## 4 Conclusions  
MVMS on absorbable mini screw for bone fixation was successfully predicted by ANN model consisting of 1 output, 3 neurons in the hidden layer, and 5 inputs. For training the network, a database was constructed based on the variation of geometric parameters and SP on the screw, according to the configuration of a full factorial design and MVMS as output, obtained by means of FEA. Since strain is accepted as the mechanical stimuli for bone remodeling [12] and knowing that limiting its maximum value within the elastic range of the material, we ensure contact between screw and bone threads avoiding problems of screw migration and breakage, the MVMS was recorded. Accordingly, the model proposed considers known values for _ID_, _LS_, _AT_, _TN_, and a desired outcome of MVMS for the screw. The relative importance of each input was calculated, _LS_ being the most influential parameter and, on the other hand, AT the one of less influence. However, _SP_ was chosen as the value to be found, when other inputs are well known, since it is of the utmost importance to avoid breakage or migration on absorbable mini screws due to inappropriate tightening. This investigation was limited to avoid complexity by the assumption of constant bone properties, despite being considered an influence factor in absorbable mini screw behavior due to the variations that bone quality can have. In addition, the screw insertion process was not taken into account to reduce the factors considered and the material of screw remained constant. Results indicates the ability of the ANN to predict the MVMS value and, also, the capability of ANNi to find an optimal value of one desired variable for a required MVMS. For the mini screw of the absorbable implant system evaluated, as LS increases, the strain decreases. This is probably due to the increment of contact surface area between the mini screw and bone. The maximum stress occurs at the neck, near the location of MVMS. As expected, due to the founds in literature about screw breakage in Section 1, the maximum stress occurs at the neck, near the location of MVMS. Other authors have studied the effect of thread or head designs of bone fixation mini screws for both metallic and absorbable materials [12; 29; 30; 31]. Nevertheless, most studies focus on optimizing one geometrical parameter, or evaluate its contribution to biomechanical response and do not consider the SP necessary for its correct installation,  
Figure 7: FEM analysis with design factor values of ANNi and calculated SP: (**a**) Strain; (**b**) Stress. which would allow avoiding subsequent surgical intervention due to screw migration or breakage. This study performs a methodology to define the appropriate SP for a known material and geometrical design of a mini screw. Furthermore, the developed methodology could be applied to find any desired input parameter. Actually, if a suitable multi-objective optimization algorithm is used, an optimal value for each geometrical variable could be obtained for a required MVMS and then its optimal SP could be found. [PERSON]-[PERSON] contributed to this work in DOE layout plANNi ng, CAD model preparation, FEA data collection, ANN database preparation and manuscript. [PERSON]-P. contributed to manuscript and selection of screw parameters. [PERSON]-S. contributed to CAD model preparation and FEA data collection. [PERSON]-G. contributed to manuscript and selection of screw parameters and material properties. [PERSON] contributed to DOE layout plANNi ng and relative importance of input variables analysis. [PERSON]-R. contributed to manuscript, CAD model preparation, FEA data collection, ANN and ANNI analysis. All authors have read and agreed to the published version of the manuscript. This research and APC was funded by Universidad Autonoma de Baja California and Universidad Autonoma de Ciudad Juarez. Not Applicable. Data Availability StatementData supporting this study are available within the article.