## 2 Materials and Methods
### Methods  
Frontal smiling photographs were taken of each patient using a Canon T3 digital camera (Canon Inc., Tokyo, Japan) assembled with a Canon 100 mm macro lens and circular macro flash (Canon Inc., Tokyo, Japan). Photographs of a posed smile were taken as part of each patient's routine orthodontic data base. Although orthodontic assistants followed a protocol, the photographs were not standardized; they were not taken at a precise fixed distance, and patients' heads were not placed in a head holder. The posed smile is voluntary and not elicited by an emotion, and it can be a learned greeting or a signal of appeasement; it can be sustained and is reliably repeatable. It is not spontaneous and is unstrained and posed. Patients were trained before the photographs (37,38). Each patient in this study had at least four photographs taken, which were reviewed to determine their acceptability and the authenticity of the unstrained posed smile. Each frame was opened in Adobe Photoshop 2020 Version (Adobe Inc., San Jose, CA, USA) and adjusted using the millimeter ruler in the frame; the calibration of all images in the software was performed according to [PERSON] et al. (39). All measurements were performed using the interpupillary line as a \begin{table}
\begin{tabular}{l l l} \hline \hline
**Inclusion Criteria** & **Exclusion Criteria** \\ \hline - & Mixed dentition: intertransitional period & - & Crani discrepancies, syndromes \\  & (presence of permanent lateral and central & or skeletal asymmetries; \\  & incisors and first permanent molars); & - & Previous orthodontic treatment; \\ - & Class 1 molar classification or mild class 2 & - & Previous traumas involving oral soft \\  & molar classification; & & and hard tissue; \\ - & Nonextraction treatment; & - & Missed tooth (traumas, caries, \\  & Minor crowing (1–4 mm) in each dental & & agenesis); \\  & arch evaluated with little index; & - & Absence of dental anomalies \\ - & Absence of crossbite; & (macrodotics or microdotics teeth); \\ - & maxillary contraction; & - & Incomplete or poor quality of records; \\ - & Pre-treatment and post-treatment records & - & Unnatural posed smiles (a smile that is \\  & available (lateral cephalosporars and & not reproducible, and therefore cannot \\  & intraoral and extraoral photographs). & be used as a reference for further \\  & & measurements). \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Inclusion and exclusion criteria applied to the sample. horizontal reference axis and its perpendicular (true vertical line) as a vertical reference (Figure 1). The appliances used for the CAs group were fabricated using the Invisalign(r) First protocol [40] (Align Technology Inc., Tempe, AZ, USA), and 22 to 40 aligners were used for each arch. Only one revision set of aligners was used. There were no restrictions on the number of attachments that could be placed; no auxiliaries other than Invisalign(r) attachments were used. Tooth movement started from the first aligner. All subjects were instructed to wear each aligner full time, excluding during meals and tooth brushing. The programmed dental movements were expansion of the first molars and simultaneous mesial, out of 1.6 and 2.6, with an addition of radiculo-buccal torque, expansion of the middle sectors of the arch; sequential radiculo-buccal torque (to follow the coronal expansion movement), alignment of the frontal group--leaving 1 mm of mesiodistal space to the deciduous canines--and adjustment of the coronal-buccal torque (to avoid making the crowns lingual). Expansion was considered adequate when an overcorrection of 2 mm per side was achieved in the posterior and middle sectors. Each aligner was changed every 7 days. Every four stages, the clinician checked for good aligner fit and the position of the attachments. The mean treatment time for the CAs group was 12 m \(\pm\) 3 m (months).