Introduction
Pedicle screws are commonly used in fusion surgeries for spine pathologies such as spondylolisthesis, tumors, spine trauma, degenerative arthritis, and revision surgeries [1–3]. The screw-based fixation system enables immediate mechanical fixation of unstable spine and has become a reference standard even for osteoporotic patients [4]. However, loosening and breakage of pedicle screws are common complications. The incidence of screw loosening post-implantation ranges from less than 1% to 15% in non-osteoporotic patients, and up to 60% in osteoporotic patients [5]. Furthermore, screw breakage is also a notable concern, occurring in 3%–7.1% of cases [6]. Loosened and broken pedicle screws can cause significant discomfort for patients, necessitating revision procedures. Studies have shown that changes in screw design can increase the screw-bone contact area, resulting in better screw-bone fixation strength [7–9]. Ongoing investigations focus on enhancing bone-screw interface strength, including the development of porous screws for improved bone-implant integration [10,11]. However, it is unclear whether these screws can withstand bending and torsion loads.
The pull-out force is regarded as the primary indicator of bone-screw fixation strength, as it reveals the mechanical behavior of the bone-implant interface [12]. However, there is no well-defined protocol to assess the efficacy of altered screw designs [13,14]. The main factors affecting the pull-out force are bone quality, screw design, and insertion techniques [13]. Bone quality can be evaluated by measuring the vertebral body’s bone density [15,16] and the anatomic characteristics of the pedicles [17]. Screw design parameters, including shape (cylindrical or conical) [18], outer diameter [19], and inner diameter [19] have been shown to impact pull-out force (Fig. 1A). Moreover, the insertion angle affects the screw-pull-out force and has been used to quantify the insertion techniques [20]. In addition, design parameters such as screw-bone interface area, degree of compacting bone (compression), and displaced diameter have been recently shown to affect pull-out strength in cancellous bone [21].
The pedicle screw traverses several bony parts with varying densities, including the lamina, pedicle, and vertebral body. Each of these structures contributes to the screw pull force, with the pedicle contributing approximately 60% to the screw pull-out strength. The vertebral body adds 5%–20%, while the anterior vertebral cortex contributes an additional 20%–25% [17]. Thus, optimizing pedicle thread profiles based on the various bony parts and their properties seems a logical approach. One study demonstrated that a reduced pitch in the pedicle region significantly increased pull-out strength compared to a single-threaded screw in human cadaveric lumbar vertebrae [22]. Another study introduced a triple-threaded pedicle screw design, which featured a finer pitch at the distal end. This innovative design improved stress redistribution to a large volume, transferring the stress from the cancellous (vertebral body) to the cortical region, reducing stress concentration [23]. These studies highlight the need for optimized thread profiles to leverage the mechanical advantage of varying bone mineral density within vertebrae.
In this study, we propose a novel poly-axial pedicle screw design tailored to vertebral anatomy and material properties. The modified design features two thread profiles for two bone types. Each thread type has a definite thread length along the screw’s longitudinal axis. A finite element (FE) analysis and design of experiments (DoE) technique were used to analyze the pedicle screw design changes. To the best of our knowledge, this study pioneers the application of these techniques for optimizing screw design. The analysis results informed the development of a novel pedicle screw. The effectiveness of the proposed design was evaluated by comparing the pull-out force with that of a clinically established pedicle screw (Medtronic Sofamore Danek USA Inc., Memphis, TN, USA) as a control device.
Materials and Methods
Study design
The study involved novel pedicle screw design, its computer simulation and analysis, and experiments using foam models as surrogates for bone. Institutional Review Board approval was not required for this study.
Design of a novel pedicle screw
A 6.5 mm diameter screw (Medtronic Sofamore Danek USA Inc.) served as the control device for comparative analysis with the proposed novel design. A three-dimensional (3D) computer-aided design (CAD) model of the screw, featuring a 6.5 mm diameter and 45 mm length, was created in PTC Creo (PTC Inc., Boston, MA, USA) for fabrication and FE analysis. The model’s geometric parameters were precisely measured up to two decimal places using micro-computerized tomographic analysis (Micro CT 40; SCANCO Medical AG, Brüttisellen, Switzerland).
In posterior surgical approaches, the screw interfaces with multiple bony structures, including the lamina, pedicle, and vertebral body. The anterior vertebral cortex contributes approximately 20%–25% to the screw’s pull-out force. Therefore, a design featuring two separate thread profiles was conceptualized: closely spaced threads for cortical bone at the proximal end and distantly spaced threads for cancellous bone at the distal end (Fig. 1B). A study on various grades of polyurethane (PU) foam found that a screw with an outer cylindrical and an inner conical diameter produces the highest pull-out force for a V-shaped thread [7]. Therefore, a cylindrical shape was chosen for the novel design.
Experimental study for control device
In clinical research, surrogate bone models made of PU are preferred over cadaveric bone models to eliminate uncertainties due to bone heterogeneity, individual size variability, and variations in bone mineral density [24]. In this study, we developed bilayer models using PU foams of distinct densities, 0.985 g/cm3 (grade 50) and 0.306 g/cm3 (grade 20), to simulate the lamina and cortico-cancellous region of the pedicle and vertebral body bones. The PU foam (V. K. Polymer Products, Nashik, India) met the requirements of the American Society of Testing Materials (ASTM F1839–08; ASTM International, West Conshohocken, PA, USA). The material properties of these foams, determined through uniaxial test using a universal testing machine (Model-2710-003; INSTRON, Norwood, MA, USA), are presented in Table 1.
The blocks of dimensions 55 mm×55 mm×48 mm (length×width×depth), with a 3 mm thick layer of grade 50 foam representing lamina, were used (Fig. 2A). The lamina foam was glued to the foam, simulating the cortico-cancellous region using epoxy resin [25]. The thickness of the lamina and cortico-cancellous region was selected based on the anatomical size of the vertebrae [26]. A stainless-steel fixture was developed to secure the bilayer model in place during testing. The pilot hole, perpendicular to the top surface of the bilayer models, was drilled using a 6.5 mm tap (Medtronic Sofamore Danek USA Inc.) at a controlled rate of 3 revolutions per minute (RPM). The control screw (6.5 mm diameter) was then inserted into the pilot hole at the same rate while being subjected to an axial load of less than 10 N, as specified in ASTM F543-17 (ASTM F543-17; ASTM International), to a depth of 39 mm using a Torsion test system (Bionix EM Torsion Test System; MTS System, Eden Prairie, MN, USA) (Fig. 2B). A longitudinal extraction load was applied to the screw head at a rate of 5 mm/min using a universal testing machine (Model-2710-003; INSTRON) (Fig. 2C). The insertion and extraction process of the pedicle screw was repeated for six samples. The resulting load-displacement curves were recorded for analysis.
Finite element analysis
All CAD modeling and FE analysis in this study were conducted using commercial software PTC Creo (PTC Inc.) and ANSYS ver. 18.2 (Ansys Inc., Canonsburg, PA, USA), respectively. A cylindrical-shaped human lamina model, with a depth of 2.8 mm, and a pedicle-vertebral body model, with a depth of 45.2 mm and an outer diameter of 10.5 mm were modeled to match the total depth of the experimental bilayer model test (Fig. 2A). The vertebral lamina’s cortical wall thickness, reported as 1.22±0.19 mm in the lumbar spine, was considered in the modeling process [26]. To ensure a conservative approach, nearly 2 times the maximum wall thickness of 2.8 mm was chosen for analysis. The screw models were assembled to a representative lamina-pedicle-vertebral model to a depth of 39 mm. Due to the high computational demands of 3D FE analysis, which required over 12 hours on high-performance computers (Windows 10 Pro, Intel i7-8700 CPU, 32 GB RAM, speed 3.20 GHz) for each 3D assembly, a two-dimensional (2D) axisymmetric analysis was employed, consistent with previous studies [27]. The screw model was assigned Ti6Al4V ELI material properties (Table 2), while material properties from Table 1 were used for the lamina and cortico-cancellous PU foam bone model. The 2D analysis employed linear triangle elements with a frictional coefficient of 0.3 at the bone-implant interface, using penalty-based contact formulation. A large deformation was enabled, and a total displacement (quasi-static) of 0.25 mm was applied to the proximal end of the pedicle screw in increments of 0.05 mm in the axial direction. The displacement boundary condition was used to determine the reaction force. A comprehensive mesh sensitivity study was performed separately for the control device, proximal and distal ends of the screw, and the final optimized design. This comprehensive study was needed due to the variation in the smallest features in different regions within the design (Fig. 3). Convergence was achieved when sequential results varied by less than 5%. The pull-out force was defined as the axial reaction force at the pre-applied displacement.
Simulation of control device
The simulation setup for the control device is shown in Fig. 4A. Following a comprehensive mesh sensitivity study, a mesh element size of 0. 2 mm was selected as optimal (Fig. 3A). To replicate physiological conditions, the outer edges of the lamina-pedicle-vertebral body bone model were constrained to restrict displacements in the X and Y directions within the global coordinate system. A unidirectional displacement was applied to the screw model in the Y direction, and the resulting reaction force was measured.
Simulations for proposed pedicle screw design
Analysis of the proximal end of the screw
A separate FE analysis was conducted to optimize thread parameters for the proximal end. A model of the human lamina with an outer diameter of 10.5 mm and depth of 5.0 mm, and a screw of 6.5 mm diameter were created. Various screw models with V-shaped threads were generated by varying the pitch and depth in 4 increments 0.2, 0.675, 0.9125, and 1.15 mm, resulting in 16 combinations (Fig. 4B). The maximum depth of 1.15 mm was determined from the control device’s thread measurement. The other values for pitch and depth were chosen to capture the effects of parameter variation. Each screw model was tested with a lamina model to a depth of 2.8 mm, using material parameters from Table 2 and bilinear material behavior [15]. A mesh element size of 0.05 mm was selected based on a sensitivity study (Fig. 3B). The outer edges of the lamina bone model were constrained in X and Y directions, and the reaction force was determined.
Analysis of the distal end of the screw
The distal end of the pedicle screw broadly engages with the pedicle and vertebral body (P-V body), composed of subcortical and cancellous bone. To streamline parameter optimization, the pedicle and the vertebral body were modeled as a single P-V body. Studies have shown that factors such as screw shape, thread shape, pitch, thread depth, and inclination angle significantly affect the pedicle screw fixation strength [19]. Therefore, we used four factors, thread shapes (A), thread depth (B), pitch (C), and trailing edge angle (D), to determine an optimum screw thread configuration. Since more than two factors were to be evaluated, a two-level full factorial DoE was conducted, with pitch ranging from 2.75 to 4 mm, depth ranging from 1 to 2 mm, trailing edge angle ranging from −5° to 30°, and thread shape type V and Buttress. The range for each factor was based on control device measurements and scientific literature.
A human P-V body model with an outer diameter of 10.5 mm and depth of 38 mm was developed. Sixteen 6.5 mm diameter screw models, generated based on factorial design parameters, were created. Each screw model was assembled with a separate P-V body model to a depth of 38 mm. The outer edges of the P-V body model were constrained in X and Y directions (Fig. 4C). Each assembly was analyzed using the material properties described in Table 2, assuming linear elastic behavior. A mesh element size of 0.1 mm was selected based on the mesh sensitivity study, and the reaction force was determined (Fig. 3C). The Minitab ver. 17.0 software (Minitab Inc., State College, PA, USA) was employed for the main effects plot, interaction plots, and analysis of variance (ANOVA) analysis.
Results
Pull-out test results for the control device
In the experimental study, six control devices (pedicle screws) with a diameter of 6.5 mm and length of 45 mm were extracted from the PU bilayer models. The load-displacement curve showed an initial increase in load, followed by a gradual decrease during extraction (Fig. 5A, B). The maximum load, defined as the pull-out force, occurred at a displacement of less than 4 mm, and this was defined as the pull-out force. Load-displacement and load-strain curves were plotted using the experimental results.
Simulation study
FE analysis for control device
The simulated pull-out force showed excellent agreement with the average experimental pull-out force from the bilayer model test. The simulation study yielded a reaction force of 1,990.5 N at a strain of 0.056 (mm/mm), while the experimental study’s reaction force (±standard deviation [SD]) was 2,082.9±175.3 N at a strain (±SD) of 0.055±0.005. This suggests that the outcome of the simulation study was within the 5% error margin, demonstrating that the FE simulation model effectively predicted the experimental test results. The constitutive model, boundary conditions, and simulations were thus validated, and a similar procedure was later used to optimize the proposed pedicle screw design.
Optimum parameters for the proximal end and distal end of the screw
Fig. 6A presents the FE analysis results for the proximal end model, showing the effects of different pitch and depth combinations on pull-out force. The pull-out force increased with the P/D ratio up to approximately 1.4 and subsequently declined as the P/D ratio increased. For the distal end model, the pull-out force of the simulation study for sixteen runs was used for the main effect plot, interaction plot, and ANOVA table in the Minitab software (Minitab Inc.). The main effect plot indicated that pull-out force varies significantly (p<0.05) with changes in factors A=type, B=depth, C=pitch, and not so significantly with D=angle (Fig. 6B). The interaction plot (Fig. 6C) showed that the combined effects of these factors significantly influenced pull-out force (p<0.05). The ANOVA analysis details the factors and their percentage contributions to pull-out force (Table 3). The adjusted R2 value of 97.50% indicated that the DoE effectively captured the variations in the data, ensuring a satisfactory model fit.
Optimized design
The P/D ratio in the range of 1 to 2, which resulted in a maximum pull-out force, was selected for the proximal end design. The distal end dimensions were selected based on full factorial analysis, which identified the following combination as optimal: buttress thread type, a large pitch of 3.5 mm, a large depth of 1.2 mm, and a trailing edge angle of −5°.
The optimized screw model of 6.5 mm diameter was assembled with the lamina and P-V body model for the simulation study using a validated FE model (Fig. 5C). The material properties were the same as listed in Table 1. A mesh element size of 0.2 mm similar to the control device analysis, was set based on the mesh sensitivity study (Fig. 3D), and the analysis conditions remained the same as in the previous analyses. The pull-out force for the optimized design was approximately 15% higher than that of the control device (Fig. 5D). A prototype for the optimized design was also developed to assess manufacturing feasibility at a cost of INR 4,500 (approximately US$ 53.48), which could be further reduced in mass production (Fig. 5E).
Discussion
In this study, the experimental test results of pedicle screw pull-out in surrogate bone models (foam) were used to validate the FE model. The FE model was found to closely predict the experimental pull-out force, demonstrating its reliability for further analysis. For comparison studies, screw design assemblies were subjected to identical analysis with boundary conditions as that of the validated FE model. This study evaluated pull-out force for a 39 mm screw purchase length, including a 2.8 mm thick lamina and a 36.2 mm length for the combined pedicle and vertebral body. The inclusion of the lamina was based on anatomical considerations and its impact on pull-out force [26]. The analysis revealed a significant increase in pull-out force in the presence of lamina, which is commonly overlooked in many studies.
The FE analysis for cortical bone revealed a bimodal distribution of P/D ratios, with two distinct peaks (Fig. 6A); the first peak occurred between 0 and 1, and the second peak occurred between 1 and 2. Notably, the pull-out force associated with the second peak was higher than the first peak but subsequently decreased as the P/D ratio increased. Further, the pull-out force was higher in cortical bone than in cancellous bone, supporting the hypothesis that high bone density results in a higher pull-out force [28].
The main effect plot suggested a strong dependency of pull-out force on type, depth, and pitch (Fig. 6B). Among these, the buttress thread type resulted in maximum force. While an increased “angle” also resulted in a high pull-out force, its effect was relatively weaker compared to the other three factors. Conversely, interaction plots revealed the multi-factor dependency of the pull-out force. Specifically, the interaction plot for type and depth indicated maximum pull-out force for buttress type and minimum for V-type thread at a depth of 1 mm (Fig. 6C). This plot also revealed that the change in type from Buttress to V decreases pull-out force for all pitch values. In contrast, the depth and pitch interaction plot showed increased pull-out force with increasing depth for all pitch values. The angle interaction plot suggests that a −5° angle with large depth (2 mm) and large pitch (4 mm) leads to maximum pull-out force. The ANOVA analysis also confirmed that individual and combined factors significantly affect cancellous bone pull-out strength, with most terms showing p<0.05. However, the thread depth cannot be infinitely increased as this would reduce the screw’s inner diameter, leading to decreased fatigue strength. Hence, the optimized design featured a thread depth within the 1.2–1.5 mm range, derived from the control device. Our analysis indicated an approximately 15% increase in pull-out strength for the proposed novel design compared to control devices. This enhancement is likely attributed to the optimized geometric parameters for different bone types, as all other test conditions remained identical for both optimized and control designs.
Further, the findings from the distal end (cancellous bone) analysis are comparable to the expandable screw study conducted in PU foam with a 0.16 gm/cm3 density and 2.3 MPa compressive strength, with a diameter of 6.5 mm and a purchase length of 45 mm. Notably, despite a yield strength of 2.01 MPa and a purchase length of 38 mm in our distal end analysis, the maximum pull-out force of approximately 1.5 kN surpassed that of non-augmented expandable screws (4 fins, 40 mm length) [29]. This enhanced performance may be attributed to the optimized parameters, suggesting that an optimized design could preclude the need for a complex manufacturing process for fins/slots. It is important to highlight that expandable type screws are susceptible to fatigue failures near the fins and are typically recommended in cases of highly osteoporotic bone [29].
Some limitations of this study should be addressed before translating the findings into clinical applications. Our investigation focused solely on pull-out force as a measure of screw-holding power, whereas actual clinical loads may involve moment loads as well. Furthermore, replicating the inhomogeneity caused by bone marrow, blood, and fat within vertebrae is challenging in foam models. We assumed these factors have a negligible impact on the outcomes. Notwithstanding these limitations, achieving high pull-out strength through design is crucial for alignment correction procedures, making this study relevant to clinical conditions. The proposed design thus needs to be further validated using animal studies. We proposed two thread types for different bone types and introduced variable inner diameters, which may increase the screw insertion torque. Although this may not significantly affect manual insertion, robotic surgery might necessitate torque calibration adjustments. This challenge could be mitigated by gradual transition at the thread junctions. Additionally, the proposed novel design has not undergone fatigue testing. Although the larger inner diameter in the proximal region is expected to improve bending strength, given its direct proportionality to the cube of the minor diameter, further investigation is required to confirm this hypothesis. Specifically, comprehensive testing is needed to evaluate the bending strength and fatigue life of the optimized design before proceeding with in-vivo studies to assess its biomechanical properties.
Despite these limitations, this study provides a crucial foundation for advancing screw-based implant research and could significantly reduce the need for repetitive prototype development and testing.
Conclusions
This study investigated the impact of design parameters on screw pull-out force and proposed two thread types for pedicle screws to harness mechanical advantage due to vertebral bone density variations. Leveraging a validated FE model and DoE techniques, we optimized design parameters for each bone type, yielding a novel design that increased the pull-out force by approximately 15% compared to the control. Notably, our findings suggest that a two-variable (pitch/depth) analysis is adequate for optimizing cortical bone design parameters, whereas a multi-variable analysis is more effective for optimizing cancellous bone design parameters. These findings indicate that this approach can optimize pedicle screw designs, reducing the need for iterative prototype testing.
Key Points
We developed a novel pedicle screw using a combination of finite element analysis and design of experiment for design optimization.
This study highlights design optimization approach for cortical and cancellous bone.
Optimized design exhibited increased pull-out force compared to the control device.
A prototype for the optimized design was developed for manufacturing feasibility.
PDF Links
PubReader
ePub Link
XML Download
Full text via DOI
Download Citation
