## 2 Materials and Methods
In each of these models, there was a simulation of a horizontal periodontal breakdown via a reduction of 1 mm of PDL and bone (from 0 to 8 mm of loss), obtaining for each of the nine intact periodonotin models nine models with various levels of bone loss (totaling 81 models analyzed in the study), Figure 1A-C. The intact periodonotin models had 5.06-6.05 million C3D4 tetrahedral elements, 0.97-1.07 million nodes, and a global element size of 0.08-0.116 mm (Figure 1A). An \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Material** & **Young’s Modulus, E (GPa)** & **Poisson Ratio, \(\
u\)** & **Refs.** \\ \hline Enamel & 80 & 0.33 & [7,10,11,13,24,25] \\ Dentin/Cementum & 18.6 & 0.31 & [7,10,11,13,24,25] \\ Pulp & 0.0021 & 0.45 & [7,10,11,13,24,25] \\ PDL & 0.0667 & 0.49 & [7,10,11,13,24,25] \\ Cortical bone & 14.5 & 0.323 & [7,10,11,13,24,25] \\ Trabecular bone & 1.37 & 0.3 & [7,10,11,13,24,25] \\ Bracket (stainless steel) & 190 & 0.265 & [7,10,11,13,24,25] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Elastic properties of materials. Figure 1: Mesh model: (**A**)—2 nd lower right premolar model with intact periodonotin, (**B**)—with 4 mm bone loss, (**C**)—8 mm bone loss, (**D**)—element warnings in dentine component, (**E**)—element warnings in PDL component, (**F**)—element warnings in bracket and enamel components, (**G**)—dentine component (red) with dental pulp-NVB (orange) and bracket (green), (**H**)—tooth (enamel-blue, dentine-red) with bracket (green) and NVB (orange), (**I**)—PDL component (grey), (**J**—enamel (blue) and bracket (green) components, (**K**–**O**) applied load vectors: (**K**)—extrusion, (**L**)—intrusion, (**M**)—rotation, (**N**)—tipping, (**O**)—translation. other aspect that must be acknowledged (i.e., due to manual anatomical reconstruction) is the presence of a reduced number of surface anomalies/irregularities in all models (Figure 1D-F), with no error warning to be found. Thus, in Figure 1D-F, some of element warnings for one of the nine intact periodontitis were displayed: D for dentine, 22 element warnings (0.004%) from 540,969 elements; E for PDL, 20 element warnings (0.00835%) from 23,970 elements; F for enamel and bracket. 17 element warnings (0.0136%) from the 124,532 elements. Nevertheless, the quasi-continuity of the models in areas affected by stress was maintained; thus, the accuracy of the simulations was found to be high. The internal control and safety check of both software (i.e., image reconstruction and finite elements analysis) do not allow the next phase of the process to be completed if errors or too many anomalies are present, an aspect that was not seen in our study. As in all earlier dental studies, the physical properties were linear elasticity, homogeneity, and isotropy; perfectly bonded interfaces; and model bases with zero displacements. All these properties were found acceptable because of their almost exclusive use in all earlier FEA studies and due to the fact that both applied forces (0.5 N) and displacements are extremely small [7; 10; 11; 13; 24; 25]. The applied forces were of 0.5 N (approx. 50 gf) directly to the base of the bracket, simulating intrusion, extrusion, rotation, translation, and tipping (Figure 1K-O). The amount of force was selected because it is small enough to be safely applied to both intact and reduced periodontitis and to produce orthodontic movements and because it allows the results obtained here to be compared with our previous FEA simulations (using the same conditions as herein) over PDL, dental pulp and NVB, and tooth [10; 11; 13]. The finite elements analysis totaled 405 simulations employing Abaqus 6.13-1 software (Dassault Systemes Simulia Corp., Stationsplein 8-K, 6221 BT Maastricht, The Netherlands) and the five most used failure criteria: Von Mises (VM), Tresca (T), Maximum Principal Tensile (S1), Minimum Principal Compressive (S3), and Hydrostatic Pressure (HP).