# Incisors Extrusion with Clear Aligners Technique: A Finite Element Analysis Study
## 2 Materials and Methods  
For this study, a CAD template of a maxillary arch, designed based on ideal proportion of teeth, was used to create six models with different attachment setups. Periodontal ligaments (PDL) for each tooth were modeled on the root shape with a thickness of 0.25 mm, as reported in the scientific literature. The aligners were made as an external offset of 0.5 mm from the surface of teeth (and eventually attachments), which is the thickness of a standard aligner, as stated as a result of repeated measurements with a Micro-CT Scan (SkyScan 1172: Bruker-microCT; Kontich, Belgium) of Invisalign aligners (Align Technology, Inc., San Jose, CA, USA) [6]. Septa between teeth were manually removed, and the aligners were refined to smooth and remove edges and undercuts. All the models were created using CAD software (SpaceClaim Corporation; Canonsburg, PA, USA) and then imported into FE software (ANSYS 18.2, Inc.; Canonsburg, PA, USA).  
In the FE software, teeth, attachments, and aligners were considered as isotropic and homogeneous materials (Table 1). Teeth and attachments were considered as one rigid body, while the difference in rigidity between enamel and dentin was not considered. With the aim of simulating the behavior of the PDL in the best possible way, it was set as a hyperelastic material. According to [PERSON] et al., the interfaces between the PDL and teeth were set as bonded contacts, while the ones between aligners and teeth were set as frictionless contacts. All the external surfaces of the PDL were linked to fixed supports to simulate the effect of the alveolar bone [7].  
After a convergence study performed on a single tooth model, mesh sizes were set at 0.09 mm for all bodies.  
Element type was set as linear for all geometries, with the quadrilateral dominant method being applied to the surface elements of teeth and aligners, while the hex dominant method was adopted for PDL elements.  
The planned extrusion was of 0.1 mm for both central and lateral incisors, and simultaneously performed. The extrusion was planned for each incisor along its own long axis.  
Six simulations were performed:  
* Without attachments (NOATT);
* With horizontal rectangular attachments only on incisors (ATT1-2);
* With rectangular attachments from second molar to canine (ATT3-7);  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Component** & **Young’s Modulus (MPa)** & **Poisson’s Ratio** \\ \hline Teeth & \(1.96\times 10^{4}\) & 0.30 \\ Attachment & \(12.5\times 10^{3}\) & 0.30 \\ Plastic Aligner & 528 & 0.36 \\ PDL & See reference & See reference \\ \hline \hline \end{tabular}
\end{table}
Table 1: Materials’ proprieties.  
ATT3-7 + optimized extrusion attachments on incisors (OTT);
* ATT3-7 + rectangular buccal horizontal attachments on incisors (RETT);
* ATT3-7 + rectangular palatal horizontal attachments on incisors (PALAT).  
Optimized attachments' shapes were derived from the one designed by Align Technology for the Invisalign system. The rectangular attachment shape was 3 \(\times\) 2 \(\times\) 1 mm, like the ones used in the ClinCheck software (Align Technology, Inc., San Jose, CA, USA).  
The adoption of palatal attachments was derived from a similar FE study by [PERSON] et al. [7]  
The following outcomes were analyzed:  
* Teeth displacement pattern;
* Aligner deformation;
* Equivalent stress of PDL;
* Contact pressure between aligner and tooth surface.