## 4 Discussion
Moreover, the anatomical accuracy of the analyzed PDL 3D models is also important (e.g., earlier studies employed models that were based on ideal anatomical data, with no mention of the mesh validating the means). There is a strict correlation between the failure criteria, boundary conditions, and anatomical accuracy of a FEA, to provide accurate results as in the engineering field [1]. Thus, if these correlations are not met, the FEA lacks accuracy [1]. There are many FEA studies in the current research flow; however, only a limited number qualify to be used for correlations (e.g., [PERSON] et al. [5] reported only 25 from 110 examined), and none completely addressed the above-mentioned issues [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. [PERSON] et al. [3; 4] assessed the differences in linear vs. non-linear reporting for intact PDL differences of 20-50% (maximally central incisor, 148,097 elements and 239,666 nodes). However, despite applying 0.2-1 N intrusion and tipping, the employed failure criteria were brittle, like S1 and S3 (with plastic deformation, no recovery of the original form, and cracking/destruction), despite assessing the biomechanical behavior of a ductile-like material (with elastic deformation and recovery of the original form). Quantitatively, their stresses were higher than here (S1, 1 KPa crucially, 0.2 N intrusion; \(-16.4\) KPa apically, 1 N of tipping/S3 \(-13.37\) KPa apically, 0.2 N intrusion; 16.4 KPa apically, 1 N of tipping). Thus, their result's accuracy is at least debatable, due to their use of brittle-like criteria instead of ductile-like criteria, which significantly alters the biomechanical behavior, as reported in other FEA simulations [21; 22]. The employed boundary conditions were isotropy, homogeneity, and linear elasticity for all model's components (except the PDL's nonlinearity). A new trend in PDL numerical simulations is to employ hydrostatic [6; 7; 8; 9; 10; 11; 12] pressure as a failure criterion, combined with the Ogden hyper-elastic model [5], with little correlation with the MHP. It must be emphasized that the hydrostatic pressure is a criterion specially created for liquids (with no shear stress), while the PDL's anatomical internal micro-structure, containing collagen fibers displayed as variously orientated dense fiber bundles with interposed NVB and rich circulatory vessels [22], is different from that of a liquid. Moreover, the Ogden hyper-elastic model was specially created to describe the non-linear behavior of complex materials, such as rubbers, polymers, and biological tissues (e.g., cells), and, due to PDL's anatomical internal micro-architecture, this model is not suitable. The boundary conditions employed were isotropy, linear elasticity, and homogeneity (except PDL with non-linearity). Thus, based on the above-mentioned issues, these FEA results raise a series of questions related to their results' accuracy. Moreover, [PERSON] et al. [6; 7; 8] reported, for intact PDLs, various optimal forces (ranging 0.28-3.31 N) for canine, premolar, and lateral incisors, with significant differences found for the same tooth (e.g., canine: rotation 1.7-2.1 N [6] and 3.31 N [8]; extrusion 0.38-0.4 N [6] and 2.3-2.6 N [7]; premolar: rotation 2.8-2.9 N [8]), which were much higher than either our 0.6-1.2 N, those reported by [PERSON] et al. [20] (0.1-1 N), or [PERSON] et al. [3; 4] (0.3-1 N). [PERSON] et al. [9; 10], employing the same hydrostatic pressure (same boundary conditions) on an intact PDL, reported, for 0.5-1 N intrusion, apical third stresses of 9.95e-00 TPa (vs. our 5.21-5.99 KPa for 1.2 N of intrusion). This huge amount of stress implies the destruction of the apical third, as this exceeded not only the 16 kPa of the MHP but also the dentine's maximum shear stress of 29-104 MPa [1], contradicting all clinically available data [20].