Model validation
The ROM data of the intact lumbar spine were compared to the results of previous studies, which were under the act of the same load as listed in Figure 5. The ROM tendency of each segment was closely correlated with the results of Chen et al[21]and Zhong et al[22]. In terms of flexion, the maximum ROM occurred at L4-5, and the maximum ROM for extension and bending was observed at L3-4 and L4-L5, respectively. The mean values for torsion were under 3°. The ROMs of the L2-L5 segments were 11.2°, 10.9°, 12.0°, and 7.1° for flexion, extension, bending, and torsion, respectively. Overall, the ROM discrepancy was within the acceptable range of error. The results of our study confirm the rationality of the model and can be further analysed.
Stress sensitivity analysis
The percentage differences in the ROM between the linear basic model and original nonlinear model, between the linear basic model and linear high-value model, and between the linear basic model and linear low-value model under flexion are displayed in Figure 6. When compared with the ROM, the differences in percentage between the linear basic model and nonlinear model were 1.32% under flexion and 1.09% under compression, which were lower than those of the linear high-value model/basic model (decreased 4.12% under flexion and 3.92% under compression, respectively) and linear low-value/basic model (increased 4.31% under flexion and 4.35% under compression, respectively).
Range of motion
In Figure 6, there was a significant reduction in the ROM at L3/4 for models a, b and c when compared with the intact model for all loading conditions. Model d slightly decreased the ROM for axial rotation and lateral bending. The supplemented fixation device provided an additional fixed effect on the fusion segment. Differences in the ROM between models a and b were not significant at less than 1° for all loading conditions. The ROM of each instrumented model is shown in more detail in Figure 7.
Flexion-extension
In Figure 7, there were no ROM differences in flexion among the four models (90.1% to 98.8% restriction). In terms of extension, model a and model b provided similar stability (97.7% and 98.4% restriction, respectively) compared with the intact model. Model c reduced the ROM of the intact model by 77.5%, and the ROM was 9.8 times greater than that of model a. Model d reduced the lowest ROM (65.3% restriction), which was less restrictive than that of model a (15.1 times).
Lateral bending
Model a and model b provided the largest reduction in the ROM, by 95.7% and 94.5% for lateral bending, compared with the intact model. Model c demonstrated less than 30% intact ROM (76.3% restriction). Similar to flexion-extension, model d reduced the lowest ROM (55.9% restriction), which was 10.3 times greater than that of model a.
Axial rotation
The largest reduction in the ROM for axial rotation ROM was found in model a compared with the intact model. However, there was no significant difference in the ROM observed within models a, b and c (73.8%, 68.3%, 64.9% restriction, respectively). Significant differences were found in model d, which merely provided 18.3% ROM restriction compared with the intact model. In addition, axial rotation ROM was the least restricted mode of kinematic behaviour.
The magnitudes of the maximum Von Mises stress in the interbody cage
The maximum Von Mises stress in the interbody cage is displayed in Figure 8. For all loading conditions, the stress of the cage was found to be largest in model b. For flexion, the maximum stress of the cage reached 172.6 MPa in model b, which significantly increased the maximum stress compared with the other models. The cage stress in model b was 13.2, 6.1, and 6.7 times greater than that in models a, c and d in terms of flexion, respectively. Similarly, the peak stress in model b was 4.8 and 2.3 times greater than that of models a and c for lateral bending and 2.0 and 1.5 times greater than that of models a and c for axial rotation. The difference was not significant between models b and d in terms of lateral bending and axial rotation.
The magnitudes of the maximum Von Mises stress on the interbody cage-L4 superior endplate interface
Under all loading conditions, model d generated the largest endplate stress among the implanted models (Figure 9). However, in terms of flexion, the maximum stress caused by model b exceeded that by models a, c and d by 3.9, 2.3 and 1.6 times, respectively. The stresses in models a and c were 40.9% and 68.9% those of model d. In terms of lateral bending, the maximum endplate stresses caused by model d exceeded those of models a, b, and c by 2.6, 3.0, and 5.4 times for left bending and 2.7, 2.5, and 1.7 times for right bending, respectively. In terms of axial rotation, the largest stress on the pedicle screw was found in model b, which exceeded models a, c and d by 1.7, 1.8 and 1.3 times, respectively.
The maximum displacement (mm) in the interbody cage
For interbody cages without supplementary fixation, the maximum displacement of the cage was found to be high in model d under all loading conditions (Figure 10). In terms of flexion, the displacement caused by model d exceeded that of models a, b and c by 121.3%, 116.8%, and 116.8%, respectively. Greater differences could be seen in lateral bending, and the displacement caused by model d exceeded that of models a, b and c by 173.8%, 225.8%, and 166.3%, respectively. In terms of extension and axial rotation, model d was slightly higher than that of the other models, but the difference was not significant.
The magnitudes of the maximum Von Mises stress on the screw-bone interface
The stress peak of the screw-bone interface was investigated to show the load distribution between the vertebrae and the spinal implants. It is important to evaluate the risk of screw loosening and migration[29]. Figure 11 summarizes the maximum Von Mises stress of the screw-bone interface for the implanted models. At the L3/4 segment, the stress was greater with the lateral instrumentation than with the posterior instrumentation under all loading conditions. In terms of flexion-extension, the stress in model c was 5.7 and 5.1 times greater than that in model a and model b, respectively. The largest stress of the screw-bone interface was found to be 617.5 MPa in model c under axial rotation, which exceeded that of model a and model b by 4.1 and 3.4 times, respectively. Greater differences could be seen in terms of lateral bending, and the stress caused by model c was 7.0 and 6.1 times greater than that of model a and model b. In addition, the stress caused by model b was slightly higher than that of model a under all loading conditions. Particularly, in terms of axial rotation, the difference was more than 30 MPa.
The magnitudes of the maximum pressure in NP-IDP of adjacent intervertebral discs
Figure 12 included the maximum pressure in NP-IDP of the superior adjacent level (L2/3) for each instrumented construct. Under all loading conditions, the L2/3 NP-IDP caused by the four models was slightly higher than that of the intact model, but the differences were not significant.