## 2 Materials and Methods  
This retrospective study was conducted following the ethical principles outlined in the Declaration of Helsinki. It received approval from the Ethics Committee of the University of L'Aquila, Italy (reference 57/2021-22) on 21 December 2021. A total of 120 patients, aged 6 to 13 years, were examined at the Dental Clinic of the University of L'Aquila. The sampling in our study was based on convenience, and no formal sample size calculation was conducted. As the study was observational in nature, the sample size was determined by the availability of willing participants during the study period. The study was registered on clinicaltrials.gov. All evaluations were performed by a single physician. Diagnostic assessments included extraoral and intraoral photographs, orthopantomography, lateral teleradiography, and intraoral scans of the dental arches. Following the case study, an individualized treatment plan was developed by the same orthodontist, based on the Indices of Orthodontic Treatment Need (IOTN) as described by [PERSON] and [PERSON] [9]. The transverse discrepancy was assessed by measuring the distance (in mm) between the palatal cusps of the upper first premolars, or if absent, between the palatal cusps of the corresponding deciduous molars.  
**The Inclusion Criteria were:**  
* Skeletal class I relationship
* Molar class I relationship
* Presence of unilateral or bilateral crossbite (falling within grade 3 IOTN index)
* Healthy periodontal status, with no signs of periodontitis or severe gingivitis
* Systemically healthy patients, without serious general diseases or contraindications for orthodontic treatment.  
**The Exclusion Criteria included:**  
* Previous orthodontic treatment
* Lack of written informed consent from a parent or legal guardian.  
As shown in Figure 1, of the 120 patients initially enrolled, 91 were excluded because they did not meet the inclusion criteria or did not provide consent. Ultimately, 29 patients were eligible and were randomly assigned to two groups using online randomization software ([[https://www.sealedenvelope.com/](https://www.sealedenvelope.com/)]([https://www.sealedenvelope.com/](https://www.sealedenvelope.com/)) (accessed on 26 April 2025) Sealed Envelope Ltd. Suite 2a, 7 th Floor--Pf City Reach, 5 Greenwich View Place, London E14 9 NN, UK. VAT number GB788228971).  
The case group, consisting of 15 patients (7 males, 8 females) with an average age of 10 \(\pm\) 1.69 years, was treated with the Eptamed Equilibrator. The control group, consisting of 14 patients (2 males, 12 females) with an average age of 10.214 \(\pm\) 1.369 years, was treated with Spark clear aligners. The transverse dimension of the arch, measured by the distance (in mm) between the palatal cusps of the upper first premolars or, if absent, the corresponding deciduous molars, was assessed using orthodontic software. Measurements were taken at baseline (T0), 6 months after the start of therapy (T1), and 1-year post-treatment (T2) by the same orthodontist.  
Participants were instructed to wear the removable devices as much as possible throughout the day and night, maintain oral hygiene, and adhere to the treatment plan, including timely mask changes and regular check-ups.  
Figure 1: Flow diagram of the progress of the two groups through the phases of this study.  
Statistical analysis was conducted using a nonparametric approach, applying the Mann-Whitney U test to maintain conservativeness. Statistical significance was set at \(p<0.05\). The results of the measurements are expressed as mean (SD). The null hypothesis posits that there are no statistically significant differences between the two treatment groups.