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			<titleStmt><title level='a'>Evaluating the biomechanical effects of pedicle subtraction osteotomy at different lumbar levels: a finite element investigation</title></titleStmt>
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				<publisher>Elsevier</publisher>
				<date>11/01/2024</date>
			</publicationStmt>
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				<bibl> 
					<idno type="par_id">10570281</idno>
					<idno type="doi">10.1016/j.spinee.2024.07.005</idno>
					<title level='j'>The Spine Journal</title>
<idno>1529-9430</idno>
<biblScope unit="volume">24</biblScope>
<biblScope unit="issue">11</biblScope>					

					<author>Niloufar Shekouhi</author><author>Sudharshan Tripathi</author><author>Alekos Theologis</author><author>Muzammil Mumtaz</author><author>Hassan Serhan</author><author>Robert McGuire</author><author>Vijay K Goel</author><author>Joseph M Zavatsky</author>
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			<abstract><ab><![CDATA[BACKGROUND: Pedicle subtraction osteotomy (PSO) is effective for correcting spinal malalignment but is associated with high complication rates. The biomechanical effect of different PSO levels remains unclear, and no finite element (FE) analysis has compared L2-, L3-, L4-, and L5-PSOs. PURPOSE: To assess the effects of PSO level on the spine's global range of motion, stresses on posterior instrumentation, load sharing with the anterior column, and proximal junctional stresses. STUDY DESIGN: A computational biomechanical analysis. METHODS: A validated 3D spinopelvic FE model (T10-Pelvis) was used to perform PSOs at L2, L3, L4 and L5. Each model was instrumented with a 4-rod configuration (primary rods + in-line satellite rods) from T11-Pelvis. Simulation included a 2-step analysis; (1) applying 300 N to thoracic, 400 N to lumbar, and 400 N to sacrum, and (2) applying a 7.5 Nm moment to the top endplate of the T10 vertebral body. Acetabulum surfaces were fixed in all degrees of freedom. The range of motion, spinopelvic parameters (lumbar lordosis [LL], sacral slope [SS], pelvic incidence [PI], and pelvic tilt [PT]), PSO force, and von Mises stresses were measured. All models were compared with the L3-PSO model and percentage differences were captured. RESULTS: Compared to the intact alignment: LL increased by 48%, 45%, 59%, and 56% in the L2-, L3-, L4-, and L5-PSO models; SS increased by 25%, 15%, and 11% while PT decreased by 76%, 53%, and 45% in L2-, L3-, and L4-PSOs (SS and PT approximated intact model in L5-PSO); Lumbar osteotomy did not affect the PI. Compared to L3-PSO: L2-, L4-, and L5-PSOs showed up to 32%, 34%, and 34% lower global ROM. The least T10-T11 ROM was observed in L5-PSO. The left and right SIJ ROM were approximately similar in each model. Amongst all, the L5-PSO model showed the least ROM at the SIJ. Compared to L3-PSO, the L2-, L4-, and L5-PSO models showed up to 67%, 61%, and 78% reduced stresses at the UIV, respectively. Minimum stress at UIV+ was observed in the L3-PSO FDA device/drug status: Not applicable.]]></ab></abstract>
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<div xmlns="http://www.tei-c.org/ns/1.0"><head>Introduction</head><p>Restoration of lumbopelvic harmony, pelvic tilt, and global sagittal balance are fundamental goals of sagittal spinal deformity correction. One of the most commonly used surgical strategies to restore sagittal balance is the pedicle subtraction osteotomy (PSO). In a PSO, the posterior elements, pedicles, and a V-shaped wedge of the vertebral body through the pedicles are resected, and the osteotomy is closed and stabilized by means of posterior fixation. PSOs are commonly performed at the L3 vertebra. However, according to Roussouly et al <ref type="bibr">[1,</ref><ref type="bibr">2]</ref>, the inferior segments (between L4 and S1) have a higher influence on lumbar lordosis and osteotomies in these regions can lead to a greater sagittal correction.</p><p>Although the PSO is a powerful surgical technique, it is associated with high rates of complications (proximal junctional kyphosis (PJK), implant failure, and pseudarthrosis <ref type="bibr">[3]</ref><ref type="bibr">[4]</ref><ref type="bibr">[5]</ref><ref type="bibr">[6]</ref><ref type="bibr">[7]</ref><ref type="bibr">[8]</ref><ref type="bibr">[9]</ref><ref type="bibr">[10]</ref><ref type="bibr">[11]</ref><ref type="bibr">[12]</ref>) and hence still remains challenging. PJK is a common complication following long segmental spinal fusion with reported rates ranging from 17% to 61.7% <ref type="bibr">[13]</ref><ref type="bibr">[14]</ref><ref type="bibr">[15]</ref><ref type="bibr">[16]</ref>. PJK is defined as a proximal junctional sagittal Cobb angle (between the upper instrumented vertebra (UIV) and 2 super-adjacent segments) of 10&#730;or higher <ref type="bibr">[14]</ref>. In severe cases, PJK can result from ligamentous disruption or fracture, which may require revision surgery. Excessive curvature correction <ref type="bibr">[17]</ref><ref type="bibr">[18]</ref><ref type="bibr">[19]</ref><ref type="bibr">[20]</ref>, abnormal preoperative sagittal parameters <ref type="bibr">[17,</ref><ref type="bibr">18,</ref><ref type="bibr">[21]</ref><ref type="bibr">[22]</ref><ref type="bibr">[23]</ref><ref type="bibr">[24]</ref>, lumbar and sacral fusions <ref type="bibr">[22,</ref><ref type="bibr">23,</ref><ref type="bibr">[25]</ref><ref type="bibr">[26]</ref><ref type="bibr">[27]</ref>, and the number of instrumented levels <ref type="bibr">[18,</ref><ref type="bibr">19,</ref><ref type="bibr">25,</ref><ref type="bibr">28]</ref> are reported as risk factors for PJK <ref type="bibr">[14]</ref>.</p><p>Previous PSO investigation has primarily focused on resultant changes in global sagittal alignment as well as relative sagittal lumbopelvic corrective potentials based on PSO level <ref type="bibr">[29]</ref>. However, as more evidence highlights the importance of restoring relative lumbar lordosis based on pelvic and spinal morphologies <ref type="bibr">[30]</ref>, in relation to mechanical complications, including PJK <ref type="bibr">[31]</ref>, an understanding of the effect of PSO level on proximal junctional stresses and load sharing with the anterior column is critically important to minimize the incidence of PJK and pseudarthrosis. The purpose of the current study was to assess the effect of PSO level on the spine's global range of motion, stresses on posterior instrumentation, load sharing with the anterior column, and proximal junctional stresses.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Material and methods</head><p>In this study, a previously validated osseoligamentous 3dimensional spinopelvic model (T10-pelvis) was used to develop 30&#730;PSOs at different vertebral levels at L2, L3, L4, and L5 <ref type="bibr">[32,</ref><ref type="bibr">33]</ref>. 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 Hyper-Mesh (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 Abaqus 6.14 (DassaultSystemes, 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.</p><p>The intervertebral discs 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 a hyper-elastic Mooney-Rivlin formulation. The sacroiliac joint was modeled using soft contact with exponential behavior. Material properties were adapted from literature and assigned to each component (Table <ref type="table">1</ref>) <ref type="bibr">[33]</ref>.</p><p>An extensive explanation of the L3-PSO model development can be found in the literature <ref type="bibr">[32,</ref><ref type="bibr">33]</ref>. A similar approach was utilized to develop 30&#730;PSOs at L2, L3, L4, and L5 levels (Fig. <ref type="figure">1</ref>). In all models, the anterior section was tied, and a surface-to-surface interaction (friction=0.46) was defined between the 2 resected segments at the posterior site.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Spinopelvic parameters</head><p>For intact and each PSO model, the following spinopelvic parameters were measured <ref type="bibr">[34]</ref>:</p><p>The angle between the superior endplates of L1 and S1. &#10146; L4-S1 lordosis: The angle between the superior endplates of L4 and S1. &#10146; Sacral Slope (SS): The angle between the superior endplate of S1 with the horizontal line. &#10146; Pelvic Incidence (PI): The morphological variable which is defined as the angle between the sacral perpendicular line with a line connecting the center of the femoral head and the center of the sacrum. &#10146; Pelvic Tilt (PT): The angle formed by a vertical reference line and the line from the sacral plate's midpoint to the femoral heads' center. &#10146; Lordosis distribution index (LDI) determines the magnitude of L4S1 lordosis relative to the total lordosis <ref type="bibr">[35]</ref> and was calculated as LDI &#188; 100 &#194; &#240;L4&#192;S1 lordosis&#222; &#240;L1&#192;S1 lordosis&#222; .</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Model instrumentation</head><p>The instrumentation (including polyaxial screws and rods) was designed in SolidWorks (Dassault Syst emes Solid-Works Corporation, Waltham, MA, USA). A 4-rod configuration was used for each PSO model (2 primary rods + 2 inline satellite rods). All models included instrumentation from T11 to the pelvis (Fig. <ref type="figure">1</ref>). Pelvic fixation with traditional iliac screws were connected to the primary rods via an iliac connector. The T11 and T10 segments were selected as the upper instrumented vertebral body (UIV) and upper instrumented vertebral body +1 (UIV+), respectively. All pedicles starting from T11 to the pelvis were instrumented bilaterally with titanium alloy polyaxial screws.</p><p>Screws were modeled in 2-parts (tulip + shaft) and connected with a ball and socket joint. The size and length of the pedicle screws for each model were selected under the guidance of the spine surgeons (Table <ref type="table">2</ref>). Shorter length pedicle screws were inserted in the vertebra adjacent to the osteotomy site to provide enough room for long rods to bypass the PSO site while short rods fixing the PSO. 8.5&#163;80 mm iliac screws were utilized (Table <ref type="table">2</ref>). Two primary rods were inserted from T11 to ilium, bypassing the levels adjacent to the PSO. The adjacent levels to the osteotomy site were then instrumented via 2 in-line recessed PSO satellite rods. All models included 5.5 mm Cobalt-Chromium primary and satellite rods.</p><p>To simulate polyaxial screws, 2 reference points were defined on the screw shaft and the tulip head, and the corresponding nodes were coupled to each reference point separately. Then a "Join and Cardan" connector was assigned between the shaft and tulip, which constrained the 2 components in U1, U2, and U3 motions and allowed 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). Primary and satellite rods were tied to the tulip in all models.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Loading and boundary conditions</head><p>Loading was applied in 2 steps. In step 1, 300 N was applied to the thoracic spine, 400 N to the lumbar spine, and 400 N to the sacrum using the follower load technique <ref type="bibr">[32,</ref><ref type="bibr">33]</ref>. In step 2, pure moments of 7.5 Nm were applied to the top endplate of the T10 vertebral body in all 3 anatomical directions. During the simulation, the acetabular surfaces of the pelvis were fixed in all degrees of freedom.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Data analysis</head><p>For each model, the spinopelvic parameters such as L1-S1 lordosis (LL), L4-S1 lordosis, sacral slope (SS), pelvic incidence (PI), and pelvic tilt (PT) were captured and compared with the intact alignment. Moreover, the LDI was calculated for each model and compared.</p><p>The T10-S1 and T10-T11 ranges of motion (ROM), along with both left and right sacroiliac joint ROMs (SIJ) within all instrumented PSO models, in flexion, extension, lateral bending, and rotation, were calculated. The SIJ ROM for each side was calculated using the difference between the angular displacements at the sacrum and ilium of the corresponding side. Furthermore, the maximum stress magnitude and location on the rods and PSO forces were recorded and compared. The maximum von Mises stresses on the anterior parts of T10 (UIV +) and T11 (UIV) vertebral bodies and the T10-T11 intervertebral discs were recorded and evaluated in all models. Given that L3-PSOs are commonly performed, the percentage differences in the aforementioned parameters were compared to this model.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Results</head></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Model validation</head><p>The L3-and L4-PSO models were validated to ensure that this model can predict previous experimental and biomechanical outcomes <ref type="bibr">[36]</ref><ref type="bibr">[37]</ref><ref type="bibr">[38]</ref>. However, due to the lack of available in-vitro studies on PSOs at L2 and L5, we were not able to validate these models.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>L3-PSO model validation</head><p>For the validation of this instrumented PSO model, the range of motion predictions for the L2-L4 instrumented models were compared to the experimental data Hallager et al <ref type="bibr">[39]</ref>. Different instrumentation techniques were used for this purpose including 2 rod and 4 rod techniques with different material properties for the rods (Titanium and CoCr rods). The FE model predictions for all motions (flexion, extension, lateral bending, and axial-rotation) as well as the normalized strains fell within the standard deviation (Fig. <ref type="figure">2</ref>), validating the L3-PSO model.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>L4-PSO model validation</head><p>For the validation of this instrumented PSO model, the range of motion predictions in the T12-S1 instrumented model were compared to the experimental data of La Barbera et al <ref type="bibr">[36]</ref>. The FE models predictions for all motions fell within the standard deviation (Fig. <ref type="figure">3</ref>), validating the L4-PSO model.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Effect of PSO level on spinopelvic parameters</head><p>Performing the osteotomy at the L4 and L5 vertebra led to the greatest lumbar lordosis corrections. Compared to the intact alignment (LL=49&#730;, Fig. <ref type="figure">4</ref>), lumbar lordosis increased by 48%, 45%, 59%, and 56% in the L2-, L3-, L4and L5-PSO models, respectively. Compared with the intact model, L4-S1 lordosis increased by 93%, 101%, in L4 and L5 PSOs while reduced by 13% and 35% in the L2 and L3 PSOs (Fig. <ref type="figure">4</ref>).</p><p>Performing an osteotomy increased the sacral slope (SS) by 25%, 15%, and 11%, in L2 L3, and L4 PSOs, respectively. The pelvic incidence (PI) did not change as a result of lumbar osteotomy while pelvic tilt reduced by 76%, 53%, and 45% in L2, L3, and L4 PSOs. The L5 PSO showed similar sacral slope and pelvic tilt as the intact alignment. Compared to the intact model LDI decreased in the L2 and L3 PSOs (37% and 28%) while increased in the L4 and L5 PSOs (76% and 81%), compared to the intact model (63%).  Screw dimension for each model was selected under the guidance of the spine surgeons. Adjacent to the osteotomy site, screw with a shorter shaft were inserted. The iliac screws were sized 8.5 &#163; 80 mm.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>T10-S1 range of motion (global ROM)</head><p>The L3 PSO showed the highest global ROM in extension and axial rotation. Compared to this model, L2, L4, and L5 showed 19%, 22%, and 20% lower ROM in extension, respectively. All models showed approximately similar ROM in flexion (differences below 2%). Compared to the L3 PSO, L4 PSO increased ROM in lateral bending (by up to 7%) while L5 PSO reduced the lateral bending ROM to the same extent. Compared to the L3 PSO, the L2, L4, and L5 PSOs reduced ROM in axial rotation by up to 32%, 34%, and 34%, respectively (Fig. <ref type="figure">5</ref>).</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Sacroiliac joint range of motion (SIJ ROM)</head><p>All models showed a small range of motion at the sacroiliac joint. The left and right SIJ ROM were approximately similar in each model.</p><p>Compared to the L3-PSO, L2-PSO model showed up to 22% and 24% lower ROM in flexion and extension while up to 97% higher ROM in lateral bending and up to 144% higher ROM in axial rotation.</p><p>Similar pattern was observed in the L4-PSO model. Compared to the L3-PSO model, ROM decreased in flexion and extension (by up to 24%) while increased in lateral Fig. <ref type="figure">3</ref>. Validation of the L4-PSO model instrumented with two rods with the in-vitro analysis of La Barbera et al. <ref type="bibr">[36]</ref>. The FE model predictions for range of motion fell within the standard deviation. Fig. <ref type="figure">4</ref>. The percentage difference of spinopelvic parameters of the PSO models with respect to the intact alignment. Compared to the intact alignment: LL increased by 48%, 45%, 59%, and 56% in the L2-, L3-, L4-, and L5-PSO models; SS increased by 25%, 15%, and 11% while PT decreased by 76%, 53%, and 45% in L2-, L3-, and L4-PSOs (SS and PT approximated intact model in L5-PSO); Lumbar osteotomy did not affect the PI.  bending and axial rotation (by up to 67% and 182% in lateral bending and left rotation). Following an L4-PSO, right SIJ ROM was reduced by 18%, compared with the L3-PSO model.</p><p>Amongst all, the L5-PSO model showed the least ROM at the SIJ. Compared to the L3-PSO model, performing osteotomy at L5 reduced the ROM at SIJ by up to 19% in flexion, 23% in extension, and up to 73% in lateral bending. Following L5-PSO, SIJ Rom was increased by up to 47% in left rotation while was reduced by 29% in right rotation.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Adjacent segment range of motion (T10-T11 ROM)</head><p>Compared to the L3-PSO model, the T10-T11 ROMs reduced by 21% in extension and up to 28% in axial rotation in L2-PSO model. In this model, the T10-T11 ROM did not change significantly in lateral bending (within 5% difference, Fig. <ref type="figure">5</ref>).</p><p>Compared to L3-PSO model, performing osteotomy at L4 increased the T10-T11 ROM in lateral bending by 9% while reduced the extension and axial rotation by 24% and up to 21%, respectively (Fig. <ref type="figure">5</ref>).</p><p>The L5-PSO showed the least T10-T11 ROM. Compared to L3-PSO, 22%, up to 15% and up to 35% lesser ROM was observed in this model in extension, lateral bending, and axial rotation, respectively (Fig. <ref type="figure">5</ref>).</p><p>All models showed approximately similar ROM in flexion as the L3-PSO model (within 5% difference, Fig. <ref type="figure">5</ref>).</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>von mises stresses on UIV, UIV &#167;1 and disc</head><p>The least stresses at UIV were observed in the L5-PSO model. The L2-PSO and L5-PSO models showed 11%-67% and 28%-78% lesser von Mises stresses than the L3-PSO model.</p><p>Compared to the L3-PSO, the L4-PSO model showed lower stresses in all ROMs (up to 61%) except left bending. Under left bending this model increased the von Mises stresses slightly (by 7%) compared to the L3-PSO.</p><p>In all models, higher von Mises stresses were observed at the T10 vertebrae (UIV+) compared to the UIV (T11) (Fig. <ref type="figure">5</ref>). Compared to the L3-PSO, L2, L4, and L5-PSOs showed 26%, 10%, and 24% higher stresses at UIV+ in extension, respectively. In flexion, L2-PSO reduced the stresses at UIV+, while L4 and L5-PSOs showed approximately similar stresses compared to the L3-PSO model (within 5% difference).</p><p>In lateral bending, all models showed approximately similar stresses at UIV+ compared to the L3-PSO model. Under axial rotation, L4-PSO increased the stresses at UIV+ by up to 9% while all other models showed approximately similar stresses as the L3-PSO model (within 5% difference).</p><p>Compared to L3-PSO, the L2-PSO model, reduced the stresses at T10-T11 annulus fibrosus (AF) by 13% in extension and up to 33% in axial rotation. However, in flexion and lateral bending, this model showed approximately similar AF stresses as the L3-PSO.</p><p>Compared to the L3-PSO, the L4-PSO showed 24% and up to 8% lesser stresses in extension, and lateral bending, respectively. However, this model showed 9% and up to 51% higher AF stresses than the L3-PSO, in flexion and axial rotation, respectively.</p><p>Compared to the L3-PSO, the L5-PSO model showed 11%, and up to 46% lesser AF stresses in extension and axial rotation, respectively. Following L5-PSO, AF stresses were approximately similar to the L3-PSO model.</p><p>FE predictions showed approximately similar T10-T11intradiscal pressure under flexion and extension in all models (within 5% difference). However, the L2-and L4-PSO models reduced the pressure by up to 23% and 37% in lateral bending, compared with the L3-PSO model. In axial rotation, the L2-PSO model showed up to 13% higher intradiscal pressure, while the percentage difference was not significant in the other 2 models compared to the L3-PSO.The L5-PSO model showed similar intradiscal pressure as the L3-PSO model in all motions (Fig. <ref type="figure">5</ref>).</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>PSO force</head><p>The maximum PSO force was observed in flexion for all models (Table <ref type="table">3</ref>). The L3-PSO model showed the maximum force across the osteotomy site. Compared to this model, the L2-PSO showed approximately similar PSO force with the percentage difference within 5%. However, the L4-PSO and L5-PSO models showed up to 13% and 11% lesser PSO force than the L3-PSO model (Table <ref type="table">3</ref>).</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Stresses on primary and satellite rods</head><p>Compared to the L3-PSO, the L2-PSO model showed up to 15% lower stresses on primary rods. The L4-PSO reduced the stresses on primary rods by 26% in extension, 20% in right bending and 11% in left rotation, compared to the L3-PSO model. However, this model increased the stresses by 16%, 21%, and 14% in flexion, left bending, and right rotation, respectively.</p><p>Compared to the L3-PSO model, the L5-PSO showed up to 47% lesser stresses on primary rods.</p><p>The L3-PSO model showed the highest stresses on satellite rods in all motions (Fig. <ref type="figure">6</ref>). Compared to this model,</p><p>Table 3 Force across the osteotomy site in models with PSOs at L2, L3, L4, and L5 vertebral bodies L2-PSO L3-PSO L4-PSO L5-PSO Extension 249.2 256 231.0 228.8 Flexion 344.7 354.2 309.0 341.1 Left Bending 292.1 301.4 269.7 279.8 Right Bending 292.7 300.2 275.0 281.6 Left Rotation 291.3 292 268.3 277.7 Right Rotation 290.3 295.4 270.9 278.1</p><p>In each model the highest PSO force was obtained in flexion. The L2and L3-PSO models showed the maximum PSO force. the L2-, L4-, and L5-PSO models showed up to 33%, 75%, and 43% lesser stresses on satellite rods, respectively. Each model demonstrated different critical stress locations, which was secondary to the difference in the rod contour in each model.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Discussion</head><p>PSO is a powerful surgical technique often utilized to correct rigid sagittal and coronal spinal deformities. However, PSOs are associated with high rates of complications, including proximal junctional kyphosis, rod / implant failure, and pseudarthrosis <ref type="bibr">[3]</ref><ref type="bibr">[4]</ref><ref type="bibr">[5]</ref><ref type="bibr">[6]</ref><ref type="bibr">[7]</ref><ref type="bibr">[8]</ref><ref type="bibr">[9]</ref><ref type="bibr">[10]</ref><ref type="bibr">[11]</ref><ref type="bibr">[12]</ref>. Thus, PSOs remain challenging, and it is essential to understand the global biomechanics, rod and proximal junctional stresses, to reduce the risk of postoperative complications that can often require revision surgery.</p><p>There are key bony, neurologic, and vascular anatomical considerations for selecting the osteotomy level. Clinically, a patient's individual spinal deformity usually dictates where corrective osteotomies are performed. PSOs are often performed at the apex of the spinal deformity, or the caudal lumbar vertebra (L3-S1) <ref type="bibr">[40]</ref>. To optimize sagittal realignment and pelvic parameters more caudal PSOs (L3, L4) are often utilized. The proximity of the more sensitive L5 nerve roots may influence the selection of a L3-PSO over a L4-PSO <ref type="bibr">[40]</ref>. Data on more distal L5-and sacral PSOs is limited and may be secondary to the challenges associated with these osteotomies. <ref type="bibr">[41,</ref><ref type="bibr">42]</ref> The deeper location of the L5 and S1 vertebra within the pelvis, proximity of the L5 nerve root and anterior vasculature to the osteotomy, and limited distal fixation points may increase the risk of periand postoperative complications. <ref type="bibr">[43]</ref> Recent clinical studies have suggested that using distal lumbar (L4, L5) and sacral PSOs can optimize lumbar lordosis, sagittal realignment, and pelvic parameters, decreasing the risk of PJK <ref type="bibr">[2,</ref><ref type="bibr">41,</ref><ref type="bibr">42,</ref><ref type="bibr">[44]</ref><ref type="bibr">[45]</ref><ref type="bibr">[46]</ref><ref type="bibr">[47]</ref><ref type="bibr">[48]</ref>. More distal PSOs (L4, L5, and S1) have the ability for greater sagittal plane realignment and improvement of pelvic parameters but may increase the risk of pre-and postoperative complications and warrant further investigation.</p><p>We hypothesized that the location of the PSO can alter spinal alignment, and local and global stresses, which can affect the surgical outcomes. Hence, this study attempts to investigate the effect of PSO level on the spine's global (T10-S1), proximal junction (T10-T11), and distal sacroiliac joint (SIJ) ROMs, stresses on the posterior instrumentation, load sharing with the anterior column, and proximal junctional stresses (UIV, UIV+1, and discs).</p><p>Given the fact that the L3-PSO is considered the most common osteotomy level, we compared different parameters across each motion with the FE predictions of this L3-PSO model (Fig. <ref type="figure">5</ref>). Compared with a L3-PSO, the data demonstrates that performing an osteotomy at the L5 segment provided the greatest rigidity, and consequently the least global ROM. This can be explained by the fact that satellite rods in a L5-PSO were attached to L4 and S1, resulting in 5 cranial segments that were anchored to the primary rods (T11, T12, L1, L2, and L3). However, in the models with cranial PSOs, such as a L3-PSO, the number of cranial vertebral segments fixed to the primary rods were reduced. Thus, the L5-PSO model demonstrated greater rigidity compared to the L3-PSO model. The L2-and L4-PSO models showed similar percentage differences of global ROM from the L3-PSO model (Fig. <ref type="figure">5</ref>).</p><p>Although a 30&#730;correction was uniformly performed in each model, performing an osteotomy at different vertebral levels changed the alignment of the spine and consequently affected biomechanics. Previous studies reveal two-thirds of the total lumbar lordosis is obtained at the lower lumbar segments <ref type="bibr">[1,</ref><ref type="bibr">30]</ref>, and performing PSOs at more caudal levels led to greater lordosis correction. Our FE predictions showed that the L4 and L5-PSO models led to the highest L1S1 lordosis corrections. Compared to the intact model, lumbar lordosis increased by 48%, 45%, 59%, and 56% in the L2-, L3-, L4-and L5-PSO models, respectively. Bourghli A, et al reported similar corresponding pattern in lumbar lordosis following L4-and L5-PSOs <ref type="bibr">[2]</ref>. Relative to the preoperative values, the L4-S1 lordosis was increased following L4 and L5-PSOs while reduced in L2 and L3-PSOs. This reduction was previously observed in the study of Pizones et al <ref type="bibr">[49]</ref>.</p><p>Additionally, PSOs at L2-, L3-, L4-, and L5 changed the sacral slope by 25%, 15%, 11%, and 0%, respectively.</p><p>In agreement with previous data, pelvic incidence did not change as a result of lumbar osteotomy while pelvic tilt was also affected by PSO level <ref type="bibr">[50]</ref>.</p><p>As indicated by Roussouly et al <ref type="bibr">[1]</ref>, lumbar lordosis can be divided into the lower and upper arcs (the upper arc extends from the apex to the inflexion point, while the lower arc extends from S1 to the apex). We observed that performing osteotomies at caudal segments lead to a larger lower arc (L4S1 lordosis). Moreover, the lordosis distribution index (LDI) calculated in each model showed that for intact, L4-, and L5-PSOs, LDI ranged from 63 to 81, while the L2-, and L3-PSOs &lt;50. Previous data reveals a greater risk for revision surgery in cases where the LDI &lt;50 <ref type="bibr">[35]</ref>. Thus, more caudal PSOs (L4 and L5) recreates a more anatomic lordosis distribution compared to more cranial PSOs (L2 and L3).</p><p>Our FE data revealed that the least SIJ ROM was observed in 2 models, the L5-PSO under flexion, extension, and lateral bending, and the L3-PSO under axial rotation. Ushirozako et al <ref type="bibr">[51]</ref> reported screw loosening in 25% of L5-PSO cases, which was significantly higher than patients undergoing an L4-PSO (8%) and L1-L3 PSOs (15%). The stiffer L5-PSO constructs may not allow for micromotion, thereby increasing the risk of screw loosening. The utilization of bilateral iliac screw fixation may mitigate the risk of screw loosening in L5-PSOs <ref type="bibr">[51]</ref>.</p><p>The development of proximal junctional kyphosis (PJK) is a common postoperative complication in adult spinal deformity (ASD) patients <ref type="bibr">[48,</ref><ref type="bibr">52]</ref>. In patients with long instrumented segmental fusions, the increased stresses at the proximal junction, can increase the risk of PJK, which may lead to proximal junctional failure (PJF) and resultant revision surgery. Previous data demonstrates that larger lumbar lordosis corrections can increase the risk of PJK <ref type="bibr">[50]</ref>, while proper rod contouring and UIV selection can be beneficial to mitigate the risk of PJK <ref type="bibr">[53]</ref>. Our FE data, reveals that the L3-and L4-PSOs demonstrates higher stresses at UIV and UIV+ compared to the L5-PSO model. Ushirozako et al <ref type="bibr">[51]</ref> demonstrated clinical results validating our FE data, in that patients undergoing an L5-PSO resulted in the lowest incidence of PJF (8.3%), compared to L4-(16%), and L1-, L2-, and L3-PSOs (20%).</p><p>Additionally, the low rate of PJK in patients with an L5-PSO could also be explained by the lowest T10-T11 ROM compared to other PSO models (Fig. <ref type="figure">5</ref>). Compared to the L3-PSO, the L2-and L4-PSOs demonstrated an increased T10-T11 ROM under lateral bending. Reducing the ROM, particularly in flexion, can decrease the load and stresses applied to the vertebral bodies, thereby reducing the risk of PJK and PJF <ref type="bibr">[2,</ref><ref type="bibr">54]</ref>. Biomechanically, caudal PSOs may be more beneficial, but bony, soft tissue, and technical considerations may limit their utility.</p><p>Rod fracture is another common complication associated with PSOs, which has been reported as high as 22% <ref type="bibr">[55]</ref>. Our data reveals that the L5-PSO model demonstrates the least von Mises stresses on the primary rods in all motions (Fig. <ref type="figure">5</ref>). These results were consistent with the retrospective study of Ushirozako et al <ref type="bibr">[51]</ref>, which showed lower incidences of rod fracture in patients with L5-PSOs, compared to L4-and L1-L3 (25% vs 56% and 30%, respectively).</p><p>The FE data for the L2-and L3-PSO models demonstrated the highest force across the osteotomy site, while the L4-and L5-PSOs revealed the least force. The decreased load applied to the anterior vertebral body in L5-PSOs, along with a reduction in distal construct length as compared to L1-L4 PSOs can increase the risk of pseudarthrosis <ref type="bibr">[49]</ref>. However, further clinical analysis is essential to validate these data.</p><p>The results of this study should be considered in the context of its limitations. These include using generic implants and neglecting the residual stresses produced as a result of rod contouring and screw/rod tightening.</p><p>Moreover, due to the lack of cadaveric validation data for L2 and L5 and given L5 0 s unique structural differences compared to other spinal levels, PSOs at this level might exhibit the most significant deviations from biomechanical/ cadaver models. Thus, the results of this study should be considered within their limitations, and further clinical investigations are necessary to fully understand the complex biomechanical environment produced by caudal osteotomies.</p><p>All PSO models were reconstructed using an intact alignment, hence relatively large LL and SS were observed in all models. The spinopelvic parameters from the current study represent the values right after the surgery and it does not consider the effect of fusion or dynamic loading at the sacroiliac joint. The estimated 30&#730;correction is an idealized maximum value and may not be clinically achievable due to the large amount of bone resected. This represents a worst-case scenario, so clinical results may differ from the FEA outcomes.</p><p>Moreover, fixing the acetabulum surfaces in all degrees of freedom affects the range of motion at the sacroiliac joint due to its kinematics. Future studies should be focused on developing a spinopelvic model with hip joint and investigate how shear forces at the sacroiliac joints affect the spine's biomechanics following a lumbar PSO.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Conclusion</head><p>Our FE data indicates that the L5-PSO resulted in the greatest lumbar lordosis, while showing the least global, SIJ, and proximal junction (T10-T11) ROMs and stresses on the primary rods, suggesting potential mechanical benefits in reducing the risk of rod breakage. However, L4-and L5-PSOs result in the least force across the osteotomy site, which may increase the risk of pseudarthrosis. Additionally, the technical considerations; the bony, L5 nerve, and anterior vascular anatomy; and the limited distal fixation points should all be considered when a caudal PSO is being contemplated. These findings provide biomechanical insights that may inform surgical planning, though further clinical investigation is essential to determine the optimal PSO level and validate these results.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Declaration of competing interest</head><p>One or more of the authors declare financial or professional relationships on ICMJE-TSJ disclosure forms. </p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>CRediT authorship contribution statement</head></div><note xmlns="http://www.tei-c.org/ns/1.0" place="foot" xml:id="foot_0"><p>N. Shekouhi et al. / The Spine Journal 24 (2024) 2191-2203</p></note>
			<note xmlns="http://www.tei-c.org/ns/1.0" place="foot" xml:id="foot_1"><p>N. Shekouhi et al. / The Spine Journal 24 (2024) 2191-2203</p></note>
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