## 2 Materials and Methods
The rate of expansion was 4-6 activations per day (0.133 mm per turn and \(\approx\)0.5-0.8 mm per day) until a diastema appeared; then, the expansion rate changed to 1 activation per day. The activation was continued until the maxillary skeletal width was equal to or greater than the mandibular width. The MSE was kept in place, with no further activation for 6 months, to retain the expansion during bone formation. Figure 1: Method used clinically and in dental casts to project the extent of maxillary skeletal expansion required. Blue line (the distance between the narrowest points of the maxillary sulcus area above the mesibuccal cusps of the first molars), maxillary width, and red line (the distance between the projected points on the mandibular buccal surfaces at the level of furcation), mandibular width, measured with a digital caliper. Figure 2: Midfacial skeletal expander II device and head of activation key (MSE II, Biomaterials Korea, Seoul, Republic of Korea). In addition to the pre-expansion CBCT, a second CBCT scan was obtained within 3 weeks of completing the expansion. The time interval between the scans was 8.1 \(\pm\) 4.8 months, and this included the time that lapsed for administrative procedures, appliance fabrication, delivery, and treatment. In order to assess skeletal outcomes induced purely by MSE, post-expansion scans were obtained before patients received any other orthodontic appliances. All subjects must also have had a final post-treatment CBCT taken at the end of orthodontic treatment, with an average treatment time of 27.6 \(\pm\) 6.9 months. The same scanner (5G; NewTom, Verona, Italy) was used for all patients, with an 18 \(\times\) 16 cm field of view, 14-bit grayscale, and a standard voxel size of 0.3 mm. Configuration of the CBCT included scan time of 18 s (3.6 s emission time) with 110 kV. In order to properly adjust the milliamperes, an automated exposure control system was used to detect the patient's anatomic density. OnDemand3D (Version 2.0, Cybermed, Daejeon, Republic of Korea) software was used to superimpose all three CBCT images, using the anatomical structures of the entire anterior cranial base [35] by automated processing to match the voxel gray-scale patterns. Once the images were properly superimposed, equivalent slices were obtained without manual adjustments for further image analysis, with distance and angular measurements described below. First, the pre- and post-expansion CBCT images (T0 and T1, respectively) were superimposed using the maxillary sagittal plane (MSP; passing through the anterior nasal spine, posterior nasal spine, and nasion), and the exact fulcrum location of each patient was identified utilizing the method described by [PERSON] et al. [32; 33]. According to [PERSON] et al., the fulcrum was located near and slightly above the external surface of the frontozygomatic suture because sutures are the weakest points of the midfacial structure during the archival movement of expansion [21]. The true rotational fulcrum on the right and left sides (rF and IF) was found using a method previously described, and the interfrontal line was established by connecting rF and IF [32; 33]. Then, the following angular measurements were performed to assess skeletal, alveolar, and dental components of expansion: (1) the frontozygomatic angle (FZA) between the interfrontal line and the line extending from fulcrum to the most external point of the zygomaticomaxillary suture, (2) the frontoalveolar angle (FAA) between the interfrontal line and the line extending from fulcrum to the alveolar bone surface at the level of distoucal root tip of the upper first molars, and (3) the frontoidental angle (FDA) between the interfrontal line and the line extending from fulcrum to the occlusal point located at the central groove of the upper first molar (Figure 3). These three angles were measured on right and left sides, and the pre-expansion value (T0) was subtracted from the post-expansion value (T1) in order to determine the treatment change for each section.