Three-dimensional finite-element analysis of a pedicle screw system combined with a titanium mesh support and fixation in the treatment of L4–5 vertebral tuberculosis

Abstract

This study aimed to assess the biomechanical stability of pedicle screws combined with titanium mesh bone grafting for spinal reconstruction and fixation during surgery for lumbar spine (L4–L5) tuberculosis using the finite-element method. A model of the L1–sacral segment of the human body was developed using the finite-element method. After verifying its effectiveness, a postoperative model was developed for treating vertebral tuberculosis at the L4–L5 level, which involved implanting an interbody titanium mesh and securing it with pedicle screws. Subsequently, the internal fixation materials and bone stress at L4 and L5 were analyzed. The verification of the finite element model proved to be effective. The titanium mesh exhibited a maximum von Mises stress of 477.9 MPa during forward bending and a minimum of 229.9 MPa during backward extension. The stress concentration was primarily observed at the cut edges, screws, and connections. Similarly, the rod experiences a maximum stress of 235.8 MPa when leaning to the right and a minimum of 101.4 MPa during backward extension. High-stress areas were identified on the screws and connecting rods. In the titanium mesh model, the maximum von Mises stresses on L4 and L5 reached 215.9 MPa during forward bending and exceeded 90 MPa in five directions. In the treatment of lumbar tuberculosis, titanium mesh fusion and pedicle screw-reinforced fixation carry the risk of prosthesis subsidence and screw breakage. Therefore, patients receiving this treatment should be cautious and avoid excessive forward and lateral flexion movements.

Introduction

Finite-element analysis (FEA) is extensively utilized in various engineering fields, including stress analysis, fluid dynamics, electromagnetism, and heat transfer, for addressing real-world issues by creating computational models. Despite initial skepticism from academics in the early 1950s, significant funding from the National Aeronautics and Space Administration facilitated the swift advancement and widespread adoption of this technology. Early FEA models were initially validated through ex vivo cadaver studies that replicated the biomechanical loads on the spine during physiological activity using pulleys and weights. Although ex vivo testing is commonly utilized in spine-related biomechanical studies, it has notable limitations, including the quality of tissue sourced from older donors, complexity of test setups, reproducibility challenges, limited biomechanical parameters, and high costs. ¹

In spinal biomechanics, FEA has emerged as an indispensable research method for analyzing load transfer, implant behavior, and degenerative or pathological conditions that are challenging to replicate experimentally. It enables quantitative prediction of stress distribution and deformation patterns under physiological loads, complementing in vitro and clinical observations.

Severe kyphotic deformity resulting from spinal tuberculosis is typically caused by the destruction of the vertebral body and intervertebral disc by Mycobacterium tuberculosis. The involvement of these structures may exacerbate nerve-related symptoms. Khanna et al. ² suggested that surgical treatment is necessary for adult spinal tuberculosis when the resulting local kyphotic deformity exceeds 60°. Following the excision of vertebral body lesions, the reconstruction of the spine’s height and stability is accomplished through various methods, such as using autologous bone, allogeneic bone, and titanium cage bone grafts. ³ Internal fixation using autologous bone and titanium, particularly cages supporting more than two vertebral lesions, has shown a high incidence of subsidence and failure. This often requires additional posterior auxiliary pedicle screw system fixation for reinforcement. ⁴ Chen ⁵ et al. analyzed 300 patients who received anterior cervical corpectomy and titanium mesh cage fusion, with 236 undergoing one-level corpectomy and 64 cases undergoing two-level corpectomy. The study evaluated titanium mesh cage subsidence, imaging findings, and clinical outcomes over a 1-month follow-up period. The results indicated that the titanium mesh cages subsided in 239 cases (79.7%). FEA provides a safe, cost-effective platform to evaluate these parameters in silico. By simulating postoperative loading conditions, it can identify potential high-stress zones, predict screw or cage fatigue, and guide optimization of surgical constructs before clinical application.

This study utilized the FEA method to develop an FE model of the human L1–S segment. In addition, a postoperative model was constructed for the management of L4–5 vertebral tuberculosis through interbody titanium mesh implantation and pedicle screw fixation. The simulation quantified von Mises stress and displacement within the cage, screws, and vertebrae under six loading modes—flexion, extension, lateral bending, and axial rotation—to assess construct stability and fatigue susceptibility. The stress conditions of the implanted internal fixation materials and fused vertebrae were analyzed to investigate their mechanical stability and offer a theoretical foundation for guiding postoperative rehabilitation exercises in clinical settings.

Materials and methods

Patients and methods

Research participant

The research participant was a 26-year-old volunteer (weight, 65 kg; height, 175 cm) ⁶ with no history of chronic low back pain and lumbar trauma. The volunteer was recruited from the Orthopedic Surgery Department of our institution and signed an informed consent form in accordance with relevant regulations, which was submitted to the institutional ethics committee for approval. All clinical research procedures adhered to the provisions of the Declaration of Helsinki.

Initially, a lumbar spine X-ray imaging was performed to rule out any spinal diseases. The imaging department of the hospital utilized a 64-slice spiral computed tomography (CT) scanner (Siemens in Erlangen, Germany), with a slice distance set at 0.625 mm for the L1–S segment. Continuous horizontal scanning was performed to acquire CT slices in the bone window display mode, and the resulting image data were exported and saved in the Digital Imaging and Communications in Medicine (DICOM) format. ⁷

Research methods

Steps to establish the normal L1–S segment FE model

1 .The DICOM file was imported into Mimics 20.0 (Materialize Inc., Leuven, Belgium), and each vertebra was selected based on the image threshold. The sacral vertebrae were selected as a whole, whereas L1–L5 vertebrae were independently segmented using specialized functions such as regional segmentation. The precise range of the vertebral bodies was delineated, and three-dimensional (3D) graphics were calculated to generate a 3D L1–S vertebral body surface model. Subsequently, an “STL” format file was generated. ⁸

2 .3-Matic 12.0 (Materialize Inc.) was utilized for constructing a more detailed and physiologically consistent 3D model. ⁹ The local smoothing function was employed to effectively smooth the imported 3D model of the vertebral body. A 1-mm thick cortical bone was generated, and an intervertebral disc model was developed.

3 .The 3D model image created using the Geomagic Studio 2015 (Geomagic Inc., USA) was imported. All surface models were processed by detecting contour lines, constructing patches, and grids, and the materialization was finalized. ⁷

4 .Hypermesh 2017 (Altair Engineering, Troy, MI, USA) was utilized to mesh the L1–S bone, L1–S intervertebral discs, and surrounding ligament structures. ⁹ Grid convergence verification was performed to ensure accuracy, and the correct elastic modulus was input based on the actual conditions to achieve a balance between accuracy and computational efficiency. ¹⁰ The study compared the maximum von Mises stress in models with element sizes of 0.5, 1.0, and 1.5 mm to the model with an element size of 0.5 mm. Convergence was achieved when the difference was <5%. The optimal vertebral mesh size was 1.0 mm, resulting in a percentage error of 2.31%. The intervertebral disc was meshed using hexahedral elements, whereas the vertebral body used a tetrahedral element. ¹¹ The FE model was assembled using Abaqus2020 (Abaqus Inc., CA, USA), incorporating material-specific properties, defining the analysis steps, applying loads, and conducting the FE simulation analysis. ¹²

5. The complete L1–S model included the cortical bone, articular cartilage, and cartilage endplate with thicknesses of 1, 0.2, and 0.5 mm, respectively.^10,13 The intervertebral disc was anatomically divided into two main components: the nucleus pulposus and annulus fibrosus. The nucleus pulposus makes up approximately 30%–40% of the intervertebral disc volume. ¹⁴ The annulus fibrosus consists of collagen fibers and a matrix arranged in five layers. It runs obliquely between the vertebral bodies at an angle of 25–45° on a horizontal plane. In a computer simulation, seven ligaments were replicated at each segment: the anterior and posterior longitudinal ligaments, ligamentum flavum, intertransverse process ligament, capsular ligament, interspinous process ligament, and supraspinous process ligament. ¹² The friction coefficient of the facet joint was defined as 0.1. Ligaments were represented using uncompressed T3D2 elements. The material properties of bone tissue were based on linear, uniform, and isotropic formulations, with relevant data sourced from the existing literature.^7,11,12,15 Soft-tissue components were modeled as linear, homogeneous, and isotropic elastic materials, acknowledging that this assumption simplifies their nonlinear viscoelastic behavior but enables computational stability. The material properties of each component are detailed in Table 1. Subsequently, these components were combined to develop an FE model representing a healthy adult spine with a normal L1–S.

Table 1.

Material properties used by the finite-element model.

Component	Young’s modulus (MPa)	Poisson ratio	Cross-sectional area (mm2)
Vertebra
Cortical bone	12,000	0.3	—
Cancellous bone	100	0.2	—
Posterior element	3500	0.25	—
Articular cartilage	10	0.4	—
Disc
Annulus fibers	360–550	—	0.15
Annulus ground substance	2	0.45	—
Nucleus pulpous	1	0.49	—
Endplate	500	0.4	—
Ligaments
ALL	7.8	—	63.7
PLL	10	—	20
LF	15	—	40
CL	7.5	—	40
ISL	10	−	30
SSL	8	—	30
ITL	10	—	1.8
Implants
Cage (titanium alloy)/connecting rod/pedicle screws	110,000	0.3	—
Bone graft	100	0.2	—

Validity verification of the FE model

The movement of the spine can be categorized into flexion, extension, lateral bending, and rotation in different planes. In this study, the lower surface of the sacrum was stabilized, whereas four specific torques were applied to the upper surface of L1 (flexion, 8 Nm; 6 Nm, extension; ±6 Nm, lateral bending; and ±4 Nm, rotation). This step was performed to determine whether the developed model aligned with the biomechanical properties of the human body, as previously outlined by Renner et al. ¹⁶ The resulting range of motion (ROM) for each direction was compared with in-vitro cadaveric data to confirm that the model reproduced physiological spinal flexibility within accepted tolerance limits. The agreement validated the mesh quality and boundary-condition fidelity before proceeding to postsurgical modeling.

FE model after spinal tuberculosis surgery

The validated FE model of the healthy spine was modified to include the pedicle-screw–rod system, titanium cage, and bone graft. Using Pro/ENGINEER (Proe) software, the pedicle screw was modeled (4.5 × 65 mm) with a 5.5 mm connecting rod. The prostheses and the nail–rod system were merged with vertebrae via Boolean operations, then remeshed in Hypermesh to generate the postoperative FE model incorporating the titanium mesh. The connecting rods were represented as straight, un-contoured elements without physiological lordosis and were assembled under a neutral alignment without applying intersegmental compression or distraction. This assumption reflects the surgical procedure used during fixation in a relaxed, load-free posture. All implant–bone interfaces were assumed perfectly bonded to simulate immediate postoperative stability, acknowledging that this condition may slightly overestimate initial fixation rigidity.

Loads and boundary conditions

The sacrum was immobilized, with a preload force of 400 N and a torque load of 7.5 Nm applied to the upper surface of L1 to replicate flexion, extension, lateral bending, and rotation movements of the spine during daily activities. ¹² These load magnitudes were chosen according to Renner et al. (2007), ¹⁶ representing typical spinal compressive and moment loads in daily activities (approximately 40–60% body weight and 6–8 Nm moment). Although active muscle forces were not included, the boundary setup replicates passive load-bearing conditions suitable for comparative FE analysis. The omission of dynamic muscle action is acknowledged as a modeling limitation. The biomechanical performance of the internal fixation system and vertebrae in the postoperative model was then evaluated.

Results

Establishment of the FE model; Pedicle screw, titanium cage, and FE model of normal human L1–S; Lumbar tuberculosis postoperative model with pedicle screw combined with titanium cage fixation

CT images of the L1–S segment from normal individuals were utilized as original data. In Mimics, 3-Matic, Geomagic Studio, and Hypermesh, a comprehensive L1–S model and two postoperative FE solid models were developed (Figure 1). The previous description of “two postoperative models” has been corrected for clarity, as only one postoperative configuration was analyzed. The postoperative model incorporated a 5.5-mm connecting rod and 4.5 × 65 mm pedicle screws, designed as straight rods without lordotic pre-contouring and applied without intersegmental compression or distraction, simulating a neutral spinal posture during fixation. This modeling assumption ensures consistent contact conditions across the cage–bone interface and reflects a typical postoperative alignment.

Figure 1.

(a, left side) Complete L1–S finite-element model. (b, right side) Spinal tuberculosis postoperative model using a titanium cage.

Validity of the model verification supported by in vitro experiments and FE model calculations conducted by Renner et al. ¹⁶

The study results indicate that the predicted activity range aligns closely with the experimental data reported in the literature. Specifically, the forward flexion range surpassed the back extension range, whereas the left and right movements exhibited similar patterns. The FE model adhered to the human body’s physiological characteristics, confirming its validity for subsequent computational simulations and analyses. After surgery, the mobility of the L4–5 fusion gap in the fixed model was <1°, signifying secure fixation and firm fusion (Table 2). This minimal residual motion confirms that the postoperative construct achieved effective stabilization and can serve as a validated foundation for stress and deformation analysis in later simulations (Figure 2).

Table 2.

Mobility of the L4–L5 vertebral body (°).

L4–5	Preoperative model	Operative model
Flexion	13.87	0.47
Extension	2.80	0.10
Left bending	6.02	0.40
Right bending	4.96	0.22
Left rotation	6.77	0.27
Right rotation	7.27	0.17

Figure 2.

Comparison of the range of motion of the current model with previously reported in vitro experimental and finite-element model data.

Internal fixation system stress

In the postoperative model, the titanium cage experienced a maximum von Mises stress of 477.9 MPa during forward flexion, with minimum stress occurring during posterior extension at 229.9 MPa (Table 3). The highest stress concentration was predominantly observed at the edge after cutting (Figure 3). Furthermore, the screws and connecting rods exhibited a maximum von Mises stress of 235.8 MPa when tilting to the right and a minimum of 101.4 MPa during backward extension. Notably, multiple high-stress areas were identified on the screws and connecting rods (Figure 3). Lastly, the L4 and L5 segments within the titanium cage model experience a maximum von Mises stress of 215.9 MPa during forward flexion, exceeding 90 MPa in five directions (Table 3). These stress magnitudes were within the mechanical tolerance of Ti-6Al-4V (yield 789–1013 MPa) and cortical bone (90–200 MPa) but approached their fatigue limits, emphasizing that repetitive bending and torsional loads could predispose the construct to progressive fatigue or microdamage under prolonged postoperative motion.

Table 3.

Stress of the internal fixation system (MPa).

Maximum von mises stress	Cage (Titanium alloy)	Pedicle screws	Vertebra (L4–L5)
Flexion	477.9	165.3	215.9
Extension	229.9	101.4	51.58
Left bending	244.9	189	105.9
Right bending	284.6	235.8	159.2
Left rotation	317.7	118.5	93.22
Right rotation	309.8	150	99.69

Figure 3.

Stress distribution diagrams of the titanium cage, screws, and connecting rods during different spinal motions: Left to right labelling (a) flexion, (b) extension, (c) left bending, (d) right bending, (e) left rotation, (f) right rotation.

Discussion

FEA is a valuable tool utilized across various industries and research disciplines. It allows for thorough testing of new designs, an inspection of components in which direct experiments are challenging, and diagnostic investigations. To understand the intricate mechanisms of the spine and its components, FE models play a crucial role. Given the complexity of the spinal structure, which includes diverse geometries, uncertain material properties, and boundary conditions, many models require simplification and idealization. This simplification process is not distinct to spine modeling. Idealization can be advantageous when dealing with uncertainty and variability. Idealization aids in deepening our understanding of complex systems by isolating and examining causal relationships while minimizing experimental variability.

With advancements in computing power, more intricate issues, such as those related to the spine, can be assessed through FE modeling. In spine research, FE modeling serves four main purposes: (a) assessing spinal health; (b) evaluating spinal changes resulting from various factors such as disease, degeneration, aging, trauma, and surgery; (c) conducting spinal assessments using instrumentation; and (d) aiding in the design and development of spine-related instruments. ¹⁷

Biomechanical analyses of various anterior and posterior surgical fixation methods for lumbar tuberculosis have been performed. Wang B et al. ¹⁸ analyzed three different approaches in L3–L5 tuberculosis, including debridement surgery with anterior bone grafts with or without titanium mesh and internal fixation with varying numbers of screws and rods. The posterior surgical methods to restore spinal stability involved transformational lumbar debridement, bone grafting, and internal fixation. By evaluating the range of motion and intradiscal pressures around the fused segment, the study aimed to compare the biomechanical effects of these approaches to assist in surgical decision-making. Results indicate that all the evaluated surgical approaches carry a potential risk of adjacent segment degeneration; however, no significant differences in the biomechanical measurements were found among the different methods.

Liu et al. ¹⁹ compared the stability and stress distribution of surrounding tissues and implants in treating lumbosacral tuberculosis using three different lumbar internal fixation methods. They constructed and validated an FE model to analyze the effects of lateral double-screw fixation of the titanium cage (group 1), posterior approach double-screw fixation of the autologous bone (group 2), and posterior approach double-screw fixation of the titanium cage (group 3). Group 4, which utilized the complete L3–S1 spine, was used for comparative purposes. Upon applying the load, the range of motion and von Mises stress of various components were recorded and analyzed. They concluded that the posterior approach of the double-screw fixed titanium cage method was effective in immediately restoring lumbosacral spine stability. It has more advantages in terms of safety and preventing screw loosening. In the present study, an FE model of the normal human L1–S was established and verified, ¹⁶ confirming its validity. This paves the way for further computational simulation and mechanical analysis.

The current model was derived from CT data of a single healthy volunteer to maintain geometric uniformity and model stability. However, this may not represent typical spinal tuberculosis patients, who often exhibit reduced bone density and altered load-bearing capacity. Therefore, the findings should be interpreted with caution, as their generalizability to osteoporotic or pathological bone may be limited. Future studies should incorporate patient-specific modeling and clinical validation to better reflect physiological variability.

In clinical settings, screw breakage is one of the factors leading to fusion failure in the pedicle screw system, with fractures commonly occurring in the middle section between the screw and screw cap. Li ²⁰ utilized the 3D FEA method to investigate the biomechanical mechanism of pedicle screws in the treatment of thoracolumbar compression fractures at the injury level. The model was subjected to various loading forces, and the stress measurements on the pedicle screws were recorded, revealing high-stress concentration at the root of the pedicle screw under different loading conditions. The study identified that, regardless of the load type applied, the maximum stress on the pedicle screws in the titanium cage combined with the pedicle screw fixation model was localized at either the nail cap-binding part or the middle section of the screw. In addition, the nail cap-binding part was the weakest point of the screw, which is prone to breakage.

The maximum von Mises stress on the titanium mesh (477.9 MPa) remained below its yield strength (789–1013 MPa) but approached the reported fatigue limit of Ti-6Al-4V (500–600 MPa). Similarly, vertebral stresses (up to 215.9 MPa) exceeded the static yield range of cortical bone (90–200 MPa) and neared its cyclic-fatigue threshold (100–150 MPa). This suggests that repetitive loading during daily activities could progressively weaken both implant and bone, highlighting the importance of minimizing fatigue-inducing motions in postoperative rehabilitation.

Previous comparative FEA and experimental reports^3,4,19 have demonstrated that combined anterior–posterior fixation and standalone cage systems differ in stress distribution and stability. Compared with these configurations, our pedicle screw + titanium-mesh construct achieved comparable fixation strength with fewer stress peaks, supporting its clinical feasibility as a single-approach solution for spinal tuberculosis.

FEA revealed that the titanium cage experiences the highest stress of 477.9 MPa when subjected to forward bending. Furthermore, the maximum von Mises stress on the titanium cage predominantly occurs at the cut edge, whereas the stress concentration is not prominent on the 3D-printed false body. The yield strength of Ti-6Al-4V ranges from 789 to 1013 MPa. ¹¹ In the pedicle screw combined with the titanium cage fixation model, the stress on the pedicle screw was the highest during forward and lateral flexion, with the greatest stress occurring during right-leaning movements at 235.8 MPa. The stress is primarily concentrated at the nail cap joint or middle section of the screw. The damage strength of the human cortical bone typically ranges from 90 to 200 MPa. ¹² The stress on the vertebrae in contact with the titanium cage exceeded 90 MPa during forward flexion, lateral flexion, and rotation, with a peak of 256.7 MPa during forward flexion. Although vertebral stresses above 90 MPa indicate a potential risk for micro-damage or subsidence, this threshold varies with bone quality. In osteoporotic or infected bone, local failure may occur even below this value. Thus, the clinical interpretation of high-stress zones should consider individual bone density and infection-induced weakening to accurately assess subsidence risk. This finding suggests a potential risk of damage to the fixed vertebrae and subsidence of the prosthesis in daily activities after surgery. Accordingly, patients who have undergone fixation with pedicle screws and titanium cage systems must refrain from engaging in forward and lateral flexion movements to prevent loosening and fractures of the internal fixation system.

Clinically, these biomechanical findings suggest that early postoperative rehabilitation should emphasize neutral spinal alignment while strictly avoiding forward flexion and right lateral bending—motions producing the highest stress levels. Gradual re-introduction of movement, guided by radiographic evidence of fusion, may reduce the risk of fatigue failure and implant loosening. Incorporating these guidelines into physiotherapy protocols can improve long-term fixation stability.

Spinal prosthetic fusion and refixation are commonly performed to provide spinal support, alleviate pain, improve spine stability, or correct spinal deformities. The postoperative model demonstrated a fixed segment mobility of 1°, indicating successful fixation. The applied boundary conditions—a 400 N axial preload and 7.5 Nm torque—were selected based on established physiological load ranges during standing and bending. ¹⁶ Although these simplify complex muscular dynamics, they adequately replicate passive loading conditions for validation. The absence of modeled active muscle forces is acknowledged as a limitation that may affect accuracy under functional loading scenarios.

This study highlights the limitations of FEA, emphasizing the importance of considering muscle strength before and after surgery to ensure the reliability of results. ¹ Although the data obtained through the FEA may not perfectly replicate real-world scenarios, they accurately reflect general trends. However, in vitro testing is necessary to obtain precise data. In addition, modeling based on individual image data may not fully capture overall individual differences, necessitating verification through multicenter controls and using large sample sizes. Furthermore, additional limitations include: (1) the use of linear elastic properties for soft tissues, which may not capture nonlinear or time-dependent behavior; (2) the assumption of perfect fusion and bone–implant interface, which may overestimate fixation stability; and (3) the omission of postoperative bone-remodeling effects, which could influence long-term mechanical outcomes.