A finite element analysis of three alternatives to C2 pedicle screw in the setting of congenital C2-3 fusion and high-riding vertebral arteries

A finite element analysis of three alternatives to C2 pedicle screw in the setting of congenital C2-3 fusion and high-riding vertebral arteries | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A finite element analysis of three alternatives to C2 pedicle screw in the setting of congenital C2-3 fusion and high-riding vertebral arteries Qiang Jian, Xingang Zhao, Yinqian Wang, Cong Liang, Xiuqing Qian, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5072741/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Objective: To investigate the biomechanical properties of three novel screw techniques for C2-3 fused vertebra with high-riding vertebral arteries (HRVAs). Summary of Background Data: There has not been an investigation into the biomechanical properties of alternatives to C2 pedicle screw in the context of C2-3 fused vertebrae and HRVA. Methods Five models were utilized to assess range of motion (ROM) and peak von Mise stress (PVMS) on the screw-rod construct. These models consisted of the following groups: C2 pedicle screw (2PS), subfacetal body screw (SBS), translaminar screw (TLS), lateral mass screw (LMS), C3 pedicle screw (3PS) fixation in the presence of HRVA and C2-3 fusion. The flexion/extension (FE), lateral bending (LB) and axial rotation (AR) on 3 planes were simulated. Results: Compared to the 2PS, the LMS and SBS exhibit similar ROM in FE and LB (<10%). The SBS reduces ROM in AR by 47.87%, while the LMS increases ROM in AR by 26.85%. Compared to 2PS, the 3PS has similar ROM in FE, LB, and AR; but increases PVMS in FE and AR by 43.62% and 29.27%, respectively, and decreases PVMS in LB by 33.81%. Compared to 2PS, the LMS decreases ROM in FE and LB by 11.93% and 14.45%, respectively; but increases PVMS in LB by 25.38%. Compared to 2PS, the SBS increases PVMS in FE, LB, and AR by 126.96%, 74.87%, and 16.97%, respectively. Although the 3PS, LMS, and SBS increase ROM in FE by 14.11%, 4.81%, and 16.89%, respectively, compared to the TLS, they decrease ROM in LB by 72.88%, 67.98%, and 67.87%, respectively, and in AR by 41.68%, 28.05%, and 70.43%, respectively. Although the 3PS and SBS increase PVMS in FE by 45.08% and 129.26%, respectively, compared to the TLS, they decrease PVMS in LB by 73.84% and 30.88%, respectively, and in AR by 8.00% and 16.75%, respectively. The LMS decreases PVMS compared to the TLS in FE, LB, and AR by 11.04%, 66.18%, and 10.77%, respectively. Conclusion: 3PS, LMS, and SBS are biomechanically feasible, may be reasonable options in the setting of congenital C2-3 fusion and high-riding vertebral arteries. C2-3 fusion high-riding vertebral arteries pedicle screw translaminar screw subfacetal screw lateral mass screw Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Congenital C2-3 fusion is a special kind of Klippel-Feil syndrome, which is often associated with congenital atlas occipitalization (AOZ) and atlantoaxial dislocation (AAD) 1–3 . Despite the presence of anatomical anomalies and aberrant biomechanical changes, there has been scarce research exploring the biomechanical characteristics of congenital C2-3 fusion. Recent reports highlight that C2-3 fusion can lead to an escalation in stress on the transverse ligament and lateral joint, potentially contributing to the development of AAD 4 . The treatment of AAD with C2-3 fused vertebrae presents both challenges and opportunities. This abnormal fusion of C2-3 vertebrae reduces the height of the cervical spine, while the abnormal AAD causes misalignment of the cervical spine. Both factors can lead to the tortuosity of the vertebral artery (VA), in turn resulting in a high-riding vertebral artery (HRVA) and eroded C2 pedicle. The presence of HRVA significantly complicates the placement of C2 pedicle/pars screws in the treatment of AAD 1 . Opting for alternatives to C2 pedicle/pars screw becomes a necessary resort. Fortunately, the increased volume of the C2-3 fused vertebrae allows for the implantation of novel alternatives 5–8 . Three special anatomical structures, C3 pedicle, fused lateral mass column and thickened C2 superior articular process, serve as additional screw insertion sites in congenital C2-3 fused vertebrae, which accommodate the C3 pedicle screw, lateral mass screw and the subfacetal body screw, respectively (Fig. 1 ). Currently, the biomechanical characteristics of the three alternatives for addressing this special anatomical anomaly remain unclear. Several cadaver studies have compared the ROM among various C1-C2 fixation techniques. Due to the unavailability of cadaveric specimens with congenital C2-3 fusion and HRVA, cadaveric studies could not be conducted. To address this, we employed finite element analysis (FEA) to scrutinize the biomechanical stability of the three alternatives in the setting of congenital C2-3 fused vertebrae with HRVA. To the best of our knowledge, there is no FEA related to screw placement in fused C2-3 vertebrae with HRVA. Materials and Methods Material A 25-year-old female inpatient who underwent transnasal endoscopic pituitary tumor resection was found to have congenital C2-3 fusion during a computed tomography scan (Philips Brilliance 64-slice scanner, Philips in Amsterdam, Netherlands). No other cervical spine disorders were found, such as disc herniation, spinal stenosis, fractures, tumors or tuberculosis. CT images were obtained in DICOM format with a resolution of 512 × 512 pixels and a slice thickness of 1.0 mm. The ethics committee approved the study. Model Construction and material properties Mimics 13.0 (Materialise Company, Belgium) was used to reconstruct the three-dimensional point cloud model. Subsequently, the model was imported into Geomagic Studio 2015 (Geomagic Inc., United States) to create editable geometric solid models. Solidworks 2016 (SolidWorks Corp., United States) was used to construct the screws and rods. The geometric solid models were then imported into Hypermesh 2017 (Altair Engineering Corp., United States) for meshing, application of boundary conditions, assignment of material properties, and definition of contact. Finally, the model was analyzed using ABAQUS 2019 (Dassault Systemes Simulia Inc., France). The cortical bone was simulated using C3D6 elements with a thickness of 1mm, while the filled trabecular bone was represented using C3D4 elements. The intervertebral discs, composed of the nucleus pulposus (60%) and the annulus fibrosus (40%) 9 , were simulated using C3D8R elements with additional hourglass control. The Jacobian ratio was constrained to be above 0.6 to control the mesh quality. The intervertebral disc was simulated using an incompressible hyperelastic material by a Mooney–Rivlin material law 10 . This simulation does not take into account density and also disregards the influence of collagen fibers 11 . Shell elements were used to model the transverse ligament with material property defined as orthotropic anisotropic 12 (Table 1 ). SPRINGA elements were used to simulate the other ligaments, including the anterior atlanto-occipital membrane, posterior atlanto-occipital membrane, cruciate ligament, apical ligament, alar ligament, tectorial membrane, anterior longitudinal ligament, posterior longitudinal ligament, ligamentum flavum, facet capsule ligament, interspinous ligament, and supraspinous ligament. These ligaments are defined as elastic‒plastic material properties 12 . Ligament failure is not involved in this study. therefore, the force-displacement curve is divided into two zones: neutral zone and elastic zone. A parabolic fitting is employed for the neutral zone, while a linear fitting is used for the elastic zone in force-displacement curve (Table 2 ). The material properties 10, 11, 13, 14 are listed in Table 1 and Table 2 . Table 1 Material property Elastic modulus/Mpa Poisson’s ratio Cortical bone 12000 0.3 Cancellous bone 500 0.3 Cartilage endplate 500 0.4 Ti (Screw and rod) 120000 0.3 Nucleus pulposus Mooney–Rivlin c1 = 0.12, c2 = 0.03 0.495 Annulus fibrosus Mooney–Rivlin c1 = 0.18, c2 = 0.045 0.45 Transverse ligament E1 = 86, E2 = 6 0.016 E1: in lateral direction, in axial plane. E2: in vertical direction, in sagittal plane. Perpendicular to E1. Table 2 Properties of ligaments Ligaments d f (mm) f f (N) d n (mm) f n (N) Parabolic coefficient Anterior atlantoaxial membrane 18.9 232 3.78 23.2 1.623695 Posterior atlantoaxial membrane 18.1 83 6.033333 8.3 0.228015 Joint capsule ligament(C0-C1) 9.9 320 3.3 32 2.938476 Joint capsule ligament (C1-C2) 9.3 314 4.65 31.4 1.452191 Joint capsule ligament (C2-C3) 9 210 3 21 2.333333 Anterior longitudinal ligament 10 300 2 30 7.5 Ligamentum flavum (C1-C2) 9.6 111 3.2 11.1 1.083984 Ligamentum flavum (C2-C3) 6 90 2 9 2.25 Apical ligament 8 214 1.6 21.4 8.359375 Alar ligament 14.1 357 2.82 35.7 4.489211 Cruciform ligament of atlas 12.5 436 2.5 43.6 6.976 Tectorial membrane 11.9 76 3.966667 7.6 0.483017 Posterior longitudinal ligament 10 80 3.333333 8 0.72 Interspinous ligament 7 37 2.333333 3.7 0.679592 Failure is not involved in this study, and thus the plastic zone and failure zone are removed; therefore, the force-displacement curve is divided into two zones: neutral zone and elastic zone. The neutral region ends in the point (d n , f n ) and the elastic region ends in the point (d f , f f ). Nonlinear surface-to-surface contact relationships were used to simulate the interaction between joints. The contacts between the facet joints and between spinous processes of C3-C5, as well as the contact between the odontoid process and the transverse ligament and between the odontoid process and the atlas, were all set as hard contacts. Research Groups We constructed the following groups: intact, unstable, C2 pedicle screw, subfacetal body screw, translaminar screw, C3 pedicle screw, and lateral mass screw groups (Fig. 2 ). The intact group comprised individuals with C0-C5 levels exhibiting congenital atlas occipitalization and C2-3 fusion devoid of AAD. In contrast, the unstable group was characterized by the removal of the cruciate ligament, alar ligament, anterior longitudinal ligament, and transverse ligament for simulating instability. Additionally, the atlantodental interval was deliberately set at more than 3 mm, thus simulating AAD. To simulate HRVAs, the VA grooves were expanded using a Boolean subtraction operation (Fig. 3 ). The C1-2/3 models was inserted by screw-rod constructs (3.5 mm in diameter). The fixation models were constructed based on the realigned unstable group configuration (Fig. 3 ). The C1 trans-arch lateral mass screws (26 mm in length) were inserted in each fixation model. The C2 pedicle screws (32 mm in length) were implanted into the C2 pedicles along with their respective directions. Similarly, C3 pedicle screws (28 mm in length) were implanted into the C3 pedicles along with their respective directions, as depicted in the schematic illustration showing the translucent pedicle region (Fig. 2 ). Subfacetal body screws (28mm in length) were implanted into the superior articular processes and vertebral body from posterior aspects with medial direction of 45°. Bilateral translaminar screws (28 mm in length) were implanted into laminas. Lateral mass screws (18 mm in length) were inserted with cephalic angle of 40° from the midpoint of fused lateral mass. The screws and rods form a common node connection, with the relationship between the implants and the vertebral bodies set as an Embed relationship. Loading and boundary conditions The inferior surface of C5 was fixed in all 6 degrees of freedom. A reference point was created on the C0 rotation axis. A distribution coupling constraint is established between this point and the upper endplate nodes. Pure torque loads of 1.5 Nm are applied at the neutral point in different directions according to the right-hand rule 15 . These torques are applied to simulate flexion and extension (FE), left and right lateral bending (LB), and left and right axial rotation (AR). Parameters The range of motion (ROM) and peak von Mise stress (PVMS) during FE, LB, and AR in three different planes were summarized. Results Model accuracy verification The segmental C1-2 ROM of intact group was 24.8° in FE, 9.1° in LB and 32.1° in AR, comparable to results from previous biomechanical study 16, 17 . The segmental C1-2 ROM of unstable group was 39.24° in FE, 11.28° in LB and 35.26° in AR, similar with the results from previous study conducted by Shao et al 18 . The ROM data obtained from the intact group and unstable group in this study showed a consistent trend and similar numerical values with previous research results 16–18 (Table 3 ). Therefore, the validity and reliability of the finite element models used in this study had been verified. Table 3 Comparison of the ROM of the C1-C2 level Groups Authors Level FE (°) LB (°) AR (°) Intact Panjabi et al. 11 C1-C2 24.4 ± 8.5 6.5 ± 2.3 56.7 ± 4.8 C3-C4 7.7 ± 5.0 9 ± 1.9 5.1 ± 1.2 C4-C5 10.1 ± 4.9 9.3 ± 1.7 6.8 ± 1.3 Ito et al. 14 C1-C2 15.3 ± 4.2 11.6 ± 10.4 63.3 ± 13 C3-C4 10 ± 4.5 8.6 ± 5.9 9.5 ± 4.9 C4-C5 14.3 ± 5.5 8.1 ± 3.8 11.5 ± 3.8 Present study C1-C2 24.8 9.1 32.1 C3-C4 8.3 5.8 7.4 C4-C5 8.0 4.6 8.0 Unstable Present study C1-C2 39.24 11.28 35.26 C3-C4 8.26 5.78 7.44 C4-C5 7.96 4.58 7.99 Shao et al. 15 C1-C2 26.24 7.50 29.3 Chun et al. 12 C1-C2 56.94 24.31 53.64 C1-2 ROM The ROM in the 5 fixation groups significantly decreased compared to that in the unstable group. The ROM values of the 5 fixation groups are shown in Table 4 (Fig. 4 ). Table 4 ROM Group FE LB AR ROM (°) C2 pedicle screw 2.39 0.32 0.71 Subfacetal body screw 2.61 0.34 0.37 Translaminar screw 2.23 1.06 1.25 Lateral mass screw 2.34 0.34 0.90 C3 pedicle screw 2.55 0.29 0.73 ROM increment (%) compared to C2 pedicle screw Subfacetal body screw 9.40 7.27 -47.87 Translaminar screw -6.40 233.89 76.32 Lateral mass screw -1.90 6.93 26.85 C3 pedicle screw 6.80 -9.46 2.83 ROM increment (%) compared to translaminar screw Subfacetal body screw 16.89 -67.87 -70.43 Lateral mass screw 4.81 -67.98 -28.05 C3 pedicle screw 14.11 -72.88 -41.68 In FE, the rank order from lowest to highest ROM was as follows: translaminar screw, lateral mass screw, C2 pedicle screw, C3 pedicle screw, and subfacetal body screw. In FE, the other fixation groups showed similar results of ROM compared to the C2 pedicle screw, all within 10%. Compared to the C2 pedicle screw, the subfacetal body, and C3 pedicle screw had increased ROM, while the translaminar screw and lateral mass screw had decreased ROM. Among them, the subfacetal body screw exhibited the greatest increase in ROM in FE, with an increase of 9.40%. Compared to the translaminar screw, subfacetal body and C3 pedicle screw increased the ROM in FE by 16.89% and 14.11%, respectively. The lateral mass screw showed a similar ROM result in FE, with an increment of 4.81%. In LB, the rank order from lowest to highest ROM was as follows: C3 pedicle screw, C2 pedicle screw, lateral mass screw, subfacetal body screw, and translaminar screw. The ROM increment compared to the C2 pedicle screw for the other fixation groups ranged from − 9.46–233.89%. Compared to the C2 pedicle screw, the C3 pedicle screw had a decreased ROM, while the other fixation groups had an increased ROM. Among them, the translaminar screw showed the largest increase, with an increment of 233.89%, and the C3 pedicle screw had the most limited ROM in LB, with a decrease of 9.46%. Compared to the translaminar screw, the subfacetal body, lateral mass and C3 pedicle screw decreased the ROM in LB with increments of -67.87%, -67.98%, and − 72.88%, respectively. In AR, the rank order from lowest to highest ROM was as follows: subfacetal body, C2 pedicle, C3 pedicle, lateral mass, translaminar screw. The ROM increment compared to the C2 pedicle for the other fixation groups ranged from − 47.87–76.32%. Compared to the C2 pedicle screw group, the subfacetal body screw had decreased ROM, while the other fixation groups had increased ROM. Among them, only the subfacetal body screw showed the smallest increase with a decrease of 47.87%, and the translaminar screw showed the largest increase with an increase of 76.32% (Table 4 ). Compared to the translaminar screw, the subfacetal body, lateral mass and C3 pedicle screws showed a decrease in ROM in AR, with increments of -70.43%, -28.05% and − 41.68%, respectively. PVMS of screw-rod construct In FE, the rank order from lowest to highest PVMS was as follows: lateral mass, translaminar, C2 pedicle, C3 pedicle, subfacetal body screw. The increase in PVMS in other fixation groups ranged from − 11.93–126.96%, compared to the C2 pedicle screw. Compared to the C2 pedicle screw, the lateral mass screw and translaminar screw reduced PVMS, while the other fixation screws increased PVMS. Among them, the subfacetal body screw led to the largest increase, with an increase of 126.96%, and the lateral mass screw led to the PVMS decrease, with a decrease of 11.93%. Compared to the translaminar screw, the subfacetal body and C3 pedicle screw increased the PVMS in FE with increment of 129.26% and 45.08%, respectively. On the other hand, the lateral mass screw decreased the PVMS in FE by 11.04%. In LB, the rank order from lowest to highest PVMS was as follows: C3 pedicle, lateral mass, C2 pedicle, subfacetal, translaminar screw. The increase in PVMS in the other fixation groups ranged from − 33.81–153.00%, compared to the C2 pedicle screw. Compared to the C2 pedicle screw, the C3 pedicle screw and lateral mass screw reduced PVMS, while the other fixation screws increased PVMS. Among them, the translaminar screw led to the largest increase, with an increase of 153.00%, and the C3 pedicle screw led to the smallest PVMS increase, with a decrease of 33.81%. Compared to the translaminar screw, the subfacetal body, lateral mass and C3 pedicle screw decreased the PVMS in LB by 30.88%, 66.18% and 73.84%, respectively. In AR, the rank order from lowest to highest PVMS was as follows: C2 pedicle, subfacetal, lateral mass, C3 pedicle, and translaminar screw. Compared to the C2 pedicle screw, the increment in PVMS for the other fixation groups ranged from 16.97–40.51%. All the fixation groups showed an increase in PVMS compared to the C2 pedicle screw. Among them, the translaminar screw had the largest PVMS increase at 40.51%, while the subfacetal body screw had the smallest PVMS increment by 16.97% (Table 5 ) (Fig. 4 , 5 ). Compared to the translaminar screw, the subfacetal body, lateral mass and C3 pedicle screw decreased the PVMS in LB by 16.75%, 10.77% and 8.00%, respectively. Table 5 Peak von Mises stress Group FE LB AR PVMS (MPa) C2 pedicle screw 293.89 195.49 219.56 Subfacetal body screw 667.01 341.85 256.82 Translaminar screw 290.94 494.59 308.51 Lateral mass screw 258.83 167.25 275.29 C3 pedicle screw 422.09 129.40 283.83 PVMS increment (%) compared to C2 pedicle screw Subfacetal body screw 126.96 74.87 16.97 Translaminar screw -1.00 153.00 40.51 Lateral mass screw -11.93 -14.45 25.38 C3 pedicle screw 43.62 -33.81 29.27 PVMS increment (%) compared to translaminar screw Subfacetal body screw 129.26 -30.88 -16.75 Lateral mass screw -11.04 -66.18 -10.77 C3 pedicle screw 45.08 -73.84 -8.00 Discussion The pedicle screw is regarded as the gold standard for posterior axis fixation using a screw-rod construct. Despite multiple studies validating its efficacy, the biomechanical properties of the two types of pedicle screws (C2 and C3 pedicel screws) remain unclear in the context of congenital C2-3 fusion. Congenital C2-3 fusion is commonly associated with HRVA in patients with AAD. Although novel alternative methods applicable to this situation have been clinically implemented, biomechanical investigations have not yet been conducted. This research presents a FEA of different screws used for C2-3 fused vertebrae with HRVA. With the widespread availability of robust screw fixation, C2 pedicle screws can achieve three-column fixation and are considered the first choice. It fixes the isthmus and pedicle and has a long screw path, and several studies have shown its biomechanical advantages 19, 20 . A cadaveric study found that C2 pedicle screws were superior to translaminar screws in AR and LB 20 . Chun, using FEA, found that C2 pedicle screws were the best because they are superior to translaminar and transarticular screws 15 . However, the biomechanical performance of C2 pedicle screws in the setting of congenital C2-3 fusion remains unclear. This study found that the ROM of C2 pedicle screws is superior to translaminar screws in AR and LB, consistent with the results obtained by Liu et al 20 . Furthermore, the PVMS on C2 pedicle screws in AR and LB is also lower than that on translaminar screws, indicating that C2 pedicle screws are still superior for use in C2-3 fused vertebrae. The use of C3 pedicle screws for C2-3 fused vertebrae was initially reported by Xiu et al. in 2014 7 . Du et al. 21 detailed the application of C3 pedicle screws in C2-3 fusion vertebrae in their reports. In C2-3 fused vertebrae, C3 pedicle screws can also stabilize three columns and achieve a long screw trajectory, providing the similar advantages as C2 pedicle screws. In the model used in this study, the lengths of the C2 and C3 pedicle screws were 32 mm and 28 mm, respectively. Therefore, it is necessary to investigate the biomechanical differences between these two screws. Currently, no studies have analyzed the biomechanics of C3 pedicle screws in C2-3 fused vertebra. Our study found that C3 pedicle screws had the least ROM and PVMS during LB. This could be attributed to the fact that the entry point of C3 pedicle screws is located more laterally, making it difficult for them to induce LB when supported by a rod, resulting in reduced ROM. Compared to the C2 pedicle screw, the C3 pedicle screw showed similar ROM in the three planes of motion, with increments of less than 10%. However, in FE and AR, it increased the PVMS by less than 50%. As a potential viable alternative, it is also necessary to investigate its differences compared to the traditional translaminar screws. Although it increased ROM by 14.11% in FE compared to translaminar screws, it significantly reduced ROM in LB and AR, with reductions of 72.88% and 41.68% respectively. Additionally, while it increased PVMS in FE compared to translaminar screws by 45.08%, it decreased PVMS by 73.84% and 8.00%, respectively in LB and AR. Therefore, C3 pedicle screws may be a biomechanically superior alternative to translaminar screws. In Xiu et al.'s study 7 , all patients achieved bony fusion. In Du et al.'s study 21 , 30 out of 33 individuals achieved fusion. This indicates that C3 pedicle screws are biomechanically reliable. Wang et al. were the first to document the application of lateral mass screws in C2-3 fused vertebrae, aimed at reinforcing the fixation of the C2 pedicle screw 6 . It fixes directly into the lateral mass, terminating at the intervertebral foramen. Currently, there is no study investigating the lateral mass screws for fused C2/3 vertebrae. Our results indicate similar ROM in FE and LB, but a 26.85% larger ROM in AR, compared to C2 pedicle screws. Given the crucial role of AR in the atlantoaxial joint, we hold some concerns regarding the lateral mass screw's resistance to AR. In comparison to the translaminar screws, it showed similar ROM in FE, and significantly reduces ROM in LB and AR by increments of -67.98% and − 28.05%, respectively. PVMS analysis revealed that the advantage of the lateral mass screw is its low PVMS, which is lower than that of the C2 pedicle screw in FE and LB. It is the only screw technique with PVMS superior to the translaminar screw in all three planes of motion. Therefore, it is inferred that its risk of screw fracture may be the lowest. This indicates that the lateral mass screw is a biomechanically feasible screw technique, may be superior to the translaminar screw. The subfacetal body screw was first reported by Patkar et al. in 2014 22 . This technique can achieve long bone purchase by angling inward toward the vertebral body 5, 23 , as demonstrated in the model of this study. Currently, there are no studies investigating the PVMS on this technique using FEA. Our study found that subfacetal body screws can effectively limit AR. This may be because the subfacetal body screw directly fixes on both sides of the odontoid process and reaches the ventral bone cortex, restricting atlantoaxial AR function, which is based on the odontoid process as the rotation axis. However, its drawback is the highest ROM and PVMS in FE. In terms of PVMS comparison, the subfacetal screw exhibited the highest PVMS, indicating the risk of screw fracture and potentially necessitating consideration for additional instrumentation reinforcement to share the stress. In addition, its strong biomechanical property of limiting rotation compensates for the shortcomings of the lateral mass screw, and the entry points of the two kinds of screw are located above and below the isthmus, respectively. This provides ideas for the combination of different screws to enhance stability. Compared to the translaminar screws, it exhibits lower PVMS in LB by 30.88% and AR by 16.75%. Compared to the C2 pedicle screws, it exhibits higher PVMS in LB by 74.87% and AR by 16.97%. In terms of ROM comparison, compared to the translaminar screws, it exhibits lower ROM in LB by 67.87% and AR by 70.43%. Compared to the C2 pedicle screws, it exhibits similar ROM in FE and LB, and decrease ROM by 47.87%. Although its ROM may be better than that of the C2 pedicle screw, its PVMS is the highest, so it cannot replace the C2 pedicle screw. Fortunately, its value was below the yield stress of titanium, and there have been no reports of screw fractures in the literature. Sushil et al. 24 , and Hou et al. 5 have reported a 100% stability rate for subfacetal screws. Therefore, the occurrence of screw fractures needs to be investigated through large clinical series. Considering its excellent ROM and the PVMS in LB and AR were smaller than translaminar screw, it may be preferable to the translaminar screws. The translaminar screw was first reported by Wright et al. in 2005 25 . In an earlier cadaveric study, C2 translaminar screws was found to be comparable to pedicle screws during FE, LB, and AR 26 . However, a clinical study by Chang revealed that translaminar screws had a higher failure rate than pedicle screws (57.1% for bilateral translaminar screws, 78.9% for unilateral translaminar screws, versus 100% for bilateral pedicle screws) 27 . Subsequent biomechanical studies shed light on this issue. An experiment by Claybrooks et al. 28 demonstrated that the ROM of translaminar screws was similar to that of pedicle screws in FE but significantly inferior in LB and AR. Our findings mainly align with Claybrooks' study, showing translaminar screws to be significantly inferior to C2 pedicle screws in LB and AR but superior in FE. This aligns with a previous FEA study conducted by Ma et al. 29 . PVMS analysis revealed the highest PVMS in LB and AR for translaminar screws compared to C2 pedicle screws. In this study, translaminar screws exhibited the poorest biomechanical performance, as evidenced by ROM and PVMS. Therefore, we consider them inferior to the three alternatives. This study has several advantages. Firstly, it is the first to investigate the biomechanical differences of various screw techniques in the setting of congenital C2-3 fusion using FEA. Secondly, previous studies modeled C2-3 fusion by obtaining CT data from normal individuals and using computer software to bind C2 and C3, which does not accurately represent the true morphology. In contrast, this study utilized CT data from patients with true congenital C2-3 fusion, providing a more accurate and realistic morphological model. Third, FEA, on the one hand, utilizes models of the same patient sample to implant different screws, eliminating intersample errors. On the other hand, computer-simulated screw placement is more precise, achieving consistent C1 screw trajectories for each model and reducing intergroup errors among different groups. Finally, FEA can calculate PVMS to assess the risk of screw fracture. This study has the following limitations: 1. The simulation of HRVA was achieved through Boolean subtraction rather than using actual patients with HRVA. In clinical surgery, different screws may be placed on both sides depending on the patient's anatomical structure. This study utilized CT data from a patient with mild deformity and bilateral symmetry to facilitate symmetrical screw placement. 2. HRVA has multiple patterns. In this study, only the isthmus height was reduced, and it could not represent all types of HRVA. 3. Congenital segmentation failure can be classified into three types based on the degree of fusion: segmentation type, partial fusion type, and complete fusion type 2 . In this study, we selected the most common form, complete fusion type, where the internal bone structure was entirely defined as cancellous bone. It is important to note that this model does not represent all fusion types. 4. The material properties and morphological characteristics (e.g., cortical bone thickness of 1 mm) adopted in this study were assumed based on data reported in the literature for normal populations, as the specific material properties of congenital C2-3 fused vertebrae and their deviations from those of normal populations remain unclear. Although instability and ligamentous deficiencies are known to exist in these patients, the exact nature of these defects is not fully understood. To simulate instability, certain ligaments were removed, and the corresponding ROM was determined based on values reported in the literature. 5. This FEA is only a numerical simulation based on one patient with limited evidence, and large-sample clinical studies are need to further verify the results. Conclusion For congenital C2-3 fusion and HRVA, C3 pedicle screws, lateral mass screws, and subfacetal body screws provide sufficient stability. All three alternatives may be reasonable options in this specific anatomical scenario. Declarations Funding: This article was supported by the Beijing Municipal Science and Technology Commission (Z191100006619040, T.F.) and the Capital Health Research and Development of Special (2020-2-8011, T.F.). Acknowledgment: none. Conflicts of Interest: none. The manuscript has been read and approved by all the authors. This manuscript has not been published or presented elsewhere in part or in entirety and is not under consideration by another journal. Research Ethics Committee approved the study. Author Contribution Qiang Jian: manuscript draft, revision. Xingang Zhao, Yinqian Wang and Cong Liang: methodology and critical revision.Xiuqing Qian: methodology.Tao Fan: supervision. References Tian Y, Xu N, Yan M, et al. Vertebral Artery Variations at the Craniovertebral Junction in "Sandwich" Atlantoaxial Dislocation Patients. Neurospine 2021;18:770-7. Jian Q, Bo X, Jian F, Chen Z. The role of clivus and atlanto-occipital lateral mass height in basilar invagination with or without atlas occipitalization. Neurosurg Rev 2024;47:404. Jian Q, Qin S, Hou Z, Zhao X, Liang C, Fan T. Individualized C1-2 intra-articular three-dimensional printed porous titanium alloy cage for craniovertebral deformity. J Orthop Surg Res 2024;19:569. Duan S, Xiao B, Cui W, et al. Finite element analysis of biomechanical changes in occipitocervical junction caused by atlanto-occipitocervical fusion and/or C2/3 fusion in Klippel-Feil syndrome. Chinese Journal of Spine and SpinaI Cord, 2021, 31(6): 540-548, 555 Hou Z, Jian Q, Fan W, Zhao X, Wang Y, Fan T. Application of C2 subfacetal screws for the management of atlantoaxial dislocation in patients with Klippel-Feil syndrome characterized by a narrow C2 pedicle and high-riding vertebral artery. J Orthop Surg Res 2022;17:495. Wang S, Wang C, Leng H, Zhao W, Yan M, Zhou H. Pedicle Screw Combined With Lateral Mass Screw Fixation in the Treatment of Basilar Invagination and Congenital C2-C3 Fusion. Clin Spine Surg 2016;29:448-53. Xiu P, Wang Q, Wang G, Wang S, Dai G, Lan Y. Morphological and clinical feasibility of C3 pedicle screw instrumentation in patients with congenital C2-3 fusion. European spine journal : official publication of the European Spine Society, the European Spinal Deformity Society, and the European Section of the Cervical Spine Research Society 2014;23:1730-6. Jian Q, Hou Z, Zhao X, Wang Y, Liang C, Fan T. A screw algorithm for congenital C2-3 fusion with high-riding vertebral arteries: feasibilities and clinical outcomes of five different fixation techniques. Neurosurgical Review 2024;47:520. Goto K, Tajima N, Chosa E, et al. Mechanical analysis of the lumbar vertebrae in a three-dimensional finite element method model in which intradiscal pressure in the nucleus pulposus was used to establish the model. J Orthop Sci 2002;7:243-6. Schmidt H, Heuer F, Drumm J, Klezl Z, Claes L, Wilke HJ. Application of a calibration method provides more realistic results for a finite element model of a lumbar spinal segment. Clin Biomech (Bristol, Avon) 2007;22:377-84. Shirazi-Adl A, Ahmed AM, Shrivastava SC. Mechanical response of a lumbar motion segment in axial torque alone and combined with compression. Spine 1986;11:914-27. Brolin K, Halldin P. Development of a finite element model of the upper cervical spine and a parameter study of ligament characteristics. Spine 2004;29:376-85. Kong D, Wang Q, Huang J, et al. A Biomimetic Structural Material with Adjustable Mechanical Property for Bone Tissue Engineering. Advanced Functional Materials 2024;34:2305412. Jian Q, Qin S, Hou Z, et al. Biomechanical differences of three cephalic fixation methods for patients with basilar invagination and atlantoaxial dislocation in the setting of congenital atlas occipitalization: a finite element analysis. The spine journal : official journal of the North American Spine Society 2025;25:389-400. Chun DH, Yoon DH, Kim KN, Yi S, Shin DA, Ha Y. Biomechanical Comparison of Four Different Atlantoaxial Posterior Fixation Constructs in Adults: A Finite Element Study. Spine 2018;43:E891-E7. Panjabi MM, Crisco JJ, Vasavada A, et al. Mechanical properties of the human cervical spine as shown by three-dimensional load-displacement curves. Spine 2001;26:2692-700. Ito S, Ivancic PC, Panjabi MM, Cunningham BW. Soft tissue injury threshold during simulated whiplash: a biomechanical investigation. Spine 2004;29:979-87. Shao M, Dai Y, Zhu W, Yu J, Lyu F. Bicortical Short C2 Pars Screw Fixation for High-Riding Vertebral Artery Provided Sufficient Biomechanical Stability: A Finite Element Study. Spine 2022;47:369-75. Lehman RA, Jr., Dmitriev AE, Helgeson MD, Sasso RC, Kuklo TR, Riew KD. Salvage of C2 pedicle and pars screws using the intralaminar technique: a biomechanical analysis. Spine 2008;33:960-5. Liu S, Song Z, Liu L, et al. Biomechanical evaluation of C1 lateral mass and C2 translaminar bicortical screws in atlantoaxial fixation: an in vitro human cadaveric study. The spine journal : official journal of the North American Spine Society 2018;18:674-81. Du YQ, Yin YH, Li T, Qiao GY, Yu XG. Can C1 lateral mass and C3 pedicle screw fixation be used as an option for atlantoaxial reduction and stabilization in Klippel-Feil patients? A study of its morphological feasibility, technical nuances, and clinical efficiency. Neurosurg Rev 2022;45:2183-92. Patkar SV. Sub-Facetal C2 Body Screw In Posterior Fixation (Goel-Harm's Technique) Of The Atlanto-Axial Joint Avoiding The Vertebral Artery. Internet Journal of Neurosurgery 2014. Singh DK, Shankar D, Singh N, Singh RK, Chand VK. C2 Screw fixation techniques in atlantoaxial instability: A technical review. Journal of craniovertebral junction & spine 2022;13:368-77. Sushil P. C2 Subfacetal Body Screw in Posterior Atlantoaxial Fixation (Goel–Harm Technique) to Avoid the Vertebral Artery. Global Spine Journal 2015;5:s-0035-1554307-s-0035-. Wright NM. Translaminar rigid screw fixation of the axis. Technical note. Journal of neurosurgery. Spine 2005;3:409-14. Gorek J, Acaroglu E, Berven S, Yousef A, Puttlitz CM. Constructs incorporating intralaminar C2 screws provide rigid stability for atlantoaxial fixation. Spine 2005;30:1513-8. Chang CC, Huang WC, Tu TH, et al. Differences in fixation strength among constructs of atlantoaxial fixation. Journal of neurosurgery. Spine 2018;30:52-9. Claybrooks R, Kayanja M, Milks R, Benzel E. Atlantoaxial fusion: a biomechanical analysis of two C1-C2 fusion techniques. The spine journal : official journal of the North American Spine Society 2007;7:682-8. Ma X, Peng X, Xiang H, Zhang Y, Zhang G, Chen B. A finite element modeling of posterior atlantoaxial fixation and biomechanical analysis of C2 intralaminar screw fixation. Chin Med J (Engl) 2014;127:1266-71. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5072741","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":430934072,"identity":"bd9deb63-ce22-4466-aa41-e0a97aeaf147","order_by":0,"name":"Qiang Jian","email":"","orcid":"","institution":"Spine Center, Sanbo Brain Hospital, Capital Medical University, Beijing, People’s Republic of China","correspondingAuthor":false,"prefix":"","firstName":"Qiang","middleName":"","lastName":"Jian","suffix":""},{"id":430934073,"identity":"78381ea5-45b6-4856-8e24-5fd9db904ed9","order_by":1,"name":"Xingang Zhao","email":"","orcid":"","institution":"Spine Center, Sanbo Brain Hospital, Capital Medical University, Beijing, People’s Republic of China","correspondingAuthor":false,"prefix":"","firstName":"Xingang","middleName":"","lastName":"Zhao","suffix":""},{"id":430934074,"identity":"874cfed1-6dfe-4bc6-8c69-04c2e5c581c3","order_by":2,"name":"Yinqian Wang","email":"","orcid":"","institution":"Spine Center, Sanbo Brain Hospital, Capital Medical University, Beijing, People’s Republic of China","correspondingAuthor":false,"prefix":"","firstName":"Yinqian","middleName":"","lastName":"Wang","suffix":""},{"id":430934075,"identity":"b2ec18bf-855f-4f0f-97db-478a0b50cf21","order_by":3,"name":"Cong Liang","email":"","orcid":"","institution":"Spine Center, Sanbo Brain Hospital, Capital Medical University, Beijing, People’s Republic of China","correspondingAuthor":false,"prefix":"","firstName":"Cong","middleName":"","lastName":"Liang","suffix":""},{"id":430934076,"identity":"75ca202c-30bc-43cb-939a-001ec5c0c878","order_by":4,"name":"Xiuqing Qian","email":"","orcid":"","institution":"School of Biomedical Engineering, Capital Medical University, Beijing 100069, China.","correspondingAuthor":false,"prefix":"","firstName":"Xiuqing","middleName":"","lastName":"Qian","suffix":""},{"id":430934077,"identity":"73bff2b9-7aba-4aa8-a83e-7455c0156fa6","order_by":5,"name":"Tao Fan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAArElEQVRIiWNgGAWjYBAC9gYg8QHKkSBKC88BBsbGGSRraeYhTQv72eOPbWrsog0OMB+8zcNgl0dYC09eYnPOseTcDQfYkq15GJKLCWqxZ8gxbM5tOADUwmMmzcNwILGBoC38bwybLcFa+L8RqUUCaAsjxBY2YrW8MZzZA/TLzMNsxpZzDJKJcViOwYcfNXa5fcebH954U2FHWAsCMIMIA+LVj4JRMApGwSjAAwB2Ezl6y+eCzgAAAABJRU5ErkJggg==","orcid":"","institution":"Spine Center, Sanbo Brain Hospital, Capital Medical University, Beijing, People’s Republic of China","correspondingAuthor":true,"prefix":"","firstName":"Tao","middleName":"","lastName":"Fan","suffix":""}],"badges":[],"createdAt":"2024-09-11 16:49:38","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5072741/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5072741/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":78867151,"identity":"bd934c1d-e2f4-4f75-94bc-6c051c5b0958","added_by":"auto","created_at":"2025-03-20 04:34:43","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":555045,"visible":true,"origin":"","legend":"\u003cp\u003eThree alternatives especially for C2-3 fused vertebrae with HRVA. (A) Posterior view of the right C3 pedicle screw starting point. (B) Lateral view of the right C3 pedicle screw starting point. (C) Lateral view of the right C3 pedicle screw. (D) C3 pedicle screw in CT with multiplane reconstruction. (E) Posterior view of the right subfacetal screw starting point. (F) Lateral view of the right subfacetal screw starting point. (G) Lateral view of the right subfacetal screw. (H) Subfacetal screw in sagittal CT. (I) Posterior view of the left lateral mass screw. (J) Lateral view of the left lateral mass screw. (K) Lateral view of the left lateral mass screw. (L) Lateral mass screw in sagittal CT. The green points indicate the entry point.\u003c/p\u003e","description":"","filename":"Figure1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5072741/v1/95880a79b9cece262bfe2db1.jpg"},{"id":78867689,"identity":"5995634f-7ff3-46aa-a6df-62bc8ec2bfe5","added_by":"auto","created_at":"2025-03-20 04:42:43","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":875299,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of the unstable group and five fixation groups\u003c/p\u003e\n\u003cp\u003e(A) The unstable group consists of models with C2-3 fusion, AAD and HRVA. Note the enlarged transverse foramen and reduced height of the isthmus. (B) The lateral view and posterior view of translaminar screw. (C) The lateral view and posterior view of C3 pedicle screw. (D) The lateral view and posterior view of subfacetal screw. (E) The lateral view and posterior view of lateral mass screw. (F) The lateral view and posterior view of C2 pedicle screw. All fixation groups underwent the implantation of C1 pedicle screws following the same trajectory.\u003c/p\u003e","description":"","filename":"Figure2.tif.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5072741/v1/a9bc582febf5f7ffd3492292.jpg"},{"id":78867160,"identity":"94d8a331-f0fa-4985-b3b9-c497afbb1404","added_by":"auto","created_at":"2025-03-20 04:34:44","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":10607419,"visible":true,"origin":"","legend":"\u003cp\u003eIllustration of model construction and research group\u003c/p\u003e\n\u003cp\u003eThe intact, unstable, and C2 pedicle groups were established for model validation and as control groups based on the C2-3 fused vertebra without HRVA. The C2-3 fused vertebra with HRVA, created using Boolean subtraction operations, was modeled into subfacetal body screw models, translaminar screw models, lateral mass screw models, and C3 pedicle screw models for subsequent finite element analysis.\u003c/p\u003e","description":"","filename":"Figure3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5072741/v1/d31430f60e54417ad616af21.jpg"},{"id":78867690,"identity":"b51a8c35-d22e-4781-b0bd-5856ecbda7f7","added_by":"auto","created_at":"2025-03-20 04:42:44","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1390927,"visible":true,"origin":"","legend":"\u003cp\u003eThe results of ROM and peak von Mises stress.\u003c/p\u003e","description":"","filename":"Figure4.tif.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5072741/v1/587d23d9ea1922bc1bd485a6.jpg"},{"id":78867154,"identity":"d5e84806-14fb-434f-a932-8e9609d02ec6","added_by":"auto","created_at":"2025-03-20 04:34:44","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":3646988,"visible":true,"origin":"","legend":"\u003cp\u003eEquivalent von Mises stress contour\u003c/p\u003e","description":"","filename":"Figure5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5072741/v1/ce2be9e856bbec6378dc0428.jpg"},{"id":83001443,"identity":"63fc7157-b19a-4be1-a3a4-a0ebf182bfdf","added_by":"auto","created_at":"2025-05-19 01:16:30","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":17779248,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5072741/v1/e917cb30-4235-42bf-956b-ed9991d5bbf1.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A finite element analysis of three alternatives to C2 pedicle screw in the setting of congenital C2-3 fusion and high-riding vertebral arteries","fulltext":[{"header":"Introduction","content":"\u003cp\u003eCongenital C2-3 fusion is a special kind of Klippel-Feil syndrome, which is often associated with congenital atlas occipitalization (AOZ) and atlantoaxial dislocation (AAD)\u003csup\u003e1\u0026ndash;3\u003c/sup\u003e. Despite the presence of anatomical anomalies and aberrant biomechanical changes, there has been scarce research exploring the biomechanical characteristics of congenital C2-3 fusion. Recent reports highlight that C2-3 fusion can lead to an escalation in stress on the transverse ligament and lateral joint, potentially contributing to the development of AAD\u003csup\u003e4\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe treatment of AAD with C2-3 fused vertebrae presents both challenges and opportunities. This abnormal fusion of C2-3 vertebrae reduces the height of the cervical spine, while the abnormal AAD causes misalignment of the cervical spine. Both factors can lead to the tortuosity of the vertebral artery (VA), in turn resulting in a high-riding vertebral artery (HRVA) and eroded C2 pedicle. The presence of HRVA significantly complicates the placement of C2 pedicle/pars screws in the treatment of AAD\u003csup\u003e1\u003c/sup\u003e. Opting for alternatives to C2 pedicle/pars screw becomes a necessary resort. Fortunately, the increased volume of the C2-3 fused vertebrae allows for the implantation of novel alternatives\u003csup\u003e5\u0026ndash;8\u003c/sup\u003e. Three special anatomical structures, C3 pedicle, fused lateral mass column and thickened C2 superior articular process, serve as additional screw insertion sites in congenital C2-3 fused vertebrae, which accommodate the C3 pedicle screw, lateral mass screw and the subfacetal body screw, respectively (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Currently, the biomechanical characteristics of the three alternatives for addressing this special anatomical anomaly remain unclear.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSeveral cadaver studies have compared the ROM among various C1-C2 fixation techniques. Due to the unavailability of cadaveric specimens with congenital C2-3 fusion and HRVA, cadaveric studies could not be conducted. To address this, we employed finite element analysis (FEA) to scrutinize the biomechanical stability of the three alternatives in the setting of congenital C2-3 fused vertebrae with HRVA. To the best of our knowledge, there is no FEA related to screw placement in fused C2-3 vertebrae with HRVA.\u003c/p\u003e"},{"header":"Materials and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eMaterial\u003c/h2\u003e \u003cp\u003eA 25-year-old female inpatient who underwent transnasal endoscopic pituitary tumor resection was found to have congenital C2-3 fusion during a computed tomography scan (Philips Brilliance 64-slice scanner, Philips in Amsterdam, Netherlands). No other cervical spine disorders were found, such as disc herniation, spinal stenosis, fractures, tumors or tuberculosis. CT images were obtained in DICOM format with a resolution of 512 \u0026times; 512 pixels and a slice thickness of 1.0 mm. The ethics committee approved the study.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eModel Construction and material properties\u003c/h3\u003e\n\u003cp\u003eMimics 13.0 (Materialise Company, Belgium) was used to reconstruct the three-dimensional point cloud model. Subsequently, the model was imported into Geomagic Studio 2015 (Geomagic Inc., United States) to create editable geometric solid models. Solidworks 2016 (SolidWorks Corp., United States) was used to construct the screws and rods. The geometric solid models were then imported into Hypermesh 2017 (Altair Engineering Corp., United States) for meshing, application of boundary conditions, assignment of material properties, and definition of contact. Finally, the model was analyzed using ABAQUS 2019 (Dassault Systemes Simulia Inc., France).\u003c/p\u003e \u003cp\u003eThe cortical bone was simulated using C3D6 elements with a thickness of 1mm, while the filled trabecular bone was represented using C3D4 elements. The intervertebral discs, composed of the nucleus pulposus (60%) and the annulus fibrosus (40%)\u003csup\u003e9\u003c/sup\u003e, were simulated using C3D8R elements with additional hourglass control. The Jacobian ratio was constrained to be above 0.6 to control the mesh quality. The intervertebral disc was simulated using an incompressible hyperelastic material by a Mooney\u0026ndash;Rivlin material law\u003csup\u003e10\u003c/sup\u003e. This simulation does not take into account density and also disregards the influence of collagen fibers\u003csup\u003e11\u003c/sup\u003e. Shell elements were used to model the transverse ligament with material property defined as orthotropic anisotropic\u003csup\u003e12\u003c/sup\u003e (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). SPRINGA elements were used to simulate the other ligaments, including the anterior atlanto-occipital membrane, posterior atlanto-occipital membrane, cruciate ligament, apical ligament, alar ligament, tectorial membrane, anterior longitudinal ligament, posterior longitudinal ligament, ligamentum flavum, facet capsule ligament, interspinous ligament, and supraspinous ligament. These ligaments are defined as elastic‒plastic material properties\u003csup\u003e12\u003c/sup\u003e. Ligament failure is not involved in this study. therefore, the force-displacement curve is divided into two zones: neutral zone and elastic zone. A parabolic fitting is employed for the neutral zone, while a linear fitting is used for the elastic zone in force-displacement curve (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The material properties \u003csup\u003e10, 11, 13, 14\u003c/sup\u003e are listed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMaterial property\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eElastic modulus/Mpa\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePoisson\u0026rsquo;s ratio\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCortical bone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e12000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCancellous bone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCartilage endplate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTi (Screw and rod)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e120000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNucleus pulposus\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMooney\u0026ndash;Rivlin c1\u0026thinsp;=\u0026thinsp;0.12, c2\u0026thinsp;=\u0026thinsp;0.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.495\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAnnulus fibrosus\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMooney\u0026ndash;Rivlin c1\u0026thinsp;=\u0026thinsp;0.18, c2\u0026thinsp;=\u0026thinsp;0.045\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTransverse ligament\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eE1\u0026thinsp;=\u0026thinsp;86, E2\u0026thinsp;=\u0026thinsp;6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.016\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"3\"\u003eE1: in lateral direction, in axial plane. E2: in vertical direction, in sagittal plane. Perpendicular to E1.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eProperties of ligaments\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLigaments\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ed\u003csub\u003ef\u003c/sub\u003e(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ef\u003csub\u003ef\u003c/sub\u003e (N)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ed\u003csub\u003en\u003c/sub\u003e (mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ef\u003csub\u003en\u003c/sub\u003e (N)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eParabolic coefficient\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAnterior atlantoaxial membrane\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e18.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e232\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e23.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.623695\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePosterior atlantoaxial membrane\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e18.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.033333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.228015\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJoint capsule ligament(C0-C1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e320\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2.938476\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJoint capsule ligament (C1-C2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e314\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e31.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.452191\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJoint capsule ligament (C2-C3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2.333333\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAnterior longitudinal ligament\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e7.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLigamentum flavum (C1-C2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e111\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e11.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.083984\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLigamentum flavum (C2-C3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2.25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eApical ligament\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e214\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e21.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e8.359375\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAlar ligament\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e14.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e357\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e35.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e4.489211\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCruciform ligament of atlas\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e12.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e436\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e43.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e6.976\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTectorial membrane\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.966667\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e7.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.483017\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePosterior longitudinal ligament\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.333333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.72\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInterspinous ligament\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.333333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.679592\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003eFailure is not involved in this study, and thus the plastic zone and failure zone are removed; therefore, the force-displacement curve is divided into two zones: neutral zone and elastic zone. The neutral region ends in the point (d\u003csub\u003en\u003c/sub\u003e, f\u003csub\u003en\u003c/sub\u003e) and the elastic region ends in the point (d\u003csub\u003ef\u003c/sub\u003e, f\u003csub\u003ef\u003c/sub\u003e).\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eNonlinear surface-to-surface contact relationships were used to simulate the interaction between joints. The contacts between the facet joints and between spinous processes of C3-C5, as well as the contact between the odontoid process and the transverse ligament and between the odontoid process and the atlas, were all set as hard contacts.\u003c/p\u003e\n\u003ch3\u003eResearch Groups\u003c/h3\u003e\n\u003cp\u003eWe constructed the following groups: intact, unstable, C2 pedicle screw, subfacetal body screw, translaminar screw, C3 pedicle screw, and lateral mass screw groups (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe intact group comprised individuals with C0-C5 levels exhibiting congenital atlas occipitalization and C2-3 fusion devoid of AAD. In contrast, the unstable group was characterized by the removal of the cruciate ligament, alar ligament, anterior longitudinal ligament, and transverse ligament for simulating instability. Additionally, the atlantodental interval was deliberately set at more than 3 mm, thus simulating AAD. To simulate HRVAs, the VA grooves were expanded using a Boolean subtraction operation (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe C1-2/3 models was inserted by screw-rod constructs (3.5 mm in diameter). The fixation models were constructed based on the realigned unstable group configuration (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). The C1 trans-arch lateral mass screws (26 mm in length) were inserted in each fixation model. The C2 pedicle screws (32 mm in length) were implanted into the C2 pedicles along with their respective directions. Similarly, C3 pedicle screws (28 mm in length) were implanted into the C3 pedicles along with their respective directions, as depicted in the schematic illustration showing the translucent pedicle region (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Subfacetal body screws (28mm in length) were implanted into the superior articular processes and vertebral body from posterior aspects with medial direction of 45\u0026deg;. Bilateral translaminar screws (28 mm in length) were implanted into laminas. Lateral mass screws (18 mm in length) were inserted with cephalic angle of 40\u0026deg; from the midpoint of fused lateral mass. The screws and rods form a common node connection, with the relationship between the implants and the vertebral bodies set as an Embed relationship.\u003c/p\u003e\n\u003ch3\u003eLoading and boundary conditions\u003c/h3\u003e\n\u003cp\u003eThe inferior surface of C5 was fixed in all 6 degrees of freedom. A reference point was created on the C0 rotation axis. A distribution coupling constraint is established between this point and the upper endplate nodes. Pure torque loads of 1.5 Nm are applied at the neutral point in different directions according to the right-hand rule\u003csup\u003e15\u003c/sup\u003e. These torques are applied to simulate flexion and extension (FE), left and right lateral bending (LB), and left and right axial rotation (AR).\u003c/p\u003e\n\u003ch3\u003eParameters\u003c/h3\u003e\n\u003cp\u003eThe range of motion (ROM) and peak von Mise stress (PVMS) during FE, LB, and AR in three different planes were summarized.\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003eModel accuracy verification\u003c/h2\u003e \u003cp\u003eThe segmental C1-2 ROM of intact group was 24.8\u0026deg; in FE, 9.1\u0026deg; in LB and 32.1\u0026deg; in AR, comparable to results from previous biomechanical study\u003csup\u003e16, 17\u003c/sup\u003e. The segmental C1-2 ROM of unstable group was 39.24\u0026deg; in FE, 11.28\u0026deg; in LB and 35.26\u0026deg; in AR, similar with the results from previous study conducted by Shao et al\u003csup\u003e18\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe ROM data obtained from the intact group and unstable group in this study showed a consistent trend and similar numerical values with previous research results\u003csup\u003e16\u0026ndash;18\u003c/sup\u003e (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). Therefore, the validity and reliability of the finite element models used in this study had been verified.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of the ROM of the C1-C2 level\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGroups\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAuthors\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLevel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFE (\u0026deg;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLB (\u0026deg;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eAR (\u0026deg;)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"8\" rowspan=\"9\"\u003e \u003cp\u003eIntact\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003ePanjabi et al. \u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC1-C2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e24.4\u0026thinsp;\u0026plusmn;\u0026thinsp;8.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e6.5\u0026thinsp;\u0026plusmn;\u0026thinsp;2.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e56.7\u0026thinsp;\u0026plusmn;\u0026thinsp;4.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC3-C4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7.7\u0026thinsp;\u0026plusmn;\u0026thinsp;5.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e9\u0026thinsp;\u0026plusmn;\u0026thinsp;1.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e5.1\u0026thinsp;\u0026plusmn;\u0026thinsp;1.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC4-C5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e10.1\u0026thinsp;\u0026plusmn;\u0026thinsp;4.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e9.3\u0026thinsp;\u0026plusmn;\u0026thinsp;1.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e6.8\u0026thinsp;\u0026plusmn;\u0026thinsp;1.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eIto et al.\u003csup\u003e14\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC1-C2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e15.3\u0026thinsp;\u0026plusmn;\u0026thinsp;4.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e11.6\u0026thinsp;\u0026plusmn;\u0026thinsp;10.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e63.3\u0026thinsp;\u0026plusmn;\u0026thinsp;13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC3-C4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e10\u0026thinsp;\u0026plusmn;\u0026thinsp;4.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.6\u0026thinsp;\u0026plusmn;\u0026thinsp;5.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e9.5\u0026thinsp;\u0026plusmn;\u0026thinsp;4.9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC4-C5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e14.3\u0026thinsp;\u0026plusmn;\u0026thinsp;5.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.1\u0026thinsp;\u0026plusmn;\u0026thinsp;3.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e11.5\u0026thinsp;\u0026plusmn;\u0026thinsp;3.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003ePresent study\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC1-C2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e24.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e9.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e32.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC3-C4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e7.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC4-C5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e8.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003eUnstable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003ePresent study\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC1-C2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e39.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e11.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e35.26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC3-C4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e7.44\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC4-C5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e7.99\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eShao et al.\u003csup\u003e15\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC1-C2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e26.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e7.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e29.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eChun et al. \u003csup\u003e12\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC1-C2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e56.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e24.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e53.64\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eC1-2 ROM\u003c/h3\u003e\n\u003cp\u003eThe ROM in the 5 fixation groups significantly decreased compared to that in the unstable group. The ROM values of the 5 fixation groups are shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eROM\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGroup\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLB\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAR\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eROM (\u0026deg;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC2 pedicle screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.71\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSubfacetal body screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.37\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTranslaminar screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLateral mass screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC3 pedicle screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.73\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eROM increment (%) compared to C2 pedicle screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSubfacetal body screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e9.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e7.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-47.87\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTranslaminar screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-6.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e233.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e76.32\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLateral mass screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-1.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e26.85\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC3 pedicle screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-9.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.83\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eROM increment (%) compared to translaminar screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSubfacetal body screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e16.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-67.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-70.43\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLateral mass screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-67.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-28.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC3 pedicle screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e14.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-72.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-41.68\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn FE, the rank order from lowest to highest ROM was as follows: translaminar screw, lateral mass screw, C2 pedicle screw, C3 pedicle screw, and subfacetal body screw. In FE, the other fixation groups showed similar results of ROM compared to the C2 pedicle screw, all within 10%. Compared to the C2 pedicle screw, the subfacetal body, and C3 pedicle screw had increased ROM, while the translaminar screw and lateral mass screw had decreased ROM. Among them, the subfacetal body screw exhibited the greatest increase in ROM in FE, with an increase of 9.40%. Compared to the translaminar screw, subfacetal body and C3 pedicle screw increased the ROM in FE by 16.89% and 14.11%, respectively. The lateral mass screw showed a similar ROM result in FE, with an increment of 4.81%.\u003c/p\u003e \u003cp\u003eIn LB, the rank order from lowest to highest ROM was as follows: C3 pedicle screw, C2 pedicle screw, lateral mass screw, subfacetal body screw, and translaminar screw. The ROM increment compared to the C2 pedicle screw for the other fixation groups ranged from \u0026minus;\u0026thinsp;9.46\u0026ndash;233.89%. Compared to the C2 pedicle screw, the C3 pedicle screw had a decreased ROM, while the other fixation groups had an increased ROM. Among them, the translaminar screw showed the largest increase, with an increment of 233.89%, and the C3 pedicle screw had the most limited ROM in LB, with a decrease of 9.46%. Compared to the translaminar screw, the subfacetal body, lateral mass and C3 pedicle screw decreased the ROM in LB with increments of -67.87%, -67.98%, and \u0026minus;\u0026thinsp;72.88%, respectively.\u003c/p\u003e \u003cp\u003eIn AR, the rank order from lowest to highest ROM was as follows: subfacetal body, C2 pedicle, C3 pedicle, lateral mass, translaminar screw. The ROM increment compared to the C2 pedicle for the other fixation groups ranged from \u0026minus;\u0026thinsp;47.87\u0026ndash;76.32%. Compared to the C2 pedicle screw group, the subfacetal body screw had decreased ROM, while the other fixation groups had increased ROM. Among them, only the subfacetal body screw showed the smallest increase with a decrease of 47.87%, and the translaminar screw showed the largest increase with an increase of 76.32% (Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Compared to the translaminar screw, the subfacetal body, lateral mass and C3 pedicle screws showed a decrease in ROM in AR, with increments of -70.43%, -28.05% and \u0026minus;\u0026thinsp;41.68%, respectively.\u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003ePVMS of screw-rod construct\u003c/h2\u003e \u003cp\u003eIn FE, the rank order from lowest to highest PVMS was as follows: lateral mass, translaminar, C2 pedicle, C3 pedicle, subfacetal body screw. The increase in PVMS in other fixation groups ranged from \u0026minus;\u0026thinsp;11.93\u0026ndash;126.96%, compared to the C2 pedicle screw. Compared to the C2 pedicle screw, the lateral mass screw and translaminar screw reduced PVMS, while the other fixation screws increased PVMS. Among them, the subfacetal body screw led to the largest increase, with an increase of 126.96%, and the lateral mass screw led to the PVMS decrease, with a decrease of 11.93%. Compared to the translaminar screw, the subfacetal body and C3 pedicle screw increased the PVMS in FE with increment of 129.26% and 45.08%, respectively. On the other hand, the lateral mass screw decreased the PVMS in FE by 11.04%.\u003c/p\u003e \u003cp\u003eIn LB, the rank order from lowest to highest PVMS was as follows: C3 pedicle, lateral mass, C2 pedicle, subfacetal, translaminar screw. The increase in PVMS in the other fixation groups ranged from \u0026minus;\u0026thinsp;33.81\u0026ndash;153.00%, compared to the C2 pedicle screw. Compared to the C2 pedicle screw, the C3 pedicle screw and lateral mass screw reduced PVMS, while the other fixation screws increased PVMS. Among them, the translaminar screw led to the largest increase, with an increase of 153.00%, and the C3 pedicle screw led to the smallest PVMS increase, with a decrease of 33.81%. Compared to the translaminar screw, the subfacetal body, lateral mass and C3 pedicle screw decreased the PVMS in LB by 30.88%, 66.18% and 73.84%, respectively.\u003c/p\u003e \u003cp\u003eIn AR, the rank order from lowest to highest PVMS was as follows: C2 pedicle, subfacetal, lateral mass, C3 pedicle, and translaminar screw. Compared to the C2 pedicle screw, the increment in PVMS for the other fixation groups ranged from 16.97\u0026ndash;40.51%. All the fixation groups showed an increase in PVMS compared to the C2 pedicle screw. Among them, the translaminar screw had the largest PVMS increase at 40.51%, while the subfacetal body screw had the smallest PVMS increment by 16.97% (Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e) (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). Compared to the translaminar screw, the subfacetal body, lateral mass and C3 pedicle screw decreased the PVMS in LB by 16.75%, 10.77% and 8.00%, respectively.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePeak von Mises stress\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGroup\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLB\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAR\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePVMS (MPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC2 pedicle screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e293.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e195.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e219.56\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSubfacetal body screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e667.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e341.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e256.82\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTranslaminar screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e290.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e494.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e308.51\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLateral mass screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e258.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e167.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e275.29\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC3 pedicle screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e422.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e129.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e283.83\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePVMS increment (%) compared to C2 pedicle screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSubfacetal body screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e126.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e74.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e16.97\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTranslaminar screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e153.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40.51\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLateral mass screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-11.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-14.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25.38\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC3 pedicle screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e43.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-33.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e29.27\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePVMS increment (%) compared to translaminar screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSubfacetal body screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e129.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-30.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-16.75\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLateral mass screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-11.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-66.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-10.77\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC3 pedicle screw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e45.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-73.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-8.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe pedicle screw is regarded as the gold standard for posterior axis fixation using a screw-rod construct. Despite multiple studies validating its efficacy, the biomechanical properties of the two types of pedicle screws (C2 and C3 pedicel screws) remain unclear in the context of congenital C2-3 fusion. Congenital C2-3 fusion is commonly associated with HRVA in patients with AAD. Although novel alternative methods applicable to this situation have been clinically implemented, biomechanical investigations have not yet been conducted. This research presents a FEA of different screws used for C2-3 fused vertebrae with HRVA.\u003c/p\u003e \u003cp\u003eWith the widespread availability of robust screw fixation, C2 pedicle screws can achieve three-column fixation and are considered the first choice. It fixes the isthmus and pedicle and has a long screw path, and several studies have shown its biomechanical advantages\u003csup\u003e19, 20\u003c/sup\u003e. A cadaveric study found that C2 pedicle screws were superior to translaminar screws in AR and LB\u003csup\u003e20\u003c/sup\u003e. Chun, using FEA, found that C2 pedicle screws were the best because they are superior to translaminar and transarticular screws\u003csup\u003e15\u003c/sup\u003e. However, the biomechanical performance of C2 pedicle screws in the setting of congenital C2-3 fusion remains unclear. This study found that the ROM of C2 pedicle screws is superior to translaminar screws in AR and LB, consistent with the results obtained by Liu et al\u003csup\u003e20\u003c/sup\u003e. Furthermore, the PVMS on C2 pedicle screws in AR and LB is also lower than that on translaminar screws, indicating that C2 pedicle screws are still superior for use in C2-3 fused vertebrae.\u003c/p\u003e \u003cp\u003eThe use of C3 pedicle screws for C2-3 fused vertebrae was initially reported by Xiu et al. in 2014 \u003csup\u003e7\u003c/sup\u003e. Du et al. \u003csup\u003e21\u003c/sup\u003e detailed the application of C3 pedicle screws in C2-3 fusion vertebrae in their reports. In C2-3 fused vertebrae, C3 pedicle screws can also stabilize three columns and achieve a long screw trajectory, providing the similar advantages as C2 pedicle screws. In the model used in this study, the lengths of the C2 and C3 pedicle screws were 32 mm and 28 mm, respectively. Therefore, it is necessary to investigate the biomechanical differences between these two screws. Currently, no studies have analyzed the biomechanics of C3 pedicle screws in C2-3 fused vertebra. Our study found that C3 pedicle screws had the least ROM and PVMS during LB. This could be attributed to the fact that the entry point of C3 pedicle screws is located more laterally, making it difficult for them to induce LB when supported by a rod, resulting in reduced ROM. Compared to the C2 pedicle screw, the C3 pedicle screw showed similar ROM in the three planes of motion, with increments of less than 10%. However, in FE and AR, it increased the PVMS by less than 50%. As a potential viable alternative, it is also necessary to investigate its differences compared to the traditional translaminar screws. Although it increased ROM by 14.11% in FE compared to translaminar screws, it significantly reduced ROM in LB and AR, with reductions of 72.88% and 41.68% respectively. Additionally, while it increased PVMS in FE compared to translaminar screws by 45.08%, it decreased PVMS by 73.84% and 8.00%, respectively in LB and AR. Therefore, C3 pedicle screws may be a biomechanically superior alternative to translaminar screws. In Xiu et al.'s study\u003csup\u003e7\u003c/sup\u003e, all patients achieved bony fusion. In Du et al.'s study\u003csup\u003e21\u003c/sup\u003e, 30 out of 33 individuals achieved fusion. This indicates that C3 pedicle screws are biomechanically reliable.\u003c/p\u003e \u003cp\u003eWang et al. were the first to document the application of lateral mass screws in C2-3 fused vertebrae, aimed at reinforcing the fixation of the C2 pedicle screw\u003csup\u003e6\u003c/sup\u003e. It fixes directly into the lateral mass, terminating at the intervertebral foramen. Currently, there is no study investigating the lateral mass screws for fused C2/3 vertebrae. Our results indicate similar ROM in FE and LB, but a 26.85% larger ROM in AR, compared to C2 pedicle screws. Given the crucial role of AR in the atlantoaxial joint, we hold some concerns regarding the lateral mass screw's resistance to AR. In comparison to the translaminar screws, it showed similar ROM in FE, and significantly reduces ROM in LB and AR by increments of -67.98% and \u0026minus;\u0026thinsp;28.05%, respectively. PVMS analysis revealed that the advantage of the lateral mass screw is its low PVMS, which is lower than that of the C2 pedicle screw in FE and LB. It is the only screw technique with PVMS superior to the translaminar screw in all three planes of motion. Therefore, it is inferred that its risk of screw fracture may be the lowest. This indicates that the lateral mass screw is a biomechanically feasible screw technique, may be superior to the translaminar screw.\u003c/p\u003e \u003cp\u003eThe subfacetal body screw was first reported by Patkar et al. in 2014\u003csup\u003e22\u003c/sup\u003e. This technique can achieve long bone purchase by angling inward toward the vertebral body\u003csup\u003e5, 23\u003c/sup\u003e, as demonstrated in the model of this study. Currently, there are no studies investigating the PVMS on this technique using FEA. Our study found that subfacetal body screws can effectively limit AR. This may be because the subfacetal body screw directly fixes on both sides of the odontoid process and reaches the ventral bone cortex, restricting atlantoaxial AR function, which is based on the odontoid process as the rotation axis. However, its drawback is the highest ROM and PVMS in FE. In terms of PVMS comparison, the subfacetal screw exhibited the highest PVMS, indicating the risk of screw fracture and potentially necessitating consideration for additional instrumentation reinforcement to share the stress. In addition, its strong biomechanical property of limiting rotation compensates for the shortcomings of the lateral mass screw, and the entry points of the two kinds of screw are located above and below the isthmus, respectively. This provides ideas for the combination of different screws to enhance stability. Compared to the translaminar screws, it exhibits lower PVMS in LB by 30.88% and AR by 16.75%. Compared to the C2 pedicle screws, it exhibits higher PVMS in LB by 74.87% and AR by 16.97%. In terms of ROM comparison, compared to the translaminar screws, it exhibits lower ROM in LB by 67.87% and AR by 70.43%. Compared to the C2 pedicle screws, it exhibits similar ROM in FE and LB, and decrease ROM by 47.87%. Although its ROM may be better than that of the C2 pedicle screw, its PVMS is the highest, so it cannot replace the C2 pedicle screw. Fortunately, its value was below the yield stress of titanium, and there have been no reports of screw fractures in the literature. Sushil et al.\u003csup\u003e24\u003c/sup\u003e, and Hou et al.\u003csup\u003e5\u003c/sup\u003e have reported a 100% stability rate for subfacetal screws. Therefore, the occurrence of screw fractures needs to be investigated through large clinical series. Considering its excellent ROM and the PVMS in LB and AR were smaller than translaminar screw, it may be preferable to the translaminar screws.\u003c/p\u003e \u003cp\u003eThe translaminar screw was first reported by Wright et al. in 2005\u003csup\u003e25\u003c/sup\u003e. In an earlier cadaveric study, C2 translaminar screws was found to be comparable to pedicle screws during FE, LB, and AR\u003csup\u003e26\u003c/sup\u003e. However, a clinical study by Chang revealed that translaminar screws had a higher failure rate than pedicle screws (57.1% for bilateral translaminar screws, 78.9% for unilateral translaminar screws, versus 100% for bilateral pedicle screws)\u003csup\u003e27\u003c/sup\u003e. Subsequent biomechanical studies shed light on this issue. An experiment by Claybrooks et al. \u003csup\u003e28\u003c/sup\u003edemonstrated that the ROM of translaminar screws was similar to that of pedicle screws in FE but significantly inferior in LB and AR. Our findings mainly align with Claybrooks' study, showing translaminar screws to be significantly inferior to C2 pedicle screws in LB and AR but superior in FE. This aligns with a previous FEA study conducted by Ma et al. \u003csup\u003e29\u003c/sup\u003e. PVMS analysis revealed the highest PVMS in LB and AR for translaminar screws compared to C2 pedicle screws. In this study, translaminar screws exhibited the poorest biomechanical performance, as evidenced by ROM and PVMS. Therefore, we consider them inferior to the three alternatives.\u003c/p\u003e \u003cp\u003eThis study has several advantages. Firstly, it is the first to investigate the biomechanical differences of various screw techniques in the setting of congenital C2-3 fusion using FEA. Secondly, previous studies modeled C2-3 fusion by obtaining CT data from normal individuals and using computer software to bind C2 and C3, which does not accurately represent the true morphology. In contrast, this study utilized CT data from patients with true congenital C2-3 fusion, providing a more accurate and realistic morphological model. Third, FEA, on the one hand, utilizes models of the same patient sample to implant different screws, eliminating intersample errors. On the other hand, computer-simulated screw placement is more precise, achieving consistent C1 screw trajectories for each model and reducing intergroup errors among different groups. Finally, FEA can calculate PVMS to assess the risk of screw fracture.\u003c/p\u003e \u003cp\u003eThis study has the following limitations: 1. The simulation of HRVA was achieved through Boolean subtraction rather than using actual patients with HRVA. In clinical surgery, different screws may be placed on both sides depending on the patient's anatomical structure. This study utilized CT data from a patient with mild deformity and bilateral symmetry to facilitate symmetrical screw placement. 2. HRVA has multiple patterns. In this study, only the isthmus height was reduced, and it could not represent all types of HRVA. 3. Congenital segmentation failure can be classified into three types based on the degree of fusion: segmentation type, partial fusion type, and complete fusion type\u003csup\u003e2\u003c/sup\u003e. In this study, we selected the most common form, complete fusion type, where the internal bone structure was entirely defined as cancellous bone. It is important to note that this model does not represent all fusion types. 4. The material properties and morphological characteristics (e.g., cortical bone thickness of 1 mm) adopted in this study were assumed based on data reported in the literature for normal populations, as the specific material properties of congenital C2-3 fused vertebrae and their deviations from those of normal populations remain unclear. Although instability and ligamentous deficiencies are known to exist in these patients, the exact nature of these defects is not fully understood. To simulate instability, certain ligaments were removed, and the corresponding ROM was determined based on values reported in the literature. 5. This FEA is only a numerical simulation based on one patient with limited evidence, and large-sample clinical studies are need to further verify the results.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eFor congenital C2-3 fusion and HRVA, C3 pedicle screws, lateral mass screws, and subfacetal body screws provide sufficient stability. All three alternatives may be reasonable options in this specific anatomical scenario.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eFunding:\u003c/h2\u003e \u003cp\u003eThis article was supported by the Beijing Municipal Science and Technology Commission (Z191100006619040, T.F.) and the Capital Health Research and Development of Special (2020-2-8011, T.F.).\u003c/p\u003e \u003cp\u003eAcknowledgment: none.\u003c/p\u003e \u003cp\u003eConflicts of Interest: none.\u003c/p\u003e \u003cp\u003eThe manuscript has been read and approved by all the authors. This manuscript has not been published or presented elsewhere in part or in entirety and is not under consideration by another journal. Research Ethics Committee approved the study.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eQiang Jian: manuscript draft, revision. Xingang Zhao, Yinqian Wang and Cong Liang: methodology and critical revision.Xiuqing Qian: methodology.Tao Fan: supervision.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eTian Y, Xu N, Yan M, et al. Vertebral Artery Variations at the Craniovertebral Junction in \u0026quot;Sandwich\u0026quot; Atlantoaxial Dislocation Patients. Neurospine 2021;18:770-7.\u003c/li\u003e\n\u003cli\u003eJian Q, Bo X, Jian F, Chen Z. The role of clivus and atlanto-occipital lateral mass height in basilar invagination with or without atlas occipitalization. Neurosurg Rev 2024;47:404.\u003c/li\u003e\n\u003cli\u003eJian Q, Qin S, Hou Z, Zhao X, Liang C, Fan T. Individualized C1-2 intra-articular three-dimensional printed porous titanium alloy cage for craniovertebral deformity. J Orthop Surg Res 2024;19:569.\u003c/li\u003e\n\u003cli\u003eDuan S, Xiao B, Cui W, et al. 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Sub-Facetal C2 Body Screw In Posterior Fixation (Goel-Harm\u0026apos;s Technique) Of The Atlanto-Axial Joint Avoiding The Vertebral Artery. Internet Journal of Neurosurgery 2014.\u003c/li\u003e\n\u003cli\u003eSingh DK, Shankar D, Singh N, Singh RK, Chand VK. C2 Screw fixation techniques in atlantoaxial instability: A technical review. Journal of craniovertebral junction \u0026amp; spine 2022;13:368-77.\u003c/li\u003e\n\u003cli\u003eSushil P. C2 Subfacetal Body Screw in Posterior Atlantoaxial Fixation (Goel\u0026ndash;Harm Technique) to Avoid the Vertebral Artery. Global Spine Journal 2015;5:s-0035-1554307-s-0035-.\u003c/li\u003e\n\u003cli\u003eWright NM. Translaminar rigid screw fixation of the axis. Technical note. Journal of neurosurgery. Spine 2005;3:409-14.\u003c/li\u003e\n\u003cli\u003eGorek J, Acaroglu E, Berven S, Yousef A, Puttlitz CM. Constructs incorporating intralaminar C2 screws provide rigid stability for atlantoaxial fixation. Spine 2005;30:1513-8.\u003c/li\u003e\n\u003cli\u003eChang CC, Huang WC, Tu TH, et al. Differences in fixation strength among constructs of atlantoaxial fixation. Journal of neurosurgery. Spine 2018;30:52-9.\u003c/li\u003e\n\u003cli\u003eClaybrooks R, Kayanja M, Milks R, Benzel E. Atlantoaxial fusion: a biomechanical analysis of two C1-C2 fusion techniques. The spine journal : official journal of the North American Spine Society 2007;7:682-8.\u003c/li\u003e\n\u003cli\u003eMa X, Peng X, Xiang H, Zhang Y, Zhang G, Chen B. A finite element modeling of posterior atlantoaxial fixation and biomechanical analysis of C2 intralaminar screw fixation. Chin Med J (Engl) 2014;127:1266-71.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"C2-3 fusion, high-riding vertebral arteries, pedicle screw, translaminar screw, subfacetal screw, lateral mass screw","lastPublishedDoi":"10.21203/rs.3.rs-5072741/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5072741/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eObjective: To investigate the biomechanical properties of three novel screw techniques for C2-3 fused vertebra with high-riding vertebral arteries (HRVAs).\u003c/p\u003e\n\u003cp\u003eSummary of Background Data: There has not been an investigation into the biomechanical properties of alternatives to C2 pedicle screw in the context of C2-3 fused vertebrae and HRVA.\u003c/p\u003e\n\u003cp\u003eMethods\u003c/p\u003e\n\u003cp\u003eFive models were utilized to assess range of motion (ROM) and peak von Mise stress (PVMS) on the screw-rod construct. These models consisted of the following groups: C2 pedicle screw (2PS), subfacetal body screw (SBS), translaminar screw (TLS), lateral mass screw (LMS), C3 pedicle screw (3PS) fixation in the presence of HRVA and C2-3 fusion. The flexion/extension (FE), lateral bending (LB) and axial rotation (AR) on 3 planes were simulated.\u003c/p\u003e\n\u003cp\u003eResults:\u003c/p\u003e\n\u003cp\u003eCompared to the 2PS, the LMS and SBS exhibit similar ROM in FE and LB (\u0026lt;10%). The SBS reduces ROM in AR by 47.87%, while the LMS increases ROM in AR by 26.85%. Compared to 2PS, the 3PS has similar ROM in FE, LB, and AR; but increases PVMS in FE and AR by 43.62% and 29.27%, respectively, and decreases PVMS in LB by 33.81%. Compared to 2PS, the LMS decreases ROM in FE and LB by 11.93% and 14.45%, respectively; but increases PVMS in LB by 25.38%. Compared to 2PS, the SBS increases PVMS in FE, LB, and AR by 126.96%, 74.87%, and 16.97%, respectively. Although the 3PS, LMS, and SBS increase ROM in FE by 14.11%, 4.81%, and 16.89%, respectively, compared to the TLS, they decrease ROM in LB by 72.88%, 67.98%, and 67.87%, respectively, and in AR by 41.68%, 28.05%, and 70.43%, respectively. Although the 3PS and SBS increase PVMS in FE by 45.08% and 129.26%, respectively, compared to the TLS, they decrease PVMS in LB by 73.84% and 30.88%, respectively, and in AR by 8.00% and 16.75%, respectively. The LMS decreases PVMS compared to the TLS in FE, LB, and AR by 11.04%, 66.18%, and 10.77%, respectively.\u003c/p\u003e\n\u003cp\u003eConclusion:\u003c/p\u003e\n\u003cp\u003e3PS, LMS, and SBS are biomechanically feasible, may be reasonable options in the setting of congenital C2-3 fusion and high-riding vertebral arteries.\u003c/p\u003e","manuscriptTitle":"A finite element analysis of three alternatives to C2 pedicle screw in the setting of congenital C2-3 fusion and high-riding vertebral arteries","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-03-20 04:34:39","doi":"10.21203/rs.3.rs-5072741/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"3750175b-d6c0-4a4f-ac7a-ee45e475f035","owner":[],"postedDate":"March 20th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-05-19T01:08:12+00:00","versionOfRecord":[],"versionCreatedAt":"2025-03-20 04:34:39","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5072741","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5072741","identity":"rs-5072741","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}