# Using FEM to Assess the Effect of Orthodontic Forces on Affected Periodontium
## 3 Results
### Lower Lateral Incisor (LLI)  
3.2.1 Equivalent Tension in the Tooth-Periodantal Ligament-Alveolar Bone Complex (\(\sigma\) ech)  
For both lower central and lateral incisors, the \(\sigma\) ech values showed linear growth, depending on the force applied when the periodontium was healthy or affected 33%. If the periodontium was affected 66%, the increase of \(\sigma\) ech showed exponential evolution. Correlation analysis showed that both the magnitude of the applied force (\(\beta\)f = 0.56, \(p\) = 0.018) and the extent to which the periodontium is affected (\(\beta\)AfP = 0.57, \(p\) = 0.017) have a significant impact on the values of \(\sigma\) ech for lower lateral incisors (Table 6).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Correlation** & **Std. Err.** & **B** & **Std. Err. B** & **t** & **\(p\)** \\
**Coefficient (Beta)** & **(Beta)** & & & & & **95\% CI** \\ \hline
**Partial correlation \(\sigma\) ech** & & & & & & \\
**vs.** & & & & & & \\ \hline Intercept & & & \(-\)837.143 & 249.0675 & \(-\)3.36111 & 0.008 \\ \hline Applied force & 0.659321 & 0.166887 & 4.260 & 1.0783 & 3.95071 & 0.003 \\ \hline Periodantal damage & 0.560924 & 0.166887 & 8.207 & 2.4416 & 3.36111 & 0.008 \\ \hline
**Partial correlation \(\sigma\) c** & & & & & & \\
**vs.** & & & & & & \\ \hline Intercept & & & \(-\)862.383 & 256.3378 & \(-\)3.36424 & 0.008 \\ \hline Applied force & 0.656882 & 0.167272 & 4.358 & 1.1098 & 3.92702 & 0.003 \\ \hline Periodantal damage & 0.562749 & 0.167272 & 8.454 & 2.5129 & 3.36427 & 0.008 \\ \hline
**Partial correlation f** & & & & & & \\
**vs.** & & & & & \\ \hline Intercept & & & \(-\)503.908 & 171.6010 & \(-\)2.93651 & 0.016 \\ \hline Applied force & 0.485140 & 0.208293 & 1.730 & 0.7429 & 2.32912 & 0.044 \\ \hline Periodantal damage & 0.611691 & 0.208293 & 4.940 & 1.6822 & 2.93669 & 0.016 \\ \hline \hline \end{tabular} \({}^{*}\) CI, confidence interval; Std. Err., standard error.  
\end{table}
Table 5: Results of the multivariate analysis—partial correlation coefficient \(\sigma\) ech, \(\sigma\) c, and f.  
3.2.2. Tension Registered in the Direction of the Applied Force--Perpendicular to the Tooth's Vestibular Surface [\(\sigma\) c]  
The MULTIVARIATE analysis identified the predictive factors in the changes of the \(\sigma\) c tension values on the direction of application of a force perpendicular to the vestibular surface of the tooth. Correlation analysis showed that both the magnitude of the applied force and the extent to which the periodontitis is affected have a significant impact on the values of \(\sigma\) ech and \(\sigma\) c (\(\beta\)f = 0.56, \(p\) = 0.018, \(\beta\)AfP = 0.57, \(p\) = 0.017 and \(\beta\)f = 0.55, \(p\) = 0.019, \(\beta\)AfP = 0.58, \(p\) = 0.016, respectively) (Table 6).  
The multivariate analysis revealed the predictive factors in changes of values of displacement as a result of applying a lingualization force. The applied force does not have a significant impact on displacement f (\(\beta\)f = 0.46, \(p\) = 0.058), but that the extent of periodontal damage significantly influenced displacement f (\(\beta\)Af.P = 0.61, \(p\) = 0.017) (Table 6).  
Figure 13: Regression line for the correlation of (**a**) \(\sigma\) ech, (**b**) \(\sigma\) c, and (**c**) f vs. applied force.  
2.3. Correlation Analysis of \(\sigma\) ech, \(\sigma\) c, and f Based on the Value of Applied Force  
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 (\(\sigma\) c \(-\) r = 0.55, \(p\) = 0.058), values of equivalent tension at the level of the tooth-periodontal ligament-alveolar bone complex (\(\sigma\) ech \(-\) r = 0.56, \(p\) = 0.054), or values of the recorded displacement (f \(-\) r = 0.46, \(p\) = 0.132) (Figure 14).  
The values of \(\sigma\) ech presented a uniform increase for no periodontal damage group and for the 33% HBL. However, for the