Biomechanical study of C2 sagittal-parallel pedicle screw versus leaning angle pedicle screw in atlantoaxial fixation: a finite element study




The atlantoaxial structure is an important motion segment in the cervical spine and atlantoaxial instability could be a life-threatening injury. The purpose of this study is to compare the biomechanical properties of the C2 sagittal-parallel pedicle screw and C2 traditional pedicle screw. combined C2 sagittal-parallel pedicle screw (C1PS + C2PPS) and C1-C2 traditional pedicle screw (C1-2PS) for atlantoaxial instability fixation.


Based on the computed tomography (CT) images, a total of 5 intact C1-2 finite element models were established and validated. On this basis, instability models were developed and two different fixation methods were applied for each model: C1 traditional pedicle screw combined with C2 sagittal-parallel pedicle screw (C1PS + C2PPS) and C1-C2 traditional pedicle screw (C1-2PS). Under the physiological load of 40 N, the 1.5 Nm pure moment was used to simulate movements of the cervical spine in flexion, extension, lateral bending and axial rotation. The von Mises stress of implants and range of motion (ROM) were analyzed and compared statistically.


In flexion and extension, the C1PS + C2PPS performed lower segment ROM (12.4% and 6.3% decreased) and stress concentration (15.9% decreased in flexion) compared with C1-C2PS. In lateral bending and axial rotation, the C1PS + C2PPS performed higher segment ROM (42.9% and 5.9% increased) and stress concentration (8.7% and 21.4% increased) compared with C1-C2PS.


Both methods were relatively safe and stable for atlantoaxial instability fixation. Compared with C1-C2PS, the C1PS + C2PPS may offer a better stability and lower risk of implant failure in flexion and extension, but C1-C2PS could perform an advantage in lateral bending and axial rotation.


The atlantoaxial junction consists of atlas (C1) and axis (C2), which is a unique structure of the cervical spine and take charge for about 50% pivot motion, flexion and extension of the cervical spine [1, 2]. Atlantoaxial instability is a very dangerous event which may occur due to physical injury, ligament laxity, tumor, tuberculosis, rheumatoid and congenital malformation [3, 4]. Most atlantoaxial instability requires surgical treatment to achieve stability and spinal cord decompression [5]. However, due to its complex anatomy structure, surgical fixation may cause a vital structure injury, such as spinal cord and vertebral artery [6]. Multiple fixation methods were reported in clinical treatment of atlantoaxial instability. The spinous process, vertebral laminar and modified posterior wiring technique were reported in the past several decades, but these techniques could not provide sufficient fixation strength [7], as it is not three column fixation method. Trans-articular screw fixation was introduced in 1992, but with an increased vertebral artery injury rate [8, 9], and it will damaged the motor function of the upper cervical. The pars screw could enhance the fixation stability [10, 11] and parsicle screw were proposed as another substitution [12]. However, the head of pars screw only reach the transverse foramen with an average length of 16 mm. Moreover, the leaning angel of parsicle screw is relatively large with an average length of 20–26 mm, and the biomechanical properties has not been verified. So, in the present, the pedicle screw (PS) was the mainstream choice for the treatment of atlantoaxial instability and showed the rigid biomechanical property in fixation [1315]. However, the soft tissue occlusion may result difficulty in placement of C2 pedicle screw during surgery. Once the screw angle deviates too much, nerves or blood vessels may be damaged directly. Wu Chao et al. proposed a novel C2 pedicle screw trajectory parallel to the sagittal plane (PPS), which could avoid tension of soft tissue and it is easier for screw placement without leaning angle. And it is feasible for about 80% patients to accommodate the C2 PPS placement. However, there is no relevant biomechanical properties of C2 PPS at present, and the stability of fixation could not only be explained by ROM of traditional cadaver study, so we conducted a finite element analysis (FEA), which has no need to worry about cadaver’s matters. Therefore, we compared the stress distribution and segment ROM between C2-PPS and C2-PS combined with C1 pedicle screw fixation for atlantoaxial instability by 5 individual FE models in this study.


Finite element model of intact atlantoaxial

This study was provided by Zigong Fourth People’s Hospital (Sichuan, China). Selection criteria: (a) patients with degenerative disease or severe ligament ossification in cervical spine were excluded. (b) patients have a history of trauma in upper cervical spine were excluded. (c) patients have a cervical dysplasia, severe rheumatic disease or tumor were excluded. (d) contrast-enhanced CT or the image had significant artifact were excluded. (e) only patients aged from 18–65 years and with normal anatomical structure in upper cervical spine were included.

There were 5 patients (3 males and 2 females, age from 32–46 years) in 59 cases from January 2022 to May 2022 who met the criteria above. The original cervical computed tomography data were exported in DICOM format from our radiology department imaging database with 0.625-mm-thickness computed tomography (CT) scans (SOMATO FORCE 128-slice spiral, Simons, Munich, Germany). All CT data were imported to Mimics software 22.0 (Materialise, Leuven, Belgium) and the atlantoaxial structure was retained by using ‘separate mask’ tool. The next steps included three-dimensional reconstruction and surface fixation. After that, the model was embedded into Geomagic Wrap 2017 (3DS System Corporation, USA) for geometry cleanup. The C1 and C2 vertebra include an internal cancellous bone and a 0.5-mm-thickness cortical bone shell. Finally, the model was imported into the SolidWorks 2016 (Dassault Systèmes, USA) for model assembly, cartilages and fixation establishment.

In the intact FEA models, the isotropic liner elastic material properties were assumed to the model and the parameters of materials were assigned according to the previous study. The ligaments that play a major role of cervical spine were determined from anatomic literature, which include transverse ligament, anterior and posterior longitudinal ligament, atlantoaxial posterior membrane, capsular ligament, flavum ligament, tectorial membrane and nuchal ligament. The spinal ligaments were simulated by spring element with tension-only (Fig. 1). The material properties were given in Table 1 [2, 16].

Table 1

Material properties and element type of the FE models


Young’s Modulus (MPa)

Poisson Coefficient

Stiffness (N/mm)

Cortical bone

12 000



Cancellous bone




Facet joint




Transverse ligament




Anterior longitudinal ligament




Posterior longitudinal ligament




Atlantoaxial posterior membrane




Capsular ligament




Flavum ligament




Tectorial membrane




Nuchal ligament




Screw and rod

110 000



For model validation, the results of range of motion (ROM) in atlantoaxial were calculated based on nodal displacement in different axes orientation and compared with the previous cadaveric experiment results and other upper cervical finite element studies under the same loading boundary conditions [1618].

Two fixation method for unstable atlantoaxial model

All ligaments of intact C1-2 model were removed to simulate the unstable atlantoaxial model according to the method by Chun, D.H., et al [2]. And the two different posterior internal fixation methods were all composed of 3.5-diameter screws and 3.2-diameter rod under the handle of the same spine surgeon in computer software. The screw threads were substituted by cylinder and the unnecessary features of screw nuts were eliminated for simplifying fixation system. The fillet feature was applied to the junction between the screw and rod in each model to avoid stress singularity happen.

Initially, the C1 pedicle screws (PS) were applied in all models, and two different screw placement methods were used in C2 vertebra, which were C2-PS and C2-PPS. C1-PS and C2-PS were placed according to the method in the literatures [19, 20]. And according to the previous study, the average length of PPS was 2 mm shorter than PS, this difference was applied to this model. The entry point of C2-PPS was about 2 mm inside of the midline of inferior facet joint and 5 mm above inferior facet joint. And the screw was parallel to the upper surface of C2 pedicle channel. Finally, the two fixation methods of unstable atlantoaxial were established: C1-2PS and C1PS + C2PPS (Fig. 2). And the models were imported to Ansys Workbench software 2020 (ANSYS, United States of America) for further analysis.

Mesh and sensitive test

All three-dimensional structures of the model were meshed by quadratic tetrahedral element (Tetra10). The mesh sensitive test was performed under the 40-N vertical loading condition. Eight meshing size were used in this test: 4, 3.5, 3, 2.5, 2, 1.5, 1 and 0.5 mm. The stress results of the screw-rod fixation were exported and plotted in Fig. 3. And the result was considered to be converged when the change of stress was smaller than 5%. As the line chart showed, once the mesh size was smaller than 1 mm, the stress reduced slightly (stress reduced by 0.93% from 1 mm to 0.5mm). In order to get a balance in computational cost and the simulation accuracy, 1 mm meshing size was used in FE models.

Loading and boundary condition

The bottom of the C2 vertebral and the bilateral inferior articular process were fully constrained in six degrees of freedom. And a vertical loading force of 40-N was applied at the upper facet joint of C1 to simulate the weight of human head. Moreover, a pure moment of 1.5-Nm was applied to the same place to simulate different body configurations. Face-to-face contact was applied to facet joints with 0.1 coefficient of friction. The other contacts were defined as bonded. After the calculation results converged, the ROMs of the C1-2 and von Mises stress of screw-rod fixation system were recorded and used for comparative analysis.

Statistical analysis

All analysis data were recorded as the Means ± Standard Deviation and performed in SPSS 19.0 (SPSS Inc, Chicago, IL, USA). Paired sample t test was used for ROMs and stress in two group for comparative study, and the P-value < 0.05 considered statistically significant. Finally, the data was presented in the form of a bar chart by the GraphPad Prism 8 software (La Jolla, USA).


Validation of FE model

The ROMs results of the intact models were compared with that of the cadaver and finite element study in the literatures [1618]. The ROMs of the model showed in a good agreement with the results of the reported literature as list in Table 2. The differences considered acceptable because of the individual variation, and the FE model could be used for the next experiment analysis.

Table 2

ROMs of intact model at C1-2 segment compared with other studies.



Zhang B*

Chuang L*

This study


12.7 ± 3.2



11.6 ± 3.3


10.5 ± 5.0



10.0 ± 2.8

Lateral bending

12.6 ± 7.0



6.1 ± 2.3

Axial rotation

37.4 ± 9.0



34.4 ± 3.1

Note: # represent for cadaver study; * represent for finite element study.

Range of motion of fixation model

The range of motions (ROM) of two fixation methods were reduced significantly compared with the intact model in all loading conditions as list in Table 3. Furthermore, the quantitative analysis showed a significant difference between the two fixation methods in all loading conditions (Fig. 4). Compared with C1-2PS models, the average ROM of C1PS + C2PPS models decreased by 12.4% and 6.3% in flexion and extension, respectively. However, it was increased by 42.9% and 5.9% in lateral bending and axial rotation, respectively.

Table 3

Comparison of C1-2PS and C1PS + C2PPS in ROM and stress.











0.51 ± 0.06

1.03 ± 0.06

0.19 ± 0.04

0.32 ± 0.03


0.45 ± 0.05

0.96 ± 0.10

0.27 ± 0.05

0.33 ± 0.04



98.56 ± 6.36

147.37 ± 13.55

81.48 ± 4.27

143.63 ± 12.64


82.81 ± 9.21

144.47 ± 5.57

88.65 ± 8.12

174.50 ± 14.42

Note: all group of data satisfied the normal distribution and express in Means ± Standard Deviation.

Stress distribution of the implants

The contour map of von Mises stress showed a similar distribution on the C1-2PS and C1PS + C2PPS models, the stress mainly concentrated at the screw tail in flexion, extension, axial rotation and concentrated at the screw-rod junction in lateral bending (Fig. 5). The stress results of implants were list in Table 3. And the quantitative analysis showed significant difference (p < 0.05) between C1-2PS and C1PS + C2PPS in all loading conditions except in extension (Fig. 4). Compared with C1-2PS models, the average stress of C1PS + C2PPS models decreased by 15.9% in flexion, while the stress increased by 8.7% and 21.4% in lateral bending and axial rotation, respectively.


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.


In general, the C1PS + C2PPS and C1-C2PS fixation methods for atlantoaxial instability are both stable technique. Compared with C1-C2PS, the C1PS + C2PPS showed a better biomechanical property in flexion and extension. And the C1-C2PS showed a better biomechanical property in lateral bending and axial rotation.





Atlas and axis


C1 pedicle screw




C2 pedicle screw


C2 pedicle screw trajectory parallel to the sagittal plane


Finite element analysis


Range of motion


Ethics approval and consent to participate

We obtained the upper cervical CT data consent from the patients to be used in our study. This study involving human CT data has been approved by the ethics committee of Zigong Fourth People’s Hospital (No. 02, 2013).

Consent for publication

Not applicable.

Availability of data and materials

The datasets used and analyzed during the current study are available from the corresponding author on reasonable request.

Competing interests

The authors declare that they have no competing interests.


No funding.

Authors' contributions

Baifang Zeng carried out the establishing of atlantoaxial models and finite element analysis, and also the drafted the manuscript. The conception and design of this research carried out by Chao Wu and also the screw placement. Binwei Qing and Danwei Shen performed the selection of data and provided useful models. The data collation and statistical analysis was conducted by Xiangyu Wang. Absolutely, all authors read and approved the final manuscript.


The support of radiology department of Zigong Fourth People’s Hospital is highly appreciated.

Authors' information

Department of Orthopedics Center, Zigong Fourth People’s Hospital, 19 Tanmulin Street, Ziliujing District, Zigong City, 643000, Sichuan Province, China.


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