# The Center of Resistance of an Impacted Maximly Canine: A Finite Element Analysis
## 1 Introduction  
There are many definitions of an impacted tooth [1, 2]. [PERSON] et al. [1] called a tooth impacted when the tooth did not erupt in the proper position of the dental arch during normal growth. [PERSON] et al. [2] defined an impacted tooth as a case in which tooth eruption was significantly delayed or there were no clinical or radiological findings that further eruption was in progress. Surveys on the prevalence of impacted teeth was conducted on all permanent teeth except the third molars in Italy [3], Korea [4], and Turkey [5]. The prevalence of impacted teeth was found to be 2.9-8.6% [3, 4, 5]. The prevalence of impacted teeth in the maxilla was 10 to 20 times higher than in the mandible [6]. In the maxilla, the canine showed the highest ratio with 69%, and in the mandible, the premolar showed the highest ratio with 56% [6]. The etiologies of the impacted teeth were diverse [7, 8], and about 70% of cases were caused by abnormal eruption pathways or localized pathologic lesions [9]. Impacted teeth require orthodontic treatment because they cause not only aesthetic problems, such as midline displacement due to the inclination of adjacent teeth, but also degenerative changes, such as root resorption of adjacent teeth, cyst formation, and loss of tooth alignment space [10]. Treatment methods include surgical exposure followed by orthodontic traction, extraction of the impacted tooth, surgical replantation, and extraction of the deciduous tooth [11]. In many cases, surgical exposure followed by orthodontic traction is performed [11]. There are two types of surgical exposure: open and closed [12]. Open surgical exposure removes the bone and soft tissue around the impacted tooth andopens the impacted area to induce a spontaneous eruption of the impacted tooth or bonds an attachment a few days after the procedure. On the other hand, closed surgical exposure is a procedure that opens the flap, bonds an attachment to the impacted tooth, and then covers the flap again and applies orthodontic forces immediately [12]. Therefore, closed surgical exposure requires more careful consideration of the orthodontic force applied to the impacted teeth than open surgical exposure. Knowing the center of resistance (COR) in the orthodontic traction of impacted teeth is important. If the orthodontic force is given to the impacted tooth without considering the COR, it may be moved in an undesirable direction or rotated, resulting in traction failure or a longer treatment period [13]. However, since the impacted tooth is inside the bone, it may be different from the COR of the erupted tooth. There have been many studies [14; 15; 16; 17] on the COR of erupted teeth. [PERSON] et al. [14] calculated the three-dimensional COR positions of about 50 maxillary first molars using the finite element method (FEM). As a result, the COR was located below and slightly distal to the trifurcation area, and the location of the COR varied as the shape of the molars varied. Above all, it was shown that the COR was a point that could vary depending on the direction of force. [PERSON] et al. [15] proved using mathematical analysis that the position of the COR moved nonlinearly depending on the shape of the root of the erupted tooth, the height of the alveolar bone, and the length of the root. However, few studies have reported on the COR of impacted teeth despite its clinical importance. Moreover, in the case of the closed surgical exposure of an impacted tooth, the COR may change depending on the stage of pericoronal tissue healing around the crown. Previous studies [18; 19; 20] on the COR of impacted teeth have been conducted on impacted teeth with exposed crowns. [PERSON] et al. [18] used the FEM to calculate the von Mises stress of the impacted canine and surrounding teeth when a palatally impacted canine with an exposed crown was pulled from a 0.019 \(\times\) 0.025 stainless steel archwire. In addition, the side effects that may occur in surrounding teeth were predicted using the FEM. [PERSON] et al.