## 2 Materials and Methods
The skull image was oriented according to NHP in the three planes of space perpendicular to each other, as shown in previous studies [19]: the transverse plane coincides with the Frankfurt plane (FH), a plane passing through two points: Orbital (Or) and Porion (Po); the sagittal plane coincides with the mid-sagittal plane (MSP), a plane perpendicular to the FH plane and passing through two points: Crista Galli (Cg) and Basion (Ba); the coronal plane coincides with the anteroposterior (PO) plane, perpendicular to the FH and MSP, passing through the right and left portion. After the orientation of the head, the virtual 2D radiograms were extracted in the following sequence:  
Lateral teleradiography, on which the cephalometric analysis, according to [PERSON], is performed  
- orthopantomography,  
- TMJ stratigraphy,  
- cross sections,  
- posteroanterior teleradiography,  
- superior and inferior submento-vertex  
- virtual reconstruction of right and left masseter muscles. Subsequently, extraoral photos (patient's face in frontal, in the right, and left side views) and intraoral photos (frontal, right, and left lateral photos, and upper and lower occlusal photos) were performed, and the dental arches were scanned using an intraoral scanner, which allows detecting details with an accuracy up to 7 \(\upmu\)m.  
The virtual setup for each subject was planned, and aligners were manufactured. At the end of clear aligner therapy (T1), extraoral and intraoral photos, pain assessments (through VAS and muscular palpation), and a CBCT scan were taken for each patient, and 2D virtual radiograms were obtained, as previously described. For each upper and lower tooth, from right to left, the first molar, the changes in root position, torque, and root length were evaluated by analyzing the cross sections at the start (T0) and the end (T1) of the treatment. Table 1 shows the number of measurements for the type of tooth of each arch taken into consideration in this study. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Tooth**} & **Measurements T0** & **Measurements T1** & **Tot. Measurements** \\  & **(n°)** & **(n°)** & **(n°)** \\ \hline Central incisor & 56 & 56 & 112 \\ Lateral incisor & 56 & 56 & 112 \\ Canine & 56 & 56 & 112 \\ First premolar & 56 & 56 & 112 \\ Second premolar & 56 & 56 & 112 \\ First molar & 56 & 56 & 112 \\ From central incisor & 336 & 336 & 672 \\ to first molar & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Number of measurements for type of tooth in each arch. The effectiveness of movement, that is, the evaluation of the sagittal root position in the alveolar bone, was performed by comparing pre-treatment and post-treatment root positions relative to the orofacial cortical plates in the cross sections at T0 and T1 stages. The sagittal root position was qualitatively evaluated in the midsagittal view according to the rating scale reported by [PERSON] et al. [20] and modified by [PERSON] et al. [21] (Figure 1): In class I, the root is positioned against the labial cortical plate (A); in Class II, the root is centred in the middle of the alveolar housing without engaging either the labial or the palatal cortical plates at the apical third of the root (B); Class III, the root is positioned against the palatal cortical plate (C); Class IV, at least two-thirds of the root is engaging both the labial and palatal cortical plates (D); and Class V, the root is positioned outside the labial cortical plate (E). Pre-treatment and post-treatment faciolingual inclinations, that is, torque, of each upper and lower tooth from right to left first molar, were measured as the angle formed by the projection of the tooth's long axis on the faciolingual plane and the line of intersection between the faciolingual and mesiodistal planes by the University of Southern California (USC) root vector analysis software program [22] (Figure 2). If the root center were lingual to the crown center, the torque measurement would be positive; otherwise, it would be negative.