## 2 Materials and Methods  
This is a retrospective study including patients in mixed dentition with maxillary transverse deficiency. The patients enrolled in this study came from private practices, and have been informed that the data resulting from their treatment will be used for research. The parents or the legal guardians of each subject of the sample had to accept an informed written consent before the beginning of dental treatment. The study was conducted in agreement with the Helsinki declaration (version, 2008). One sample was treated with Invisalign First and the other one was treated using a 6 mm screw and 450 g force Leaf Expander. The Invisalign First treated patients were 30: 15 females and 15 males with an average age of 8.4 \(\pm\) 1.2 years and a range of treatment between 8 and 12 months. The expansion protocol performed on this group was as follows:  
1. [label=(0)]
2. Mesial out derotation of the upper first molars with the control of root buccal torque, if needed;
3. Sequential expansion first of the upper permanent molars and then of all remaining teeth in the arch;
4. Each expansion stage did not exceed 3 mm;
5. The aligners were changed every week for a total use of indicatively 24 aligners, and the check up was every 6 weeks. The Leaf Expander treated sample (tooth-borne expander anchored on the second deciduous molars with extension arms to canines) was composed by 38 patients: 19 females and 19 males with an average age of 8.2 \(\pm\) 1.3 years and with a range of treatment of approximately 8 to 10 months. The two samples have been paired so that at T0 there were no differences regarding age, maxillary discrepancy, molar and canine diameters. In both samples, the inclusion criteria were:  
* Age between 6 and 10 years;
* Mixed dentition;
* First upper molars completely erupted;
* Adequate data collection (photos, radiographs, study casts);
* Transversal discrepancy less than 3 mm. Exclusion criteria were:  
* no previews orthodontic treatment;
* no cranio-facial district development anomalies. For each patient, initial records were collected for the case study, as is normally routinely performed: medical history, intra ed extra oral photos, cast models, OPG and Tele X-rays. In particular, for the Invaslign First group digital impressions were taken at T0 with an iTero intra-oral scanner (iTero; Align Technologies, San Jose, CA, USA), whereas for the Leaf Expander group a Trios 3 Shape scanner was used (Trios(r) 3 Cart wired, 3 Shape, Copenhagen, Denmark). The files, after a proper conversion, were subsequently uploaded on two specialized measurement software applications: \"Maestro 3D Ortho Studio-version 6.00.00.20000\" and \"Minics Innovation Suite 22\". The following measurements were taken into consideration [26; 27]:  
* Deciduous upper canines gingival width (53-63G): linear distance between the center of the upper deciduous canines palatal surface in contact with the gingival margin. * First deciduous upper molars gingival width (54-64G): linear distance between the center of the upper first deciduous molars palatal surface in contact with the gingival margin. * Second deciduous upper molars gingival width (55-65G): linear distance between the center of the upper second deciduous molars palatal surface in contact with the gingival margin. * First permanent upper molars gingival width (16-26G): distance (mm) between the inner part of the upper first permanent molars palatal surface. * Deciduous upper canines dental width (53-63): distance (mm) between the edges of the cusps of the upper deciduous canines. * First deciduous upper molars dental width (54-64): distance (mm) between the edges of vestibular cusps of the upper first deciduous molars. * Second deciduous upper molars dental width (55-65): distance (mm) between the edges of the mesio-vestibular cusps of the upper second deciduous molars. * First permanent upper molars dental width (16-26): linear distance between the edges of the mesio-vestibular cusps of the upper first permanent molars.