## 4 Discussion  
In this study, we compared the stability of the spine in several cases by simulating the procedure of posterior spinal fusion in patients with vertebral fractures and calculating equivalent stress in each case. The spine generates moments through various motions. In this study, the average ROM and equivalent stress generated by the four basic motions of the spine were classified as the motion average stress, and the stability of the spine was evaluated using this stress. First, the correct ROM after spinal fixation surgery directly affects the stability of the spine and spinal implants and improves a patient's quality of life. The occurrence of excessive ROM increases stress on the adjacent disk and potentially increases the risk of developing adjusted segment degeneration (ASD) [54]. Conversely, if the ROM is low, the intervertebral load transfer is not smooth due to excessive fixation [55]. Hence, the optimal criterion for ROM after spinal fixation was set as the ROM of the intact model in the study. We found T11-L1-L2 fixation using a PS led to the optimal ROM; the average ROM was \(-0.87^{\circ}\), which differs from that of the intact model but is similar to that of the intact model at the maximum possible extent. Conversely, the lowest ROM was observed in T11-L1-L2 fixation using a CS, potentially because the load generated from the upper part might not be transferred correctly due to excessive fixation. Figure 8: Equivalent stress applied to IVD via pure moment: (**a**) equivalent stress of IVD in flexion, (**b**) equivalent stress of IVD in extension, (**c**) equivalent stress of IVD in lateral bending, and (**d**) equivalent stress of IVD in axial rotation. Second, increased stress applied to the screw of the spinal implant increases the possibility of fixation failure due to screw damage. The vertebra of the fractured vertebral segment loses load transmission and support, and thus the load applied to the fixation screw increases. When a PS was used in the simulation in this study, the stress applied to the screw in the fractured state exceeded that in the normal state. The highest stress generation point of the screw is around the screw head. A spinal rod is connected to the screw head, and this process has a complex shape. The stress concentration can occur during contact due to deformation because of load transfer. To prevent this stress concentration, it is necessary to modify the screw head design such that the spinal rod does not contact the vertebral arch maximally or modify the screw trajectory [17]. The equivalent stress applied to a CS is lower in the fractured state than in the normal state because of the small screw diameter and trajectory characteristics of a CS. In general, the bending moment of a CS received by the screw stress is lower than that of a PS due to the relatively short screw length. Therefore, in the case of long-segment fixation, it is expected that the risk of damage to the spinal implant is significantly lower in a CS than in a PS. When the lowest stress occurs in the screw, T10-T11-L1-L2 is fixed using a CS, and a significant difference is absent even in T10-T11-L1 fixation using a PS. Third, high stress on the PIB can increase the possibility of damage to the vertebra with lower stiffness than the screw and cause screw fixation failure. The stress applied to the PIB at the fractured state was the highest at T11-L1-L2 fixation using a CS and lowest at T10-T11-L1-L2 fixation using a CS. This result was similar to the result of the stress on the screw. In the case of a PS, the stress in the fractured state consistently exceeded that in the normal state. However, when using a CS, the stress tendencies before and after fractures were different in the same fixation method. T10-T11-L1 fixation using a CS exhibited a high ROM and low screw and PIB stress. Conversely, compared to other cases, T11-L1-L2 exhibited a lower ROM and lower stress on the screw but higher stress on the PIB.