## 2 Materials and Methods  
### Study Design and Type of Participants  
A retrospective study on changes of the skeletal and dental structures before and after maxillary expansion obtained by an RME and a Leaf expander was performed using lateral radiographs of subjects treated at Fondazione IRCCS Ca' Granda, Ospedale Maggiore Policlinico Milan between January 2019 and August 2020.  
The Ethical Committee of the Fondazione IRCCS Ca'Granda, Ospedale Maggiore Milan--Italy (Protocol No.: 573/15) approved the present study protocol. Patients' parents or their guardians signed an informed consent form, allowing us to use diagnostic records for research motivations.  
Records consisted of lateral cephalograms obtained before and after maxillary expansion of patients that underwent orthodontic treatment at the Department of Biomedical, Surgical and Dental Sciences.  
The inclusion criteria for the samples of this observational retrospective study were as follows: good state of health; subjects with maxillary transverse deficiency (MTD) with unilateral/bilateral posterior crossbite; mixed dentition; age between 7 and 9 years old; an RME and a Leaf expander anchored on the upper deciduous second molars; patients before the pubertal peak of growth (CVM 1-3) [14].  
Exclusion criteria were: lack of postexpansion lateral cephalograms; poor radiographic quality; patients with previous orthodontic treatment, hypodontia in any quadrant excluding third molars; inadequate oral hygiene; craniofacial syndromes or cleft lip or palate.  
The lateral cephalometric head films were taken as follows: the first was taken no more than two months before the cementation, and the second was taken immediately after removing the appliance, approximately in a time period between 9 and 12 months from the beginning of the treatment. The RME requires a specific period of time from the last activation to stabilize orthopedic results. The overall mean duration, including active treatment and the retention phase, lasts 10 months according to the literature [15] and approximately 9 months with the Leaf expander [9].  
According to [PERSON] et al. [16], the prepubertal age was chosen because it is the most indicated period to resolve maxillary hypoplasia. Greater and more stable skeletal changes occur in subjects undergoing maxillary expansion during this particular stage of development.  
A total of 23 patients treated with the rapid maxillary Hyrax expander and 20 subjects treated with the Leaf expander met the inclusion criteria and were included in the test groups.  
The Leaf expander group consisted of 9 males (mean age = 7.5 \(\pm\) 0.9 years old) and 11 females (mean age = 8.2 \(\pm\) 0.6 years old). The mean distance between the two lateral radiographs was 10.2 months.  
The RME group of the present study was composed of 11 males (mean age = 7.8 \(\pm\) 0.6 years old) and 12 females (mean age = 8.1 \(\pm\) 0.5 years old). The mean distance between the two lateral radiographs was 10.8 months.  
The control group consisted of 19 untreated subjects: 10 males (mean age = 7.4 \(\pm\) 0.8 years old) and 9 females (mean age = 7.7 \(\pm\) 0.9 years old) who met the inclusion criteria. These patients did not receive any orthodontic treatment before taking the first lateral radiographs, and not even in the period between the first and the second. The two lateral cephalospor were taken as control to assess skeletal growth, as the parents refused a maxillary expansion treatment. The mean distance between them was 11 months.