## 2 Materials and Methods  
The study was conducted in accordance with the Declaration of Helsinki and approved by the Ethics Committee of KENIMUS, Approval Code: N\({}^{\circ}\) 2873. Approval Date: 4 May 2022. The study is based on the results of digital measurements on 3D models of 33 patients (12 male and 21 female) treated by the team over the past two years with a digitally planned and printed expander. The number of patients included in the study is over 30, which is important for the statistical calculations included in the study's design. For both males and females, the appropriate time for treatment is during mixed dentition and early permanent dentition (before and at the start of the peak of adolescent growth), and treatment efficacy is likely to vary between the sexes depending on growth activity. The bone growth period is conventionally determined in practice by the maturity of the cervical spine, and in cases of doubt, a CBCT examination of the maxilla is performed to determine the maturity of the sutures before orthodontic treatment is planned. The mean age of the patients was 13.39 years. Twenty-six (78.8%) of the patients were in the period of permanent dentition formation, and 7 (21.2%) were in mixed dentition (Table 1). The criteria used for the inclusion of patients in the study are:  
1. Complete documentation at each stage (initial phase, finished first treatment phase with RME, finished treatment and achieved satisfactory result, retention phase). 2. Informed consent, presented, discussed, and accepted treatment plan (non-extraction treatment) certified by the signature of the patient (or parent). 3. Strictly followed treatment protocol, without missed appointments for control. \begin{table}
\begin{tabular}{c c} \hline \hline
**Variable** & **RME (\(\boldsymbol{n}\) = 33)** \\ \hline Mean age \(\pm\) SD (years) & 13.39 \(\pm\) 3.97 \\ Gender—number (\%) & \\ Males & 12 (36.4) \\ Females & 21 (63.6) \\ Dentition—number (\%) & \\ Mixed & 7 (21.2) \\ Permanent & 26 (78.8) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Distribution of the participants in the study—by gender, age, and type of dentition. 4. Digital documentation before and after each stage and at the end of treatment (digital models without double images, all tooth surfaces visible, no missing areas in the scan). The rapid maxillary expansion of all the patients is the initial phase (first phase) of main treatment, which includes active treatment with fixed techniques during the period of active growth and development in puberty. Complete documentation is necessary for longitudinal study design and the assessment and evaluation of treatment results. Digital documentation before and after each stage is a powerful tool for accurate measurements. The STL digital models have not been influenced by any deformation over time. Strictly followed treatment protocols guarantee that the outcomes are due to treatment requirements and are not influenced by any patient's noncompliance. All the patients fills out the informed consent form in order to follow the protocols for good dental practice and to fulfils the ethical committee requirements. Clinical protocol: The rapid maxillary expansion appliance used is individually planned and fabricated for each patient on a 3D model obtained after an intraoral scan. The design of the appliance is constructed so that the expansion screw is closer to the molars. The design of the appliance was made with Exocad software (Exocad DentalCAD 3.0 Galway) and was printed with CAM technology from Co-Cr alloy by laser sintering of the metal (Figure 1). The appliance was bonded to the distal teeth in the maxilla. The patient and accompanying parent are trained to activate the device. Activation takes place once a day at a fixed time--evening. The treatment clinical protocol includes 20-28 activations. The parents should turn the expansion screw per % of its full rotation (0.25 mm per activation).