## 2 Materials and Methods
### Orthodontic and Surgical Procedures  
At the first visit (T0), clinical records were collected, consisting of the following: (1) general and dental anamnesis; (2) extraoral and intraoral orthodontic clinical examination; (3) pathological clinical examination; and (4) visual analogue scale (VAS) and muscular palpation to estimate the pain intensity ratio on each patient's face and neck.  
Each patient underwent a CBCT scan using Planmeca Promax(r) 3D MID unit (Plammeca Oy, Helsinki, Finland) according to a low-dose protocol with these parameters: an acquisition time of 15 s, 80 kVp, 5 mA, 35 microSievert (uSv), a field of view (FOV) of 240 \(\times\) 190 mm, and normal image resolution [34]. The patient's CBCT was performed with the head oriented according to the Natural Head Position (NHP). After X-ray scanning, DICOM (Digital Imaging and Communications in Medicine) image files were processed using Dolphin Imaging 3D software v. 12.0 (Dolphin Imaging and Management Solutions, Chatsworth, CA, USA) for storage and interpretation. After the orientation of the head, the virtual 2D radiograms were extracted. Subsequently, extraoral photos (each patient's face in frontal, right-side, and left-side views) and intraoral photos (frontal, right, and left lateral photos and upper and lower occlusal photos) were taken, and the dental arches were scanned using an intraoral scanner.  
The subjects underwent pre- and post-surgical orthodontic treatment; two patients were treated with straight-wire fixed appliances (patient 3 and patient 4), and two were treated with clear aligners (patient 1 and patient 2). The patients treated with clear aligners changed the aligner every 14 days and wore it for at least 22 h/day. The pre-surgical orthodontic planning stage included decompensatory mechanics, leveling, and the alignment of teeth. In the clear aligner cases, the orthodontic brackets with Kobayashi hooks were bonded before surgery, and the refinement aligners were planned after the surgical operation and worn in the post-surgical phase. At the end of pre-surgical orthodontics, the surgical guides were made through a digital workflow that included the use of CBCT scans and intraoral scanners.  
All patients were operated upon under general anaesthesia.  
The choice between single jaw surgery and bimaxillary surgery was based on the cephalometric analysis carried out using Dolphin software and on the soft tissue profile analysis: bimaxillary surgery was performed when there was a discrepancy \(\leq\)0 degrees between the angles SNA and SNB and a notable disharmony on an aesthetic level.  
Three patients underwent bimaxillary orthognathic surgery (Le Fort I osteotomy of the maxilla associated with bilateral sagittal split osteotomy), whereas one patient (patient 2) underwent only bilateral sagittal split osteotomy. The bone segments were locked with rigid fixation using osteosynthesis plates and screws in all participants. One year after surgery (T1), extraoral and intraoral photos and a CBCT scan were taken for each patient. The 2D virtual radiograms were obtained, as previously described. Among 2D virtual radiograms, the pre- and post-surgical lateral teleraliographies were used to perform hard and soft tissue cephalometric measurements. The acquisition of post-surgical data was performed one year after surgery, that is, when a complete recovery of the soft tissues was achieved.  
In patients treated with aligners, pre-surgical therapy lasted 15 months for patient 1 and 21 months for patient 2; post-surgical treatment lasted 33 months for patient 1 and 25 months for patient 2. On the other hand, in patients 3 and 4 treated with fixed appliances, pre-surgical treatment lasted 3 years, and post-surgical treatment lasted 6 months.