# Alternative Pedicle Screw Design via Biomechanical Evaluation
## 3 Mechanical Strength of the New Design
### Numerical Testing for Pull-Out Strength
#### 3.2.2 FEA Results and Discussion  
The established FEA model was used to evaluate the stress state of the lumbar vertebrae and the pedicle screw. Three types of pedicle screws were used in the analysis, the results of which were compared with each other (Figures 8-10 and Table 5).  
In the integrated model, resistance to pull-out force is mainly given by the pedicle screw, with some by the bone. The maximum Von-Mises stress in the model matched that on the screw surface. However, the maximum Von-Mises stress calculated at the proximal part of the pedicle was approximately half of that for all of the integrated models. This means that the maximum stress on the screw surface was generated and transmitted to the pedicle and then to the vertebra.  
For all three models, the magnitudes of the stress against the pull-out force were allowable because they did not exceed the strength of each material. The maximum stress in the pedicle screws was smaller than the strength of Ti-6 Al-4V ELI (900 MPa), while the stress at the proximal part of the pedicle decreased by 52%, 59%, and 44% from the maximum for the single-threaded, double-threaded, and proposed designs, respectively. Hence, the maximum stress in L4 was lower than the cortical bone's strength (50-150 MPa) [26]. Therefore, it can be concluded that the three types of pedicle screws showed appropriate mechanical robustness against the pull-out force and had appropriate stress distribution from the screw to the bone.  
We can conclude that the alternative dual screw design is appropriate for improved convenience during surgery and, even though the screws were slightly more stressed than the others, their mechanical robustness values were similar. However, the alternative screw design could be improved to lower the stress concentration and maximum stress. In all the analysis results, the maximum stress on the vertebrae occurred properly in the cortical bone, which is a deep region of the spine. The maximum stresses on the pedicle screw all appeared in the shank between the head and the thread due to the stress concentration caused by the sudden change in the cross-sectional area of the screw from the head to the shank. Therefore, design modification is needed to ensure that the cross-sectional area from the head to the shank changes more gradually and smoothly. The alternative pedicle screw incurs around 20% more stress than the conventional designs. This means that the stress on the quadruple thread underneath the shank is higher, which in turn increases the stress on the shank as a whole. The stress could be lowered if a somewhat longer quadruple thread was employed in the alternative dual thread.  
Figure 7: Simulation conditions: (**a**) the boundary conditions and (**b**) the loading conditions for the pull-out force.  
Figure 8: FEA results for a single-threaded pedicle screw: Top is the pedicle screw, left is L4 and the pedicle screw, and right is L4.  
Figure 9: FEA results for the double-threaded pedicle screw: Top is the pedicle screw, left is L4 and the pedicle screw, and right is L4.  
Figure 10: FEA results for the proposed pedicle screw: Top is the pedicle screw, left is L4 and the pedicle screw, and right is L4.