In this model, one of the premolars is missing. The load vector (\(\mathcal{T}\)) is from the hook of the MSDs to the mandibular molar. For the CM3D, the hook is on the canine side, so \(\mathcal{T}\) was more tilted due to the smaller \(\beta\). canine along the X direction but induced a mildly higher force on the molar, especially the JVB. The reaction moments on the canine and molar following each MSD are shown in Figure 4a,b, respectively. The magnitude of the tipping moment on the canine about the X direction induced by the JVB was 12.52 N\(\cdot\)mm (90%) and 15.50 N\(\cdot\)mm (92%) less than the ones by the CM3D and CM3D Clear, which were 14.0 N\(\cdot\)mm and 16.9 N\(\cdot\)mm, respectively. Nevertheless, the tipping moment on the canine induced by the JVB was in the opposite direction of that induced by the CM3D and CM3D Clear. The magnitude of the rotational moment about the Z direction induced by the JVB was 6.78 N\(\cdot\)mm (70%) and 8.40 N\(\cdot\)mm (74%) less than the ones induced by the CM3D and CM3D Clear, which were 9.7 N\(\cdot\)mm and 11.3 N\(\cdot\)mm in the opposite direction. The buccal-lingual moment on the canine about the Y direction induced by the JVB and CM3 Ds was kept at the same level at about 6.0 N\(\cdot\)mm to 7.0 N\(\cdot\)mm. On the molar, the tipping moment about the X direction induced by the JVB was 12.83 N\(\cdot\)mm (290%) and 14.46 N\(\cdot\)mm (326%) more than the ones by the CM3D and CM3D Clear, which were 4.42 N\(\cdot\)mm and 3.80 N\(\cdot\)mm. The rotational moment on the molar about the Z direction induced by the JVB was 8.98 N\(\cdot\)mm (187%) and 10.8 N\(\cdot\)mm (366%) higher than the ones by the CM3D and CM3D Clear, which were 4.79 N\(\cdot\)mm and 2.95 N\(\cdot\)mm. The magnitude of the buccal-lingual moment on the molar induced on all MSDs was negligible, even though the direction of moment by the JVB was opposite to others. In summary, the JVB induced significantly less tipping and rotational moment on the canine, while significantly higher on the molar, compared with the other two MSDs. The von-Mises stress distribution in MSDs from the buccal and lingual view is shown in Figure 5. The stress concentration was observed near the hook structure for all MSDs. The area average was taken on the surface of MSDs, which was bonded with the teeth.