Finite element analysis (FEA) began to be applied to the medical field in the late 1960s, which started the trend of biomechanical research by computer simulation. Unlike in vitro study of ROM data, it has unique advantages in studying the stress distribution of instruments, bone structure and soft tissues, and which can clearly show the local force transmission and stress distribution in all part of internal fixation. Moreover, the FEA would not be limited by the lack of specimens, and multiple types of experiment could be performed on the same model repeatedly without deformation or damage. In this study, the three-dimensional models were established based on fine-cut CT original data to ensure the accuracy of FE models. The main ligaments of atlantoaxial were established by using spring elements and the intact models were validated by the previous cadaver study and finite element studies. Furthermore, the influence of stress singularity is noted in this research. Theoretically, stress singularity is bound to occur at the place where the geometric topology changes dramatically, and the stress will increase unlimitedly if the mesh size continues to be subdivided. This will lead to failure to find the most suitable density of mesh, and results in a not credible data of stress. We notice that under the same loading condition, the results would vary greatly among different finite element studies, which the maximum stress ranged from 48–974 MPa [2, 18, 21]. This phenomenon may be due to the stress singularity effect or the utilization of liner unit in model mesh. According to the theory of finite element method, quadratic element is more accuracy than linear element in capturing stress results. To address this matter, we deployed a fillet feature in the screw-rod junction with a small radius which could not significantly change the structure of the implants, and the mesh sensitive test run successfully with a converged result. The mesh size was controlled in 1 mm with quadratic tetrahedral element (Tetra10), considering the cost of the computing resource and calculation accuracy. Finally, we completed a comparative study of 5 groups of models and obtained the results with statistical differences. Compared with a single FE model, the results would have less individual difference and a better reliability.
Under the different physiological loads, the ROMs of both type of fixation method were reduced significantly, which were almost less than 1 degree. In flexion and extension loading conditions, the ROMs of C1PS + C2PPS model were less than that in C1-C2PS significantly (P < 0.05). The results showed that C1PS + C2PPS has a greater ability to restrict the ROM in sagittal plane movements. However, in lateral bending and axial rotation, the ROMs of C1PS + C2PPS were greater than that in C1-C2PS significantly (P < 0.05). And in lateral bending, the difference was 42.9%, which mean C1-C2PS has obvious advantages in this loading condition. But the average lateral bending ROM were 0.19 and 0.27 in C1-C2PS and C1PS + C2PPS, which may not be significant differences clinically. Generally, these differences are consistent with the characteristics of the PPS and PS trajectory, in which the more consistent the screw direction and torque direction, the more rigid fixation are obtained.
According to the contour map of the stress distribution, the stress mainly concentrated at the posterior part of the screw-rod system. Compared with the C1-C2PS group, the C1PS + C2PPS showed a lower stress concentration on implants in flexion significantly (15.9% reduction) but showed no significant difference in extension, which indicated the C1PS + C2PPS may could reduce the risk of internal fixation failure in sagittal plane movement under physiological loads. However, the C1PS + C2PPS showed higher stress concentration on implants in lateral bending (8.7% increased) and axial rotation (21.4% increased), which suggests that C1PS + C2PPS are less able to disperse stress concentration in these physiological loads. This indicated that in the sagittal plane movements, the C2 PPS could better reduce the stress concentration, but C2 PS has advantages in lateral bending and axial rotation with that. Again, this difference was consistent with the difference in ROM reduction, which may cause by the same reason. Generally, the maximum stress ranged from 81.5 MPa to 174.5MPa under the different physiological loads in this study, and the yield strength of titanium alloy material is about 795–827 MPa, and the ultimate strength is about 860–896 MPa [22], which indicate that the two internal fixation methods are both relatively safe and reliable.
The limitation of this study include: (a) this study only covers computer simulation process, which carried out in an ideal situation. Furthermore, we need to implant the C2PPS into the cadaver models to evaluate its biomechanical properties. (b) this finite element analysis was a statics analysis, which simulate in normal physiological activity of cervical spine. However, the activity of human cervical vertebra is a complex process, which needs more perfect analytical methods to reveal the mechanical properties of C2PPS in the future.