Biomechanical comparison of multi-rod constructs by satellite rod configurations (in-line vs. lateral) and screw types (monoaxial vs. polyaxial) spanning a lumbar pedicle subtraction osteotomy (PSO): is there an optimal configuration?

Multi-rod constructs are used commonly to stabilize pedicle subtraction osteotomies (PSO). This study aimed to evaluate biomechanical properties of different satellite rod configurations and effects of screw-type spanning a PSO. A validated 3D spinopelvic finite element model with a L3 PSO (30°) was used to evaluate 5 models: (1) Control (T10–pelvis + 2 rods); (2) lateral satellite rods connected via offsets to monoaxial screws (LatSat-Mono) or (3) polyaxial screws (LatSat-Poly); (4) in-line satellite rods connected to monoaxial screws (InSat-Mono) or (4) polyaxial screws (InSat-Poly). Global and PSO range of motions (ROM) were recorded. Rods’ von Mises stresses and PSO forces were recorded and the percent differences from Control were calculated. All satellite rods (save InSat-Mono) increased PSO ROM and decreased primary rods’ von Mises stresses at the PSO. Lateral rods increased PSO forces (LatSat-Mono:347.1 N; LatSat-Poly:348.6 N; Control:336 N) and had relatively lower stresses, while in-line rods decreased PSO forces (InSat-Mono:280.1 N; InSat-Poly:330.7 N) and had relatively higher stresses. Relative to polyaxial screws, monoaxial screws further decreased PSO ROM, increased satellite rods’ stresses, and decreased PSO forces for in-line rods, but did not change PSO forces for lateral rods. Multi-rod constructs using in-line and lateral satellite rods across a PSO reduced primary rods' stresses. Subtle differences in biomechanics suggest lateral satellite rods, irrespective of screw type, increase PSO forces and lower rod stresses compared to in-line satellite rods, which had a high degree of posterior instrumentation stress shielding and lower PSO forces. Clinical studies are warranted to determine if these findings influence clinical outcomes.


Introduction
Lumbar pedicle subtraction osteotomies (PSO) are powerful surgical techniques to correct rigid and severe coronal and sagittal spinal malalignment. While providing significant correction, they are associated with a relatively high rate of short-and long-term complications [1,2]. Two of importance are pseudarthrosis and rod breakage, which have been reported as the most common postoperative complications and frequent indications for revision operations [2][3][4][5][6][7][8][9][10][11]. In an attempt to decrease their rates, a variety of supplementary surgical techniques have been evaluated and implemented. These have included multi-rod constructs stabilizing the PSO, interbody cages adjacent to the PSO, and varying rod materials and diameters spanning the PSO [4,10,[12][13][14][15][16][17].
Multi-rods constructs can be achieved using either "satellite" rods (rods not connected to the primary rods) and/or "accessory rods" (rods connected to the primary rods) [18]. The first report of a multi-rod construct across a PSO was by Gupta et al. [4] who utilized a laterally based satellite rod connected to a posted pedicle screw system (i.e., monoaxial screws that connect to rods via slotted connectors, which are secured to the screw shaft via a locking nut) above and below the PSO. Lateral satellite rods can be particularly useful from a surgical perspective, as they provide temporary stabilization while the PSO is being performed, facilitate closure of the osteotomy site (symmetric and/or asymmetric), and serve as the final fixation rods across the PSO without needing to be exchanged. As posted screw systems are now antiquated, the senior author has adapted the laterally based satellite rod technique of Gupta et al. using modern polyaxial screw systems by connecting a rod laterally to the screws above and below the PSO site via lateral offset connectors (Fig. 1).
As lateral satellite rod constructs have yet to be studied biomechanically and prior multi-rod biomechanical analyses have only focused on in-line satellite rods (Fig. 1) and accessory rods, the purpose of this study is to evaluate the biomechanical properties of in-line vs. laterally based satellite rods with different screw types (monoaxial vs. polyaxial) adjacent to a lumbar PSO site.

Methods
A previously validated three-dimensional osseoligamentous spinopelvic finite element model (T10-pelvis) with a 30° PSO at L3 was used [15]. The intact model was reconstructed from computed tomography (CT) scans of a human spine using MIMICS (Materialize Inc., Leuven, Belgium) software. IAFE-MESH (University of Iowa, Iowa) and HyperMesh (Altair Engineering, Michigan, USA) were used to create hexahedral elements (C3D8) of the vertebrae and tetrahedral elements (C3D4) of the pelvis. The meshed components were assembled in the Abaqus 6.14 (Dassault Systemes, Simile Inc., Providence, RI, USA). The spinal and sacroiliac ligaments were modeled using truss elements. In the vertebral body, a layer of 0.5 mm cortical bone was simulated to surround the cancellous bone [15,19].
The intervertebral disks were composed of annulus fibrosis and nucleus pulposus. The annulus fibrosis was simulated using a solid ground substance (C3D8 elements) reinforced with rebar elements (embedded with ± 30° angles). The nucleus pulposus was modeled using C3D8 elements with hyper-elastic Mooney-Rivlin formulation [15,20]. The sacroiliac joint was modeled using soft contact with exponential behavior [15,21]. Material properties were assigned to each component based on the literature (Table 1) [15].
The PSO model utilized in this study was previously performed and validated [15]. The anterior section was tied, while at the posterior, a surface-to-surface interaction (friction = 0.46) was defined between the two resected segments [15].
The instrumentation including rods, pedicle screws, and lateral connectors was designed in SolidWorks (Dassault Systems, SolidWorks Corporation, Waltham, MA, USA) and imported into Abaqus for model development. Each pedicle screw was modeled in two parts (tulip and shaft) connected with a ball and socket joint. The pedicles at T10, T11, and T12 were instrumented with 6.5 × 40 mm polyaxial screws. At L1 and L5, 6.5 × 45 mm polyaxial screws were used. Adjacent to the osteotomy site (L2 and L4), 6.5 × 40 mm screws were inserted. The S1 pedicles and iliac screws were sized 7.5 × 50 mm and 8.5 × 80 mm polyaxial screws, respectively. In the "Control" model, two bilateral 5.5 mm cobalt-chromium rods were connected all screw tulips from T10 to the pelvis. In all of the other 4 constructs (multirod; see below), primary rods were connected to the screws' tulips from T10 to ilium, except at L2 and L4 where the satellite rods were connected.

FE model development
The mesh convergence study was performed in two steps. First, a three-point bending simulation was performed on a single screw shaft and seed sizes were reduced until the difference between the yield loads obtained from two subsequent seed sizes was less than 5%. Second, the LatSat-Mono model was used to perform the mesh convergence study on the rods. Seed sizes were reduced until the percentage difference between the forces across the PSO site was below 5%. In all levels except the PSO site, the shaft and tulip components were assembled and inserted under the guidance of spine surgeons. To accommodate the primary rods over the satellite rods, the primary rods were bent less than the satellite rods and the screws above and below the PSO site (i.e., L3 and L5) were recessed deeper than the other screws (i.e., T10, T11, T12, L1, L2, and S1). To keep the curvature of the rods similar in models with mono-and polyaxial screws the screw shafts were aligned with the tulip heads at the PSO site. Different interactions were defined between the screw shaft and the tulip head; in models with monoaxial screws, the tulip head was tied to the shaft. To simulate polyaxial screws, the same procedure was used as literature [22]. First, two reference points were defined on the screw shaft and the tulip head and the corresponding nodes were coupled to each reference point. Then, a "Join-Cardan" connector was assigned between the shaft & tulip which constrained the two components in U1, U2, and U3 motions and allows for a relative rotation between these components (UR1, UR2, and UR3). Moreover, a surface-to-surface interaction was defined between the tulip and shaft (friction = 0.4 [23]). Rods were tied to tulip and lateral connectors.
A two-step analysis was performed. In step 1, follower loads were applied using wire elements (with axial connector type) which followed the curvature of the thoracolumbar segments. A 300 N connector load was applied to the thoracic (150 N to left and right side) and a 400 N connector load was applied to the lumbar spine (200 N to left and right side). Additionally, a concentrated force with the magnitude of 400 N was applied to the sacrum to account for the body weight and muscle forces [15]. In step 2, pure moments of 7.5 Nm were applied to the top endplate of the T10 vertebra in all anatomical directions. In both steps, the acetabulum surfaces of the pelvis were fixed in all degrees of freedom.

Data analysis
For each configuration, the range of motions (ROM) of T10-S1 (global) and L2-L4 (PSO) were recorded at the second step. The von Mises stresses on the primary/satellite rods were recorded and the percentage differences to the primary rods in the Control model were calculated. Due to the complexity in loading and geometry of the lumbar spine PSO model, von Mises stresses, instead of individual components of stress, were used as von Mises stress is a commonly used criterion for yielding or fracture under complex loading. The critical stress locations were recorded and compared among all models. For each model, the force acting at the osteotomy site in flexion motion was captured.

T10-S1/global range of motion
Data on T10-S1 ROM are presented in Fig. 3. Use of satellite rods in any configuration (in-line and lateral) decreased T10-S1 ROM in flexion-extension and lateral bending [15].    Table 2 and Fig. 5. Compared to in-line configurations, lateral rods decreased stresses on primary rods to a similar extent, but had considerably lower stresses themselves. Compared to the Control model, reduction in primary rods' von Mises stresses was similar between lateral and in-line configurations. Satellite rods provided greatest percent reduction in von Mises stresses on primary rods during flexion and lateral bending. Lateral satellite rods' von Mises stresses were considerably less than the von Mises stresses on in-line satellite rods. For all satellite rods, von Mises stresses were greatest during  flexion and lowest during extension. Of note, InSat-Mono was the only construct to demonstrate an increase in stresses on the primary rods in extension (+ 13.15%) compared to the Control (Table 2). Also, the data demonstrated that polyaxial screws at the osteotomy site (LatSat-Poly & InSat-Poly) resulted in lower stresses on satellite rods compared to models with monoaxial screws for both lateral and in-line configurations ( Table 2). In the four-rod configurations, two critical stress locations were observed: adjacent to the PSO site and at the L5-S1 level. The critical stress location was observed on primary rods for all multi-rod constructs at the PSO site except during lateral bending and extension where the maximal stresses were adjacent to L5-S1. Additionally, the InSat-Mono model showed slightly higher stresses on the satellite rods than the primary rods.

Force at the PSO site (Table 3)
Data on forces at the PSO site are presented in Table 3. Compared to the Control, lateral satellite rods increased the force across the osteotomy site. In contrast, in-line satellite rods (most notably InSat-Mono) showed lower PSO forces than the Control construct. While screw types above and below the PSO did not result in a difference in PSO forces for lateral satellite rods, monoaxial screws with in-line rods (InSat-Mono) had 50 N lower PSO forces than polyaxial screws with in-line rods (InSat-Poly).

Discussion
Multiple prior studies have evaluated the relative biomechanical behaviors of in-line satellite rods and accessory rods, but none have evaluated the biomechanics of lateral satellite rod constructs across a lumbar PSO. As such, the study presented herein investigated the relative biomechanical effects of lateral versus in-line satellite rods with different screw types (monoaxial vs. polyaxial) adjacent to a lumbar PSO site using a well-accepted validated FE model for long thoracolumbar spine instrumentations. These results are consistent with prior reports, but also add unique information to the literature on biomechanics of multi-rod constructs for lumbar PSOs, particularly lateral satellite rods.
Our FE predictions showed that using satellite rods (inline and lateral) reduced von Mises stresses on primary rods at the PSO compared to the Control model, which is in agreement with prior reports [9,[12][13][14][24][25][26][27]. This benefit appears to be in part secondary to allowing primary rods to be undercontoured at the PSO site. Gupta et al. reported that when the osteotomy site is closed by satellite rods independent from the primary rods, a sharp curvature at the apex of the primary rods is avoided, which eventually will lead to less primary rod stresses and theoretically lower rates of rod breakage [4]. This was demonstrated by Gelb et al. who found that in-line satellite rods across a PSO decreased primary rod stresses, as the satellite rods allowed the primary rods to be undercontoured by 14.2° [17,28]. As the vast majority of rod fractures occur at the level of the PSO [6], this effect of satellite rods on reducing primary rod stresses is important.
Lateral and in-line satellite rod configurations' reduction on primary rod stresses appears to be a result of different biomechanical effects on the PSO site. We found that lateral satellite rods increased PSO ROM in flexion and extension, which resulted in less von Mises stress on the lateral satellite rods and increased force at the PSO site. This is in contrast to in-line satellite rods, which resulted in decreased force at the PSO likely as a consequence of the in-line rods creating a relatively stiffer construct across the PSO site (less PSO ROM relative to the lateral satellite rods, particularly with monoaxial screws). This relative increased stiffness transferred the forces and stress from the PSO site to the in-line satellite rods, as evidenced by the considerably higher von Mises stresses observed on the in-line satellite rods themselves. These data suggest that the lateral satellite rods, irrespective of screw type, create a better biomechanical environment across the PSO site compared to in-line satellite rods, as the forces are transferred away from the lateral and primary rods and to the anterior vertebral column [11]. This is postulated to be biomechanically favorable for the PSO site, as increased PSO forces should promote bone-healing and fusion at the osteotomy site and decrease the chances of non-union compared to the in-line configurations, a theory also supported by La Barbera et al. [11]. This currently is purely a theory, and has yet to be proven. As such, it deserves further investigation. Note that ROM from T10 to S1 is Table 3 The forces across the osteotomy site under flexion for different configurations simulated in this study Using laterally based satellite rods increased the PSO force while the in-line satellite rods decreased the force at the osteotomy site compared to the Control model not altered appreciably by any satellite rod configuration, which is likely secondary to the fact that the control and the four satellite rod configurations all include rods that stabilize the spine from T10 to the pelvis and that the satellite rods only span 2 levels (L3-L5).
Our results on the effects of screw type (monoaxial vs. polyaxial) used to stabilize satellite rods across the PSO provide an added dimension to the discussion in the prior paragraph. Consistently, monoaxial screws in this study created a stiffer PSO site relative to polyaxial screws, as evidenced by decreased PSO ROM in all directions for both types of satellite rods. This relative decreased ROM afforded by monoaxial screws was subsequently manifested in higher von Misers stresses on satellite rods for both types of satellite rods. While this stress shielding by the posterior instrumentation resulted in significantly lower PSO forces for in-line satellite rods with monoaxial screws (56 N less than controls) compared to in-line rods with polyaxial screws (5 N less than controls), there was no difference in forces across the PSO site for lateral satellite rods with monoaxial screws compared to lateral rods with polyaxial screws. In fact, the lateral satellite rods with monoaxial screws resulted in an increase in PSO forces, the values of which were similar to lateral satellite rods with polyaxial screws. Given the anterior load sharing afforded by the lateral satellite rod constructs, they appear to offer superior biomechanical PSO environments relative to in-line satellite rod configurations. These data suggest that LatSat-Mono may offer the best biomechanical PSO environment, while the InSat-Mono creates the most unfavorable biomechanical PSO environment.
The results of this study should be considered in the context of its limitations. These include the lack of range of motion data for the cadaveric spine with lateral satellite rod configurations, simulation performed with no muscle forces, and using uncomplicated geometries of the implants and simplified contact and constraints. Moreover, the residual stresses produced as a result of rod contouring and screw/rod tightening were not considered. Specifically, the interconnections of the screws, rods, lateral connectors, and anatomy were all in ideal conditions, which is almost never the case clinically. The lack of motion between the lateral satellite rods and the connectors may have stiffened the lateral satellite rods making them appear better when in practice those interconnections may create a less stiff construct over the PSO. As such, future investigations should ideally incorporate movement between the rod and connector or screw and connector. Our finding that satellite rods affect more than just reducing ROM across the PSO in flexion deserves further scrutiny. It may imply that the moment is not about the instantaneous axis of rotation of the PSO and perhaps posterior to it, which may or may not be physiologic. Alternatively, satellite rods' effects on biomechanics may also be influenced by other factors, including rod characteristics (i.e., diameter, material, bend magnitude). Additionally, as utilization of laterally based satellite rods is relatively new for PSO closure and stabilization, we are unable to comment upon the clinical significance of our observed biomechanical differences and relative long-term clinical performance of the different instrumentation configurations evaluated in this study. Of note, however, all techniques have been performed safely and without any notable clinical differences in the short-term. Despite these limitations, the advantageous biomechanical data of laterally based satellite rods observed in our study are noteworthy when considered in the context of the purported benefits imparted by lateral satellite rods on the surgical workflow while performing a lumbar PSO [i.e., providing temporary stabilization while the PSO is being performed, facilitating closure of the osteotomy site (symmetric and/or asymmetric), and serving as the final fixation rods across the PSO without needing to be exchanged].

Conclusion
In this FE analysis of a L3 PSO, multi-rod constructs using in-line and lateral satellite rods reduced stresses on primary rods at the PSO site. This was afforded by different relative distributions of forces and stresses on the PSO site and satellite rods between the two satellite rod configurations. Specifically, lateral satellite rods distributed forces more advantageously (increased PSO forces and low von Mises stresses on the satellite rods-low degree of stress shielding on posterior instrumentation) compared to in-line satellite rods (decreased PSO forces and high von Mises stresses on the satellite rods-high degree of stress shielding on posterior instrumentation). Monoaxial screws created a particularly favorable biomechanical PSO environment when combined with lateral satellite rods, but unfavorable biomechanical conditions when combined with in-line satellite rods. As the biomechanics differences observed between the constructs in this study are subtle, these data deserve further attention through additional in vitro and clinical studies.
Authors' contributions All authors made substantial contributions to the conception or design of the work, the acquisition, analysis, or interpretation of data, drafted the work or revised it critically for important intellectual content, approved the version to be published, and agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.
Funding The work was supported in part by NSF Industry/University Cooperative Research Center at UCSF, The University of Toledo, and The Ohio State University (www.nsfcdmi.org).
Availability of data and materials All data generated or analyzed during this study are included in this published article.

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Code availability No software application or custom code was utilized.

Conflicts of interest
The authors have no conflicts of interest to declare that are relevant to the content of this article.
Ethics approval As the study involved no patient or clinical data, no ethical approval was required.
Consent to participate As the study involved no patient or clinical data, consent to participate was not required.

Consent for publication
As the study involved no patient or clinical data, consent for publication was not required.
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