## 2 Materials and Methods  
This pilot study was approved by the Unit Internal Review Board (2020-0205). Patients attending the Unit of Orthodontics and Pediatric Dentistry of the University of Pavia for orthodontic treatment were enrolled in the study, with written consent for performing CBCT being obtained from their parents [31]. The inclusion criteria were: patients with mono- or bilateral crossbite, need for Hyrax RME or Haas treatment, and indication for CBCT to evaluate the upper arch (maximillary displaced canines, presence of artifacts in the preliminary orthopantomography or other conditions that require CBCT for a complete diagnosis). The sample size calculation (alpha = 0.05; power = 95%) was performed considering \"maximillary internormal distance\". The sample size calculation (alpha = 0.05; power = 80%) was performed considering \"ANB angle\" as a primary outcome. An expected mean of 4.16 with a standard deviation of 1.4 was hypothesized, with an expected difference between the means of 1.65 [25]; therefore, 11 cephalometric tracings per group were required for the study [32]. Eleven patients were enrolled: eight females (age 6.4 \(\pm\) SD years) and three males (age: 12.4 \(\pm\) SD years). Considering the tooth eruption stage for each patient, Hyrax RMEs were used on 10 patients. The RMEs were cemented onto the second primary molars on six patients, to the first permanent molars on three patients, and to the first permanent molars and premolars in one patient. One patient was treated with a Haas RME. A CBCT scan was performed before treatment (T0) and was repeated 6 months after the end of orthopedic therapy (T1). As CBCT is becoming more commonly used to quantitatively assess the effects of RME to overcome the limitations of 2D radiographs [33], it was necessary to repeat the CBCT 6 months after the end of the therapy to accurately assess the effects of the RME, especially on the transverse plane, such as the amount of disjunction of the alveolar bone and the dento-alveolar tipping of the first upper molars [34]. According to the protocol, two activations per day were required [35; 36]. The duration of the active therapy was, on average, 3 weeks, and at the end of the activation time, the expanders were blocked with resin, metal or brass ligatures. It was necessary to wait at least 6 months after the removal of the expander to perform a new CBCT in order to prevent any image distortion during the scan. CBCTs at T0 and T1 were performed on each patient by the same operator using the same i-CAT machine (Imaging Science International, Hatfield, PA, USA), with a radiation dose of 2.5 mSv [37]. The following X-ray machine parameters were set: Tension: 120 kVP, Intensity: 3-7 mA, Focal spot: 0.5 mm, Voxel: 0.4 mm, Pixel: 0.4 mm, Grayscale: 14 bits, Scan time: 20 s, Detector material: amorphous silicon flat. Two programs were used in this study: Simplant OMS (version 2.1.3, Materialise NV, Leuven, Belgium) (Figure 1) and Delta-Dent (version 2.3, Outside Format, Pandino, Italy) (Figure 2). Both programs create radiological images in DICOM format that grant the capability to evaluate anatomical structures with more precision and without artifacts [38]. The operator can rely on visual and auditory support to optimize landmark positioning [1; 3]. The section for the reconstruction of the DICOM images was set to start from 0.5 mm. The operator traced 25 landmarks, of which 19 were skeletal and 6 dental, enabling the programs to perform cephalometric measurements for the sagittal, vertical and transverse analysis [39; 40].