Biomechanical effect of cage position combined with bilateral pedicle screw xation in the osteoporotic lumbar spine of oblique lumbar interbody fusion: a nite element analysis

Background: The inuence of cage position on postoperative cage subsidence has been paid increasing attention. The best cage position in oblique lumbar interbody fusion (OLIF) is still unclear. This study aimed to evaluate the biomechanical effects of different cage positions with stand-alone (SA) methods and bilateral pedicle screw xation (BPSF) in the osteoporotic lumbar spine after OLIF. Methods: A nite element (FE) model of an intact L3-L5 lumbar spine was constructed. After validation, an osteoporosis model (OP) was constructed by assigning osteoporotic material properties. SA models (SA1, SA2, SA3) and BPSF models (BPSF1, BPSF2, BPSF3) in which a cage was placed in the anterior, middle and posterior third of the L5 superior endplate (SEP) were constructed at the L4-L5 segment of the OP. The L4-L5 range of motion (ROM), the stress of the L5 SEP, the stress of the cage and the stress of xation were compared among the different models. Results: According to the degree of ROM of L4-L5, the stress of the L5 SEP and the stress of the cage for most physiological motions, the SA and BPSF models were ranked as follows: SA2 (cid:0) SA1 (cid:0) SA3, BPSF2 (cid:0) BPSF1 (cid:0) BPSF3. In BPSF2, the stress of xation was minimal in most motions. At the same cage position, the ROM of L4-L5, the stress of the L5 SEP and the stress of the cage in the BPSF models were signicantly reduced compared with those in SA models; compared with SA2, BPSF2 had a maximum reduction of 83.24%, 70.71% and 73.52% in these parameters, respectively. Conclusions: Placing the cage in the middle third of the L5 SEP for OLIF could reduce the maximum stresses of the L5 SEP, the cage and the xation, which may reduce the risk of postoperative cage subsidence, endplate collapse and xation fracture in the osteoporotic


Background
Lumbar interbody fusion (LIF) is the classic technique used to treat lumbar degenerative disease and can be achieved through multiple approaches, and each approach has advantages and disadvantages. With the development of precise and minimally invasive surgical techniques, many minimally invasive LIF procedures have emerged. In recent years, oblique lateral interbody fusion (OLIF) has been highly praised because it has been reported to yield great surgical results [1][2] . However, it is worth noting that the incidence of postoperative cage subsidence and even endplate collapse due to osteoporosis or excessive injury of the endplate is approximately 8.3%~9.4% [1.3] . A relevant anatomical study [4] con rms that the width of the epiphyseal rim varies across regions. The width of the rims in the lateral region of the endplate, in the anterior region and in the posterior region are approximately 7.3 mm, 5.6 mm and 3.3 mm, respectively. Therefore, the contact area between the OLIF cage and the epiphyseal ring varies by the cage position, but few studies on the effect of cage position on the biomechanics of the lumbar spine have been conducted in osteoporosis patients.
In this study, OLIF osteoporosis models with different cage positions, stand-alone (SA) methods and bilateral pedicle screw xation (BPSF) were created. By analyzing the lumbar biomechanics, we can theoretically select a more reasonable cage position, identify the advantages of BPSF in the osteoporotic lumbar spine and provide reference information for clinicians.

Construction of the normal intact lumbar nite element model and osteoporosis model
In this study, we selected an adult male with no history of lumbar disease. CT scans of his lumbar spine were performed with 0.625-mm-thick slices (Siemens, Germany). The data obtained in the DICOM format were imported into Mimics 17.0 (Materialise, Leuven, Belgium) to reconstruct the L3-L5 model. Next, the L3-L5 model was imported into Geomagic Wrap 2017 (3D Systems, Inc., South Carolina, USA) for hole lling, smoothing, polishing, simpli cation, surface construction and other processing steps. Then, cancellous bone, cortical bone, intervertebral discs, cartilage endplates and facet joints were The nucleus pulposus accounted for 30%-50% of the disc volume [6] . The thickness of the cartilage endplate and cortical bone was 1 mm, and the thickness of the facet joints was 0.2 mm [7] . Spinal ligaments (including the anterior longitudinal ligament, posterior longitudinal ligament, ava ligament, interspinous ligament, supra-spinous ligament, intertransverse ligament and facet capsular ligament) were modeled by spring units that were subjected to only tension. The material properties of the models were derived from previous studies [8][9][10] (Table 1). The osteoporosis model (OP) were modi ed from the normal intact model by adjusting material properties. Osteoporosis was induced by reducing the elastic moduli of the cancellous bone by 66% and those of the cortical shell, endplates, and posterior elements by 33% [5] . The soft tissue structures remained unchanged (Table 1).

Construction of the OLIF FE model
The cage and BPSF were created in SolidWorks 2016 (Fig. 2). The length, width and height of the cage were 50 mm, 17 mm and 10 mm, respectively, with an 8-degree sagittal angle. The rectangular plane instead of the serrated plane was used. The length of the pedicle screws was 50 mm, and the diameter of these screws was 6.5 mm. The rods were 53 mm in length and 5.5 mm in diameter. The OP was assembled with the cage and BPSF. Moro et al. [11] divided the area between the anterior and posterior edges of the vertebral body into zones I, II, III, and IV. In this study, the L5 superior endplate (SEP) was equally divided into four parts, and the demarcation points were recorded as a, b and c. The intersection of the maximum transverse and longitudinal diameter of the cage was recorded as central point A. The long axis of the cage was placed parallel to the transverse diameter of the L5 SEP, and A overlapped with a, b and c (Fig. 3). Then, SA models (SA1, SA2, SA3) and BPSF models (BPSF1, BPSF2, BPSF3) with a cage placed in the anterior third (zones ~ ), middle third (zones ~ ) and posterior third (zones ~ ) of the L5 SEP were created (Fig. 4).
In all OLIF models, L4-L5 was considered the operative segment, and the cage was implanted as a single unit on the left side. The nucleus pulposus, annulus brous and cartilage endplate were removed. The cage and BPSF material properties are listed in Table 1.

Boundary conditions, loading methods and biomechanical evaluation
The contact type of facet joints was set to "frictional", and the frictional coe cient was 0.2; the contact types of the other components were set to "bonded". The inferior surface of L5 was xed. An axial preload of 400 N and a 10 Nm moment were imposed on the superior surface of L3 to simulate 6 physiological motions: exion/extension, right/left lateral bending and right/left axial rotation [12][13] . The range of motion (ROM) of L4-L5, the stress of the L5 SEP, the stress of the cage and the stress of the xation were analyzed and compared to investigate the biomechanical effects of different cage positions with SA and BPSF.

Model validation
The ROMs (L3-L4 and L4-L5) were compared with the results of previous cadaveric study [14] and FE study [15] (Fig. 5). We found that our results were close to theirs. Therefore, the normal intact lumbar FE model in the current study could be used for further analysis.

L4-5 ROM
Compared with the ROM of the OP, that of SA1 was more than 28.29% smaller, and the ROMs of SA2 and SA3 were more than 43.06% and 39.83% smaller, respectively, during all motions. The SA models listed in decreasing order in terms of ROM during most motions were as follows: SA3 SA1 SA2. The ROMs of BPSF1, BPSF2 and BPSF3 were more than 80.56%, 80.92% and 84.13% smaller, respectively, during all motions. The BPSF models listed in decreasing order in terms of ROM during all motions except for extension were as follows: BPSF3 > BPSF1 > BPSF2 (Fig. 6).
ROM differed the most between BPSF1 and SA1 in exion, as ROM in BPSF1 was 89.37% smaller. ROM differed the most between BPSF2 and SA2 in exion, as ROM in BPSF2 was 83.24% smaller. ROM differed the most between BPSF3 and SA3 in exion, as ROM in BPSF3 was 74.28% smaller.

Stress of the L5 SEP
The SA models listed in decreasing order in terms of the maximum Von Mises stress of the L5 SEP during all motions except extension were as follows: SA3 > SA1 > SA2. The stresses of SA1 and SA2 were the highest in exion, and the stress of SA3 in exion was second only to that in right lateral bending, which reached 79.39 MPa. The BPSF models listed in decreasing order in terms of the maximum Von Mises stress of the L5 SEP were as follows: BPSF3 > BPSF1 > BPSF2. The stresses of BPSF1, BPSF2 and BPSF3 in exion and right lateral bending were signi cantly higher than those in other motions, while the stresses were the lowest in extension (Fig. 7).
The L5 SEP maximum stress differed the most between BPSF1 and SA1 in extension, as the stress was 71.98% lower in BPSF1. Compared with the L5 SEP maximum stress of SA2, that of BPSF2 differed the most in extension, as it was 70.71% smaller. The L5 SEP maximum stress of BPSF3 differed the most from that of SA3 in extension, as it was 53.13% smaller. The maximum Von Mises stress of the L5 SEP was mainly concentrated in the region of the epiphyseal ring of the endplate in contact with the cage. Figure 8 shows the cloud map of L5 SEP stress in the OLIF models in exion.

Stress of the cage
The SA models listed in decreasing order in terms of the maximum Von Mises stress of the cage in all motions except extension were as follows: SA3 SA1 SA2. The stresses of SA1, SA2, and SA3 were the highest in exion and lowest in left axial rotation. The BPSF models listed in decreasing order in terms of the maximum Von Mises stress of the cage were as follows: BPSF3 > BPSF1 > BPSF2. The stresses of BPSF1, BPSF2, and BPSF3 were the highest in exion and lowest in extension (Fig. 9).
The cage maximum Von Mises stress of BPSF1 differed the most from that of SA1 in extension, as it was 78.38% smaller. Compared with the cage maximum Von Mises stress of SA2, that of BPSF2 differed the most in extension, as it was 73.52% smaller. The cage maximum Von Mises stress of BPSF3 differed the most from that of SA3 in extension, as it was 54.16% smaller. The maximum Von Mises stress of the cage was mainly concentrated in the region in contact with the epiphyseal ring of the endplate. Figure 10 shows the cloud map of cage stress in the OLIF models in exion.

Stress of the xation
The BPSF models listed in decreasing order in terms of the maximum Von Mises stress of the xation were as follows: BPSF3 > BPSF2 > BPSF1 in exion and BPSF1 > BPSF2 > BPSF3 in extension. The xation stress of BPSF2 was the lowest in other motions (Fig. 11). The maximum Von Mises stress of xation was mainly concentrated at the junction of the pedicle screws and rods. Figure 12 shows the cloud map of xation stress in the BPSF models in left axial rotation.

Discussion
Lumbar interbody fusion (LIF) is an effective treatment for various spinal diseases [16][17] and is the most widely used surgical procedure [18] , but complications such as excessive blood loss, muscle denervation, iatrogenic muscle disorders and soft tissue injury are unavoidable [2] . OLIF, which was rst reported by Silvestre et al. [19] in 2012, uses the natural space between the psoas major muscle and the abdominal aorta for the surgical approach and has been widely used in recent years for indirect decompression and interbody fusion in patients with lumbar degenerate disorders due to its advantages of yielding less trauma, less perioperative bleeding and a lower incidence of neurological complications [20][21][22] . Although good clinical results of SA OLIF have been reported [23][24][25] , lumbar degenerate disorders have been reported mostly in elderly patients, and complications such as subsidence and migration of the cage after surgery should not be neglected. For patients with dual-energy X-ray absorptiometry (DEXA) T scores of less than − 1.0, posterior instrumentation is often required [26] .
In recent years, scholars have paid increasing attention to the in uence of cage position on postoperative cage subsidence. Studies [27][28] have reported that the rigidity of the central region of the endplate is signi cantly less than that of the peripheral region, which is called the epiphyseal ring, from L1 to S1. Therefore, cage position is an important factor of cage subsidence and endplate collapse. However, the best cage position remains unclear. Barsa et al. [29] found a lower cage subsidence rate near the anterior part of the intervertebral space. Abbushi et al. [30] concluded that the medio-medial cage position shows the highest migration rate, and the lowest migration and highest fusion rate are seen when the cage is in the posteromedial position. Thus, the authors suggested posterior medial cage placement for PLIF.
However, Ko et al. [31] found that the rate of cage subsidence increases with a more posterior cage position. A previous study [27] shows that the inferior endplate is approximately 40% stronger than is the superior endplate, and the subsidence probability of the superior endplate is signi cantly higher than that of the inferior endplate [32][33] . Therefore, we analyzed the stress of the L5 SEP and cage to evaluate the effect of cage position on the biomechanics of the osteoporotic lumbar spine.
In the present study, the ROMs of the SA models and BPSF models were more than 28.29% and 80.56% smaller in all motions, respectively. This indicated that both SA and BPSF could provide stability for the surgical segment. The stresses of the L5 SEP and cage were the lowest when the cage was placed in the middle third of the L5 SEP and were the highest when the cage was placed in the posterior third in both the SA models and the BPSF models. This result may be related to the contact area between the cage and the endplate changing according to the cage position during lumbar movement; the larger the contact area was, the smaller the stress. The stress of the xation was also the lowest in most motions when the cage was placed in the middle third of the L5 SEP, which may be related to the fact that different cage positions affect mechanical properties such as the moment arm and torque of the bilateral pedicle screw xation. Kim et al. [34] thought that cage positioning and the application of greater compressive load are two reasons for the high risk of cage subsidence. Based on these results, placing the cage in the middle third of the L5 SEP could help reduce the maximum stresses of the L5 SEP, the cage and the xation, which may be bene cial for reducing the risk of postoperative cage subsidence, endplate collapse and xation fracture, regardless of whether SA or BPSF is performed. This position is consistent with the cage placement recommended in the Guidelines for the clinical application of lumbar oblique lateral interbody fusion [35] . The guidelines also point out that whether or not to apply SA technology should be decided on the basis of whether the application of a cage alone can provide su cient stability [35] . In our study, the L4-L5 ROM, the stress of the cage and the stress of the L5 SEP were smaller under all motions in the BPSF models than those of the SA models, especially in exion and extension. This suggested that the SA method could not provide su cient stability under some motions. In contrast, BPSF could signi cantly increase the stability of the surgical segment and reduce the stresses of the cage and L5 SEP in all motions, which could improve the safety of OLIF surgery in osteoporotic lumbar spine. This may be the reason why the BPSF group had a lower incidence of cage settlement than did the SA group in the study by Zeng et al. [25] . It is also worth noting that almost all surgical models showed the largest stress values for the cage and endplate in exion, so few bending movements should be performed after OLIF surgery.
In addition to considering the factors of subsidence when placing the cage, it is also necessary for clinicians to restore sagittal balance and induce su cient indirect decompression. Kepler et al. [36] concluded that anteroposterior cage placement is an important intraoperative determinant of postoperative alignment; anterior placement leads to larger angles of lordosis, while middle/posterior placement has a minimal effect on sagittal alignment. The authors also thought the rate of new neurologic de cits postoperatively after placement of the cage in the posterior part of the disc space may become signi cant. Park et al. [37] suggested that placing the cage within the anterior third of the disk space is better for restoring the segmental angle without compromising the extent of indirect neural decompression achieved with LLIF if the height of the cage is large enough. Jin et al [38] found that cages are located mostly in the middle third of the vertebral body, signi cantly increasing the posterior disk space height and foraminal height compared with those in the anterior cage position. However, another study [39] proposes that increases in disk height and foraminal and canal areas are not dependent on cage positioning within the disk space; as intraoperative placement of a cage in the central portion of the disk is an easier and safer technique, central placement may be preferable in a clinical setting.
According to the clinical experience of our team, SA OLIF is preferred during the rst-stage operation, and the degree of improvement in the patients' symptoms and imaging ndings observed postoperatively are used to determine whether to perform the two-stage operation combined with posterior pedicle screw xation. In this study, we recommend that if the images taken between the two operations shows that the cage has migrated toward the posterior part of the disc space, posterior pedicle screw xation should be performed to reduce the risk of postoperative complications.
In this study, an osteoporotic lumbar spine model was created, and the results were informative. However, our study has some limitations. The FE models were simpli ed. The residual discs of the surgical segments and musculoskeletal segments were not modeled, and ligaments were replaced with springs, which differ from biological ligaments in terms structure. Furthermore, the lumbar spine varies across individuals, and the present study was based on a model of the lumbar spine for analysis, so the results have yet to be validated in a clinical study.

Conclusion
The cage position should be selected according to the speci c conditions. For the osteoporotic lumbar spine, the cage should be placed in the middle third of the disc space. For the lumbar spine with signi cant sagittal imbalance, the cage should be placed in the anterior third of the disc space so that it helps to restore sagittal balance and does not affect the extent of indirect decompression. If the cage migrates toward the posterior part of the disc space after the rst-stage operation, a second-stage operation combined with posterior pedicle screw xation should be performed in a timely manner. Compared to SA OLIF, BPSF can provide su cient stability for the surgical segment in the osteoporotic lumbar spine and may reduce the incidence of postoperative endplate collapse, cage subsidence and posterior internal xation fracture.