## 2 Materials and Methods  
Institutional review board approval (#829885) from the University of Pennsylvania was approved prior to collecting any CBCT information. CBCT scans of 54 untreated Caucasian adult patients (12 males and 42 females) between the ages of 18 and 65 were obtained from a private orthodontic practice with an I-CAT machine (Imaging Sciences International, Hatfield, PA, USA) in 0.3 mm voxel size. The inclusion criteria were: (1) no prior orthodontic treatment; (2) minimal dental wear; (3) no missing teeth other than third molars; and (4) less than 5 mm crowding per arch. The exclusion criteria were: (1) presences of remaining primary dentition; (2) posterior crossbite; (3) crowns or significant restorations on any first molars; (4) extensive dental restorations and wear; and (5) craniofacial deformities. The sample size was pre-determined based on the previous studies [3; 4]. In addition, the sample size was calculated based on an alpha significance level of 0.05 and 80% power to detect an effect size (\(\rho\)) of 0.36 between measurements. The power analysis showed that at least 46 patients were needed. Using Dolphin Imaging 3D software (version 10.5, Dolphin Imaging and Management Solutions, Chatsworth, CA, USA), each image was oriented so that the occlusal plane was parallel to the floor. To extract a two-dimensional (2D) lateral cephalogram, each scan was compressed from the right outermost portion of the patient's head to the center of the left central incisor, as described by [PERSON] et al. [12]. This 2D extracted lateral cephalogram was used to make vertical cephalometric measurements. The following measurements were taken and evaluated for each patient's lateral cephalograms: FMA (FH to mandibular plane, in degrees), SN-GoGn (SN to GoGn, in degrees), and PFH:AFH (poster facial height to anterior facial height ratio):  
* Porion (Po): the most superior point of the external auditory meatus. * Orbitale (Or): the most inferior point of the orbital rim. * Sella (S): the geometric center of the pituitary fossa located by visual inspection. * Nasion (N): the most anterior point of the frontonasal suture. * Gonion (Go): the mid-point between the best fit lines tangent to the posterior and inferior border of the mandible. * Gnathion (Gn): the midpoint between the most anterior and inferior points of the symphysis. * Menton (Me): the most inferior point on the mandibular symphysis. * Frankfort horizontal (FH) plane: the line connecting the porion and orbitale. * Mandibular plane: the line tangent to the lower border of mandible. * SN: the line connecting the sella and nasion. * GoGn: the line connecting the gonion and gnathion. * Poster facial height to (PFH): S to Go* mm (*constructed Gonion). * Anterior facial height (AFH): N to Me**mm (**Menton). * Frankfort-mandibular plane angle (FMA): the angle formed by the intersection of the FH plane and the mandibular plane. * SN-GoGn: the angle between a line through sella to nasion and a line through gonion and gnathion. The axial section at the mandibular first molar was taken at the furcation. In this view, the anteroposterior and mesolateral midpoints were determined. The sagittal section at the mandibular first molar was confirmed at the line through the midpoint of mesiodistal crown width and midpoint between mesial and distal roots at 1/3 the distance from apex. The coronal section obtained at 0.5 mm slice was to measure tooth and bone inclination. Separate left and right coronal sections were taken for higher accuracy. Tooth inclination was obtained by measuring the angle between the vertical line and a line made by connecting the midpoint of the buccal and lingual cusp tips and the midpoint of the buccolingual width at the level of the cementoenamel junction, as described by [PERSON] and [PERSON] (Figure 1a,b) [3]. Alveolar bone inclination was also measured in the same 0.5 mm coronal section obtained to measure first molar inclinations.