# Three-Dimensional Force Characterizations in Maximly Molar Distalization: A Finite Element Study
## 4 Discussion  
This work quantified the 3D reaction force and moment on the canine and molar induced by the application of different MSDs by extracting the reaction force and moment on the contact region between the teeth and maxilla. The important reaction forces or moments related to the tooth movement, extrusion, tipping, and rotation were quantified for the canine and molar, the two teeth connected with the MSDs. Three MSDs, the JVB, CM3D, and CM3D Clear, were implemented in this work. A comparative study was conducted to study the influence of the structural design of the MSD on the reaction force and moment induced on each tooth. The results show that the maxillary molar would undertake more force and moment through structural modification of the orthodontic devices, i.e., moving the hook structure from the canine end to the middle of the bar. To the author's best knowledge, this work is the first-time 3D mechanical characterization of the reaction force and moment for these typical MSDs in Class II malocclusion treatment was conducted. The mechanistic understandings from this work will shed light on the optimal design of the MSDs. The quantification of the treatment effects of MSDs is essential for an expected tooth movement trend. In this work, the treatment effects of different MSDs in terms of reaction force and moment are quantified. A two-dimensional study by Dr. [PERSON]'s group showed that the total resultant extrusion force along the vertical force increased from 3.38 to 4.97 oz by moving the hook structure from the end of the CM3 Ds to the middle of the JVB [20]. This work shows that the JVB induced less extrusion force on the canine compared with CM3 Ds. Obviously, by changing the location of the hook structure from one end to the middle of the MSD, more load was undertaken by the molar tooth in both force and moment. The JVB induced considerably higher extrusion force on the molar, which was negligible in the CM3 Ds. The JVB induced significantly less tipping moment and rotational moment compared with the CM3 Ds but significantly higher on the molar. These observations indicate that different portions of force can be allocated to each tooth by changing the location of the hook structure. In addition, we also noticed that the reaction force on the canine along the distal direction showed a negative value compared with the CM3 Ds, indicating that the arc structure of the JVB may induce a trend that the molar and canine move farther apart from each other and the canine moves backward when the distance of the molar and canine reaches a certain value. Such a trend is not observed in the other two CM3 Ds. The forces on the molar teeth help correct Class II malocclusion by distalizing the molar. In addition, the distal tipping of the mesial cusp may help in Class II correction. However, the extrusive forces and the mesial tipping of the molar may open the bite, which is needed in deep-bite corrections, since it is found commonly in Class II malocclusion [42]. The stress distribution in the MSDs also agreed with the quantified reaction force and moment. The bracket structure of the JVB showed a higher stress than that of the CM3 Ds, indicating a higher resultant reaction force on the molar. The minimal stress observed on most parts of the CM3 Ds, except on the canine pad, indicated that most of the load was undertaken by the canine. Of notice, with the bar and the bracket connected with a simple pin-point structure, the gap between the bar and the socket may affect force transfer from the hook to the socket and tooth, which will lead to the overestimation of the reaction force. The CM3D Clear was developed with medical-grade polymer for aesthetic purposes, while the structure was softer than the metallic material [40]. Although a minimal difference was observed in this study, it may have a significant effect considering the long-term reaction, especially in terms of tooth movement. The use of a soft material may result in less force transmission from the canine to the molar.