## 2 Materials and Methods
The topographical mesh distribution for elements warnings was 201 (0.0039%) of 5,117,355 for the bone, 63 (0.00677%) of 930,023 for the tooth-bracket-PDL, 39 (0.00586%) of 665,501 for the tooth bracket, 26 (0.00459185%) of 566,221 for the dentine, and 17 (0.0141469%) of 120,168 for the enamel-bracket elements. The internal controls and safety checks of both software models (i.e., the image reconstruction and the finite element analysis) do not allow the next phase of the process if errors or too many anomalies are present, an aspect that was not seen in our study. Each of the nine models was subjected to a gradual horizontal periodontal breakdown of 1 mm, ranging from 0 to 8 mm bone loss, thus obtaining a total number of eighty-one models with intact and reduced periodontitis. The FEA simulations (a total of 486) were performed in Abaqus 6.13-1 software (Dassault Systemes Simulia Corp., Stationsplein 8-K, 6221 BT Maastricht, The Netherlands). Five orthodontic movements were simulated over dental tissue (extrusion, intrusion, rotation, tipping, and translation) under three loads of 0.6 N (approx. 60 gf), 1.2 N (approx. 120 gf), and 2.4 N (approx. 240 gf). The boundary condition assumptions were isotropy, homogeneity, and linear elasticity (as in all above-mentioned FEA studies), with perfectly bonded interfaces and the base of the models enclosed (Figure 2). Fixed boundary conditions (i.e., encastre) were imposed at the bottom of the models (i.e., the translations of the FE nodes were restricted; thus, the rotations were also zero). To our understanding, these conditions are representative of and relevant to the studied issues. The failure criterion used were the non-homogeneous ductile materials' Tresca and the homogenous ductile materials Von Mises criteria. The load manager conditions selection was as follows: step procedure--static, general; load type--pressure; load status--created in step, distribution--uniform; magnitude--depending on the surface area; and amplitude--ramp. The Abaqus boundary condition manager selection was as follows: step procedure--static, general; boundary condition type--symmetry/antisymmetric/encastre; boundary condition status--created in step. Although the numerical domain was large (around 6 million FE), the analysis time was reasonable, due to the following considerations: linear elastic analysis (no change in structural stiffness), a small amount of force per each load increment (thus, the stress concentrations are avoided), stable mesh with a negligible number of poor shaped FE, and perfect bond between the biological parts. The load selection of 0.6 N was motivated by the fact that it was lower than 1 N (mechanically important), and closer to the loads selected for other simulations in our research project. 1.2 N was selected, since it was a little bit higher than 1 N and was double the first one. 2.4 N was selected, being the double of the second one, and closer to the other above-mentioned FEA studies, to enable correlations. The simulations displayed qualitative (color-coded projections of the maximum amount of stress--red/orange = high, yellow-green = moderate, blue = low) and quantitative (in KPa) results for PDL and correlated them with the 16 KPa of MHP to evaluate the ischemic and resorptive risks during the periodontal breakdown process. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Material** & **Young’s Modulus, E (GPa)** & **Poisson Ratio, v** & **Refs.** \\ \hline \hline \multicolumn{1}{c}{} & 80 & 0.33 & [1,21–25] \\ \multicolumn{1}{c}{} & 18.6 & 0.31 & [1,21–25] \\ \multicolumn{1}{c}{} & Pulp & 0.0021 & 0.45 & [1,21–25] \\ \multicolumn{1}{c}{} & PDL & 0.0667 & 0.49 & [1,21–25] \\ \multicolumn{1}{c}{} & Cortical bone & 14.5 & 0.323 & [1,21–25] \\ \multicolumn{1}{c}{} & Trabecular bone & 1.37 & 0.3 & [1,21–25] \\ \multicolumn{1}{c}{} & Stainless steel & 190 & 0.265 & [1,21–25] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Elastic properties of materials.