## 1 Introduction  
Maxillary transverse deficiency (MTD, or maxillary hypoplasia) is a common problem that affects the normal development of the maxillofacial complex. Therefore, the early diagnosis and correction of MTD are essential to achieve a normal transverse skeletal relationship between maxilla and mandible [1].  
The incidence of MTD ranges from 8.5% to 22% [2] in children and adolescents. MTD is usually associated with a unilateral or bilateral crossbite [3], a generalized lack of space in the maxillary arch, and crowding because the jaw is narrow compared with the rest of the craniofacial structures. These conditions can be treated using an RPE as described by [PERSON] (1860) [4]. The RPE appliance is used in growing patients because the ossification of the MPS increases with age and occurs earlier in girls than in boys [5]. In terms of sex, the mean age of ossification of the MPS girls is 16 years and 18 years in boys, as described by [PERSON] in 1975 [6]. However, [PERSON] in 1980 reported that MPS fusion occurs at the age of 14-15 in females and 15-16 in males [1]. The maturation stages of the MPS are not directly related to chronological age, as reported in numerous studies [7, 8]. The hand and wrist method (HMM) [7] and cervical vertebrae method (CVM) [8] are the conventional indexes chosen to determine the possibility of maxillary expansion. [PERSON] (2013) [9] introduced a new index by observing CBCT images, and suggested that maturation of the MPS can be Classified into five stages (A, B, C, D, E). There are three types of MPS disjunction: RPE (with dental support), MARPE (miniscrew-assisted rapid palatal expansion with skeletal support) [10], and SARPE (surgically-assisted rapid palatal expansion) [11]. MARPE and SARPE are used in fused MPSs or compromised dental support.  
MPS fusion Classification using CBCT provides reliable parameters for the clinical decision between conventional (RPE) and unconventional (MARPE, SARPE) methods. According to [PERSON] et al., (2013) [9], there are five stages of MPS maturation. Stages A (straight high-density sutural line, with no or little interdigitation) and B (scalloped appearance of the high-density sutural line) are frequently noted up to the age of 13 years; stage C (parallel, scalloped, high-density lines that were close to each other, separated in some areas by small, low-density spaces) is typically observed from 11 to 17 years (rarely in younger or older patients). Patients in stages D (fusion completed in the palatine bone, with no evidence of a suture) and E (anterior fusion in the maxilla) might be better treated by SARPE because fusion of the MPS already has occurred.  
The introduction of cone beam computed tomography (CBCT) in orthodontics allows a quantitative evaluation of BD using Hounsfield units (HU) [12], and an accurate analysis concerning sagittal and vertical growth patterns, which helps to make the decision about whether to use conventional (RPE) or unconventional maxillary expansion methods (MARPE or SARPE).  
The present paper aims to measure mean bone density (BD) values of the midpalatal suture (MPS) in order to predict an accurate estimation of the MPS's response to expansion therapy using a rapid palatal expander (RPE) appliance, as related to sex (males and females), vertical skeletal patterns (hypodivergent, normodivergent, and hyperdivergent), and sagittal skeletal patterns (Class I, Class II, and Class III).  
The first null hypothesis predicts no differences between males and females in terms of BD in the ROI. The second null hypothesis predicts that there are no differences between different vertical skeletal patterns in terms of BD in the ROI. The third null hypothesis predicts no differences between different sagittal skeletal patterns in terms of BD in the ROI. The fourth null hypothesis predicts that there are no differences between the two time points (T0 and T1) in BD in the ROI.