## 2 Materials and Methods  
This retrospective study was performed at the University of California at Los Angeles (UCLA), with approval by the ethics committee (IRB number 17-000567). Pre-expansion CBCT images from 14 randomly selected patients successively treated with MSE (Biomaterials Korea, Seoul, Republic of Korea) with mean age of 20.4 \(\pm\) 3.5 years were obtained. All patients were diagnosed with maxillary transverse deficit and treated at the orthodontic clinic, UCLA School of Dentistry, under the supervision of one clinician. Orthodontic treatment, including bonding of brackets and other appliances, was carried out after the completion of MSE expansion and acquisition of post-expansion CBCT. At the end of orthodontic treatment, the post-treatment CBCT was obtained. The selection criteria included (1) diagnosis of transverse maxillary deficiency; (2) patient records with CBCT images obtained at 3 time points: pre-expansion (T0), within 3 weeks after active expansion (T1), and at the end of orthodontic treatment (T2); (3) absence of any craniofacial irregularity; and (4) no orthodontic treatment precedent. The average time interval was 8.1 \(\pm\) 4.8 months between pre-expansion and post-expansion CBCT and 19.5 \(\pm\) 7.3 months between post-expansion and post-treatment. Average total treatment time between pre-expansion and post-treatment CBCT was 27.6 \(\pm\) 6.9 months. The transverse deficiency was diagnosed using coronal cuts from each subject's initial CBCT according to [PERSON] et al. [32]. The maxillary bone width was determined by the distance between the right and left bony points at the level of the mesibuccal root tips of the upper first molars (usually the narrowest part of the maxilla). Mandibular bone width was defined as the distance between the right and left bony buccal surfaces at the level of the lower first molar function. If the mandibular width was greater than the maxillary width, a transverse discrepancy was diagnosed. Clinically and in dental casts, the maxillary width is defined by the distance between the left and right most concave points along the maximillary vestibule above the mesibuccal cusps of the first molars [34]. The mandibular width is defined as the distance between the left and right buccal surfaces over the lower first molar function. The amount of difference among these values also projects the extent of maxillary skeletal expansion required (Figure 1). Taking measurements on study models can be completed before and during the expansion in order to assess the bone relationship. The expansion was stopped once adequate expansion had been achieved, and the maxillary bony width became wider than the mandibular width for optimal occlusion after dental decompensation. The furcation is most likely the center of rotation for mandibular molars when compensated; therefore, the width between the buccal points over the furcation was used as the projected mandibular width after lower dental uprighting. The maxillary molars are generally buccally flared, and decompensation by uprighting the maxillary molars causes the maxillary dental arch to construct. The most concave area of the maxilla is often at the apex of the maxillary molar, and controlled tipping with fulcrum at the apex is required for decompensation, unlike for mandibular molars. The MSE II device (Figure 2) has a jackscrew unit (16.15 mm in length, 4.5 mm in width, and 14.15 mm in depth) with four parallel holes (1.8 mm in diameter) for micro-implant insertion and two soft supporting arms on each side, which are soldered to the molar bands for stabilizing MSE during the expansion. The body of MSE is positioned between the zygomatic buttress bones, usually located lateral to the first molars. Four micro-implants (1.8 mm in diameter and 11 mm or 13 mm in length) were bicontically inserted through the palatal bone. The posterior placement and bicontical engagements promote posterior and superior expansion of the maxillary process, which in turn produce the archival expansion described in previous studies [21; 32; 33].