# Using FEM to Assess the Effect of Orthodontic Forces on Affected Periodontium
## 4 Discussion  
Currently, there is no consensus as to what the optimal force for orthodontic tooth movement should be; however, most agree that it is up to 1 N [21; 22]. Although this may be true theoretically, in practice it is difficult to control and assess the precise force applied to every tooth. As the force magnitude increases, so do the potential unwanted side effects such as undesired tooth movements, external apical root resorption, hyalinization, and patient discomfort [21; 23; 24]. Due to the inconsistencies in the literature and because of the theoretical nature of the study, we considered various force magnitudes in our simulation, up to 5 N, to illustrate the effect on periodontal tissues of different force magnitudes on various scenarios of bone loss. In the case of 1 N force, we noted that when the profound periodontitis tissues are intact, the forces are evenly distributed along the central region of the root of the central lower incisor, both on the buccal and lingual areas. As the periodontal tissues start to break down, the stress concentrates to a narrower area, mostly around the tooth's center of rotation. Finally, as the bone loss reaches 66% the crown of the tooth is lingualized, while the root is bucally inclined. The area of maximum tension is in the vestibular apical third. Even though in all three scenarios the force magnitude was the same (1 N), the biomechanical behavior of the tooth was different due to the contrasting periodontal status: intact, moderate, and severe periodontal breakdown. Our results were similar to those found in the literature that considered orthodontic tooth movement on an intact desmodontium and observed that the stresses were concentrated in the apical root area in the case of the application of a purely intrusive, extrusive, or rotational force [25; 26; 27; 28]. For the tipping movement, the main stress area was situated at the alveolar crest while for bodily movement, it was throughout the desmodium [25]. In contrast, others have argued that the morphology of the alveolar bone dictated the stress-strain observations and due to the nonlinear behavior of the desmodontium different areas of compression and tension cannot be detected; thus, light continuous forces are recognized as intermittent by the periodontal ligament [29]. In the case of an affected desmodontium, one study reports results similar to ours in the case of applying a 1 N force on an incisor and showed that as the severity of the bone loss upsurges the amount of tooth movement increased to a maximum of 2.60 mm [30]. The lateral lower incisor has similar patterns of stress distribution and movement to the central incisor; as bone loss aggravates, so does the lingualization of the teeth. If the periodontal tissue is intact, it is able to absorb and compensate for the heightened forces to a certain degree, even those exceeding the accepted physiological values for orthodontic tooth movement. However, in the case of a reduced periodontium lingualization is observed, in this case the tissues are no longer able to compensate, and the areas of maximum stress  
Figure 14: Regression line of the correlation (**a**) \(\sigma\) ech, (**b**) \(\sigma\) c, and (**c**) f vs. applied force. are unevenly distributed. [PERSON] et al. considered both linear and nonlinear models of the periodontal ligament of a mandibular premolar and after applying extrusive and tipping forces examined the minimum and maximum principal stresses and von Mises stresses in the desmodontium. When the periodontium was given nonlinear mechanical properties, the stresses were substantially different from the uniform thickness model; in the apical and cervical area the stresses were significantly increased when compared to the linear model [31]. Considering the fact that in our study the periodonotin was linear, a nonlinear analysis might yield even more dramatic results in the case of reduced bone level. Optimal orthodontic movement should be calibrated to the degree of periodontal disease progression.