# Three-Dimensional Force Characterizations in Maximly Molar Distalization: A Finite Element Study
## 1 Introduction  
Class II malocclusion, a classification of dental misalignment, occurs when a discrepancy exists between the position of the mandible and the maxilla. The condition is prevalent among orthodontic patients and can lead to functional and aesthetic issues if left untreated [1, 2]. Different orthodontic appliances and procedures have been developed for the treatment of Class II malocclusion [3, 4]. To achieve the necessary forces to move teeth into their correct position, orthodontic appliances are typically used. Several functional and removable appliances have been employed, such as braces and archwires [5], twin block appliances [6], Bionator appliances [7], and Forsus (3M) [8]. Orthodontists select the appliances based on the specific needs of the patient with the ultimate goal of achieving function, aesthetics, and stable occlusion. The clear aligners have been increasingly adopted in the treatment for malocclusion among adults because the aesthetic clear aligner causes less mouth irritation and requires shorter dental appointments [9, 10]. Even though treatment with a clear aligner is shorter than that with braces, some studies have indicated that the clear aligner may not provide enough occlusion contacts, torque control, and retention [11]. In addition, [PERSON] and [PERSON] reported the duration of sequential molar distalization with aligners to be excessively long (21 \(\pm\) 3 months) [12]. The clear aligners can be combined with various types of auxiliaries prior to aligner treatment, such as the Carriere(r) Motion 3D (CM3D) by Henry Schein Orthodontics(r) (Carlsbad, CA, USA) appliance, to enhance the correction forces [13] and minimize the occupation of the oral cavity, which improvespatient comfort and speech compared with conventional appliances such as braces [14]. The CM3D appliance is one type of maxillary segmental distalizer (MSD), which contains a straight bar with a bondable pad with a socket at the molar end, a bondable pad with a hook at the canine end, and intermaximillary elastics [13; 15]. The straight bar and the pad with a socket work together to connect the maxillary canine and molar, the bondable pad with a hook is attached to the mandibular molar, and then the intermaximillary elastics are used to link the hooks on the bar and the bondable pad. The intention is to rotate the upper molars and pull the maxillary teeth backwards. The treatment allows for orthodontic movement without the use of miniscrews, thus avoiding risks of root injuries [16], failure [17], or fracture [18]. The CM3D is effective in correcting Class II malocclusion but also causes tooth extrusion and lower incisor proclination [13; 15]. Recently, an innovative design, the JVBarre (JVB) by Rocky Mountain Orthodontics(r) (Franklin, IN, USA), was developed to achieve less canine extrusion and molar tipping [19]. Compared with the CM3D, the JVB is designed to have a curved bar with a centrally located hook. The intention is to reduce the extrusion force and rotational moment on the canine but increase molar rotation for Class II correction [20]. The optimization of these orthodontic devices relies on the quantitative characterization of the reaction force and moment induced by the appliances, while the 3D force characterization still lacks [19]. Finite element analysis (FEA) is a powerful tool in evaluating orthodontic devices, usually in terms of the stress and strain in the dentition following placement of miniscrews [21; 22; 23; 24; 25], archives [26; 27; 28], or clear aligners [29; 30]. A comparative study utilizing FEA showed that the occlusal force induces different displacement and stress distribution in Class I, II, and III malocclusion [31]. The influence of the cross-sectional shape of ribbon archwires with edgewise and round wires on intermaximillary traction in Class II malocclusion treatment was comprehensively studied with FEA simulation [32]. The results showed that the larger size leads to less mandibular dentition movement.