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Finite element study of the impact of pedicle screw density on the biomechanical response of a Lenke 1AN scoliotic curve
∗Corresponding author: Andre P. Mazzoleni. a_mazzoleni@ncsu.edu
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Received: ,
Accepted: ,
This article was originally published by Reed Elsevier India Pvt. Ltd. and was migrated to Scientific Scholar after the change of Publisher.
Abstract
Abstract
Benefits of increasing screw density in posterior instrumentation used to treat a scoliotic deformity are demonstrated using a three-dimensional finite element model (FEM) of the thoracolumbosacral spine.
The FEM represents a Lenke 1AN scoliotic deformity with a 50° Cobb angle and 20° apical vertebral rotation. The curve is corrected with bilateral pedicle screw fixation and 75 separate randomized screw distributions.
Total construct screw density, concave rod screw locations at T6, T10, T11 and T12, and convex rod screw locations at T7 and T12 each correlate strongly with reductions in postoperative Cobb angle (P < 0.05). Apical vertebral rotation is greatly impacted (reduced) by screws placed at the apical vertebra on both concave and convex rods (P < 0.05). Under pure moment loading, intersegmental micromotion is generally reduced when motion segment screw density is increased, with the exception being the upper instrumented joint.
These results suggest that increasing the screw density of posterior constructs used to treat a Lenke 1AN scoliotic deformity may improve the de-rotation correction with better postural restoration, reducing the risk of future complications including pseudarthrosis.
Keywords
Finite element analysis
Scoliosis
Pedicle screw
Micromotion
1 Introduction
Scoliosis is a complex, three-dimensional (3D) deformity of the spine characterized by a coronal plane Cobb angle greater than 10°.1 This condition is usually accompanied by rotation of the vertebral column and can begin in childhood or adulthood.2 Treatment options for adolescent or adult scoliosis can range from conservative choices such as bracing, exercise, and physical therapy to surgical techniques.3
Surgical techniques to treat scoliosis generally include anterior, posterior, and combined methods.1 Harrington instrumentation was first used in surgical scoliosis correction after World War II.4 Since then, advancements in scoliosis research have led to pedicle screw fixation becoming a dominant operative choice. The primary goal in scoliosis correction is a stable balanced spine and, depending on patient symptoms, spinal fusion with posterior instrumentation is a viable treatment,5 though complications exist. Even while considering modern surgical techniques and instrumentation, pseudarthrosis rates in primary fusion for adult idiopathic scoliosis have been estimated to be as high as 17%.6 Implications of pseudarthrosis of the spine include chronic pain, instability and instrumentation failure, which may necessitate revision surgery.7,27
Major causes of pseudarthrosis are inadequate surgical techniques and insufficient demobilization of the motion segment.7,27 Increased micromotion between bone and interbody cage implant, and elevated strain levels at desired fusion sites are known to adversely affect bone formation.8,9 Minimization of micromotion where fusion is targeted is an important consideration in the design of posterior constructs for surgical scoliosis treatment. Pedicle screw density is hypothesized to significantly affect the small, relative movements between adjacent vertebra (i.e., micromotion).
Pedicle screw density (SD) – the number of pedicle screws used per vertebral level – is a choice made largely based on surgeon experience and preference and can vary from 0 to 2. In the treatment of scoliosis with posterior instrumentation and pedicle screw fixation, there are competing clinical opinions on the optimum SD and configuration including both low- and high-density constructs. To achieve optimum deformity correction and curve stability, successful fusion at each desired level is critical, and may be complicated by excessive micromotion. In this paper, the significance of SD relative to initial postoperative curve correction is quantified as well as SD at each level relative to segmental micromotion resulting from standardized loading conditions. The results of this study are intended to provide insight into the impact that pedicle SD can have on the stability of the postoperative scoliotic spine and on the potential for excessive micromotion which can have detrimental effects on bone formation and solid fusion.
2 Methods
2.1 Non-scoliotic finite element model
The present study utilizes a 3D finite element model (FEM) of the human thoracolumbosacral spine which has been developed and validated in prior research.10,11 The model geometry is based on average anatomical dimensions of key spinal landmarks12 and is developed using Solidworks 2016 (Dassault Systems SA, Waltham, Massachusetts). Analysis is performed using ANSYS 18.2 (ANSYS, Canonsburg, Pennsylvania). Each vertebra is comprised of an outer shell representing the cortical bone and an inner region reflecting the trabecular bone and includes the posterior elements. The rotational and translational flexibility of each motion segment is achieved with 6-degree-of-freedom (DoF) elastic joints attached to the lower and upper end plates of each adjacent pair of vertebral bodies. The translational and rotational load-deflection characteristics of each motion segment from T1 to the sacrum are assigned using values from cadaveric and computational studies from the literature and includes the stiffening effect of the rib cage.10,13–16 These elastic joints accurately simulate the stiffness contributions provided by the soft tissue and ligaments of the spinal column and are a common choice in scoliotic spine modeling using the finite element method.17 This FEM (including posterior instrumentation to be discussed later) is comprised of 127579 nodes and 67742 elements, utilizing higher order tetrahedral structural solid finite elements and shell finite elements with quadratic displacement behavior. A complete discussion of the development and validation of this FEM can be found in Warren et al. (2021).
2.2 Scoliotic finite element model
To simulate the surgical placement of spinal instrumentation used in surgery to correct a scoliotic spine, scoliosis curve type and severity must first be defined. The curve type chosen for this study is 1AN, based on the Lenke Classification system for adult idiopathic scoliosis.18 This represents a main thoracic curve type with lumbar modifier ‘A’ and a normal thoracic sagittal profile. Consistent with common surgical practice, the proximal and distal fusion levels chosen for this study are T5 and L1, respectively.19 Titanium pedicle screws are placed bilaterally with 4.75 mm diameter titanium rods.20
The geometry of the non-scoliotic FEM is then modified to represent a Lenke 1AN curve with a Cobb angle of 50° as measured in the coronal plane between the upper and lower end plates of the T5 and L1 vertebral bodies, respectively (Fig. 1). An apical vertebral rotation angle of 20° into the convexity of the lateral curve is also modeled as is typical of scoliotic deformities.21,28 Material properties of the 3D components of the model are presented in Table 1. Regarding posterior instrumentation, pedicle screws are placed bilaterally at the distal and proximal instrumented levels (T5 and L1). The remaining levels will have screws distributed randomly. A total of 75 unique pedicle screw distributions will be studied.
| Part | Young's Modulus (MPa) | Poisson's Ratio |
| Vertebral Bones | ||
| Cortical Bone | 12,000 | 0.3 |
| Cancellous Bone | 100 | 0.2 |
| Posterior Bone | 3,500 | 0.25 |
| Sacrum | 3,500 | 0.25 |
| Spinal Instrumentation | ||
| Rods and Pedicle Screws | 110,000 | 0.3 |
| Lumbar Intervertebral Discs | ||
| Elastic Joints | Nonlinear translational and rotational stiffness based on Warren et al. (2020) | |
| Thoracic Intervertebral Discs | ||
| Elastic Joints | Translational and rotational stiffness based on Liebsch et al. (2017), Ignasiak et al. (2016) | |
| Thoracolumbar Junction | ||
| Elastic Joints | Translational and nonlinear rotational stiffness based on Couvertier et al. (2017), Ignasiak et al. (2016) | |
| Lumbosacral Joint | ||
| Elastic Joints | Translational and nonlinear rotational stiffness based on Panjabi et al. (1994), Ignasiak et al. (2016) | |
2.3 Boundary and loading conditions
Simulation of the installation of posterior instrumentation is performed in such a way as to reproduce the loads induced in the spine (and the installed instrumentation) by the intraoperative correction performed by an orthopedic surgeon, as described below. The 6-DoF elastic joints representing each motion segment in the non-scoliotic FEM above are preloaded with prescribed moments which create an initial “loaded” state for each joint. These moment “preloads” are based on the load-deflection characteristics of each joint and the 3D angle of rotation necessary to displace each joint in the non-scoliotic model into a scoliotic geometry (with a Cobb angle of 50° and an axial rotation of the apical vertebra of 20°), i.e., these preloads represent the restoring moments (from ligaments, soft tissue, etc.) that would result from a surgeon using surgical tools to maneuver a scoliotic spine (as described above) into a straightened position. To calculate the loads induced in the spine by the intraoperative correction performed by an orthopedic surgeon, posterior instrumentation described above is then added to the model prior to activation of the moment preloads. Then, the preloads are activated, and these loads attempt to return the spine to its prior scoliotic geometry while being resisted by the implanted posterior instrumentation. Resulting displacements and loads acting on the spinal anatomy and implanted instrumentation will thus be those of a scoliotic spine geometry that is being held in a corrected position by instrumentation implanted via a surgical process. The sacrum is fixed and the T1 vertebral body is set free to translate in the caudocranial direction during this simulation, allowing possible changes in the length of the spine with curve correction. This procedure is performed 75 times with unique and randomized pedicle screw configurations. Postoperative Cobb angle, as measured between T5 and L1, as well as angle of rotation of the apical vertebra, is recorded for each screw configuration.
After each simulation of instrumentation placement, and after curve correction is recorded, pure moments of 7.5 Nm are then applied individually to the cranial end of the T1 vertebra in flexion/extension, lateral bending, and axial rotation. Variation in segmental micromotion is recorded for each load application (flexion/extension, lateral bending, and axial rotation) and for each randomized screw configuration. During the moment loading, the sacrum remains fixed and the T1 vertebra is allowed to translate and rotate in all directions.
2.4 Model sensitivity to geometry and material properties
Spine soft tissue and bone mechanical properties are highly subject-specific and will vary from one patient to the next. It follows that motion segment and whole spine flexibility is likewise subject-specific. This model is developed using dimensional and material property data from various cadaveric and in vitro studies on healthy spine specimens. Research has shown scoliosis patients to have significantly different spine geometries in certain areas of the curve as compared to healthy individuals (e.g., scoliotic discs in the primary curve are taller and thinner than in healthy subjects) which would suggest that scoliotic spines may be more flexible.22 The simulations described herein will be performed twice more, once with the motion segment stiffness values (translational and rotational) decreased by 25% and once with the stiffness values increased by 25%. Paired t-test analysis will be performed on the results of the 3 sets of simulations to determine the significance of any observed variance in biomechanical and instrumentation response. Paired t-test analysis will be performed on both 100% and 75% stiffness results, and on 100% and 125% stiffness results.
3 Results
3.1 Postoperative curve correction
Table 2 illustrates the statistical significance of each pedicle screw location relative to its impact on the quality of curve correction of the scoliotic spine. Quality of curve correction refers to the immediate post-operative Cobb angle following instrumentation placement, where the smaller the post-operative Cobb angle, the higher the quality of curve correction. Impact of total construct SD on quality of curve correction is also provided. The upper and lower instrumented vertebra are T5 and L1 (screws are always present). Additional pedicle screws placed at T6, T10, T11 and T12 on the concave rod and at T7 and T12 on the convex rod substantially reduce the postoperative Cobb angle (P = 4E-3, 0.048, 0.02, 3E-7 for screws at T6L, T10L, T11L, T12L, respectively and P = 2E-3, 0.04 for screws at T7R, T12R, respectively). Screws placed at the apical vertebra (T9) also provide significant benefit relative to axial rotation of the postoperative spine model (P = 2E-17, 3E-4 for screws at T9L, T9R, respectively). Postoperative Cobb angle also correlates strongly with SD, i.e., increases in SD lead to reductions in Cobb angle (P = 3E-6).
| Result | Screw Density | Concave Rod – Pedicle Screw Installation Location | ||||||
| T6L | T7L | T8L | T9L | T10L | T11L | T12L | ||
| Cobb Angle | 3E-6 | 4E-3 | 0.91 | 0.79 | 0.91 | 0.048 | 0.02 | 3E-7 |
| Vertebral Rotation | 0.93 | 0.87 | 0.68 | 0.22 | 2E-17 | 0.24 | 0.09 | 0.12 |
| Result | Convex Rod – Pedicle Screw Installation Location | ||||||
| T6R | T7R | T8R | T9R | T10R | T11R | T12R | |
| Cobb Angle | 0.81 | 2E-3 | 0.93 | 0.23 | 0.92 | 0.57 | 0.04 |
| Vertebral Rotation | 0.87 | 0.75 | 0.36 | 3E-4 | 0.69 | 0.07 | 0.92 |
3.2 Segmental micromotion
Figs. 2 through 5 illustrate the impact of SD at each motion segment on the relative amount of rotational micromotion under the movements of flexion, extension, lateral bending, and axial rotation. Between the T6 and T12 vertebral bodies, reductions in micromotion are significant (P < 0.002) when SD of the motion segment of interest increases from a minimum possible value of 0 to a maximum possible value of 2 during flexion, extension, lateral bending and axial rotation. The exception to this is seen at T7-T8 in Figs. 2 and 3 (flexion and extension) where increases in micromotion are experienced with increasing motion segment SD, but these increases are relatively minor (as is the micromotion itself). The lower instrumented motion segment for the simulations conducted in this paper is T12-L1 and the minimum SD for T12-L1 is 1. Increasing SD to 2 does not appreciably affect micromotion due to flexion or extension, but reduces micromotion due to lateral bending by 8%, and increases micromotion due to axial rotation by 3%. The upper instrumented motion segment in this study is T5-T6 which similarly includes a minimum SD of 1. Increasing SD to 2 at T5-T6 produces increases in micromotion of 49%, 41%, 17% and 29% for flexion, extension, lateral bending and axial rotation as compared to a SD of 1; possible factors contributing to this phenomenon are discussed later.
3.3 Sensitivity Analysis
Results in Table 2 and in Figs. 2 through 5 were computed twice more, once with motion segment stiffness decreased by 25% and once with motion segment stiffness increased by 25%. Paired t-test analysis was performed comparing both 100% and 75% stiffness results, and 100% and 125% stiffness results. The null hypothesis of μD=0 is tested where μD represents the average difference between the 100% stiffness data point and the corresponding 75% stiffness (or 125% stiffness) data point. For each t-test, P > 0.05 which indicates that there is no statistically significant difference between results of the 100% stiffness and 75% stiffness simulations, or between the 100% stiffness and 125% stiffness simulations.
4 Discussion
Competing opinions exists in the literature and in clinical applications with regards to pedicle screw distribution used in the surgical treatment of scoliosis with posterior instrumentation.23–25 Each implant distribution is met with unique results in terms of quality of curve correction and postoperative spine stability. Achieving optimal spinal alignment can minimize risk of postoperative complications and can preclude the need for future revision surgeries. Table 2 demonstrates the importance of total construct screw density (SD) relative to the correction of the deformity in the coronal plane. Cobb angle is significantly improved as SD increases. Additionally, certain individual screw placement locations provide considerable benefit to the initial postoperative spinal alignment. Fig. 1 demonstrates that screws placed on the concave rod near the cranial and caudal ends of the construct – T6, T10, T11, T12 – affect substantial improvement in Cobb angle. Only half as many screws on the convex rod, however, are statistically beneficial to the postoperative Cobb angle – screws placed at T7 and T12. This suggests that increasing SD on the concave rod, as compared to the convex rod, is more important for achieving an optimal coronal plane spinal alignment. Conversely, Fig. 1 and Table 2 suggest that apical vertebral screw placement is less important for minimizing Cobb angle post-surgery. As scoliosis is a three-dimensional deformity, proper alignment must also consider the vertebral rotation into the convexity of the curve that typically presents with the condition. These results show that unlike coronal Cobb angle correction, screws placed at the apical vertebra are particularly important for axial de-rotation of the spinal column.
Proper spine alignment following surgery is important for a variety of reasons, including mitigation of the risk of future complications stemming from an improper alignment. For many patients, including the adolescent population, improving posture and self-image is another major motivation for pursuing surgical treatment of scoliosis.26 A proper alignment of the spinal column can be as important from a social perspective as it is from a personal health standpoint. Understanding the motivation of the patient and considering the results of the simulations in this paper together suggest that increasing SD in posterior instrumentation for treatment of scoliosis may be vitally important for patient health and satisfaction.
When posterior instrumentation with spinal fusion is used to treat a patient with scoliosis, the immediate and long-term health of the patient is of paramount importance. Pseudarthrosis is a complication that can challenge patient health and is associated with insufficient demobilization of the motion segment. Data in Figs. 2 through 5 represent the effectiveness of motion segment demobilization with respect to motion segment SD. For most instrumented motion segments, rotational micromotion as a result of each direction of movement is reduced as SD of the segment under consideration is increased. Between T6 and T12, the only exception to this relationship is at T7-T8 during flexion and extension where rotation of the joint increases slightly as SD increases from a minimum of 0 to a maximum of 2. Reviewing Figs. 2 and 3, the magnitude of rotation at T7-T8 is smaller in all cases than any other vertebral segment. So, while rotation at this level may increase slightly as SD increases, its magnitude is 39% lower than the next smallest recorded magnitude of rotation for all other joints.
Motion segments T5-T6 and T12-L1 exhibit slightly different relationships with SD as compared to the remaining joints. Rotations at T12-L1 are generally higher than at any other location along the spine model. This is likely a result of being the lowest joint in the model and the joint closest to the point of fixation. Comparing a SD of 2 to 1, rotations at T12-L1 are largely unaffected. Values decrease slightly (8%) during lateral bending and increase slightly (3%) during axial rotation. Motion segment T5-T6 is the only joint that exhibits increases in rotation for each movement with increases in SD. During flexion and extension, rotational micromotion increases by as much as 49% when increasing SD from 1 to 2. Increases during lateral bending and axial rotation are less. This joint is unique from the others in the spine model in that this is the point of load application and there are no other instrumented segments in the cranial direction. Additionally, rotational joint stiffness is lowest at T5-T6 as compared to all other joints from T6-L1. This may contribute to the unique relationship seen between SD and rotation at this joint.
5 Limitations
A simplified modeling technique has been used for the instrumentation in these simulations. Screws are modeled as cylinders with bonded contact between screw face and the posterior elements along the spine. Also, the interaction between screws and cortical/trabecular bone material that occurs as the screw is inserted into the vertebra is neglected. This was done to facilitate the parametric nature of the simulations and allow easy removal and replacement of screws within the model at each level. This paper performs numerous simulations, and results are averaged and evaluated for statistical significance (as discussed in the Sensitivity Analysis section of this paper). As results are normalized to 1.0, the relative changes or differences in results for various configurations are the main concern instead of magnitude of the results presented, i.e., the relative differences in results should not be adversely impacted by the method of screw modeling used in this research as it is applied to all screw locations. Hence, while some simplifying assumptions have been made to facilitate the parametric simulations, the validity of the conclusions drawn after analyzing the results is not considered to be impacted by these simplifications.
6 Conclusions
The results of this study suggest that the probability of maximizing patient health and satisfaction may be increased by using high SD posterior instrumentation in the treatment of a Lenke 1AN scoliotic deformity. Increasing SD produces better postoperative spinal alignment which can mitigate the risk of future complications and increase patient aesthetic satisfaction which can be tremendously important to the individual. Decreased micromotion is also associated with increasing SD. Risk of pseudarthrosis may be minimized by more effectively demobilizing the desired motion segments to better allow for bone formation to occur. Considerable attention is paid to minimizing implant density in the existing research on this topic due to economic, patient surgical risk, and other factors, but long-term health and satisfaction of the patient is vitally important, and the results of this study suggest that both may be maximized by a trend toward increasing implant density.
Sources of funding
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
Other statements
The contents of this manuscript have not been and will not be submitted for publication elsewhere.
Institutional review board approval/patient consent
Not applicable.
CRediT authorship contribution statement
Justin M. Warren: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing – original draft, Visualization. Lloyd A. Hey: Resources, Writing – review & editing. Andre P. Mazzoleni: Conceptualization, Resources, Writing – review & editing, Supervision, Project administration.
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