Biomechanical comparison of three stand-alone lumbar cages — a three-dimensional finite element analysis

A three-dimensional nonlinear model of the lumbar spine was constructed from L1 to L5 levels (Figure 2). The lumbar geometry was reconstructed from 1-mm computed tomography scans of a middle-aged male. The CT-scanning images of only one vertebra were used to build the entire lumbar column. The other vertebrae were duplicated and spanned by the intervertebral discs that were manually developed by the CAD software. This makes the vertebral bodies, posterior elements, and associated processes quite similar in shape and size. The pre-procedures of the lumbar FE model were established using ANSYS, Ed.9.0 software (ANSYS Inc., Canonsburg, PA, USA). The INT model was an osseo-ligamentous lumbar spine which includes the vertebrae, intervertebral discs, endplates, posterior elements, and all seven ligaments. The eight-node solid elements were used for modeling the cortical bone, cancellous bone, posterior element, and endplate. The material properties of all tissues were assumed to be homogeneous and transversely isotropic [22]. The intervertebral disc consisted of annulus ground substance, nucleus pulpous, and collagen fibers embedded in the ground substance. The nonlinear annulus ground substance was simulated by using the hyper-elastic Mooney-Rivlin formulation [23]. In the radial direction, twelve double cross-linked fiber layers were defined to decrease elastic strength proportionally from the outermost layer to the innermost. The collagen fibers in different annulus layers were strengthened by the weight factor using the approach from a previous study by the current authors [20]. The weight factors of the elastic modulus were 1.0 at outermost layers, 1–3, 0.9 at layers 4–6, 0.75 at layers 7–9, and 0.65 at the innermost layers, 10–12. The nucleus pulpous was modeled as an incompressible fluid with a bulk modulus of 1666.7 MPa by eight-node fluid elements [22].

No morphological change in vertebrae was simulated in this study. Only decrease in vertebral strength was assumed to model the biomechanical property of the osteoporotic bone. There were two vertebral strengths simulated in this study: normal and osteoporotic models. Compared to the normal bone, “osteoporosis” was defined as a decrease of 66% in the elastic modulus for cancellous bone and a decrease of 33% for the cortical bone [24]. All seven ligaments and collagen fibers were simulated by two-node bilinear link elements with uniaxial tension resistance only, which were arranged in an anatomically correct direction [25]. The cross-sectional areas of each ligament and material properties of the spine were obtained from previous studies (Table 1) [20, 22, 23, 25]. The facet joint was modeled with sliding and non-penetrating behavior using an eight-node surface-to-surface contact element which can slide between three-dimensional target surfaces. The initial gap between a paired facet was kept within 0.5 mm and the coefficient of friction was set at 0.1 [20, 22].

The Latero cage can be interlocked with a bent lateral plate that is inserted parallel to the coronal plane and into the vertebral bodies, thus preventing cage loosening. The SynFix cage consists of a trapezoid frame incorporated with an anterior plate and screws to stabilize the cage body. The Stabilis cage is a trapezoid frame with a threaded cylinder at the middle region to increase the bone-purchasing ability. Without the serrated anchorages, the final ALIF model of the SynCage-Open cage is further instrumented with bilateral pedicle screws to enhance the construct stability. The models of all cage systems were established by SolidWorks, Ed. 2012 software (SolidWorks Corporation, Concord, MA, USA). The spikes of the Latero cage and the screw threads of the SynFix cage were omitted to simplify numerical calculation (Figure 1).

For ALIF simulation, the L3-4 level of the INT model underwent partial discectomy and total nuclectomy. For the SynFix, Stabilis and SynCage-Open models, the anterior approach was used to remove the anterior longitudinal ligament, anterior and a half inner layer of the annulus, and the entire nucleus pulpous. For the Latero model, the lateral approach was adapted to remove the lateral and a half inner layer of the annulus and the entire nucleus pulpous. All the other ligaments of the three models were preserved.

Accordingly, the Latero, SynFix, Stabilis, and SynCage-Open peek cages were modeled and inserted into the L3-4 level. The friction coefficient of the bone-cage interfaces was 0.8 to mimic a serrated surface for the initial stability of the trapezoid frame [14]. The SynCage-Open model was supplemented with bilateral transpedicular fixation. In the SynCage-Open and SynFix models, the pedicle screw (6-mm diameter) and locking screw (4-mm diameter) were respectively modeled with three-dimensional beam elements. The bone-screw interfaces were assumed to be fully bonded to simulate intimate bone-screw purchase. The numbers of elements and nodes were 98,988/135,786, 112,087/253,492, 114,849/162,169, and 106,436/180,875 for the Latero, SynFix, Stabilis, and SynCage-Open models, respectively. The material properties of the ALIF cages, supplementary components, and transpedicular fixator were listed in Table 1.

Only vertical compression onto the lumbar top can potentially lead to excessive movement of the lumbar column [16]. In this study, the follower load was used to constrain each motion segment of the lumbar model with the two-node truss elements that induce contractions for a given temperature change [26]. In principle, the ideal follower load remains tangent to the spine curve, and each spinal segment is loaded in nearly pure compression without artifact motions. Using the trial-and-error method, the attached points of truss elements were modified to optimize the follower load path approximated through the instantaneous center of rotation at each motion segment [27]. This study cautiously decreased the temperature of the truss elements to produce a 400-N follower load for minimizing the ROM of each motion segment (<0.2°). Subsequently, a 10-Nm moment was applied to the lumbar top to simulate flexion-extension, left/right lateral bending, and left/right axial rotation, respectively. During simulation, the bottom of the L5 vertebral body was fixed completely. The comparison indices were intersegmental ROM, facet force, and stresses of annulus, implant, and endplate. The annulus stress is the stress of the ground substance. From the biomechanical viewpoint, the annulus fibers are mainly responsible for the tension. However, the ground substance can bear the various loads that always exist within the intervertebral discs. Previous in vitro studies demonstrated that a disc may prolapse under certain load combinations of flexion, lateral bending, axial rotation, and axial compression [28‐30]. Only the stress of the annulus fibers cannot provide the sufficient information about the disc loads. Consequently, this study uses the stress of the ground substance as the index of the disc prolapse and herniation.

The convergence test consisted of three mesh qualities: 4,750 elements / 4,960 nodes for the coarse model, 27,244 elements / 30,630 nodes for normal model, and 84,594 elements / 94,162 nodes for the finest model. For the finest mesh quality, the changes in total ROM were respectively within 1.03% in flexion (< 0.2°), 4.39% in extension (< 0.5°), 0.01% in torsion (<0.2°), and 0.001% in lateral bending (< 0.1°). Consequently, this study used the finest model to evaluate the biomechanical behaviors of the INT and ALIF models under four physiological motions.

For model validation, the ROM changes in five levels of the INT model were compared with the experimental results of Rohlmann’s study [27]. Under 3.75- and 7.5-Nm moments with 150-N preload, a previous study [31] by the current authors showed data of the current INT model within the extreme values of Rohlmann’s results. Under a 10-Nm moment with 150 N preload, however, the predicted ROMs of this study were 6° to 11° less than those of the in vitro tests under flexion. This might be explained by the differing preload applications of the current (pressure preload) and earlier in vitro tests (vertical preload) [12, 14]. The pressure preload applied a compressive force of 150 N that was always perpendicular to the lumbar top. However, the compression of the vertical preload was consistently orthogonal to the horizontal plane during lumbar motion. Consequently, the pressure preload resulted in a much lower bending moment compared with the vertical preload. In torsion, the facet contact force of the INT model ranged between 121 to 130 N and the values were within the ranges of earlier studies [25, 32]. This indicated that the INT model was well verified for further simulation of the four ALIF models. In total, there were nine models (one intact, four instrumented × two bones) and six motions simulated in this study.

Referring to Panjabi’s ALE formula [33], the restricted ROM of the instrumented model was compared with the corresponding ROM value of the INT model (Figure 3).

The A + P model had the maximal capability in restricting ROM from −76.5% to −93.8% in all motions. The Latero model performed ROM control similar to that of A + P, and superior to that of the SynFix model in flexion and extension. Moreover, the Latero model performance was similar to that of the SynFix model in bilateral axial rotation and left lateral bending, but inferior in right lateral bending. The asymmetrical design of the Latero model with the vertebral plate placed on the left side explained the different behaviors in left versus right lateral bending. The Stabilis model had the lowest values in all motions, especially in controlling lateral bending (−21.0%) and extension (−10.6%). This finding is consistent with the result of the previous study by the current authors [14].

For the osteoporotic lumbar, the percentages of restricted ROM at the surgical level for all models were also shown in Figure 3. Under the osteoporotic condition, the percentages of restricted ROM consistently decreased for all models. The percentages of change rate were 2.7% ~ 10.8% in the Latero, 9.7% ~ 15.9% in the SynFix, 4.4% ~ 13.0% in the Stabilis, and 4.8% ~ 8.2% in the A + P models. The maximal change rate was around 10% in the Latero (10.8%) and A + P (8.2%) models, and slightly higher in the SynFix (15.9%) and Stabilis (13.0%) models. Under the osteoporotic condition, the A + P model still had 70% of ROM control; while the Latero model had weaker control in right lateral bending (−25.9%, versus − 36.7% in normal bone), the SynFix model had weaker control in extension (−38.0%, versus − 50.7% in normal bone), and the Stabilis model had even weaker control in extension (−6.2%) and lateral bending (−8.0%).

ROM control of the adjacent levels under normal and osteoporosis conditions for all models were shown in Figures 3a-c. Under both conditions, the percentages of ROM change rate were less than 12.3% at L2-3, and less than 15.8% at the L4-5 level as compared to the INT model. The difference of ROM change rates was small at the adjacent levels of each model under normal and osteoporotic conditions.

Referring to Panjabi’s formula [33], the normalized percentages of the maximum annulus stress at the surgical level of all models were shown in Figure 4a. At the surgical level, the normalized annulus stress and intersegmental ROM can be well correlated for each model. The Latero model had maximum annulus stress similar to the A + P model, and was superior to the SynFix model in flexion and extension. It was also similar to the SynFix model in bilateral axial rotation and left lateral bending, but inferior in right lateral bending.

Under the normal condition, the annulus stress distribution of the four instrumented models was shown in extension, right and left lateral bending (Figures 5a-c). The Latero had annulus stress distribution similar to the A + P model in extension (Figure 5a), similar to the Stabilis model in right lateral bending (Figure 5b), and similar to the SynFix model in left lateral bending (Figure 5c). The Stabilis model showed the highest annulus stress in all motions, with the stress being concentrated at the posterior annulus in extension (Figure 5a) and at the lateral annulus in bilateral lateral bending (Figures 5b, c). In contrast, the annulus stress was more evenly distributed in the other three models. However, at the adjacent L2-3 and L4-5 levels, there was no obvious difference in annulus stress distribution among the four instrumented models.

The facet contact forces at the surgical and adjacent levels of all models are shown in extension and bilateral rotation (Figures 6a-c). The A + P model had nearly zero facet contact force at the surgical level in all motions, because the relative motions of the facets joint were restricted by the pedicle screw. In extension, the Latero model could control most of extension (−91.6%) and there was little force shifted to the facet joints (Figure 6a). In bilateral axial rotation, the facet contact force of the Latero and SynFix models were similar, because both devices had similar capability in controlling axial rotation (Figures 6b-c). The highest values of facet contact force at the surgical level of the Stabilis model could be explained by the poorer control of extension and axial rotation. At the adjacent levels, there were small differences (<15.0 N) of facet contact force among the four models in extension and axial rotation (Figures 6a-c; left: left facet and right: right facet).

The maximum stresses sustained by the integrated parts of three stand-alone cages were shown in Figure 4b. The locking screws of the SynFix model had higher stress than the vertebral plate of Latero and the threaded cylinder of Stabilis models in all motions. The ratios of maximum stresses at the integrated parts among Latero, SynFix and Stabilis models were 1: 9.6: 2.7 in extension, 1: 2.9: 0.2 in right lateral bending, and 1: 2.2: 0.4 in right axial rotation, respectively. The maximum stress at the integrated parts of the Latero model was similar to that of the Stabilis model in left lateral bending and left axial rotation.

The stress distribution at the integrated part of the three stand-alone models was shown in extension, right lateral bending, and right axial rotation (Figures 7a-c). In these three motions, the stress was concentrated at the base of the locking screws in the SynFix model; while the stress was evenly distributed over the vertebral plate in the Latero model and the threaded cylinder in the Stabilis model.

Since cage subsidence most commonly occurs at the lower endplate of the upper vertebra [2], only the maximum stress on the L3 endplate was calculated. All models consistently showed that the maximum stress occurs at the top surface of the L3 vertebra (Figure 8). The adjacent endplate of the Latero model was more stressed than the other models in axial rotation. Among all motions, the L3 endplate was most stressed in flexion at the SynFix model. In extension, the stress ratios of the contact surface on L3 between the three stand-alone cage models in extension equal to 1:1.07:1.15 in Latero, SynFix, and Stabilis, respectively. The aforementioned stress ratios were 1:1.47:0.53, 1:0.48:0.53 and 1:0.31:0.34 in flexion, left axial rotation and right axial rotation, respectively. The highly stressed endplate of the Latero model in axial rotation might be attributed to the smaller contact surface of the Latero cage.