## 4 Discussion  
Our FEA study assessed the differences between the only two failure criteria that are biomechanically suited for dental tissue numerical studies (due to their acknowledged ductile resemblance) [1]. Additionally, by approaching the boundary condition issues, our study aimed to improve the accuracy of FEA dental studies. The present analysis was conducted on 81 3D models (with 0-8 mm bone loss) and 486 FEA simulations. This research was the first of this type to investigate the boundary conditions used in the FEA, correlated with the proper material-based failure criteria and with the MHP. Both analyzed criteria (Tresca and VM) displayed similar qualitative stress distribution areas for all three loads, levels of bone loss, and orthodontic movements. Quantitatively significant differences were seen. For both criteria, the quantitative amounts of stress doubled (1.2 N) and quadrupled (2.4 N) when compared with 0.6 N, with Tresca being 15% higher than VM, as expected [1; 21; 22; 23]. The stress and ischemic and resorptive risks increase were directly correlated with bone loss and load increase. The rotation, translation, and tipping were the most stressful movements for the PDL and the most prone to ischemia and further periodontal resorption. All quantitative stresses were lower than the maximum amount of physical properties of the tooth and the surrounding periodontitis components [27; 28; 29; 30]. In both intact and reduced periodontitis, qualitatively, the rotation, translation, and tipping caused the most stress in the cervical third of the PDL (an area less vascularized than the other two thirds), while the intrusion and extrusion, despite being the least stressful, caused stress across the entire PDL (in agreement with clinical behavior). This stress distribution needs to be considered when dealing with various levels of bone loss, since, if the same applied load is kept for bone loss as for an intact periodontitis, the amount of stress is higher and the ischemic and resorptive risks progressively increase. Thus, 1.2 N can be safely applied to an intact periodontitis, while 2.4 N could produce mild to moderate ischemic and resorptive risks in the cervical third of the PDL (especially for the rotation, translation, and tipping movements), due to the reduced vascularization when compared with the apical third. It also must be noted that, clinically, there are rarely pure orthodontic movements (as here) and, usually (due to their combination), the amount of combined stress is lower than here. The same load amount (0.6-1.2 N) was also safe for extrusion and intrusion for the reduced periodontitis, since a smaller stress exceedance of the MHP was displayed, and only in the cervical third of the PDL. Mild to moderate ischemic risks were predictable for a 2.4 N load with more than 4 mm of loss, since the stress exceedance was seen across the entire PDL (especially in the cervical third). For the other three more stressful movements (i.e., rotation, translation, and tipping), 1.2 N seemed to be safe for up to 4 mm of loss, whereas, after this level, moderate ischemic and resorptive risks were visible for the cervical third of the PDL (e.g., where qualitative stress display was visible). However, 2.4 N seemed to produce moderate risks for the cervical third of the PDL, especially after 4 mm of loss (due to the high exceedance of the MHP ranging from 5 to 17 times). Based on the above results, 4 mm of periodontal loss seems to be a reference point in orthodontic treatment, signaling an increase in the ischemic and resorptive risks if the same applied loads are kept as for an intact periodontium. Thus, after 4 mm of loss, to avoid any degenerative risks (i.e., pulpal and periodontal), a load of more than 1 N (approx. 100 gf) should be carefully considered, especially for movements of rotation, translation, and tipping. These results agree with [PERSON] et al.