## 3 Results
### Development of the Artificial Neural Network (ANN) Model  
Behavior of the mechanical system bone tissue--orthopedic implants under static and dynamic load is a complex problem and could not be reduced to a simple deformation under load problem due to the following considerations:  
* Bone tissue is a material with complex mechanical properties, significantly different from those of the implant device (Young modulus highly anisotropic [50], shear and bulk modulus, elastic limit, homogeneity, and isotropy). * Screw assembly between the bone and the implant introduces complex effects that cannot be fully accounted for analytically. Load is transferred between bone and implant device by means of screws, which undergo complex stresses, especially bending and shear. A complex stress field occurs in the bone tissue in the vicinity of the screw insertion region. * L plate and PLS plate devices are somewhat similar regarding the implant deformation under load. However, the HEF is different in many aspects from the first two. On the other hand, PLS plate and HEF perform similarly from a mechanical point of view with the difference that PLS is an internal fixator, requiring open surgery while HEF is a minimally invasive implanting technique. * Although standard implant insertion surgical procedures are in place, minor differences in terms of screw position, anatomic particularities of the bone, fracture particularities, surgeon experience and preferences and several other factors introduce a random component of the bio-mechanical behavior of the implant device--bone system. * It appears from Figure 12a-c that the standard deviation (scattering of data points around mean value) tends to increase as the applied force increases. This is a clear indication that random factors with varying influence exist. Due to the reasons presented above, the implant deformation as a function of compressive force cannot be reduced to a simple linear (or nonlinear) deformation under load problem. Instead, an algorithm that accounts for statistical variations is expected to produce more accurate results. Artificial Neural Networks (ANN) is considered a machine learning algorithm appropriate for this type of problem. A standard ANN architecture with one input layer, one hidden layer and one output layer was selected with logistic sigmoid as activation function. Input parameters delivered to the ANN were (1) the force applied to the implant and (2) the implant type. The model output parameter was the implant deformation. The ANN training algorithm was Levenberg-Marquardt, which offers a trade-off between fast convergence and efficiency. MATLAB R2018a ANN toolbox was used to generate the ANN model. The input data set was divided in 70% training, 15% validation and 15% testing. The performance criteria used in the training algorithm was selected Mean Squared Error. The minimum number of neurons in the hidden layer for which the network performed well was 5 and the learning rate was 0.5. The data set observed the general recommendations for designing the training set: \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Implant Type**} & \multicolumn{2}{c}{**Correlation Coefficient**} \\ \cline{2-3}  & **Pearson** & **Spearman** \\ \hline L plate & \(-0.9989\) & \(-1.0000\) \\ PLS plate & \(-0.9993\) & \(-0.9996\) \\ Hybrid external fixator & \(-0.9988\) & \(-0.9993\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Pearson and Spearman correlation coefficients. In Figure 13, the coordinates of the markers are represented by the actual (experimental) values of the implant deformation (\(x\) axis) and the ANN predicted values of the implant deformation (\(y\) axis). The lines represent the linear fit of the actual value--ANN predicted value with the following parameters (Table 4):  
To compare the actual (measured) values of the ID with the ANN predicted values, the ANN model was be used to generate a set of values (for the same set of input values) in such way that a comparison was made possible.