Pedicle screw fixation is commonly used in spinal instrumentation surgeries to connect rods to vertebrae in order to correct spine alignment, stabilize vertebrae, and reach an arthrodesis.1 To be effective, the pedicle screw constructs must withstand intraoperative loading and physiological forces due to daily postoperative activities.
In current practice, numerous screw designs (various screw shaft threads and shape, screw heads articulated with the screw shaft, materials) and insertion and manipulation techniques afford the surgeon many options. However, there is little consensus on the selection of an optimal type of screw, size, and trajectory (insertion point, tapping, and screw alignment) depending on vertebra dimension and shape and bone mechanical properties. These choices are determined at the discretion of the surgeon on the basis of his/her experience and practice.2,3 Computer-assisted surgery systems guide surgeons, in real-time, to properly insert the screws through the pedicles,4 but the insertion strategy itself, generally, remains empirical.
In vitro experiments, such as axial pullout tests, provide significant insight into the biomechanics of screw-bone interactions and failure forces. Several surgical parameters have been studied such as the trajectory and entry point.2 However, experimentations reveal limitations in terms of interindividual variability (bone density, pedicle morphology, etc.) and reproducibility. Also, the surgical techniques used during those tests can significantly affect mechanical strength.5
Such limitations in determining the optimal parameters for obtaining strong pedicle screw fixation could be overcome by finite element analysis.6 A few finite element models (FEM) have been developed, but most fail to take into account local geometric details and advanced mechanical properties such as plastic deformation, bone fracture, material properties distribution, and contact friction at the bone-screw interface. Previous models focused either on detailed pedicle models7 or on simplified complete vertebra models,8 which did not permit studying the detailed effects of every screw design parameter and insertion trajectory individually or combined simultaneously.
The objective of this study was to analyze the bone-screw mechanical interaction and test several parameters such as the pedicle screw size, thread design, insertion point and trajectory that could minimize the risk of instrumentation failure using a detailed FEM of an instrumented vertebra.
MATERIALS AND METHODS
For this study, 2 different existing multiaxial screws were used with different thread patterns (Fig. 1) from the CD Horizon spinal systems (Medtronic Inc., Memphis). The first screw (CD HORIZON LEGACY screw) was a cylindrical equally spaced single-lead thread screw, whereas the second (CD HORIZON OSTEOGRIP screw) had a slightly conical inner core and the pitch of the distal part was dual-lead thread (double pitch in the pedicle region). In addition, the single-lead thread screw crests were thicker and had spherical bases, whereas the dual-lead thread screw crests were thinner and had conical bases.
Two different screw lengths (40–50 mm) and screw diameters (6.5–8.5 mm) were tested. The screws were virtually positioned and placed through the pedicle following the free-hand localization technique, which used anatomic landmarks on vertebrae during an open surgery.9 The entry point was enlarged by removal of the superficial cortical elements simulating the use of a bone rongeur or a burr.10 The screw tapping was modeled using a boolean operation method to remove bone at the future location of the screw. Two common trajectories [anatomic (AN) and straightforward (SF)2,3] were tested for each screw (Fig. 1).
A design of experiment (DOE) was performed to biomechanically investigate both the individual and combined effects of the thread type, lengths, diameters, and insertion trajectories on the fixation strength of the pedicle screws. Each parameter had 2 extreme values, as described above. A DOE is a statistical method enabling to determine whether there is a statistically significant effect that a particular factor exerts on the dependent variables of interest.11 The DOE was based on a Box, Hunter, and Hunter full plan with 4 factors leading to 16 runs. The statistical analysis was performed using Statistica 8 (StatSoft Inc., Tulsa). Because of the determinist aspect of FEM simulations an α acceptance of <0.01 was chosen for significance.
The geometry used for the FEM was built from computed tomography scan images of an L3 vertebra (contiguous slices of 0.6 mm thick) of a 50th percentile human volunteer (European, 32 y old, 75 kg, 1.75 m) with no known spinal pathology to obtain a “generic shape.” The vertebra (Fig. 2) was modeled by taking into account the separation of the trabecular and cortical bone with realistic regional thickness from morphologic measurements.12,13 The pedicles were 13 mm in height and 11 mm in width, whereas the cortical bone thickness varied from 1.0 to 1.5 mm. The vertebra FEM was meshed with 4 node tetrahedral elements of 0.5 mm characteristic length in the peri-implant region (region of interest) and 1 mm characteristic length in the farther regions. The mesh distribution was refined through a convergence study to adapt to the region of interest and minimize the number of nodes to satisfactorily balance accuracy and computer resources. The external surface of the screws was modeled as a shell with characteristic triangular elements of 0.5 mm. The triangle-based elements were chosen for their ability to comply with complex geometry and their nonwarpage properties. The model as a whole contained ∼50,000 nodes (∼250,000 elements).
Rigid body properties were applied to some node groups of the model away from the region of interest and to all nodes of the screw, thus reducing computational time. The screw was considered rigid due to the high material property gradient at the interface, which was several times higher than the bone. These assumptions were verified to have marginal impact on the results. The bone/screw interface was modeled using a point/surface penalty method for the contact interface with a Coulomb-type friction coefficient of 0.214 and a minimal gap of 0.05 mm.
The cortical and trabecular bones were considered as homogenous isotropic materials. Their properties were estimated from a previous study using an inverse finite element method based upon experimental tests performed on fresh postmortem elderly human subjects.15 The model integrates an elastoplastic material law (Johnson-Cook) to simulate bone failure (Table 1).16 Thus, before plastic deformation occurs (equivalent stress<yield stress), the material behaves as linear elastic. During plastic deformation, the equivalent stress was computed using the relation σ=a+bεpn, where σ is equivalent stress, a is yield stress, b is hardening modulus, εp is plastic strain (true strain), and n is hardening exponent. Once the failure plastic strain (εmax) of a given element locally was reached, failure occurred and the corresponding element deleted, thus simulating the bone fracture.
Boundary and loading conditions were applied to simulate screw pullout as described in the ASTM-F543 standard.17 This specific test was performed to assess the biomechanical strength of the screw anchorage by applying a ramped axial tensile force to the screw until total pullout. The external nodes of the anterior part of the vertebral body were fixed to simulate rigid embedment. In addition, a constraining slide link condition was applied to the whole screw (leaving only the translation in the screw axis free) to simulate the effect of fixation with the loading shaft and avoid any off-axis displacement.
The simulations were performed using the explicit dynamic FEM solver RADIOSS v5.1 (Altair Engineering Inc., Troy) with a kinetic relaxation scheme to perform a quasi-static analysis. The stresses along the screw threads during the pullout were analyzed. The initial stiffness and the peak pullout force extracted from the computed load-displacement curve were compared with available previously published experimental data18–21 for model validation.
The computed load-displacement curves exhibited a nonlinear behavior (Fig. 3), which could be divided into 3 zones. In the first part of the curve (zone A), the bone-screw construct followed a linear elastic stiffness slope, without bone damage or failure. Once yield strength was reached (zone B), bone element failure commenced at the local level in the peri-implant area and plastic deformation occurred. The stiffness decreased as plastic strain failure was reached on bone elements, which contributed to an eventual total loss of bone-screw stiffness. Screw failure occurred at the end of zone B at the level of the peak pullout force. Zone C showed a decrease in stiffness and pullout force until the screw was totally pulled out of the bone.
Compared with previously published data, the simulated initial stiffnesses (1327–4800 N/mm) were slightly higher than that obtained experimentally on human cadaveric vertebrae (1100 –2700 N/mm),18,19 whereas the simulated peak pullout forces (220 –750 N) were within the published range (218–840 N).20,21 The discrepancy between the experimental values can be explained by the natural variability of human subjects (due to age and bone quality, vertebra size, and level), the difference in screw design, and also by the poor reproducibility of such experiments.20–22
In the bone structure, the Von Mises stress distribution revealed high stresses at each thread, most pronounced at the tip of the screw and in the pedicle isthmus area. The overall fracture pattern initiated in the trabecular bone, around the screw tip, and propagated to the head of the screw until total pullout. Differences in the stress distribution pattern between the 2 thread profiles were observed (Fig. 4). The cylindrical single-lead thread screw revealed an even bone stress distribution from tip to head, with higher stress reported at the tip of the screw and in the pedicle isthmus area. At the same pullout force, the conical dual-lead thread screw showed an irregular stress distribution with several stress concentration zones at each thread of the trabecular section distally.
The DOE analysis revealed significant effects (P<0.01) for all tested major factors (ie, the type, diameter, length, and trajectory of the screw) on both of the indices studied (Fig. 5). Screw diameter consistently had the highest effect on anchorage strength. Pareto charts report the effects of the tested design parameters, ordered in rank of importance using the “t values.” Looking at peak pullout force response, the significant effects in descending order included screw diameter, insertion trajectory, thread type, and screw length. The resulting initial stiffness and peak pullout force were highly correlated (r2=0.84), thus showing that one is a good indicator of the other.
The study of the interaction between individual parameters showed significant effects for screw trajectory combined with thread type and screw trajectory combined with diameter. The AN trajectory allowed larger diameter screws to be placed, in addition to longer screws (Fig. 5). Other combinations of factors did not reveal significant effects, as their effects were only linear predictions of the individual variables.
The response distribution box plots (Fig. 6) indicated that the highest initial stiffnesses and peak pullout forces were obtained when the screw was longer (50 mm) and with a larger diameter (8.5 mm). The SF trajectory exhibited better biomechanical anchorage than the AN trajectory. Better anchorages were obtained with the cylindrical single-lead thread screw than the dual-lead thread screw with the slightly conical diameter.
Screw diameter had the greatest impact on anchorage performances, which is consistent with previous biomechanical studies showing that a screw’s major diameter determines pullout strength.23 The major diameter is directly related to crest height, thus to the contact surface with the bone, leading to better anchorage. Furthermore, the increase of screw diameter in the isthmus of the pedicle leads to a closer connection with the cortical (harder) bone. For instance, a few crests of the 8.5 mm screw were gripping the cortical bone in the pedicle region (without cortical wall violation). The pedicle fill could have been another index of interest in addition to the pedicle diameter, but a single vertebra only was used in this study; therefore the filling ratio would be quite the same.
At a given size, the dual thread screw had a reduced anchorage capability as compared with the single thread screw. This could be explained by the crest design and height, which are different for the same major diameter. The single-lead thread screw type has a spherical and even thread base contrary to the dual-lead thread screw type, which has a spherical thread base in the pedicle region and a conical thread base in the trabecular region. The effect of these designs resulted in different stress distribution and concentration spots for each type of screw (Fig. 4). The stress concentration spots near the distal threads in the dual thread screw design led to an earlier bone fracture, thus weaker anchorage of the dual-lead thread screw. However, the simulated bone fracture occurred at a high force level (500–600 N), such that any difference should not be an issue during “normal” intraoperative correction maneuvers or postoperative functional loads, but could be a problem in the case of excessive loads.24 This study focused only on axial forces; no conclusion could be made on the different loads as could be applied to screw intraoperatively or postoperatively.
The screw profile (conical vs. cylindrical) also has an influence on screw performance, as inferred by the work of Abshire and colleagues18 and Hsu and colleagues25 who determined that conical screws and dual-lead thread screws improve the insertion torque. It seems intuitive that a higher insertion torque is correlated to higher peak pullout force;23,26 however, it has been demonstrated that insertion torque is not a good predictor of pullout force as the relations are screw and geometry specific.27,28 The results of the current study, revealed a reduced performance when using a screw with a conical profile. It is important to note that this factor was dependent on the thread type, meaning the results are a combination of both the screw profile and thread type.
The screw insertion process is generally preceded by a pretapping step using a smaller diameter than the screw. This study did not take into account the effect of pressfit and pedicle deformation29 during screw insertion, which has an effect on screw anchorage.30 This initial stress state might have an impact if other insertion techniques are investigated, particularly related to the tapping process. Further work is needed to understand the influence of the screw insertion to implement the stress and bone deformation.
The screw diameters used for this current study were larger than those generally used during corrective surgeries. The larger screws were chosen to accommodate the pedicle size of the model. To complete this investigation, further studies with a wider variety of lengths and diameters and vertebrae types should be performed.
The SF trajectory leads the screw threads closer to the cortical wall, which could explain the increased stiffness and pullout force resulting in better anchorage. As the cortical bone layer has a major effect on screw anchorage,21 its interaction with the screw trajectory and diameter is particularly important.
The simulated fracture patterns, beginning around the tip of the screw and propagating to the head, suggest that higher stresses occurred first in the areas around the tip and the pedicle isthmus. This result is contrary to predicted failure mechanisms from threaded assembly theory,31 which describes the higher-stress area as the contact area around the 3 first inserted threads bearing 70% of the total load. The computed results showed a more uniform distribution of contact forces along the screw shaft with an increasing trend in the screw tip area. This discrepancy was also reported in other numerical studies on screw pullout in bone structures,32,33 which agree with the reported results. Such a divergence could be explained by the material property gradient between bone and screw, but also by the differences in thread design between industrial and medical screws. The results suggest that the threaded assembly theory, used for standard industrial screws,31 may not be adequate for pedicle screw design anchored in bone.
The initial toe-region was not considered in this study as it represented a numerical effect of the contact interface definition. Although this phenomenon is observable in experimental curves, it only represents the early effects of loading and has no outlook on the biomechanical performance of the screws.
Even though the geometry used represents a “generic” vertebra shape, the material properties were derived from a finite element inverse method using lumbar vertebrae harvested from elderly subjects (∼70 y old). This is consistent with most reported experimental tests, mainly performed on elderly and osteoporotic vertebrae.18–21
The bone material properties used in the model resulted from a finite element inverse method of slow dynamic compression tests,15 which may explain the higher stiffness values that were numerically obtained. The conditions of mechanical property extraction (axial compression) were different from the conditions described in this study; however, it was assumed that the bone properties were isotropic. This assumption might lead to higher anchorage because bone properties have lower Young modulus in the transverse directions than in the axial direction.34 Furthermore, the model was intended to be used for relative comparisons and not as an absolute prediction tool, thus diminishing any numerical-experimental disparity issues.
The elastoplastic material law (Johnson-Cook) used in this study assumes that the bony structures are isotropic and have a homogenous distribution. In reality, the pedicle and the vertebral body have a complex and irregular bone distribution12,13,35 leading to anisotropic properties. Further investigations implementing heterogeneity in bone properties could be an alternative to investigate such effects. Alternative methods to model more accurately the complex internal bone structures such as micro Finite Element Analysis33 or Smoothed Particle Hydrodynamics exist, but require higher computational resources.
This study only focused on the behavior of individual screws under axial loading. Any effects on triangulation screw pairing or instrumentation assembly were not taken into account in the current study. The intended use of this model was to perform relative comparisons using a DOE approach, rather than absolute value analyses. The model created was extracted from a healthy man with no known spinal pathologies or deformities and the material properties were considered as ideal (homogenous and no osteoporosis). At this current state, no extrapolation should be made for deformed pedicles or osteoporotic vertebrae. Additional work would be required to modify this generic model to a more personalized one, in terms of geometry and material properties.
The DOE determined that the diameter of the screw had the highest impact on mechanical anchorage. The simulated cylindrical single-lead thread screws presented better biomechanical anchorage than the conical dual-lead thread screws in axial loading conditions. The trajectory promoting closer connection with the cortical bone provided a better mechanical anchorage.
A detailed and realistic FEM of an instrumented lumbar vertebra was developed to analyze and compare screw designs and trajectories. The developed comprehensive FEM is a valuable tool to analyze the pedicle screw biomechanics. It is a promising alternative to complex, expensive and specimen-specific in vitro experimental tests.
The recommendations provided can improve single screws performance under axial loading. Further studies should be undertaken to refine and fully validate this model, and to examine other types of loads as well as whole construct effects. The model could also be adapted to further analyze patient-specific characteristics, such as osteoporotic or deformed vertebrae. Looking to the future, this ideology could lead to a computerized testing platform for new implant designs or as a surgery-planning tool to help clinicians.
1. Lenke LG, Kuklo TR, Ondra S, et al. Rationale behind the current state-of-the-art treatment of scoliosis (in the pedicle screw
era). Spine. 2008;33:1051–1054.
2. Dhawan A, Klemme WR, Polly DW Jr. Thoracic pedicle screws: comparison of start points and trajectories. Spine. 2008;33:2675–2681.
3. Lehman RA Jr, Polly DW Jr, Kuklo TR, et al. Straight-forward versus anatomic trajectory technique of thoracic pedicle screw
fixation: a biomechanical analysis. Spine. 2003;28:2058–2065.
4. Nottmeier EW, Seemer W, Young PM. Placement of thoracolumbar pedicle screws using three-dimensional image guidance: experience in a large patient cohort. J Neurosurg Spine. 2009;10:33–39.
5. Brown BS, McIff TE, Glattes RC, et al. The effect of starting point placement technique on thoracic transverse process strength: an ex vivo biomechanical study. Scoliosis. 2010;5:14.
6. Wagnac E, Michardiere D, Garo A, et al. Biomechanical analysis of pedicle screw
placement: a feasibility study. Stud Health Technol Inform. 2010;158:167–171.
7. Zhang QH, Tan SH, Chou SM. Effects of bone materials on the screw pull-out strength in human spine. Med Eng Phys. 2006;28:795–801.
8. Chen CS, Chen WJ, Cheng CK, et al. Failure analysis of broken pedicle screws on spinal instrumentation
. Med Eng Phys. 2005;27:487–496.
9. Modi HN, Suh SW, Fernandez H, et al. Accuracy and safety of pedicle screw
placement in neuromuscular scoliosis with free-hand technique. Eur Spine J. 2008;17:1686–1696.
10. Gaines RW Jr. The use of pedicle-screw internal fixation for the operative treatment of spinal disorders. J Bone Joint Surg. 2000;82-A:1458–1476.
11. Montgomery DC. Design and Analysis of Experiments. 1997;Vol. 7New York: Wiley.
12. Hirano T, Hasegawa K, Takahashi HE, et al. Structural characteristics of the pedicle and its role in screw stability. Spine. 1997;22:2504–2510.
13. Silva MJ, Wang C, Keaveny TM, et al. Direct and computed tomography thickness measurements of the human, lumbar vertebral shell and endplate. Bone. 1994;15:409–414.
14. Liu CL, Chen HH, Cheng CK, et al. Biomechanical evaluation of a new anterior spinal implant. Clin Biomech. 1998;13suppl 140–45.
15. Garo A, Arnoux PJ, Wagnac E, et al. Calibration of the mechanical properties in a finite element model of a lumbar vertebra under dynamic compression up to failure. Med Biol Eng Comput. 2011;49:1371–1379.
16. El-Rich M, Arnoux PJ, Wagnac E, et al. Finite element investigation of the loading rate effect on the spinal load-sharing changes under impact conditions. J Biomech. 2009;42:1252–1262.
17. ASTM Standard F543-07. Standard Specification and Test Methods for Metallic Medical Bone Screws. ASTM International, West Conshohocken, PA; 2009.
18. Abshire BB, McLain RF, Valdevit A, et al. Characteristics of pullout failure in conical and cylindrical pedicle screws after full insertion and back-out. Spine J. 2001;1:408–414.
19. Inceoglu S, McLain RF, Cayli S, et al. Stress relaxation of bone significantly affects the pull-out behavior of pedicle screws. J Orthop Res. 2004;22:1243–1247.
20. Mehta H, Santos E, Ledonio C, et al. Biomechanical analysis of pedicle screw
thread differential design in an osteoporotic cadaver model. Clin Biomech. 2012;27:234–240.
21. Santoni BG, Hynes RA, McGilvray KC, et al. Cortical bone trajectory for lumbar pedicle screws. Spine J. 2009;9:366–373.
22. Pfeiffer M, Gilbertson LG, Goel VK, et al. Effect of specimen fixation method on pullout tests of pedicle screws. Spine. 1996;21:1037–1044.
23. Cho W, Cho S, Wu C. The biomechanics of pedicle screw
-based instrumentation. J Bone Joint Surg. 2010;92:1061–1065.
24. Wang X, Aubin CE, Labelle H, et al. Biomechanical analysis of corrective forces in spinal instrumentation
for scoliosis treatment. Spine. 2012;37:1479–1487.
25. Hsu CC, Chao CK, Wang JL, et al. Increase of pullout strength of spinal pedicle screws with conical core: biomechanical tests and finite element analyses. J Orthop Res. 2005;23:788–794.
26. Kwok AWL, Finkelstein JA, Woodside T, et al. Insertional torque and pull-out strengths of conical and cylindrical pedicle screws in cadaveric bone. Spine. 1996;21:2429.
27. Inceoglu S, Ferrara L, McLain RF. Pedicle screw
fixation strength: pullout versus insertional torque. Spine J. 2004;4:513–518.
28. Okuyama K, Abe E, Suzuki T, et al. Can insertional torque predict screw loosening and related failures? An in vivo study of pedicle screw
fixation augmenting posterior lumbar interbody fusion. Spine. 2000;25:858–864.
29. Inceoglu S, Kilinçer C, Tami A, et al. Cortex of the pedicle of the vertebral arch. Part I: deformation characteristics during screw insertion. J Neurosurg Spine. 2007341–346.
30. Defino HLA. Study of the influence of the type of pilot hole preparation and tapping on pedicular screws fixation. Acta Ortop Bras. 2007;15:200–203.
31. Guillot J. Assemblages par Elements Filetes. Modelisations et Calcul. Techniques de l’Ingénieur, Tome 1 B5560 à B5562, Paris, France; 1987.
32. Chatzistergos PE, Magnissalis EA, Kourkoulis SK. A parametric study of cylindrical pedicle screw
design implications on the pullout performance using an experimentally validated finite-element model. Med Eng Phys. 2010;32:145–154.
33. Wirth AJ, Müller R, Harry van Lenthe G. The discrete nature of trabecular bone microarchitecture affects implant stability. J Biomech. 20121060–1067.
34. Schmidt H, Heuer F, Drumm J, et al. Application of a calibration method provides more realistic results for a finite element model of a lumbar spinal segment. Clin Biomech. 2007;22:377–384.
35. Defino HLA, Vendrame JR. Role of cortical and cancellous bone of the vertebral pedicle in implant fixation. Eur Spine J. 2001;10:325–333.