## 2 Materials and Methods  
The present retrospective study was conducted on patients who were treated consecutively by the same operator. The collected data were anonymously recorded, and the statistical analysis was conducted blindly (blindness was obtained by eliminating every reference to the group from the elaboration file). This study includes 116 initial patients, with ages ranging from 7 to 46 years (mean age 14.51 years). The criteria adopted for the inclusion in the study were as follows: the presence of maxillary transversal deficit; no previous orthodontic treatment; no orthognathic surgery performed; no extractions; absence of agenesis, congenital pathologies and cranio-maxillofacial malformations; use of a hybrid device for palatal expansion using two miniscrews placed in the anterior area of the palate; and a complete set of pre- and post-therapy models. Therapy was defined as treatment with maxillary expansion first and subsequent multi-bracket therapy. Based on these criteria, 48 patients were excluded, and 68 were evaluated for the study. The ages of the patients included in the study varied from 7 to 27 years old (mean age 13.45). The sample was divided into three groups based on CVM stage at the start of treatment, using the CVM method as an assessment of midpalatal suture maturation [24]. Group 1 (CS1-CS2) included 21 patients (mean age 10.21, SD 1.34), Group 2 (CS3-CS4) included 28 patients (mean age 13.37, SD 1.37) and Group 3 (CS5-CS6) was composed of 19 patients (mean age 17.14, SD 3.48) (Figure 1). TeleRx and STL models of dental arches were obtained for each patient, both at the beginning and the end of the treatment. Each patient underwent an orthodontic therapy where the first step was a palatal expansion by means of a hybrid expander; afterwards, the therapy was completed with a multi-bracket appliance (BioQuick, Forestadent, Germany). The type of screw chosen for each device was Orthopal (8 mm length, 1.7 mm diameter). The number of activations of the hybrid device varied from 1 to 3 activations per day. Activation days varied from 7 to 23 days, until the operator was evaluated to have reached a proper upper transversal dimension. All the patients were treated with an MBT prescription bracket for the upper incisors and standard Edgewise prescription for the posterior teeth. Expansion values were observed at the end of treatment on digital models. The following dental elements of the upper jaw were considered in the evaluation of the dental transversal variations: canine, premolars and first molar. Three points were considered for each element:  
* Cusp: buccal cusp was considered. For the first molar, the point was placed on the meso-vestibular cusp. * Centroid: the center of the occlusal table. * Lingual point: the most palatal point at the level of the tooth collar. The distance in millimeters (Figure 2) was calculated between the respective points on the teeth of the contralateral arch on the 3D models, both pre- and post-treatment. The measurements were performed by two operators. A sample of 10 patients was examined to detect the accuracy of the measurements. Both operators evaluated the cusp-cusp, centroid-centroid and lingual point-lingual point distances at the level of the first upper molars. The obtained values were compared to each other, using Pearson's correlation index. A correlation index value equal to +1 indicates a perfect positive correlation. A correlation index equal to 0.998 was obtained. Dental torque values were observed at the end of treatment on digital models. The torque value was obtained through the OnyxCeph software ([[https://onyxceph.eu/en/](https://onyxceph.eu/en/)]([https://onyxceph.eu/en/](https://onyxceph.eu/en/)) Image Instrument (accessed on 18 January 2024), Chemnitz, Germany) following these steps:  
1. The crowns of the dental elements were selected with the 'Segmentation' option. 2. When the crowns were selected, the following commands were entered: 'Segment crowns' > 'Separate crowns' > 'Complete separation'. Figure 1: Study flow chart.