# Using FEM to Assess the Effect of Orthodontic Forces on Affected Periodontium
## 4 Discussion
Strain of anterior teeth is reported to be concentrated in the cervical region at the top of the alveolar crest, and it increases even more as the bone level decreases. Moreover, this strain increases even more in subjects with excessively inclined anterior teeth This is a common side effect that is usually addressed during orthodontic therapy of periodontally compromised patients. To avoid the deformation of the alveolar ridge crest in these cases, [PERSON] and [PERSON] recommend displacements of less than 0.18 mm for normal alveolar bone, 0.15 mm for 1/3 resorption, and 0.10 mm for 1/3-1/2 resorption [32]. The values of displacement resulting from the application of force maintain a significant linear increase in our study, coupled with the increase in the magnitude of the applied force, with no significant differences for no periodontal disease and 33% bone loss. However, in the 66% bone loss, the values of f are significantly greater, both compared to the intact periodontium and to the 33% group, depending on the magnitude of the applied force. One study that analyzed the biomechanical properties of desmodontium to assess intrusion through orthodontic force of 0.5, 1, and 3 N found that the location and the applied force levels were statistically significant in their effects on the modulus; the apical part also had greater stiffness. In this study, however, the authors proposed a heterogenous periodontium in which the modulus varied in relation to location [33]. The maximum equivalent tension in the tooth-periodontal ligament-alveolar bone complex (\(\sigma\) ech) is most affected by the magnitude of the applied force; close behind is tension in the direction of the force (\(\sigma\) c), but the displacement values (f) were not affected significantly by the magnitude of the applied force. Another significant aspect that must be taken into account is orthodontic appliance placement [34]. Research has pointed out that increasing the length of the brackets' hook can reduce the stress on the periodontal ligament. Thus, a 7 mm-long hook delivered 22 kPa, while a bracket without a hook, 80 kPa. Moreover, by the apical angulation of the applied force from 0\({}^{\circ}\) to 30\({}^{\circ}\) there was a diminution on the effect of the periodontium stress profile [35]. A more streamlined tooth movement can be obtained, with less stress along on the desmodontium, by simply increasing the length of the bracket hook due to the application of the force closer to the center of resistance. In the lower incisor model, the maximum equivalent tensions and tensions in the direction of the applied force show linear growth when the periodontium is healthy or affected 33%; however, if the periodontium is affected 66%, the increase shows an exponential progression, with significant higher values than those encountered in cases in which the periodontium was unaffected or affected to a lesser degree. Multivariate analysis yielded the predictive factors in the changes of the \(\sigma\) ech and \(\sigma\) c values in the tooth-periodontal ligament-alveolar bone complex. The magnitude of the applied force and the extent to which the periodontium is affected have major impact in the case of lower incisors. However, in the case of displacement as a result of applying a lingualization force, correlation analysis showed that only the extent of periodontal damage significantly influences displacement, but the applied force does not. We also showed that none of the analyzed parameters was significantly influenced by the magnitude of the applied force, values of the tension recorded in the direction of force application, values of equivalent tension at the level of the tooth-periodontal ligament-alveolar bone complex, or values of the recorded displacement. A similar study to ours in design that analyzed a lower premolar model assessed the compressive stress quantitatively and qualitatively in periodontium for a model of gradual periodontal breakdown (0-8 mm) under orthodontic movements.