# Estimation of Distances in 3D by Orthodontists Using Digital Models
## 2 Method
### Materials  
The estimations of distances were carried out on 5 3D digital models (obtained with Insignia(r) software), derived from 5 clinical cases (Figure 2). The choice of these 5 cases (also used in the study by [PERSON] et al.) was based on the objective of allowing the practitioners to make estimations on a varied panel of orthodontic malocclusions comprising all of the types of dental-maximillary dysmorphisms in the three dimensions of space. The characteristics of the different malocclusions are reported Table 1.  
The digital models were displayed on the same computer, by the same operator, and under the same conditions for each of the 31 practitioners. The participants had the option to change the orientation of the view of the model. The collection of distance estimates was carried out as follows: after observing the virtual models of each clinical case on the screen, the practitioner verbally gives their distance estimates for each of the 7 variables to the operator, who writes them down in a table.  
\begin{table}
\begin{tabular}{c c} \hline Case no. 1 & Class I with moderate crowding of the arch \\ \hline Case no. 2 & Class II with pronounced incisor supraclusion \\ \hline Case no. 3 & Class II with a significantly increased overjet \\ \hline Case no. 4 & Class II incisor infraclusion \\ \hline Case no. 5 & Class II with malposition of the mandibular incisors \\ \hline \end{tabular}
\end{table}
Table 1: Presentation of the five clinical cases used in our study.  
Figure 2: The five clinical cases used for distance estimation.  
The variables to be estimated:  
For each of the models, each practitioner had to estimate 7 quantifiable variables. These estimates were carried out on the 5 virtual models mentioned (5 \(\times\) 7 = 35 estimates by orthodontist) without the possibility of making direct measurements (they were only estimates). The variables selected were similar to those of the study by [PERSON] et al. [46]:  
These variables were the following (Figure 3):  
* Crowding of the mandibular arch: the amount of space required for proper alignment of the teeth in the arch (volumetric reconstitution, intra-arch measurement);
* Spee's curve--the curve formed by the projection in a sagittal plane of the buccal cusps of the mandibular teeth (vertical dimension, intra-arch measurement);
* Antero-posterior symmetry of the first permanent maxillary molars (teeth 16 and 26) while taking their mesial side as a reference (sagittal dimension, intra-arch measurement);
* Inter-molar distance of 16/26 (horizontal dimension, intra-arch measurement): distance separating the mesiobuccal cusp of the first permanent maxillary molars (teeth 16 and 26);
* Right canine class according to [PERSON]'s classification [47] based on the mesiodistal relationship of the teeth (sagittal dimension, inter-arch measurement);
* Overjet of 11/41--the gap as assessed on to the occlusal plane between the buccal side of the mandibular incisors and the occlusal edges of the central maxillary incisors (sagittal dimension, inter-arch measurement);
* Alignment of 11/41--Alignment of the mandibular incisors by their opposing maximalies (vertical dimension, inter-arch measurement).  
The question that we wanted to address was the performance of the orthodontist's estimate compared to the measurements made with software whose reliability in this regard has been demonstrated and which can, therefore, serve as a reference. Indeed, the reliability and precision of the measurements made using different software have already been demonstrated [47; 48; 49]. The actual measurements were calculated for each case by the same operator using the Insignia(r) software (ORMCO Corporation: Brea, CA, USA) and then verified by a second operator.  
For each of the 7 variables, the difference in the absolute value between the estimation of the measurement by the practitioner and the measurement of the variable carried using the Insignia(r) software was determined.  
Figure 3: Presentation of the seven estimated variables.