# The Effectiveness of Dental Protection and the Material Arrangement in Custom-Made Mouthguards
## 3 Results
### Overall Displacements
#### 3.1.2 Mouth Components  
Table 5 shows the main information of the teeth displacements regarding the mean and range values. The higher displacements appear in the two central incisors in all models, i.e., in the loading region. Moreover, the distribution pattern of the displacement field in all three directions was similar between models. Figure 5 represents the pattern distribution of the magnitude of displacement in all models. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Displacement** & **Model** & **Mean \(\pm\) SD (\(\mu\)m)** & **Min/Max (\(\mu\)m)** \\ \hline \multirow{3}{*}{x-axes} & CMG & \(-0.20\pm 1.26\) & \(-8.33/1.212\) \\  & FMG & \(-0.65\pm 2.39\) & \(-21.39/2.58\) \\  & HMG & \(-20.105\pm 85.42\) & \(-1480.7/62.63\) \\ \hline \multirow{3}{*}{y-axes} & CMG & \(-0.76\pm 1.12\) & \(-2.33/5.71\) \\  & FMG & \(-1.73\pm 1.97\) & \(-4.83/10.46\) \\  & HMG & \(-50.14\pm 68.19\) & \(-815.17/48.45\) \\ \hline \multirow{3}{*}{z-axes} & CMG & \(-0.144\pm 0.85\) & \(-5.29/3.09\) \\  & HMG & \(-0.06\pm 2.11\) & \(-10.08/9.35\) \\ \cline{1-1}  & HMG & \(-2.74\pm 31.96\) & \(-208.70/89.20\) \\ \hline \multirow{3}{*}{Magnitude} & CMG & \(1.62\pm 1.26\) & \(0.18/9.94\) \\ \cline{1-1}  & HMG & \(3.48\pm 2.31\) & \(0.65/21.61\) \\ \cline{1-1} \cline{2-4}  & HMG & \(69.21\pm 105.38\) & \(3.69/1688.50\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mean and range of displacements for the different mouthguard protections. Figure 4: Histograms of the distributions found for the movement antero-posterior, i.e., in the direction of the x-axis, in all mouthguards. Figure 6 shows the numerical variation of the average teeth displacement with the load intensity. Although the dentition of the four models presented similar behavior, i.e., the average displacement value increases with the increase of the applied force, the HMG model is the one that stands out for giving lower values, and the NMG model for presenting higher values. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Displacement** & **Model** & **Mean \(\pm\) SD (\(\mu\)m)** & **Min/Max (\(\mu\)m)** \\ \hline \multirow{4}{*}{x-axes} & NMG & \(-0.023\)\(\pm\) 0.047 & \(-0.558/0.060\) \\  & CMG & \(-0.019\)\(\pm\) 0.0388 & \(-0.441/0.061\) \\  & FMG & \(-0.018\)\(\pm\) 0.034 & \(-0.419/0.049\) \\  & HMG & \(-0.008\)\(\pm\) 0.015 & \(-0.066/0.036\) \\ \hline \multirow{4}{*}{y-axes} & NMG & \(-0.116\)\(\pm\) 0.107 & \(-0.747/0.004\) \\  & CMG & \(-0.110\)\(\pm\) 0.099 & \(-0.679/0.004\) \\  & FMG & \(-0.096\)\(\pm\) 0.088 & \(-0.608/0.003\) \\  & HMG & \(-0.008\)\(\pm\) 0.015 & \(-0.175/0.006\) \\ \hline \multirow{4}{*}{z-axes} & NMG & \(0.005\)\(\pm\) 0.022 & \(-0.080/0.155\) \\  & CMG & \(-0.012\)\(\pm\) 0.023 & \(-0.134/0.026\) \\  & HMG & \(-0.003\)\(\pm\) 0.019 & \(-0.071/0.036\) \\  & HMG & \(-0.003\)\(\pm\) 0.010 & \(-0.045/0.017\) \\ \hline \multirow{4}{*}{Magnitude} & NMG & \(0.125\)\(\pm\) 0.112 & \(0.0004/0.931\) \\  & CMG & \(0.118\)\(\pm\) 0.101 & \(0.0004/0.799\) \\ \cline{1-1}  & FMG & \(0.103\)\(\pm\) 0.089 & \(0.0003/0.726\) \\ \cline{1-1}  & HMG & \(0.072\)\(\pm\) 0.045 & \(0.0003/0.178\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mean and range of displacements of the teeth in the different models. Figure 5: Pattern distribution of the magnitude of displacement field: (**a**) in the NMG model; (**b**) in the CMG model; (**c**) in the FMG model; (**d**) in the HMG model. Table 6 shows the average and the range values of displacements in the maxilla and in the soft tissue. Again, the results show that the HMG model is the one that stands out for presenting lower values of the magnitude of displacement in the maxilla bone and higher values in the soft tissue. Figure 7 shows the main differences among the distributions of the displacement magnitude in the soft tissue of all models.