Evaluation of S2 alar and traditional S1 pedicle 1 fixation for severe lumbar spondylolisthesis in 2 different bone mineral densities: a finite element 3 analysis

Background: Lumbar spondylolisthesis is a common disease in older 15 populations. The surgical treatment of spondylolisthesis has a history of more than 50 16 years, with L5-S1 screws widely used in clinical practice to reduce slippage and 17 fusion. However, some patients with severe lumbar spondylolisthesis and Conclusion: Extending fixation to the S2 wing can significantly improve internal 40 fixation device stability and reduce the risk of intraoperative and postoperative 41 fractures while avoiding injury to the sacroiliac joint, reducing the difficulty of 42 surgery and the risk of injury to surrounding tissues. It is a reasonable plan for the 43 treatment of moderate and severe lumbar spondylolisthesis with osteoporosis. 44


Introduction 47
Lumbar spondylolisthesis is a deformity that occurs between the lumbar 48 vertebrae and the relative adjacent vertebrae, mainly consists of horizontal 49 displacement, and is one of the most common spinal deformities. Wiltse et al. 50 classified lumbar spondylolisthesis into six types based on the causative factors: 51 dysplastic, isthmic, degenerative, traumatic, pathological and iatrogenic [1] . Severe  In 1986, Matthiass proposed lever reduction using pedicle screws and a rod 58 fixation system [2] . Since then, with the development of internal fixation materials and 59 4 / 30 clinical practice, the application of pedicle screws in the treatment of lumbar 60 spondylolisthesis has gradually become widespread. However, problems such as 61 screw loosening, iatrogenic fracture and broken internal fixation devices have not 62 been satisfactorily solved, especially screw loosening in osteoporotic patients. Severe 63 osteoporosis is a significant cause of internal fixation failure, such as pedicle screw 64 loosening and pull-out after spinal fusion surgery [3][4][5] . Spondylolisthesis often occurs 65 in the L5/S1 segment because there is a high degree of mobility at the L4-S1 66 segment, joining the rigid sacropelvic unit. Failure of instrumentation frequently 67 begins at the sacrum, which is the site of maximum stress [6] . The reported failure 68 rate of S1 pedicle screws is approximately 44% [6][7][8] . Thus, extension of the 69 instrumentation to the distal sacrum or iliac wings has gained increasing interest. 70 Alternatives to the single use of S1 screws include the addition of S2 alar screws and 71 S2 alar-iliac screws.

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Finite element analysis (FEA) is a mathematical and physical computational 73 method that can analyze objects of various shapes by building multiple tiny units and 74 simulating changes that occur during the stressing process [9] . FEA has already been 75 applied to characterize the complex biomechanical properties of the lumbar vertebrae 76 in previous studies [10,11] . Nevertheless, to the best of our knowledge, few studies have 77 illustrated the detailed biomechanical mechanisms of L5-S1 and L5-S2 alar fixation in 78 spondylolisthesis patients with osteoporosis.

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The aim of this study is to compare L5-S1 reduction and fixation methods and 80 explore whether extending the fixation to include the S2 alar can significantly 81 improve the stability of the internal fixation device by FEA.  both sides of the S1 vertebra (Fig. 1). The spikes and features were deleted, 100 smoothing was performed with a polygon mesh, and the triangles were made more 101 uniform in size. Then, a patch was generated using the following tools: Construct derived from the literature [12][13][14][15] , as specified in Table 1 Table 1. In the L5-S1 fixation model, the S1 screw path stresses were unevenly 157 distributed, with the main stresses concentrated on the upper contact surface at the tail 158 of the screw path and the lower contact surface at the front of the screw path.

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Nevertheless, in the L5-S2 alar model, the stresses were relatively dispersed, and the 160 main stresses were distributed at the caudal lateral side of the screw path (Fig. 4). In 161 the low BMD model, when the bone of the S1 screw path reached the yield stress (2.2 162 MPa), the load in the L5-S1 model was 355.58±11.5 N, which was in accordance 163 with previously reported data [16] . Meanwhile, the corresponding load of the L5-S2   The internal fixation stress distribution of the L5-S1 model and the L5-S2 alar 188 model is shown in Figure 3. In the L5-S1 model, the maximum stress was 189 concentrated at the tail of the screw, while in the L5-S2 alar model, the maximum 190 stress was concentrated on the connecting rod near the S1 screw (Fig. 6). In the low 191 BMD model, when the S1 bone yielded, the stress at the tail of the L5-S1 model  Table 3.   3. S1 screw path deformation 207 In the L5-S1 model, the most obvious deformation of the S1 path was on the 208 upper contact surface of the tail, followed by the lower contact surface of the anterior 209 segment of the screw path. The deformation of the middle and rear screw path was the 210 least, and the internal and external deformation was similar. In the L5-S2 alar model, 211 the largest deformation was located at the tail of the screw path, and the overall 212 distribution was relatively uniform (Fig. 7). Regardless of BMD, when the S1 screw    In the current surgical treatment of lumbar spondylolisthesis, L5-S1 internal 232 fixation is mostly reported for reduction; this method has been widely used for many 233 years with proven efficacy, but it also has shortcomings. Due to the short force arm 234 and relatively concentrated stress, this L5-S1 reduction method based on the lever 235 principle is prone to S1 screw loosening in patients with moderate to severe 236 spondylolisthesis, especially in the case of osteoporosis [17] . In response to this 237 problem, surgical approaches continue to be explored and modified, including 238 extended internal fixation to S2, sacroiliac joint fixation and iliac fixation [18] . From a 239 biomechanical point of view, extended methods must be able to increase the stability 240 of the internal fixation device and provide greater power for lifting and reduction.

241
However, each extended internal fixation method still has some flaws. The use of 242 sacroiliac screw fixation inevitably leads to sacroiliac joint damage, loss of sacroiliac 243 joint mobility, and increased long-term risk of chronic sacroiliac pain [19] . Due to the 244 anatomy of the S2 pedicle, which is relatively short and close to the anterior internal frequently reported in older patients with osteoporosis [20][21][22] . To the best of our 250 knowledge, there is a paucity of studies that have examined the biomechanical 251 differences between L5-S1 and L5-S2 alar fixation in severe spondylolisthesis with 252 different BMDs.

253
This study presents a preliminary biomechanical evaluation of L5-S1 and L5-S2 254 alar fixation with different BMDs to analyze the intraoperative reduction stress 255 distribution in severe lumbar spondylolisthesis patients with osteoporosis via FEA.

256
Regarding the yield load of the S1 screw path, in the L5-S1 fixation method, when 257 lifting and repositioning the site of lumbar spine slippage, the stress was concentrated 258 on the tail of the S1 screw path. Because of the thinner cortex of the sacrum compared 259 to that of other vertebrae, excessive concentrated stress could lead to screw loosening 260 or even internal fixation failure. This may also explain why screw loosening often 261 occurs in the tail segment. Nevertheless, in the S2 alar fixation method, the S1 screw 262 path stress was uniformly distributed. When the bone in the S1 screw path yielded, the 263 average load of the L5-S2 alar model was 86.9%-111% higher than that of the L5-S1 264 model, which could significantly improve the reduction ability and S1 screw stability, 265 especially in the low BMD group. This result could be observed more visually in the 266 reduction load-BMD diagram (Fig. 5). When the BMD and the load required for 267 reduction were below the "L5-S1" line, fixation with both 4 screws and 6 screws 268 could achieve reliable stability. However, when the BMD and the load required for 269 reduction were between the "L5-S1" and the "L5-S2 alar" lines, the L5-S1 fixation Regarding the stress of internal fixation, analysis of the S1 internal fixation stress 283 in both models revealed that the S1 screw stress was concentrated at the tail of the reached. When subjected to the same reduction load, the stress of the S1 screw tail in 291 the L5-S1 model was much higher than that in the L5-S2 alar model, predicting a 292 higher risk of screw bending or even fracture. In the L5-S2 alar fixation model, the 293 stress was highest on the connecting rod near the S1 screw, reaching 319-942 MPa at 294 yield in different BMDs. However, it was still lower than the highest stress (423-945 295 MPa) of the S1 screw in the L5-S1 model at the same density. Therefore, the 296 following can be concluded: 1. at the same BMD, the L5-S2 alar model had a higher 297 risk of titanium rod deformation or even fracture, while the L5-S1 model had a higher 298 risk of screw fracture; and 2. when the bone yield stress was reached, the risk of 299 titanium rod deformation in the L5-S2 alar model was still lower than the risk of 300 screw fracture in the L5-S1 model, which further proved that the overall structure of 301 the L5-S2 alar model was more stable.

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Regarding S1 screw path deformation, as the reduction load increased, there the L5-S2 alar model was 60% to 100% higher than that in the L5-S1 model, while 310 there was no significant difference in the maximum screw path deformation between 311 the two models. The above results indicate the following: 1. with the same reduction 312 effect (i.e., the same reduction load was applied) and the same BMD, in the L5-S2 313 alar model, the deformation of the S1 screw path was dispersed and uniform, while in 314 the L5-S1 model, local bone destruction at the front and tail ends of the screw path 315 easily occurred due to stress concentration; 2. when the bone yielded, the degree of 316 screw path deformation had little correlation with bone density, according to Table 4; 317 and 3. S1 screw loosening could occur with relatively minor bone destruction in the 318 L5-S1 model, whereas it occurred with further bone compression in the L5-S2 alar 319 model, indirectly proving that the L5-S2 alar model was more stable.