## 2 Materials and Methods  
Study design: A retrospective study was performed on an orthodontic sample of pediatric patients with suspected OSAS and treated with RPE to further evaluate the functional effects on nasal resistance using active anterior rhinomanometry (AAR) with an ATMOS Rhino 31 rhinomanometer (Figure 1). This study was conducted from an initial sample of 235 orthodontic patients, with a positive orthodontic history for oral breathing and/or snoring, provided by the same private practice (M.M). Specifically, the presence of the following: oral breathing related to obstructive cause (hypertrophy of adenoids and/or tonsils; hypertrophy of turbinate; septal deviation) or non-obstructive cause; disturbed sleep; and OSAS. All patients underwent a first orthodontic examination after otorhinic evaluation with a final diagnosis of mouth breathing. Participants: From the initial sample, a first selection of patients was made by applying the following exclusion criteria: age less than 5 years or greater than 12 years, dento-cranial facial deformities in general, dental abnormalities, orthodontic treatment already performed  
Figure 1: ATMOS Rhino 31. The rhinomanometer is equipped with operational buttons, electromechanical pressure transducers, amplifiers, and analog-to-digital transducers. It features a display for real-time monitoring and visualization of results, as well as an integrated printer. Additionally, it consists of a measuring probe with olives or a mask for recording airflow; a pressure probe, a flexible tube, or a tube with nasal adapter to record pressure differences; and a handle for gripping. or in progress; and the above inclusion criteria: contraction of the upper maxilla with a need to expand at least 5 mm, positive history of oral respiration. Study size: The sample recruited consisted of 122 children, aged 5-12 years, 53 males and 69 females. Data Collection: For each patient, at time T0 (pre-treatment), an active anterior rhinomanometry with mask (AAR) was conducted by the same operator (G.S.) to examine respiratory function. Specifically, the ATMOS Rhino 31 rhinomanometer was used in the present study to test nasal respiratory pressure and respiratory airflow. This device enables real-time monitoring of airflow trends by synchronous recording of pressure and flow difference. In addition, each patient underwent the Scales for sleep-related breathing disorders Questionnaire (SRDB) or Pediatric Sleep Disorders Questionnaire (PSQ-SRDB), completed by the parent, in order to validate the orthodontic history of OSAS. Moreover, intra- and extra-oral photos, imprints for study models, RX OPT, and TLL were performed for each subject. These records permitted confirmation of the diagnosis of upper jaw contraction, continuing with orthodontic treatment based on the application of a rapid palatal expander of the type Hyrax or Pendex on deciduous or permanent dentition. The protocol calls for the device to be activated 0.25 mm per day until, clinically, contact is detected between the palatal cusp of the upper first molar or upper deciduous second molar with the buccal cusp of the lower first molar or lower deciduous second molar. At this point, the expander is left in place for at least 4 months. If at T0 (pre-expansion) the AAR was clinically significant, the exam is repeated by the same operator (G.S.) at T1 (post-RPE), corresponding to a period of three months after screw fixation. Indeed, the purpose of the present study is to determine the magnitude of improvement on respiratory function by evaluation of nasal resistance values and the concomitant evolution in terms of sleep quality and OSAS. Because of this, the questionnaires, to be completed by the parent and mentioned above, were again administered at T1. Changes between pre- and post-treatment in nasal resistance to airflow were assessed in order to examine any improvement induced by the application of RPE on respiratory function.