1 Introduction

The use of C1 (atlas) screws, specifically C1 lateral mass (LM) screws, is a safe and effective treatment option for upper cervical instability but carries risks, including injury to the paravertebral venous plexus and vertebral artery during placement.^1–3 However, the need for preoperative angiographic evaluation to delineate vascular anatomy may increase procedural complexity and risk. Various techniques have been developed to address C1-occipital condyle and atlanto-axial instability, such as C1 lateral mass and C1 pedicle screwing. Occipito-C1 and atlanto-axial instability may result from congenital malformations, fractures at C1-C2 or occipito-C1 due to trauma, deformities caused by rheumatoid arthritis (e.g., pannus formation), infections, and degenerative diseases.^4–7

The paravertebral venous plexus is the most common source of bleeding, and a frequent complication associated with C1 screw techniques.⁸ This complication affects the surgical site and the screwing technique, increases patient blood loss, and prolongs operation time. Other complications of C1 fixation include proximity to the greater occipital nerve, excessive manipulation of the C2 nerve root during surgery and caudal traction, postoperative occipital neuralgia, and C1 posterior arch fracture. While the risk of injury to ventral structures during C1 screw insertion is rare, it still poses a significant risk. Therefore, to minimize the risk of complications associated with C1 fixation, we recommend the use of the modified C1 lateral mass screw technique (unicortical) as reported by Pan et al.⁹ and Lee et al., in 2013.¹⁰

Despite several proposed insertion angles for posterior C1 lateral mass screws, no clear consensus has been established regarding the optimal entry point, superior and medial angle of the C1 lateral mass. To address this issue, virtual 3D reconstruction methods such as volume or surface rendering are used to create a detailed 3D model that can be manipulated through rotation and sectioning to provide a better understanding of structural complexity. The purpose of this study is to evaluate the insertion angle of one of the posterior C1 lateral mass screw techniques with precision. This is achieved by examining the atlas through 3D reconstruction of 80 real patients' atlases. The objective is to determine the entry point, insertion angles, and length of C1 lateral mass screws to minimize the risk of injury to the vertebral artery, spinal cord, or nerve roots during instrumentation. Finite Element Analysis (FEA) has become an essential computational tool in the design, evaluation, and optimization of medical screw fixation systems. By breaking down a complex physical structure into smaller, manageable elements, FEA allows both engineers and clinicians to simulate and analyze how screws interact with bone under various loading conditions.^11–13

FEA has emerged as a key tool in advancing orthopedic screw fixation by driving improvements in implant design, modeling complex bone–screw interactions, and enhancing patient-specific preoperative planning. In implant design optimization, FEA enables researchers to explore how variations in screw geometries—such as thread pitch, length, major diameter, and profile—affect load distribution and fixation stability; studies have shown that simulated performance can closely mirror experimental results, providing a robust foundation for refining implant parameters.^14–16 Moreover, FEA is crucial for simulating the intricate interplay between screws and the anisotropic, heterogeneous bone matrix—allowing for detailed mapping of stress distributions and identification of potential failure zones, a process that is vital for ensuring long-term implant integrity and reducing complications.^17,18 In addition, by integrating patient-specific imaging data, FEA supports personalized preoperative planning, enabling surgeons to virtually test different screw placements and fixation strategies before entering the operating room; this technique not only refines surgical technique but has also been demonstrated to contribute to shorter operation times and improved clinical outcomes in procedures such as osteotomy fixation.^19,20

In this study, FEA was employed to develop a geometric approach for determining the optimal entry point, angulation, and depth of the LM screw, thereby preventing injuries to adjacent structures during screw fixation procedures. For this analysis, we used the C1 vertebrae of 80 patients who presented to our hospital with cervical pathology but no pathology in the upper cervical region. We created 3D models of the vertebrae using computerized tomography (CT) images and applied the C1 posterior lateral mass screws. Since preserving bone integrity is critical,^21–23 the stress distribution results obtained via FEA were used to evaluate the optimal medial angle derived from the geometrical approach. Various geometrical dimensions, including the optimal entry point, superior and medial angles, and depth of the screw, which were then classified into different age groups and genders were obtained.

2 Materials and method

2.2

2.2 Generating 3D models

CT scan images were transferred as Digital Imaging and Communications in Medicine (DICOM) format to 3D Slicer (US National Institutes of Health (NIH) open-source software, 4.11.20210226 version. C1 correlated DICOM images were selected section by section for volume rendering. C1 related areas were mapped to axial, sagittal, and coronal planes slice by slice. 3D models were created from these selected areas as shown in Fig. 1.

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Fig. 1 3D model generation of C1 from CT scans, selection of C1 related areas section by section related to (a) axial plane, (b) sagittal plane, and (c) coronal plane. (d) 3D model of C1 as a result of combination of all selected areas, € atlas (C1 vertebra) general view and main dimensions; length, width and height.

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2.3

2.3 Measurements

Measurements were made on both 3D DICOM images and 3D models for cross-checking purposes. No major difference was observed between the two different approaches. Fig. 1. (e) shows general dimensions; length, width, and height are measured on 3D models. Fig. 2. (a) Illustrates the location of the medial and transverse plane location on C1. Fig. 2. (b) Displays the position of the medial angle (β), Fig. 2. (c) Indicates transverse angle (α) and functional screw depth (FSD). There are several measurements required to calculate medial, transverse angle and functional screw depth. Fig. 2. (d) shows the essential measurements. The right-side lateral mass dimensions are length (y1) and width (x1). Distance between anterior arch end points is x2, the width of the upper vertebral foramen is x3, and the vertical gap between x2and x3 is y2. ε is the angle that shows the slope of the lateral mass posterior. The trajectory of the screw is shown in Fig. 2(e) in 3D, transverse, and sagittal planes.

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Fig. 2 (a)Demonstration of transverse and sagittal planes, x-axis and y-axis are located on the transverse plane of C1, the sagittal plane dwells on z-axis and y-axis, (b) Medial angulation is between lateral mass screw path and median sagittal plane, co-coordinate origin located on mid point of the anterior tubercle, (c) Access point according to Lee method, transverse angle is measured angulation between the axis through access point to mid point of anterior tubercle on z-axis, ε is the angle between frontal plane and posterior lateral mass, this angulation is used to calculate FSD, (d)Anatomical measurements on C1 atlas required to calculate medial angle, y1 is lateral mass length on y-axis (y1 is taken 2 mm less from both ends since screw thread is not functional on the entry point because of the notch and pointed screw tip), x1 is lateral mass width on x-axis, x2 and x3 are respectively top and bottom width of foramen for dens on x-axis, y2is foremen for dens length on y-axis, MPD is distance between midpoint of tuberculum posterius and access point on y-axis, (e) trajectory of the latera mass screw.

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3 Results

Results and analysis of the data are summarized in Table 1. There were 40 men (range 18–40 and 40–80 age) and 40 women (range 18–40 and 40–80 age) in this study. The average age was 49,6 years. No upper cervical pathologies were observed in any of these patients. The reference entry point for lateral mass screw application was performed according to Lee et al.

C1 (atlas) vertebra morphological anatomy measurements (Table 1), according to the data we obtained, width was 44.71 ± 3.56 mm in the combined group, 44.14 ± 3.11 mm in the combined subgroup between the ages of 18–40, and it was calculated as 45.28 ± 3.76 mm in the combined subgroup of 40–80 ages. Length calculated from the C1 vertebra transverse process endpoints is average 78.73 ± 5.90 mm in the combined group, 79.45 ± 5.26 mm in the 18–40 age combined subgroup, and 78.01 ± 5,96 in the 40–80 age combined subgroup, 96 mm was found. When morphological anatomical measurements of C1 vertebra height were calculated; the average value was found to be 21.53 ± 2.78 mm in the combined (male and female) group, 21.73 ± 2.92 mm in the combined 18–40 age group, and 21.34 ± 2.66 in the 40–80 age group.

Entry point determination for men and women are evaluated together (combined); the average distance from the midline (posterior tubercle of C1) to the screw entry site (junction of the inferior part of the posterior arch and the midpoint of the lateral mass) was 20.27 ± 1.48 mm, between the ages of 18–40, it was 20.44 ± 1.42 mm, and between the ages of 40–80, it was 20.09 ± 1.49 mm. The combined (male and female) superior angle value is 16.73 ± 4.37° on average, and in the 18–40 age subgroup this value was 15.62 ±4° (Table 2).

In the lateral mass screw technique, medial angle values were 20.75 ± 3.84° in the combined group (male and female), 20.67 ± 3.89° in the 18–40 age subgroup, and 20.83 ± 3,81° in the 40–80 age subgroup. In the C1 lateral mass screw technique, whose entry point was determined according to the Lee method, the functional screw length was 21.16 ± 2.37 mm in the combined group, 20.86 ± 2.76 mm in the combined subgroup between the ages of 18–40, and 40–80 years in the combined subgroup it was measured as 21.46 ± 2.13 mm (Table 2).

Stress distribution is an important factor in terms of bone integrity under loading.^23,24 Crack initiation may occur around the stress consecration regions.^22,25,26 According to FEA analysis results, lateral mass screw medial angle influences the amount of maximum stress and stress distribution when applying 50 N (N) pulling force along the screw direction. Fig. 3. Shows stress distribution between the screw and lateral mass inside wall as a function of medial angle. Stress concentration points are formed when the medial angle is lower than 15° and higher 25° due to variable distance between lateral mass side wall at the spinal canal outer surface. Stress concentration area is observed at the region where the posterior arch merges to lateral mass when the medial angle is lower than 15°. Similarly, merging point of anterior arch and lateral mass is critical when medial angles are more than 25°. Also, the amount of maximum stress is significantly influenced by the medical angle. Fig. 4. Presents maximum stress that obtained as a function of medial angle for left and right side. The lowest maximum stress is obtained where medial angle = 21° for the left side as 3.82 Mega Pascal (MPa) and medial angle = 22° for the right side as 3.92 MPa. Different transverse angle conditions were applied to the FEA models; however, the stress distribution results revealed no significant variations among the angulations.

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Fig. 3 FEA results of stress distribution analysis of the lateral mass screw pulling on C1 with 50 N load as a screw pulling force.

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Fig. 4 Medial angle effects on max stress created while pulling the lateral mass screw on C1. The minimum max. stress is obtained where medial angle = 21^ofor left side, and medial angle = 22^ofor right side.2.

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A geometrical approach was employed to calculate the medial angle, transverse angle, and functional screw depth to identify the optimal medial angle that maintains a consistent distance between the screw and the medial wall of the lateral mass, while ensuring a uniform stress distribution and minimal stress on C1. Medial angle (β) was taken parallel to the lateral mass medial wall to avoid possible stress concentration region on posterior arch under loading. Fig. 5. Shows the compression of different medial angle screw trajectories on the cross-section of the medial plane.

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Fig. 5 Comparison of different medial angle (a) 10° and (b) 21°. Smaller angle weakens the posterior arch and lateral mass connection.

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Lee et al. developed a method to determine the entry point of the lateral mass screw 4. The entry point is right below the posterior arch and midpoint of lateral mass on the sagittal plane. A small notch is created to construct a screw trajectory in this technique. Fig. 2€. shows the typical screw path for the lateral mass screw.(1)MedialAngle=tan−1(x3−x22y1)(2)FunctionalScrewDepth=y1cos(−ε)cos(ε−α)cos(β)

Medial angle (β) and functional screw depth were calculated by Eq. (1) and Eq. (2) with length and angle measurements on the atlas for 80 samples. α was measured by deriving the angle between the line through the access point and midpoint of the anterior tubercle and axial plane as demonstrated in Fig. 2(c and d).

4 Discussion

Rigid fixation of C1 with lateral mass screws has become an increasingly popular technique for fixing the upper cervical spine.¹⁰ Many studies have attempted to define the optimal medial angulation for C1 lateral mass screw placement, but their methodology did not allow for a definitive conclusion. The use of a proper entry point, medial and superior angulation of C1 lateral mass screws can help minimize the risk of injury to the spinal cord, vertebral artery, nerve roots, internal carotid artery, and C1 vertebral bone fracture.

The entry point for C1 lateral mass screwing technique was first published by Goel et al., in 1994.²⁷ In 2001, Harms et al. modified this technique with the development of the polyaxial screw rod system.²⁸ However, inferior retraction of the C2 root and the surrounding venous plexus during surgery may result in excessive bleeding and C2 ganglion injury.^9,10,29 Additionally, the proximity of the greater occipital nerve and the venous plexus increases the risk of occipital neuralgia as a possible complication of C1 lateral mass fixation.⁹

Another accepted C1 stabilization technique is the C1 peduncular screw technique defined by Tan et al., in 2003.²⁸ However, this technique has a risk of injury in the part where the vertebral artery runs over the C1 arch.^28,30 Additionally, since bicortical access is made in this technique and the C1 posterior arch is thin, fractures may occur at the screw entry site or posterior arch during the procedure. Huang et al. have indicated that the C1 peduncle screw technique is difficult to apply because the posterior arch thickness becomes thinner in the vertebral artery groove section.³¹

As the starting point of our study, we found that Lee et al.’s technique is suitable. It does not damage the C2 root and ganglion, has few occipital neuralgia complications, is far from the vertebral artery, and does not cause a C1 bone fracture. One important point to note is that revision may be necessary during surgery. A fracture in the posterior arch of C1 or at the screw entry point reduces the possibility of screw revision, thus affecting surgical usability.

Regarding medial and superior angles, some studies have suggested that the medial trajectory should not exceed 30° to avoid penetrating the spinal cord (SC).³² Rocha et al. (2007) conducted a study on 20 cadaver C1 vertebrae, where they applied the lateral mass screw technique, and the results showed that the mean maximum angle of medialization was 16.7 ± 1.3°, and the mean maximum superior angulation was 21.7 ± 4.7°. In their study, Rocha et al. determined the entry point as the posterior wall of the lateral mass and used the inferior part of the posterior arch for the convenience of 4 mm screw placement. In 2009, Serkan et al. conducted a C1 study on 40 cadavers and found the ideal medial angulation to be 13.5 ± 1.9° and the maximal medial angulation to be 29.4 ± 3.0°. They also determined the ideal sagittal angle to be 15.2 ± 2.6° and the maximal cephalic angle to be 29.6 ± 2.6°.³³

In 2020, Hung et al. conducted a study on 120 patients using computed tomography to assist in placing C1 lateral mass screws. The study found that the maximal medial angle on the right side was calculated to be 36.7 ± 2.9° and 36.5 ± 2.7° on the left side. The superior angle measurement was calculated as 49.7 ± 4.2° on the right side and 49.6 ± 4.0° on the left side.³⁴

The length of a screw varies depending on several factors, including the starting point, as well as the vertical and sagittal angulations of the screw. For instance, in the C1 peduncular screw technique over the posterior arch, the average screw lengths were reported as 33.9 ± 2.7 mm by Resnick et al.,³⁰ 28.9 ± 2.4 mm by Tan et al.,²⁸ 31.0 ± 3.0 mm by Ma et al.,³⁵ and 30.2 ± 2.2 mm by Christensen et al..³⁶ Additionally, James et al.³⁷ found that the screw length in the peduncular screw technique ranged from 29 to 34 mm depending on the applied technique in their 2013 study. Moreover, Rocha et al.³³ reported that the ideal screw length for the lateral mass screw technique ranged from 26 mm to 34 mm when placed bicortically.

Our study aimed to evaluate the clinical feasibility of utilizing the C1 lateral mass screw technique in surgical procedures. In this study, the midpoint of the inferior lateral mass and the junction of the posterior arch were identified as the appropriate entry point. The midpoint of tuberculum value calculated for the lateral mass technique was 20.27 ± 1.48 mm. Notably, utilizing this entry point offers several benefits, including reduced retraction of the C2 root and minimal contact after screw placement, decreased risk of exclusion of venous structures and reduced bleeding, low probability of C1 posterior arch fracture during screw placement, and minimal risk of contact with the C1 and vertebral artery.

The convenient medial angle was determined to be 20.75 ± 3.84°, calculated by measuring the angle between the lateral mass midline and the C1 median line. Implementing this angle in surgical procedures can help reduce excessive load on the lateral mass bone walls and prevent the occurrence of fractures or burst. Furthermore, the FEA conducted in this study revealed that the left side exhibited the lowest maximum stress of 3.82 MPa when the medial angle was set to 21°, while the right side exhibited the lowest maximum stress of 3.92 MPa when medial angle was set to 22°.

The superior angulation technique involved aiming for the sagittal plane of the midpoint of the anterior tubercle. The mean angle value calculated for the lateral mass technique was found to be 16.73 ± 4.37°. This superior angulation can help minimize the risk of injury to the C1 root, and particularly the vertebral artery. In a study by Murakami et al.,³⁸ 3D C1 tomography of 177 individuals revealed that the internal carotid artery (ICA) was located in front of the C1 lateral mass in 64.4 % of cases, with 54.6 % of cases located on the outer side of the lateral mass 1/3. The appropriate screw length for the C1 lateral mass screw technique varies depending on the screw angle and entry point, and incorrect placement can lead to injury to anterior structures. In our study, the screw length was determined to be 21.16 ± 2.37 mm after evaluating the entry point and angles. It should be noted that our measured functional screw depth (21.16 ± 2.37 mm) represents only the intraosseous portion. To align the C1 screw head with the C2 screw construct, an additional 8–9 mm of threaded shaft is typically required for posterior extension. Thus, the total screw selection length approximates 29–38 mm, in line with previously reported values.^26–32 Our study did not directly compare population-average–based planning with individualized planning in clinical settings. Future research should assess our recommended metrics against patient-specific navigation in terms of operative time, accuracy, and complication rates.

5 Conclusion

Despite numerous studies and literature reviews on C1 atlas screw techniques, there is still no consensus in surgical practice. The anatomical limitations and intraoperative and postoperative complications associated with these techniques continue to be debated, making it challenging to determine the ideal method and technique for C1 atlas screw stabilization. In this research, we used computer-generated 3D models to perform a comparative geometric analysis, developed based on the stress distribution results observed during screw pullout, using FEA of the Lee et al. technique, one of the C1 screw fixation methods. This study demonstrates that combining precise geometric planning with FEA enhances the safety and efficacy of C1 lateral mass screw fixation. While our population-averaged entry points and angulation values offer useful reference data, we acknowledge that significant inter-individual anatomical variation exists. These averages are not intended to supplant patient-specific preoperative imaging and intraoperative decision-making, which remain the standard of care in modern spinal surgery. A favorable entry point—at the midpoint of the inferior lateral mass and posterior arch junction—along with calculated medial (20.75 ± 3.84°), resulted in reduced stress concentrations and minimized risk to adjacent neurovascular structures. These results align with previous anatomical and biomechanical findings, supporting the utility of FEA in refining screw trajectories. The integration of patient-specific modeling underscores the potential for improved surgical planning and construct stability.

CRediT authorship contribution statement

Mehmet Selim Demirtas: 3D model work, 3D Printing, finite element analysis, formulation. Densel Arac: Problem Defination, Conceptualization, Investigation, Writing – original draft. Fatih Keskin: Problem Defination, Material Image Selection and Deletion.

Informed consent

Participants were provided with information regarding the utilization of medical images for scientific research in accordance with the Privacy of Personal Health Data Processing and Protection Regulations (20/10/2016–29863) established by the Ministry of Health of the Turkish Republic.

Compliance with ethical standards

During the entire duration of this Agreement, the Provider is required to adhere to all relevant rules, regulations, and directives of The Ministry of Health of the Turkish Republic. See Regulation on Processing and Protecting The Privacy of Personal Health Data (20/10/2016–29863).

Ethical approval

The research was conducted with the approval letter (decision: 2022/3842) from the Ethics Committee of Necmettin Erbakan University.

Funding

This work received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Funding

There is no finical support for this study.