# Estimation of Distances in 3D by Orthodontists Using Digital Models
###### Abstract  
In the field of orthodontics, digital dental arch models are increasingly replacing plaster models in orthodontic diagnostics. This change in interface from physical plaster models to digital image-based models raises the question of how orthodontists interpret intra- and inter-arch relationships from an image on a screen. In particular, the issue of the accuracy of the distances estimated on numerical models is crucial since the estimation of distances is the basis of the therapeutic decision-making process. Studies have shown that distances were well estimated on plaster models, but no study has verified this point on numerical models. This is the question that our study addresses. The experimental protocol consisted of collecting estimates of measurements made by orthodontists using digital models. The reliability of these measurements was then assessed by comparing them to the actual physical distances. We asked 31 orthodontists (19 women and 12 men; an average age of 37 years) to generate 3D model-based measurements of seven different elements: mandibular congestion, the maxillary interpolar distance, Spee's curve, 16/26 symmetry, the right canine class, overbite, and overbite. These values were then compared to the actual measurements calculated using Insignia software (ORMCO Corporation: Brea, CA, USA), using single sample \(t\)-tests. This test makes it possible to compare a distance estimated by the participants with a reference value, which corresponds here to the real distance. The results indicate that, overall, the distance estimates made on the 3D models differ significantly from the actual distances measured using the Insignia software. This was particularly so for mandibular crowding (test value = 0; t (30) = 10.74; \(p\leq 0.01\)), test value = 1; t (30) = 6.23; \(p\leq 0.01\)). Although no study has focused on distance estimation on numerical models in the field of orthodontics, our results agree with the conclusions of studies showing that distances are not estimated in the same way in real environments and virtual environments. Additional studies will make it possible to identify more clearly the parameters (individual factors, equipment, etc.), which make it possible to improve the estimation of distances in the practice of orthodontics. In any case, these studies are necessary to improve the training of future practitioners in the use of virtual models for decision-making and to support them in the digital transition.  
Orthodontics; digital models; virtual reality; distance estimation +
Footnote †: journal: Applied Sciences  
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among others. Today, medicine is one of the most important areas of application of virtual reality [4], for example, for diagnosis or therapeutic planning. Indeed, advances in medical imaging and advances in computing power have made simulated images much more realistic and much faster to generate, thus allowing the reconstruction of three-dimensional anatomical entities and offering practitioners the possibility to interact directly with this imagery [4].  
Many fields of health are concerned, such as, for example, the treatment of a painful chronic handicap. Techniques using progressive motor imagery and VR can help manage the fear of moving or help make a movement that would normally be too painful [5]. VR is also used to treat anxiety disorders such as phobias [6], where an interactive space is created in which the patient is confronted with his situation or his phobic object. In addition, in the field of surgery, a remote control makes it possible to act on a virtual model by means of a virtual robot: the actions are first carried out in the virtual environment before being transmitted to the operator performing the operation, thereby allowing the procedure to be tested before being performed on the patient [7]. There are also various applications for the learning and training of medical personnel based on surgical simulators and software exploration of the human body [8].