## 1 Introduction
Nevertheless, this technique has some limitations which involve manual landmark identification and the stability of the reference areas used for the superimposition. Finite element analysis (FEA) is a computational technique that has been applied the most to understand the transfer of the force from the application point to the alveolar structures via the PDL, and FEA allows the calculation of biomechanical parameters such as force, pressure and thermal changes obtained on biomaterials and human tissues and that can be hardly measured in vivo [14]. Finite element simulation could lead to a prediction of the biomechanical effects of different orthodontic appliances; a previous study evaluated the effects of a rapid maxillary expansion on the craniofacial skeleton of a patient with unilateral cleft lip and palate to individuate the application of points of force for a better expansion using a three-dimensional finite element model [15]. With the aim of identifying the mechanics of the teeth whose movement is planned, as well as the effects on dental elements that act as anchorage, there have been few attempts to study tooth-aligner interactions by finite element models (FEM) [16; 17; 18]. Some studies have investigated the effects deriving the M:F ratio from the presence and type of attachments when a translation movement is planned. Regardless of the attachment, movement occurs initially by tipping, while the pair of forces for root control and uprighting only occurs later if attachment is present; when there is no attachment, tipping is the only expected result [19]. Moreover, an overhanging attachment appears to be able to control unintentional tooth movement better than general attachment [20]. Another key point is the position of the attachment: during incisor extrusion, a rectangular palatal attachment could improve the biomechanics and therefore the effectiveness of the planned movement [21]. As we have seen, one of the main features of orthodontic aligners that characterize the force transfer from the aligner to the tooth is the auxiliary elements, like attachments, divots and power ridges. Their geometrical features and positions strongly affect the load transfer and therefore the tooth movement [22]. For this reason, it would be desirable to optimize their features using numerical methodologies, such as the finite element method (FEM). Numerical methodologies would allow orthodontic behaviors to be simulated. In recent years, research activities have been focused on the analysis of traditional orthodontics, contrary to what was carried out for the biomechanical modelling of aligner treatments [23]. A patient-specific 3D finite element model (FEM) was developed to analyze the biomechanical response using different auxiliary elements to correct malocclusion. The patient anatomy was digitally reconstructed by merging optical 3D scanning and Cone-Beam Computed Tomography (CBCT), thus providing an accurate model comprising tooth crowns, roots periodontal ligaments (PDLs) and alveolar bone. The orthodontic appliance was modelled by exploiting Boolean operation through AutoCAD(r)(r)(r), Q.104.0.0 AutoCAD 2020.1.2, [[https://www.autodesk.com/](https://www.autodesk.com/)]([https://www.autodesk.com/](https://www.autodesk.com/))) to replicate the appliance manufacturing process. FEA simulated the interactions between anatomical tissues and appliance structures, enabling both the geometrical and mechanical attributes of the appliance to be tuned to gain the target tooth movements. In the current literature, there is not any example of a specific clinical case treated with an aligner configuration chosen according to an FEA simulation: the aim of the current paper was to simulate the rotation movement of a maxillary canine for a specific clinical case by using three different aligner configurations, and to predict with a fully digital workflow the most efficient aligner design and auxiliaries.