## 2 Materials and Methods
It was done by the parents until optimal transverse contacts were achieved between the posterior upper and lower teeth. After the expansion, there was a 3-month retention period before the expander was removed. Follow-up appointments are scheduled once a month to monitor the results and follow the clinical protocol. For the purposes of this investigation contemporary and reliable methods are used, which is possible through the new technologies that are incorporated into daily practice. All patients were scanned with an intraoral scanner and 3D models were generated and stored in STL format. The intraoral scanner was calibrated, with calibration tool, every week to provide the accurate digital model. Scans were performed before starting treatment (phase 1), after completion of the expansion phase (phase 2) and at the end of orthodontic treatment (phase 3). After removal of the RME appliance (phase 2), the patients are photographed, and a control frontal cephalogram is performed. The methodology is described in detail as follow:  
Biometric protocol: The following parameters were measured on all digital models of all 33 participants in the study:  
* PA--the perimeter of the upper dental arch (twelve teeth--from the right first permanent molar to the left first permanent molar). The measurement is made from a point positioned in the middle of the distal side of the first molar. The orthodontic software itself positions the arch on the alveolar crest and determines its shape, based on the information from the initial and final points and three additional points--two placed in the middle of the medial side of the first premolar and one located at the contact  
Figure 1: Clinical protocol—(**a**) initial phase; (**b**) digital model of printed appliance; (**c**) adapted and fixed appliance; (**d**) state after completion of activation. point between the central incisors. In the mixed dentition cases, the middle of the medial side of the first deciduous molar was used (Figure 2);
* aP--the perimeter of the anterior segment--from the distal surface of the canine to the distal surface of the opposite canine (deciduous or permanent)--six teeth measured with orthodontic software (Figure 2); when canines are not present, measurements are taken from the medial surface of the first premolars or first deciduous molars. * PP--width of maxilla in the area of the premolars. The two points are in the middle of the central fissure, under the mediovestibular tubercul. In mixed dentition, when first premolars are not fully erupted, this parameter is not measurable (Figure 2);
* MM--width of maxilla in the area of the molars (Figure 2);
* L--length of the maxillary dental arch, measured from a point on the vestibular surface of the central incisors to a line connecting points in the middle of the distal surface of the first permanent molar (Figure 3);
* I--length of the anterior segment of the dental arch, measured from a point on the vestibular surface of the central incisors to a line connecting points in the middle of the medial surface of the first premolar (Figure 3);
* w--the width of the anterior segment--a straight line connecting points in the middle of the medial surface of the first premolar (Figure 3). The described measurements were performed identically during the treatment phases: (1) before treatment; (2) at the end of the first phase (RME); and (3) at the end of treatment with brackets. In order to differentiate the same type of measurement in the different stages, the following designations are applied: the numerical sign after the letters indicates the phase: 1--before treatment (PA1, aP1, PP1, MM1, L1, 11); 2--the phase after the first appliance (PA2, aP2, PP2, MM2, L2, l2); 3--the end of treatment (PA3, aP3, PP3, MM3, L3, l3).