## 3 Results
### Statistical Analysis Results
MSE \[=\left(\sum\limits_{\text{j}=1}^{\text{P}}\sum\limits_{\text{i}=1} ^{\text{N}}\left(\text{d}_{\text{ij}}-\text{y}_{\text{ij}}\right)^{2}\right)/ \left(\text{N}\cdot\text{P}\right)\] \[\text{r}^{2} =\frac{\Sigma(\text{x}_{\text{epi}}-\text{\overline{x}}_{\text{ exp}}).(\text{y}_{\text{net}}-\text{\overline{y}}_{\text{net}})}{\sqrt{\Sigma(\text{y}_{ \text{epi}}-\text{\overline{y}}_{\text{exp}})^{2}}(\text{\overline{x}}_{\text {net}}-\text{\overline{y}}_{\text{net}})^{2}}\]  
\[\text{E}_{\text{p}}=\frac{\text{Y}_{\text{exp}}-\text{Y}_{\text{net}}}{\text {Y}_{\text{exp}}}\cdot 100\]  
The key step is to validate the network, by comparing its answers with data that was not used in the training stage. The closer the MSE is to zero and the closer the r\({}^{2}\) is to 1, the higher the network performance. Table 2 shows the constructed ANN topologies and their performances. The number of training epochs used was 50,000 for all neural networks. Transfer functions such as SigmoidAxon were used, and the training process took less than 5 min. The best results were obtained in the training stage with the ANN network (21:35:4). In the validation stage (Figures 5 and 6), if we consider a confidence interval of \(\pm\)25%, we find that excellent results are obtained except for the Average GCL for which the errors are higher. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Network** & \multirow{2}{*}{**MSE**} & \multirow{2}{*}{**r\({}^{2}\)**} & \multirow{2}{*}{**E\({}_{\text{p}}\)(\%)**} \\  & **Topology** & & & \\ \hline
1. & ANN (21:7:4) & 0.004794 & 0.935800 & 18.00 \\ \hline
2. & ANN (21:14:4) & 0.000105 & 0.998700 & 4.00 \\ \hline
3. & ANN (21:21:4) & 0.000002 & 0.999970 & 0.36 \\ \hline
4. & ANN (21:28:4) & 0.00000 & 0.999996 & 0.12 \\ \hline
5. & ANN (21:35:4) & 0.00000 & 1.00000 & 0.059 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Different types of ANN tested and their performance in the training stage. Figure 5: Comparison of experimental results with those provided by the ANN network (21:35:4) in the validation stage (**a**) (MD-experimental), (**b**) (experimental PSD). The positioning of the points near the center line indicates a very good correlation. In the validation stage, Figures 5 and 6 compare the values of the output parameters calculated by ANN network (21:35:4) model with the experimental values. The positioning of the points near the center line indicates a very good correlation of the experimental data with those calculated with the neural model (output parameter model = experimental value). Most of the points are close to the center line for the MD, PSD, and linear CD output parameters. Larger deviations are highlighted for the Average GCL output parameter. The best-performing validated neural models can be used to make predictions outside the experimental field. With the same network, predictions were made for new data not used in the training and validation stages. The new data had the same type of input and output data. In fact, the network was verified on data from new patients who did not participate in the initial evaluation, presented in Table 3, and the results obtained by using the network (Table 3). The results are also excellent except for the Average GCL for which the errors are higher (Figures 7 and 8). If we consider a confidence interval of \(\pm 25\%\), the results offered by the network are similar to the experimental ones for the three parameters (MD, PSD, C/D) (\(-4.5\) DB, \(2\)-\(4\) DB, \(0.6\)-\(0.7\)). As a remark, it is necessary to expand the database in order to increase the accuracy of the network prediction.