## 2 Materials and Methods  
Study Design and Participants: This cross-sectional study was conducted using cone-beam computed tomography (CBCT) images from the archives of the Department of Medical, Oral, and Biotechnological Sciences at the University \"G. D'Annunzio\" in Chieti. A total of 500 Italian patients aged between 17 and 60 years of age were included, with a balanced distribution of 250 males and 250 females. The sample was selected from patients who presented for orthodontic diagnosis and treatment planning.  
17-29 years: 121 scans (24.2%)  
30-39 years: 127 scans (25.4%)  
40-49 years: 123 scans (24.6%)  
50-60 years: 129 scans (25.8%)  
Ethical Considerations: The study received ethical approval (number 23) from the Independent Ethics Committee of the Hospital of Chieti. All procedures were conducted in accordance with the European Union Good Practice Rules and the Helsinki Declaration. Written informed consent was obtained from all participants for the use of their images and data.  
Inclusion and Exclusion Criteria: Patients were included if they were aged 17 years or older (under 60 years old) and had no history of congenital craniofacial syndromes, cervical spine trauma, or surgery. Exclusion criteria comprised the following:  
* Insufficient image quality (e.g., due to patient movement);
* Region of interest cut-off;
* Presence of congenital lip and palate anomalies or other craniofacial syndromes;
* History of trauma or surgery in the cervical spine;
* Non-Italian nationality.  
Imaging Protocol: All CBCT scans were acquired using a Pax-Zenith 3D CBCT machine (Vatech Corporation Ltd., Hwaseong, Republic of Korea) following a low-dose acquisition protocol. The parameters included the following:  
* Field-of-view (FOV): 240 \(\times\) 190 mm;
* Normal resolution quality;
* Tube voltage: 80 kVp;
* Tube current: 5 mA;
* Acquisition time: 15 s.  
Patients were positioned with the Frankfurt plane parallel to the floor, and a 360\({}^{\circ}\) rotation scan was performed with a duration of 15-20 s. The raw data were then processed into multiplanar and three-dimensional images using Dolphin imaging software (12.0.9.58, Dolphin Imaging & Management Solutions, Chatsworth, CA, USA).  
Image Analysis: To determine the presence and type of APAD, each CBCT image was individually assessed by the authors. Discrepancies in evaluation were resolved through consensus or by consulting a third observer. Only images where all observers agreed on the presence or absence of APAD were included in the final analysis. To prevent evaluation fatigue, no more than 50 images were analyzed in a single session.  
Classification and Measurement: APAD was classified according to the system proposed by [PERSON] et al. (1994) [6] and is illustrated in Figure 1, which categorizes anomalies into five types based on morphological characteristics:  
* Type A: Failure of posterior midline fusion of the two hemiarches;
* Type B: Unilateral defect;
* Type C: Bilateral defects;
* Type D: Absence of the posterior arch with a persistent posterior tubercle;
* Type E: Absence of the entire posterior arch, including the tubercle.  
For cephalometric analysis, the NHP (Natural Head Position) orientation was set using Dolphin software (12.0.9.58), which included three reference planes:  
1. The transverse plane coinciding with the Frankfurt plane (FH), passing through Orbital (Or) and porion (Po);
2. The sagittal plane coinciding with the mid-sagittal plane (MSP), perpendicular to the FH and passing through the Crista galli (Cg) and Basin (Ba);
3. The coronal plane coinciding with the anteroposterior (PO) plane, perpendicular to the FH and MSP, and passing through the right and left porion.  
Data Recording and Analysis: All findings and measurements were recorded using Microsoft Excel version 16.0 for Windows 10. The prevalence and distribution of APAD types were analyzed, with particular attention paid to the occurrence of any associated conditions such as Ponticulus Posticus.