## 4 Discussion
Other studies, using the same above-mentioned conditions, reported lower amounts of stress for the apical and cervical thirds of an intact PDL, i.e., 10-20 KPa [11], \(-5.8\) KPa [5] for tipping, and \(-4.7\) KPa [5] for intrusion, when 0.25 N were applied. Higher amounts of stress were reported by [PERSON] et al. [22] for 0.5 N of intrusion (\(-13.68\) KPa apically, and 18.86 KPa acrically), when performing a comparative study among five failure criteria. [PERSON] et al. [12], in a recent study with the conditions of 0.1-1.5 N of intrusion, a maxillary central incisor, linear elasticity, homogeneity, and isotropy, hydrostatic stress, and S1, reported that results with assumed isotropy, homogeneity, and linear elasticity as boundary conditions were closer to clinical and animal studies, despite other studies [3; 4; 5; 13] reporting the opposite. Nevertheless, hydrostatic and S1 failure criteria are not suitable for FEAs of PDL. Moreover, they reported no stress in the cervical third of the PDL for intrusion (which is biomechanically incorrect). The [PERSON] FEA studies (which were mechanically and behaviorally better for PDL [1; 21; 22; 23; 24; 25]) also employed isotropy, homogeneity, and linear elasticity/non-linear elasticity, and reported variable results (both qualitative and quantitative) when correlated with the present results. [PERSON] et al. [13] investigated 1 N of extrusion in the PDL (with uniform vs. non-uniform thickness, linear vs. non-linear, VM, and S1/S3) of a lower premolar, reporting a higher amount of stress for linear non-uniform thickness (17.7 Kpa vs. 14.8 Kpa, the middle thirds), with a similar stress distribution, but with the highest stress in the apical third (vs. in the cervical third in the current study). The non-linear non-uniform PDL displayed the highest stress of 29.3 KPa apically (while measuring 0 KPa in the middle and 8.99 KPa in the cervical thirds). Our present stress distribution for extrusion displayed stress across the entire PDL, with the highest amount of stress being 11.64 KPa excrically and 5.21 KPa in the middle and apical thirds for 1.2 N, disagreeing with [PERSON] et al. 's [13] simulation. The 1 N tipping for a non-uniform and non-linear PDL reported 6.34 Kpa of stress apically and 6.49-8.86 KPa excrivedly vs. 2.69 KPa apically and 21 KPa excrivedly in the present study for 1.2 N. [PERSON] et al. [13] reported differences between the linear (the cervical and middle thirds' stress) vs. non-linear (apical third stress) for ductile-like VM. The reported quantitative differences were variable, being up to 2.4 times higher for the non-linear brittle-like S1 apical stress when compared with the linear, and lower for the non-linear in the middle third. These results contradicted [PERSON] et al. [3; 4], [PERSON] et al. [1; 21; 22; 23; 24], and the present distribution. However, it must be remembered that their lower premolar model consisted of only 1674 elements and 5205 nodes, artificially designed, with a sample size of one vs. the more complex models (e.g., 6.05 million here, and 239,666 nodes and 148,097 elements in [PERSON] et al. 's [3; 4]). [PERSON] et al. [5], in a recent systematic review study (1999-2019), assessing the constitutive models of PDL and with MHP correlations, found only 25 FEA studies of PDLs (most of them are also referenced here) from a total of 110, with only 10 assessing the correlation's quantitative results with MHP, 20 studies assuming linear elasticity, 3 studies hyper-elasticity, and 1 study non-linearity. He also analyzed an idealized premolar (VM, S1, S3, hydrostatic pressure), considering isotropy, linearity, and homogeneity for all models' components (except the PDL considered non-linear), with 1.67 million elements, and under 0.25 N-2.25 N of intrusion and tipping. There was no discussion, however, about the suitability and accuracy for the PDL study of these failure criteria from a physical-mechanical viewpoint (as above-mentioned).