S2 Alar Iliac Screw and S1 Pedicle Screw Fixation for the Treatment of Sacral Fractures : A Finite Element Study

Background: Five different sacral fracture xation methods were compared using nite element (FE) analysis to study their biomechanical characteristics. Methods: Denis type I sacral fractures were created by FE modeling. Five different xation methods for the posterior pelvic ring were simulated: sacroiliac screw (SIS), lumbopelvic xation (LPF), transiliac internal xator (TIFI), S2-alar-iliac (S2AI) screw and S1 pedicle screw xation (S2AI-S1), and S2AI screw and contralateral S1 pedicle screw xation (S2AI-CS1). Four different loading methods were implemented in sequence to simulate the force in standing, exion, right bending, and left twisting, respectively. Vertical stiffness, relative displacement, and change in relative displacement were recorded and analyzed. Results: As predicted by the FE model, the vertical stiffness of the ve groups in descending order were S2AI-S1, SIS, S2AI-CS1, LPF, TIFI. In terms of relative displacement, S2AI-S1 and S2AI-CS1 groups displayed a smaller mean relative displacement, although the S2AI-CS1 group exhibited greater displacement in the upper sacrum than the S2AI-S1 group. The SIS group displayed a moderate mean relative displacement, although the displacement of the upper sacrum was smaller than that of the S2AI-CS1 group. The LPF and TIFI groups displayed larger mean relative displacements. In terms of change in relative displacement, the TIFI and LPF groups displayed the greatest uctuations in their motion, while the SIS, S2AI-S1, and S2AI-CS1 groups displayed smaller uctuations. Conclusion: Compared with SIS, unilateral LPF and TIFI, S2AI-S1 displayed the greatest biomechanical stability of the FE models and can be used as a new method for the treatment of sacral fractures. When the S1 pedicle screw insertion point on the affected side is damaged, S2AI-CS1 can be used as a good alternative to S2AI-S1.

stability of the FE models and can be used as a new method for the treatment of sacral fractures. When the S1 pedicle screw insertion point on the affected side is damaged, S2AI-CS1 can be used as a good alternative to S2AI-S1.

Background
Sacroiliac screws (SIS) and lumbopelvic xation (LPF) have been widely used clinically as two conventional methods for the treatment of posterior pelvic ring injuries, but both methods have limitations [1][2][3][4]. Sacroiliac screw placement with a residual displacement of 10 mm or more can endanger adjacent neural and vascular structures [1]. In addition, the reported incidence of sacroiliac screw loosening is as high as 17.3%, and that of screw failure is 11.8% [2]. There are many postoperative complications in the clinical practice of LPF, such as incision infection, screw prominence, implant failure, and reoperation [3,4]. Long-term xation of the lumbar vertebrae is prone to lower back discomfort [4].
Transiliac internal xator (TIFI) has the advantages of being minimally invasive and having low postoperative infection rate, although it still cannot prevent local skin discomfort caused by screw protrusion [5].
To reduce the problems caused by the protrusion of the iliac screws, the S2-alar-iliac (S2AI) technique has been proposed to replace the iliac screw in lumbosacropelvic xation [6,7]. The S2AI screw is 15 mm deeper than the iliac screw, which makes it less prominent [6]. Biomechanical testing of S2AI screw xation resulted in comparable stability versus traditional iliac screw [8]. Furthermore, the S2AI screw technique has fewer postoperative complications than the iliac screw technique [9]. However, the S2AI screw technique is mainly used in spine-related operations [10,11], and there are few studies [12,13] that applied the S2AI screw technique to treat posterior pelvic ring injuries. In these studies [12,13], the lumbar spine was xed, which would limit normal lumbosacral movement.
For Isler type I sacral fractures, the lumbosacral joint is considered to be preserved and therefore has a certain degree of stability [14].The purpose of surgery is only to resolve pelvic instability. We propose the S2AI screw and the ipsilateral S1 pedicle screw xation (S2AI-S1) as a new internal xation method to address the problems in LPF, such as high invasiveness to soft tissue, and those related to the xation range [15]. This short-segment xation method maintains the mobility of the lumbar spine and resolves concerns about adjacent segment disease. In addition, we propose another con guration that is to x the S2AI screw with the contralateral S1 pedicle screw (S2AI-CS1). However, it is still unclear whether the new internal xation methods can meet the requirements of biomechanical stability for the treatment of sacral fractures. Furthermore, the differences in biomechanical stability between new internal xation methods and traditional xation methods remain to be elucidated.
The aim of this study was to investigate the biomechanical stability of S2AI-S1, S2AI-CS1, SIS, LPF, and TIFI for the treatment of Denis type I sacral fractures through nite element (FE) analysis.

Materials And Methods
CT data of the lumbar spine and pelvis were collected from a healthy male volunteer (30 years old, 175 cm, 70 kg, normal bone structure, no tumors, no deformities, no lumbar spine and pelvic structural damage). The CT imaging data were processed using . The thicknesses of the cortical bone and endplates in the FE model were assumed to be 1.3 mm and 0.8 mm, respectively [19]. The thickness of sacral cartilage and iliac cartilage in the sacroiliac joint were 1.8 mm and 0.9 mm, respectively. The gap between the two cartilages was 0.3 mm [20] ( Table 1). All the bony parts and implants were meshed using a 10-node tetrahedron element. In the FE models, the contact condition between sacroiliac joint cartilage was de ned as friction contact, and the friction coe cient was 0.015 [21]. Meanwhile, a friction coe cient of 0.3 was applied between the interaction surfaces of fractures [21]. The interfaces between the superior and inferior articular processes, between the plates/bars and the screws, and between the screws thread part and bone were modeled with a bonded contact.
Denis type I models (right side) were obtained respectively by grid line segmentation. The ligaments were injured as follows: Denis type I sacral fracture accompanied injuries of the LPSL and part of the SPSL. The anterior pelvic ring destruction resulted in injuries of the interpubic disc, superior pubic ligament, and arcuate pubic ligament.
The anterior pelvic ring was xed with a plate, and the methods of xing the posterior pelvic ring were as follows: in the SIS group, a half-thread hollow screw (7.3 mm × 75 mm) was placed horizontally into the S1 segment. In the S2AI-S1 and S2AI-CS1 groups, the S2AI screw (7.5 mm×80 mm) was inserted according to the method in the literature [22], and then connected to the S1 pedicle screw with a rod ( Fig. 1.a-b). Unilateral LPF was formed by connecting L4-L5 pedicle screws and an iliac screw (7.5 mm×80 mm), and TIFI was formed by connecting iliac screws on both sides. In the FE model, the long screws close to the fracture line were de ned as the main screws, while the others were secondary screws.
For the boundary condition, a standing posture with two legs was simulated: the acetabulum on both sides was xed with 6 degrees of freedom. For the loading condition, a vertical force of 500 N was applied on the top surface of the L4 to simulate the upper body weight. According to spinal three-column theory, the upper endplate of L4 shares 85% of the load, and the bilateral superior articular facets of L4 share 15% of the load [16]. In addition, exion was simulated by a 500 N vertical load and a 10 Nm moment of forward sagittal direction [21]. Right bending was simulated by a 500 N vertical load and a 10 Nm moment of right lateral direction. Left twisting was simulated by a 500 N vertical load and a 10 Nm moment of left horizontal rotation direction.
The vertical stiffness of each group was calculated based on the vertical displacement of the center point of the upper surface of S1 (vertical stiffness = 500N/vertical displacement). Four pairs of points ( Fig. 2) on both sides of the fracture line were selected for calculation of the relative displacement (RD) of the fracture. The RD was used to evaluate the stability effect of each group of internal xation on the sacral fracture model. The smaller the RD, the better the stability of the xation. In addition, changes in the relative displacement caused by three types of motion with respect to standing were calculated, to evaluate the range of uctuation in the relative displacement of motion conditions relative to standing conditions. (Additional le 1)

Results
The mesh convergence study

The vertical stiffness of the FE models
The vertical displacement (Z-axis) of the center point of the upper surface of the S1 vertebral body in the SIS, LPF, TIFI, S2AI-S1, and S2AI-CS1 groups were 0.7119 mm, 0.9861 mm, 1.0694 mm, 0.6864 mm, and 0.7491 mm, respectively. According to the stiffness calculation formula, as predicted by the FE model, the vertical stiffness of the ve groups in descending order were S2AI-S1, SIS, S2AI-CS1, LPF, and TIFI. respectively. The maximum von Mises stress values of all the implants were less than the yield stress of titanium [25]. (Fig. 3.a-e). Under 500 N vertical stress, the maximum von Mises stresses of the bone around the main screw in the SIS, LPF, TIFI, S2AI-S1, and S2AI-CS1 groups were 31.

Relative displacement and change in relative displacement
Using four different loading methods, the mean RD (mm) of the ve groups in descending order were TIFI, LPF, SIS, S2AI-CS1, and S2AI-S1 (except that the mean RD of LPF in exion and twisting left was greater than for TIFI) (Fig. 4a-d). The RD of the LPF and TIFI groups displayed a decreasing trend from point 1 to point 3, but an increasing trend from point 3 to point 4. The RD of the SIS group exhibited an increasing trend from point 1 to point 4. The RD of the S2AI-S1 and S2AI-CS1 groups displayed a decreasing trend from point 1 to point 2, but an increasing trend from point 2 to point 4. The RD of the S2AI-CS1 group at point 1 was greater than that of the S2AI-S1 and SIS groups, while the RD at point 2 to point 4 was similar to that of the S2AI-S1 group but smaller than the SIS group. (Additional le 2-5) Compared with standing, the change in relative displacement of the SIS, S2AI-S1, and S2AI-CS1 groups for three different movements uctuated less. For the LPF group, the change in relative displacement during exion was large, while in right bending and left twisting they were small. For the TIFI group, the change in relative displacement was larger in exion and left twisting, while smaller in right bending (Table 2). LPF: Lumbopelvic xation ; TIFI: Transiliac internal xator ; SIS: sacroiliac screw ; S2AI-S1: S2-alariliac screw and S1 pedicle screw xation ; S2AI-CS1: S2-alar-iliac screw and contralateral S1 pedicle screw xation.

Discussion
An unstable pelvic fracture is a severe injury that is the cause of high mortality and morbidity [27]. Due to complex local anatomy, unique biomechanics, and poor bone quality, the xation of sacral fractures remains a challenge [28]. A key aspect of sacral fracture repair is su cient stability to counterbalance translational and rotational forces in the vertical and horizontal directions [3]. In addition, to improve the quality of life of patients following surgery, sacral implants should also minimize adverse effects on patients. In the present study, static FE analysis methodology that is widely accepted by the community was used to evaluate the stability of ve internal xation methods on sacral fracture. The results of simulation show that the new internal xation methods for the treatment of Denis type I sacral fractures can meet safety and stability requirements.
In a biomechanical study, Acklin et al. found that under Denis II sacral fracture model with vertical loading, the average axial stiffness of SIS was greater than that of unilateral LPF [29]. Although a Denis type I fracture model was used in the present study, the results of the simulation were consistent with those in the literature. In an FE analysis study, Song et al. found that unilateral LPF could not provide su cient horizontal and rotational stability for patients with unilateral sacral fractures [30]. In the present study, the change in relative displacement of the unilateral LPF uctuated greatly in exion compared with standing, indicating that unilateral LPF is potentially unstable. In another study, Vigdorchik et al. found that the stiffness of the SIS was greater than the pedicle screw construct (namely TIFI) under the sacroiliac joint injury model [31]. Although a Denis type I fracture model was used, the stiffness of SIS which is greater than TIFI in our study was consistent with the result of Vigdorchik et al.
A higher maximum von Mises stress indicates that the model has a higher risk of implant failure [32].
According to the results of the simulation (except SIS), the LPF group displayed a greater risk of implant failure, occurring at the connection between the iliac screw and rod. This con rms previous clinical studies which found that implant failure usually manifests as disengagement of the screw to rod connector [33]. The TIFI and S2AI-CS1 groups displayed a moderate risk of implant failure at the shaft and junction of the head and main screw. The S2AI-S1 group exhibited a lower risk of implant failure which also occurred at the shaft and the junction of the head and secondary screw.
Higher stresses on the bone around the screw may lead to screw loosening and secondary fractures [21]. Based on the results of the simulation, the SIS group has a higher risk of screw loosening than the LPF group. In a cyclic loading experiment by Acklin et al., SIS was found to be more prone to loosening than LPF [29], consistent with our prediction. Furthermore, the main screws were predicted to have a greater risk of loosening than the secondary screws. For the main screws, the S2AI-CS1 and SIS groups had a higher risk of screw loosening, the S2AI-S1 and LPF groups displayed a moderate risk of screw loosening, while the TIFI group had a lower risk of screw loosening. For the secondary screws, the S1 pedicle screw in the S2AI-S1 group has a higher risk of loosening than other screws. Therefore, it is believed that the disadvantage of S2AI-S1 is a relatively increased risk of loosening of the secondary screw. When comparing the S2AI-S1 group with the S2AI-CS1 group, the ipsilateral S1 pedicle screw had a greater in uence in reducing the maximum von Mises stress for the S2AI screw than the contralateral S1 pedicle screw.
According to the mean RD values, the overall stability of the ve internal xation methods in the FE models, in descending order are: S2AI-S1, S2AI-CS1, SIS, LPF, and TIFI. Considering that unilateral LPF and TIFI are insu cient for stability of the posterior pelvic ring, it is considered necessary to add a sacroiliac screw to unilateral LPF or TIFI to enhance stability, as demonstrated in previous studies [29,34]. The RD of different points reveals that a fracture is more stable the closer it is to a screw (S2AI screw/Sacroiliac screw). This indicates that a single-segment S1 sacroiliac screw provides limited stability for the lower sacrum. A number of researchers have suggested adding an S2 sacroiliac screw for biplanar stability [19,35]. Since the S2AI-CS1 group had greater RD at point 1 and point 4 than the S2AI-S1 group, the former was slightly less stable when used in sacral fractures than the latter. In addition, although the overall stability of the S2AI-CS1 group for sacral fractures was superior to that of SIS, the stability of the upper sacrum was slightly worse.
The change in relative displacement reveals the principal reason for the difference in stability. TIFI and unilateral LPF are methods that can achieve indirect stabilization of sacral fractures through a screw-rod system, while SIS, S2AI-S1, and S2AI-CS1 can provide direct xation of sacral fractures using screws. According to the AO principles of fracture management, xation of the fracture interface using screws could create a preload [36]. This preload would compress the fracture and prevent separation, while friction between the fracture surfaces and between the screw and bone would oppose displacement due to shear [36]. By comparing the relative changes in displacement for three types of motion, the TIFI and LPF groups displayed greater uctuations during motion, while the SIS, S2AI-S1, and S2AI-CS1 groups exhibited only small uctuations. This indicates that the SIS, S2AI-S1, and S2AI-CS1 groups can achieve absolute stability for the fracture, while the TIFI and LPF groups can only achieve relative stability.
This study con rmed the role of the new internal xation in the stability of Denis I sacral fractures. The invasiveness of LPF and problems with the xation range [15] (limitation of mobility of lumbar vertebrae, adjacent segment disease, and the need for implant removal) suggest that S2AI-S1 may be a bene cial method for internal xation. Compared with TIFI, S2AI-S1 is not only expected to improve in biomechanical stability, but also eliminate the problem of screw protrusion. Although S2AI-S1 may not be as minimally invasive as SIS [37], the former has better biomechanical stability and a lower risk of screw loosening than the latter. Considering that S2AI-CS1 is slightly less stable in the upper sacrum and that the main screw has a higher risk of loosening, such xation is not recommend as the rst choice. When the S1 pedicle screw insertion point on the affected side is damaged, S2AI-CS1 can be used as a good alternative to S2AI-S1. Although the new internal xation method can meet the safety and stability requirements, patients are advised to avoid premature weight bearing to prevent implant loosening and loss of reduction.

Limitations
Nevertheless, some potential limitations related to this study should be noted. First, the biomechanical results obtained through nite element analysis are inadequate to fully con rm the stability of S2AI-S1, which needs to be further veri ed by cyclic loading experiments on cadaver bone models. Second, the screw in this experiment used simpli ed processing to reduce the calculation time and analysis error due to stress concentration. However, to obtain accurate stress distribution on the screw and the bone around the screw, the screw thread should be considered in the FE model [38]. Third, in this study, only the main ligaments were simulated, but in practice, some other ligaments and muscles may still play a role [39]. Therefore, there may be some differences between our simulation data and cadaver bone model data. Finally, the present study used CT data from a normal male pelvis for development of the FE model, and no anatomical differences between individuals were considered.

Conclusion
Compared with SIS, unilateral LPF, and TIFI, S2AI-S1 displayed the best biomechanical stability of the FE models and can be used as a new method for the treatment of posterior pelvic ring injuries. When the S1 pedicle screw insertion point on the affected side is damaged, S2AI-CS1 can be used as a good alternative to S2AI-S1.

Declarations
Ethics approval and consent to participate: This study was approved by the Ethics Committee of the Nanfang Hospital of Southern Medical University (NFEC-2019-256). Informed consent was obtained from the participant included in the study.

Consent for publication:
Not applicable Availability of data and materials: All data generated or analysed during this study are included in this published article and its supplementary information les Competing interests: The authors declare that they have no competing interests Funding: Figure 1 The FE models of new internal xation method. a. S2AI-S1 model. b.S2AI-CS1 model.

Figure 2
Four observation points in the FE model. Points 1 and 4 were located at the upper and lower ends of the sacrum, respectively. Point 2 was located at the intersection of the horizontal midline between S1 and S2 posterior sacral foramen and the fracture line. Point 3 was located at the intersection of the horizontal midline between S2 and S3 posterior sacral foramen and the fracture line.

Figure 3
Stress distribution of the ve implants under standing condition. a. LPF group, the maximum equivalent stress was located at the connecting rod near the iliac screw head. b. TIFI group, the maximum equivalent stress was located at the junction of the right iliac screw head and shaft. c. SIS group, the maximum equivalent stress was located at the middle of the screw. d. S2AI-S1 group, the maximum equivalent stress was located at the junction of the S1 pedicle screw head and shaft. e. S2AI-CS1 group, the maximum equivalent stress was located at junction of the S2AI screw head and shaft.