## 1 Introduction  
Sleep-disordered breathing (SDB) indicates breathing difficulties during sleep time; it is a disorder characterized by prolonged increased upper-airway resistance and partial or complete upper-airway obstruction, which compromise the pulmonary ventilation or the sleep quality [1]. SDB refers to increased upper-airway resistance, from primary snoring to obstructive sleep apnea (OSA) [2, 3]. Several studies examined anatomic differences between SDB subjects and healthy nasal breathers using traditional cephalometric tracing, model analysis, and three-dimensional (3D) radiography [3, 4, 5, 6, 7, 8, 9]. [PERSON] et al. suggested that children with a high hard palate and long oval-shaped face are highly likely to have sleep-disordered breathing [9]. Model analysis revealed that SDB patients had a narrower maxilla and mandible compared with the control group; the tongue could compensate for the reduced inter-arch dimensions, assuming a more upward and backward position [7, 10, 11]. The most common cause of SDB is adenotonsillar hypertrophy. Children with adenotonsillar hypertrophy are usually treated with adenotonsillectomy, but the surgery itself may cause a narrower epipharyngeal air space and a more poorly developed maxilla, which may predispose children to sleep-disordered breathing, with a continuum of severity, varying from snoring to obstructive sleep apnea [12]. For this reason, rapid maxillary expansion (RME) is considered a treatment option as part of an orthodontic procedure for managing this respiratory disorder [13; 14; 15; 16], since RME is a painless treatment [17] that can simultaneously correct transverse maxillary deficiency and widen the floor of the nasal cavities. This, in turn, leads to a drastic and immediate reduction in air resistance, facilitating a normal nasal breathing pattern, with possible explanation of the mandibular and hyoid bone advancement, which may explain the anterior traction of the tongue, in turn increasing the posterior dimension of the respiratory tract and reducing its resistance, consequently improving nocturnal breathing quality, while also influencing the periodontal status of mouth breathing subjects [18]. Regarding treatment timing with RME, it has been reported that early mixed dentition is the ideal phase, to prevent subsequent anatomical changes that may later occur in skeletal and soft tissues, such as the stabilization of morphological characteristics of a long and narrow uvula, increase in palatal vault dimensions, presence of a cross or open bite, abnormal position of canines and molars, and generalized crowding [11; 19; 20]. Rapid maxillary expansion in pediatric patients with obstructive sleep apnea is associated with an increase in the maxillary transverse dimension and widening of the nasal cavities, mostly evaluated on 3D analyses [13; 16; 21; 22]. Additional dental effects include uprighting of the maxillary incisors, with a reduction in the angle between the sella-nasion plane and the axis of the upper incisor; moreover, the upper incisors tend to extrude. As a result, cephalometric variations of overbite and overjet can be observed.  
Thus, the aim of this study was to evaluate cephalometric variables concerning dento-skeletal changes and airway dimensions in SDB children treated with rapid maxillary expansion, compared with healthy children treated with RME for malocclusion.