## 3 Results  
In this paper, we are varying geometric parameters and pretension of an absorbable mini screw used for bone fixation in an absorbable screw-plate system. The database, as observed in Table 3, includes 32 configurations based in a DOE layout and was split into 2 parts. The 80% data correspond to learning stage and the other 20% were used for testing the network. The recorded output obtained from FEM analysis was the MVMS value. The strain concentrated regions were similar in all the simulations and MVMS for each configuration was found in the shaft, as shown in Figure 5.  
Figure 5: Strain distribution in screw for (**a**) Simulation 4, and (**b**) Simulation 8. Inputs and outputs were normalized from 0.1 to 0.9 and, after that, the values of biases, weights and number of neurons in hidden layer were calculated in the training stage using Matlab tool for neural networks. The resulting configuration of the ANN was with 5 neurons in input layer, 3 neurons in hidden layer and 1 neuron in output layer. Table 4 gives the obtained parameters for weights and biases that best fit the ANN model. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{4}{*}{_Wi_} & \multicolumn{2}{c}{**1 Output, 3 Hidden Neurons, 5 Inputs (_l = 1, s = 3, K = 5_)} & \multirow{4}{*}{b1} & \multirow{4}{*}{b1} \\ \cline{2-5} \cline{5-6}  & \(W_{\text{(s,1)}}\) & \(W_{\text{(s,2)}}\) & \(W_{\text{(s,3)}}\) & \(W_{\text{(s,4)}}\) & \(W_{\text{(s,5)}}\) & \\ \cline{2-5} \cline{5-6}  & \(3.26294\) & \(5.47101\) & \(-1.19592\) & \(-9.87149\times 10^{-1}\) & \(-1.96785\) & \multirow{2}{*}{b1} \\ \cline{2-5} \cline{5-6}  & \(-2.14904\) & \(-1.06270\) & \(-4.12154\) & \(7.75643\times 10^{-1}\) & \(1.81929\times 10^{-1}\) & \(-4.89210\times 10^{-1}\) \\ \cline{2-5} \cline{5-6}  & \(-2.81372\times 10^{-1}\) & \(-1.17328\) & \(4.07900\times 10^{-2}\) & \(9.97168\times 10^{-1}\) & \(4.71938\times 10^{-1}\) & \(-1.16479\) \\ \cline{2-5} \cline  
The MVMS can be calculated by Equation (7), which includes the coefficients obtained from the ANN. \[\text{MVMS}=2\bigg{[}\frac{W_{o(1,1)}}{1+e^{X_{1}}}+\frac{W_{o(1,2)}}{1+e^{X_{2}}} +\frac{W_{o(1,3)}}{1+e^{X_{3}}}\bigg{]}-\Big{(}W_{o(1,1)}+W_{o(1,2)}+W_{o(1,3)} \Big{)}+b2_{1,1} \tag{7}\]  
where:  
\[X_{1}=-2\Big{(}w_{i(1,1)}\cdot\text{ID}+w_{i(1,2)}\cdot LS+w_{i(1,3)}\cdot AT +w_{i(1,4)}\cdot SP+w_{i(1,5)}\cdot TN+b1_{(1,1)}\Big{)} \tag{8}\]  
\[X_{2}=-2\Big{(}w_{i(2,1)}\cdot ID+w_{i(2,2)}\cdot LS+w_{i(2,3)}\cdot AT+w_{i(2,4)}\cdot SP+w_{i(2,5)}\cdot TN+b1_{(1,2)}\Big{)} \tag{9}\]  
\[X_{3}=-2\Big{(}w_{i(3,1)}\cdot ID+w_{i(3,2)}\cdot LS+w_{i(3,3)}\cdot AT+w_{i( 3,4)}\cdot SP+w_{i(3,5)}\cdot TN+b1_{(1,3)}\Big{)} \tag{10}\]  
Figure 6 shows the comparison between MVMS from the numerical solution and predicted values from the ANN. Data were compared with linear regression model obtaining an R\({}^{2}\) of 0.9938. The obtained MSE was of 9.6925 \(\times\) 10\({}^{-7}\). The intercept-slope test was run with a confidence level of 99%. The results are presented in Table 5. As is observed, the confidence level is reached due to a 0 and 1, found between intercept and slope limits. Based on these findings, it is concluded that the ANN proposed model is capable to accurately predict the MVMS. Using (6), we calculate the relative importance for each input. All variables have a strong effect on the output. Furthermore, LS is the most influential parameter (37.85%), followed by ID (21.71%) and SP (13.95%), while TN (13.69%) and AT (12.8%) are the least. The effect of LS and ID on MVMS is due to the increasing or decreasing the contact area between the mini absorbable screw and bone. Thread number and angle of the thread shape have a relative low contribution to MVMS value. Nevertheless, to ensure the success of mini absorbable screw plate system, the adequate SP must be applied on the mini screw to avoid breakage or migration due to inadequate installation.