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. 2022 Sep 9;101(36):e30419. doi: 10.1097/MD.0000000000030419

Biomechanical characteristics of 2 different posterior fixation methods of bilateral pedicle screws: A finite element analysis

Yulei Ji a, Qiaolin Zhang a, Yang Song a,b, Qiuli Hu a,✉, Gusztáv Fekete c, Julien S Baker d, Yaodong Gu a,*
PMCID: PMC10980486  PMID: 36086784

Background:

To explore the biomechanical characteristics of 2 posterior bilateral pedicle screw fixation methods using finite element analysis.

Methods:

A normal L3-5 finite element model was established. Based on the verification of its effectiveness, 2 different posterior internal fixation methods were simulated: bilateral pedicle screws (model A) were placed in the L3 and L5 vertebral bodies, and bilateral pedicle screws (model B) were placed in the L3, L4, and L5 vertebral bodies. The stability and stress differences of intervertebral discs, endplates, screws, and rods between models were compared.

Results:

Compared with the normal model, the maximum stress of the range of motion, intervertebral disc, and endplate of the 2 models decreased significantly. Under the 6 working conditions, the 2 internal fixation methods have similar effects on the stress of the endplate and intervertebral disc, but the maximum stress of the screws and rods of model B is smaller than that of model A.

Conclusions:

Based on these results, it was found that bilateral pedicle screw fixation in 2 vertebrae L3 and L5 can achieve similar stability as bilateral pedicle screw fixation in 3 vertebrae L3, L4, and L5. However, the maximum stress of the screw and rod in model B is less than that in model A, so this internal fixation method can effectively reduce the risk of fracture. The 3-dimensional finite element model established in this study is in line with the biomechanical characteristics of the spine and can be used for further studies on spinal column biomechanics. This information can serve as a reference for clinicians for surgical selection.

Keywords: bilateral pedicle screws, finite element analysis, internal fixation, lumbar spine, spinal biomechanics

1. Introduction

With the continuous progress of population aging in China, the number of patients with lumbar degenerative diseases is increasing, and surgery has become the treatment of choice for more patients.[1,2] Spinal fractures are very common, accounting for 5% to 6% of systemic fractures. Spinal injuries often occur in the thoracolumbar segment, accounting for 28% to 58% of spinal injuries.[3,4] Thoracolumbar fractures often lead to patients with thoracolumbar instability.[5,6] If internal fixation treatment is not carried out in time, it will further lead to the aggravation of spinal cord injury and paralysis of the corresponding segments, causing huge losses and burdens to patients, their families, and society. The spinal pedicle screw internal fixation system meets the biomechanical requirements of spinal fixation and can effectively fix the anterior, middle, and posterior spine. It is the most common method to provide spinal stability in clinic.[7,8] In the 1970s, Raymond and Saillant [9] first applied this method to treat vertebral fractures.

In the past, the use of in vitro experiments to study the effects of different internal fixation methods has been limited.[10,11] In recent years, with the development of computer technology, the use of the finite element method to study the mechanical properties of internal fixation devices has been widely recognized.[12,13] In the 1970s, Belytschko et al[14] successfully established a 2-dimensional finite element model of the lumbar intervertebral disc using radiographs and applied the finite element method to the biomechanical analysis of orthopedics for the first time. In 1988, Goel et al[15] successfully established a complex 3-dimensional finite element model of the lumbar spine through computed tomography (CT) scanning data for the first time. The finite element method can replace the traditional biomechanical experiment to a considerable extent, control the experimental conditions, and simulate the mechanical situation in the state of living body movement.[16–18] The finite element analysis of pedicle screws can accurately reflect the mechanical conditions of screws, screw bone complexes, screw systems, and vertebral bodies, and can comprehensively analyze loads of vertebral bodies at different angles, stress patterns, and motion states.[19,20]

In our study, the L3-L5 segment finite element model of the human body was established using the 3-dimensional finite element method, and the effectiveness of the model was verified. By comparing the biomechanical differences between bilateral pedicle screws inserted into the L3 and L5 vertebral bodies and the L3, L4, and L5 vertebral bodies in the same normal spinal model, we hope to determine which of these 2 different pedicle screw fixation methods could have better biomechanical stability in thoracolumbar fractures through biomechanical experiments. The experimental results provide better guidance for pedicle screw placement in clinics.

2. Materials and Methods

2.1. Model construction

A healthy female volunteer with no spinal-related diseases (age, 50 years; height, 163 cm; weight, 4 kg) was selected for this study. The study was conducted by the guidelines of the Declaration of Helsinki and was approved by the Committee of Ningbo University (code ARGH20211213). After obtaining informed consent, the subject was scanned with 64 slice spiral CT for the L1-L5 segments of the lumbar spine, with a scanning interval of 1 mm and 294 layers. The DICOM format images were obtained and imported into Mimics 20.0 (Materialise, Leuven, Belgium). Through threshold segmentation, region growth, and manual modification, a 3-dimensional geometrical model of the L3-L5 segments of the lumbar spine was generated and then imported into Geomagic Studio 2013 (3D Systems, South Carolina, United States) for surface smoothing. The IGES format files were further into SolidWorks2020 (Dassault Systèmes, Massachusetts, United States) to set the parameters through the surface guide, improve the characteristic line, and establish the intervertebral disc entity. A pedicle screw with a diameter of 8 mm and a length of 55 mm and a connecting rod with a diameter of 8 mm and a length of 50 mm was introduced for assembly.[21] Finally, 3-dimensional solid lumbar models of L3-L5 segments with 2 different fixation methods were generated, as shown in Figure 1.

Figure 1.

Figure 1.

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The lateral and back view of the lumbar spine models.

2.2. Material properties and mash generation

The established spine models were imported into ANSYS Workbench 19.2 (ANSYS, Inc., Canonsburg, PA) for mash generation. All components have meshed with tetrahedral solid elements with a 2-mm element size. As shown in Table 1, all the assigned materials were obtained from previous studies and idealized as homogeneous and isotropic linear elastic materials. We then established the positions of the lumbar anterior longitudinal ligament, posterior longitudinal ligament, ligamentum flavum, interspinous ligament, supraspinous ligament, intertransverse ligament, and articular capsule ligament based on their anatomical position and structure.[22] The physical properties of the ligament are simple as a spring, so the ligament is set as a linear tension spring element to assign the structural stiffness of the main ligaments, such as the anterior and posterior longitudinal ligaments and the interspinous ligament. According to the physiological and anatomical model of the lumbar spine, the fibrous ring and nucleus pulposus of the intervertebral disc were not separate under load, so the contact setting between them is “bonded.” The vertebral body and intervertebral joint can slide under a certain load, so the contact condition of the vertebral body and the intervertebral joint is set to “friction.” The friction coefficient was determined to be 0.01, owing to the presence of SF.

Table 1.

Material properties of the lumbar finite element model.

Young modulus (MPa) Poisson ratio Stiffness (N/mm)
Cortical bone 12,000 0.3
Cancellous bone 100 0.3
endplate 25 0.25
Annulus fibrosis 4.2 0.453
Nucleus pulposus 1 0.499
Articular cartilage 50 0.3
Nails and rods 110,000 0.3
Anterior longitudinal ligament 8.75
Posterior longitudinal ligament 5.83
Supraspinous ligament 15.38
Interspinous ligament 0.19
Ligamentum flavum 15.75
Intertransverse ligament 2.39
Cystic ligament 10.85
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2.3. Boundary and loading conditions

The boundary condition constrains the lower edge of the L5 vertebral body and fixes the movement of the lower end of the L5 vertebral body in all directions. A reference point was established on the upper surface of the L3 vertebral body and 2/3 of approximately 300 N axial pressure and 10 N·m moment of human body mass were applied to simulate the 6 motion states of lumbar load-bearing and lumbar flexion, extension, left bending, right bending, left rotation, and right rotation.[23] The ROM of the vertebral body and maximum equivalent stress of the endplate, intervertebral disc, and pedicle screw was observed.

2.4. Model validation

In this study, model validation was carried out according to previous literature and in vitro experimental results. During the verification, the lower surface of the L5 vertebral body was fixed, and the upper edge of the vertebral body was simulated with normal upper-body stress of 150 n. Under vertical stress of 150 n, 10 nm forward flexions, extension, lateral bending, and rotation stress were applied to the upper surface of the vertebral body and compared with the previous research ROM to verify the effectiveness of the model.[24]

3. Results

3.1. Finite element model

The established normal spine finite element model includes 125,521 C3D4 solid elements, 233,023 nodes, and 3-dimensional finite element models of L3-5 vertebral bodies with 2 different backward entry modes. The finite element model includes various fine reconstructed vertebral bodies, intervertebral discs, upper and lower articular cartilage, ligaments, and other anatomical structures.

3.2. Validation of the intact model

For the normal L3-5 finite element model established in this study, the ranges of flexion, extension, side bending, and rotation under 10 nm torque are shown in Table 2, and they are consistent with the results of previous studies.[25–27] Simultaneously, the value of the normal model provides the base value for 2 different reconstruction models for reference.

Table 2.

Comparison of range of motion between this study and previous studies in all loading motions.

Anteflexion/extension Lateral bending Rotation
Zheng et al[38] 11.1° 7.6° 3.8°
Cai et al[39] 8.03° 7.5° 4.16°
Qin et al[40] 17.43 ± 2.68° 17.41 ± 4.17° 8.65 ± 2.66°
Our study 12.84° 8.03° 6.4°
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3.3. ROM of the entire lumbar spine

Under a load of 300 N vertical downward force and 10 nm moment, the lumbar spine moved in 6 directions. The activity ranges of the 2 different reconstruction models and the normal models in flexion, extension, lateral bending, and axial rotation are shown in Table 3. In general, all posterior fixation techniques can reduce the range of motion of the fusion segment related to completing the configuration. Compared with the normal lumbar model, the range of motion in the direction of lumbar flexion, extension, lateral flexion, and axial rotation of the 2 models was lower than that of the normal model. Compared with the normal model, the forward flexion of model A is reduced by 91%, the extension is reduced by 99%, the left bending is reduced by 94%, the right bending is reduced by 95%, and the left rotation is reduced by 89%, and the right rotation is reduced by 89%. Compared to the normal model, model B had 91% less flexion, 99% less extension, 95% less left bending, 96% less right bending, 90% less left rotation, and 91% less right rotation. Under the 6 working conditions, the ROM values of Models A and B were similar.

Table 3.

Comparison of range of motion in flexion and extension, side bending, and axial rotation.

Normal model Model A Model B
Flexion 12.03° 1.11° 1.1°
Extension 7.73° 0.01° 0.01°
Left lateral bending 7.24° 0.41° 0.36°
Right lateral bending 7.85° 0.4° 0.35°
Left axial rotation 5.75° 0.63° 0.55°
Right axial rotation 6.08° 0.64° 0.56°
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3.4. Stress distribution of intervertebral disc

The stress comparison of the lumbar intervertebral discs is shown in Figures 2 and 3. Under the 6 working conditions of flexion, extension, lateral bending, and axial rotation, the maximum stress of the intervertebral disc of the 2 new models was lower than that of the normal model, and the maximum stress of the intervertebral disc of model A was similar to that of model B. Taking the flexion state as an example, in the vertical loading state, the stress of the intervertebral disc is concentrated in the rear half, the compressive stress near the pedicle is the largest, and it gradually decreases from back to front, and the compressive stress at the front edge of the intervertebral disc is minimal. During flexion movement, the stress in the anterior area of the intervertebral disc is large and compressive. In contrast, in the posterior extension position, the posterior side of the intervertebral disc is under compressive stress, and the anterior side is under tensile force; during lateral flexion, the intervertebral disc compression area has large stress and is under compressive stress, which gradually decreases to the opposite side and becomes a tensile force, as shown in Figure 4.

Figure 2.

Figure 2.

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Stress comparison of L3/4 intervertebral disc.

Figure 3.

Figure 3.

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Stress comparison of L4/5 intervertebral disc.

Figure 4.

Figure 4.

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Stress distribution of intervertebral disc during flexion.

3.5. Stress distribution of endplate

A comparison of the maximum peak values of the endplates of the 2 reconstruction models under various physiological activity ranges is shown in Figure 5. In these 6 states, the maximum stresses of the endplates of models A and B were significantly reduced compared with the normal model, and the maximum stresses of the endplates of model A and model B were similar. In all the loading modes, the stress tended to be more concentrated at the edge of the endplate.

Figure 5.

Figure 5.

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Stress distribution of endplate.

3.6. Stress distribution of screws and rods

The maximum equivalent stresses of the pedicle screws in the 2 models under different working conditions are shown in Figure 6. In the flexion state, the maximum stress of the screw of model B was 9.8% less than that of model A, and the maximum stress of the rod of model B was 2.7% less than that of model A. In the extension state, the maximum stress of the screw of model B was 10.7% less than that of model A, and the maximum stress of the rod of model B was 3.2% less than that of model A. In the left bending state, the maximum stress of the screw of model B was 1% smaller than that of model A, and the maximum stress of the rod of model B was 6.8% smaller than that of model A. In the right bending state, the maximum stress of the screw of model B was 1.8% less than that of model A, and the maximum stress of the rod of model B was 8% less than that of model A. In the left rotation state, the maximum stress of the screw of model B was 3.9% less than that of model A, and the maximum stress of the rod of model B was 10.9% less than that of model A. In the right rotation state, the maximum stress of the screw of model B was 4.4% less than that of model A, and the maximum stress of the rod of model B was 10% less than that of model A. The screw stress of the model gradually increased from the screw head to the root. The stress near the screw root reached the maximum value, and the maximum value appeared on the inner side of the screw, which was consistent with the common position of screw fractures in the clinic. The minimum value of screw stress in the 2 models appeared in the extension.

Figure 6.

Figure 6.

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Stress distribution of screw.

4. Discussion

In this study, the imaging data in DICOM format were obtained by spiral CT, the image data were processed and optimized by Mimics software, and the model optimization and grid processing were carried out using 3-Matic of Mimics software. The pedicle screw internal fixation system was simulated and established using SolidWorks software, and a 3-dimensional lumbar finite element model was constructed by importing the finite element software ANSYS. The placement of pedicle screw internal fixation during the operation was simulated, and the corresponding finite element model was constructed, which can be accurate and effective and can calculate the biomechanics of the finite element model. From the results, this model vividly simulates the structure of the human lumbar spine bone and soft tissue and accurately simulates the stress of the involved lumbar spine under different working conditions.[28–30]

Under different motion states, the range of motion of the 2 new lumbar models is significantly smaller than that of the normal model, indicating that the screw rod internal fixation system plays a significant role in limiting the range of motion of the vertebral body and that the screw rod internal fixation can effectively maintain the stability of the spine. Comparing the stress changes of the model before and after internal fixation, it can be seen that the nail rod internal fixation system makes the stress transfer of the lumbar spine concentrated on the nail body and reduces the stress load of the lumbar spine’s structure, such as the endplate, intervertebral disc, and pedicle, which shows that it can effectively prevent the premature degradation of lumbar-related structures.[31–33] The biggest advantage of the pedicle screw rod internal fixation system is that it produces immediate stability, which provides a prerequisite for patients to carry out postoperative rehabilitation training and related functional exercises as soon as possible, which is particularly important for the functional recovery of surgical patients.[34–36] However, by observing the force on the posterior internal fixation system under different states, the placement of the screw rod internal fixation caused excessive stress concentrated on the pedicle screw. If excessive stress is concentrated on the pedicle screw for a long time, it causes a large load on the screw. Therefore, this is consistent with broken nails caused by stress fatigue in some patients after long-term activity.[37–39]

This experiment verified that the pedicle screw internal fixation system has an obvious effect on the lumbar spine and that its role in maintaining stability can reduce the probability of spinal instability. In this experiment, both models produced stress concentration at the root of the screw and the connection of the screw rod, which is consistent with the position of internal fixation failure and fracture commonly observed in the clinic.[40–42] In this study, it was found that the minimum value of the screw stress in each model occurred during extension. Under 6 working conditions, the maximum stress of the screw and rod of model B was less than that of model A, indicating that the screws and rods in this internal fixation method are less likely to be broken. In Model B, the middle pedicle screw experienced less stress than the screws at both ends of the head and tail, and the overall stress of the lower screw was higher than that of the upper screw. In general, the transmission of force is always attenuated from top to bottom[43]; however, when it is blocked by fixation, the stress is mainly concentrated here, and the middle part plays the role of supporting the transmission force.[44] Therefore, the middle screw was relatively less stressed, the stress of the upper and lower screws was more obvious, and the stress of the lower screw was greater. This result indicated that the relative stress of the intermediate screw was low. In the process of clinical placement of the intermediate screw in the future, can the intermediate screw be replaced by other internal fixation, such as a hook, which only needs to be firmly connected with the vertebral body to some extent, and there is no need to fix like pedicle screw, which can reduce the trauma required for screw placement on the one hand, and it is more economical on the other hand.[45]

Through this experiment, it was found that the mobility of models A and B is similar under 6 working conditions, which shows that the stability of the pedicle screw fixation model in the L3 and L5 vertebral bodies can be similar to that in the L3, L4, and L5 vertebral bodies. It can be seen from Figure 6 that both models A and B show a large maximum stress value when the rotating side bends, especially in the rotating state, while it is relatively small in the bending and extension states. The sagittal plane of the longitudinal axis formed by the pedicle screw may be consistent with the sagittal plane of the lumbar spine for the flexion and extension movement of the lumbar spine,[46,47] so the internal fixation stress is small, while the rotation of the lumbar scoliosis is an activity in the horizontal plane of the coronal plane, forming a large included angle with the sagittal plane of the longitudinal axis formed by the pedicle, so it has large shear stress.[48] Therefore, clinically, in the case of no fusion, we should try to reduce activities such as lumbar lateral bending rotation, especially the rotation movement. If there is a significant lateral bending rotation movement with the participation of torque, the possibility of internal fixation failure is high.[49] Although this difference in stress does not have a decisive impact on the operation, the long-term stress concentration will lead to fracture of pedicle screws due to fatigue, which will bring a series of potential risks after the operation, which is not conducive to the stability of the entire internal fixation system.[50,51]

The intervertebral disc is an important load center and buffer structure for spinal function. It plays a key role in the spinal movement, bearing, and transmission of various loads.[52,53] It is also a prone site for lumbar diseases.[54,55] From the relationship between the maximum effective stress of the intervertebral disc and the loading mode, among the 6 loading modes, the increase in the intervertebral disc stress caused by the forwarding bending moment was the most obvious, followed by lateral bending and rotation, and the intervertebral disc stress was the smallest during extension. It shows that flexion is most likely to cause chronic injury and degeneration of the intervertebral disc; Lateral bending and rotation activities are the second, and posterior extension activities are the most beneficial to the intervertebral disc. The intervertebral disc stress shows that under the 6 working conditions of flexion, extension, left and right lateral bending and left and right rotation, the 2 internal fixation methods have similar effects on the stress of the intervertebral disc. The stress is mainly concentrated at the edge of the intervertebral disc, and the stress on the compression side is relatively concentrated and diffused to the tensile side, which is consistent with the biological mechanical characteristics of the lumbar spine.[56 The results of this study show that the fiber ring of the lumbar intervertebral disc becomes larger, and there is an obvious stress concentration under the 6 working conditions. When twisting, the stress of the annulus fibrosus is mainly concentrated in the lateral rear, which also indirectly proves that the rupture of the annulus fibrosus and prolapse of the nucleus pulposus is caused by the excessive stress of the annulus fibrosus of the intervertebral disc; that is, the protrusion of the lumbar intervertebral disc often occurs on the posterolateral side, which is one of the important causes of human lumbar diseases.[57]

Regardless of which segment of the lumbar spine is fixed, the stress of the lower screw, especially the screw vertebral body interface and screw rod connection, is the largest. In the case of long-term nonfusion, the fracture risk was the highest.[58] The pedicle screw fracture observed in the clinic is mostly concentrated near the lowest nail tail cap.[59] Therefore, to reduce the risk of internal fixation failure, we can try to take a variety of methods: on the one hand, fusion is necessary. After fusion, the internal fixation stress can be reduced, and the possibility of fatigue fracture caused by long-term nonfusion fretting can also be reduced to a certain extent.[60] At the same time, the placement of inferior screws can be improved, such as using screws with better materials or pedicle screws with thicker diameters when the pedicle diameter allows.[61] Screw-in pedicle screws should be used as much as possible to reduce the part exposed outside the bone while ensuring that they do not penetrate the anterior wall of the vertebral body and have an appropriate length (it is generally considered that the distance from the pedicle puncture point to the intersection line between the pedicle axis and the anterior edge of the vertebral body is 80%[62–64]), it reduces the risk of fracture.

However, there are still shortcomings in the application of this model. First, the conditions set for the convenience of the experiment may not be consistent with the actual situation. For example, the nail rod and vertebral body are completely elastically fixed without relative movement, and the friction coefficient between joint surfaces may also be inconsistent with the actual situation; second, the exogenous stability factors of the spine, such as muscle, are ignored, and some structures are simplified; actual degenerative conditions such as bone loss, ligament relaxation, and intervertebral disc elasticity weakening in the vertebral body model are not considered, and the material parameters used are all normal values, so the specific accurate figures calculated may be different from reality.[65,66] However, under the same experimental conditions, a general trend represented by the 2 internal fixation stress distributions can be well simulated, which meets previous research standards: the simulation cost is relatively low, there is no risk to patients, and the results are also convincing, which has a certain guiding significance for clinical practice. This will play an important role in further understanding the biomechanics of these 2 internal fixation methods. It can not only help surgeons choose the best interbody fusion technology for specific patients but also optimize implants, which helps to reduce postoperative complications and recovery time. In addition, it also has significance for the rehabilitation exercise guidance of postoperative patients.

5. Conclusion

The finite element model established in this study conforms to the biomechanical properties of the spine, and it has been verified that the model is effective. The 2 internal fixation systems improve the stability of the lumbar spine and reduce the stress on the endplate and intervertebral disc. These 2 fixation methods have similar effects on the stress of the endplate and intervertebral disc, but the maximum stress of the screw and rod of model B is smaller than that of model A, so this internal fixation method can effectively reduce the risk of fracture, as it provides a reference value for clinicians to choose surgical methods.

Author contributions

All the authors contributed substantially to the manuscript. YJ and YG were responsible for the conceptualization. YJ, QZ, and YS were responsible for the investigation and methodology. YJ, QZ, YS, and QH were responsible for the formal analysis and writing of the original draft. GF, JB, and YG were responsible for writing – reviewing & editing, and supervision. All authors have read, provided feedback, and approved the submitted version.

Conceptualization: Yulei Ji, Yaodong Gu.

Formal analysis: Qiuli Hu, Yulei Ji, Qiaolin Zhang, Yang Song.

Investigation: Yulei Ji, Qiaolin Zhang, Yang Song.

Methodology: Yulei Ji, Qiaolin Zhang, Yang Song.

Supervision: Gusztáv Fekete, Julien S. Baker, Yaodong Gu.

Writing – original draft: Yulei Ji, Qiaolin Zhang, Yang Song, Qiuli Hu.

Writing – review & editing: Gusztáv Fekete, Julien S. Baker, Yaodong Gu.

Abbreviations:

CT =
computed tomography
ROM =
range of motion

The study was conducted by the guidelines of the Declaration of Helsinki and was approved by the Committee of Ningbo University (code ARGH20211213).

Informed consent was obtained from all the participants involved in the study.

This study was sponsored by the Zhejiang Provincial Key Research and Development Program of China (grant no. 2021C03130), the Zhejiang Provincial Natural Science Foundation of China for Distinguished Young Scholars (grant no. LR22A020002), Public Welfare Science & Technology Project of Ningbo, China (grant no. 2021S134), Basic Scientific Research Funds of Provincial Ningbo University (SJWY2022014), and K. C. Wong Magna Fund of Ningbo University.

The authors have no conflicts of interest to disclose.

The data that support the findings of this study are available upon reasonable request from the corresponding author. The data were not publicly available because of privacy or ethical restrictions.

How to cite this article: Ji Y, Zhang Q, Song Y, Hu Q, Fekete G, Baker JS, Gu Y. Biomechanical characteristics of 2 different posterior fixation methods of bilateral pedicle screws: A finite element analysis. Medicine 2022;101:36(e30419).

Contributor Information

Yulei Ji, Email: jiyulei@hotmail.com.

Qiaolin Zhang, Email: 2011042033@nbu.edu.cn.

Yang Song, Email: yang.song@uni-obuda.hu.

Gusztáv Fekete, Email: fg@inf.elte.hu.

Julien S. Baker, Email: jsbaker@hkbu.edu.hk.

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