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OPEN

Load‑sharing biomechanics
of lumbar fixation and fusion
with pedicle subtraction osteotomy
Luigi La Barbera1*, Hans‑Joachim Wilke2, Maria Luisa Ruspi3, Marco Palanca3,
Christian Liebsch2, Andrea Luca4, Marco Brayda‑Bruno4, Fabio Galbusera5 & Luca Cristofolini3
Pedicle subtraction osteotomy (PSO) is an invasive surgical technique allowing the restoration of awell-balanced sagittal profile, however, the risks of pseudarthrosis and instrumentation breakage
are still high. Literature studied primary stability and posterior instrumentation loads, neglecting theload shared by the anterior column, which is fundamental to promote fusion early after surgery. The
study aimed at quantifying the load-sharing occurring after PSO procedure across the ventral spinal
structures and the posterior instrumentation, as affected by simple bilateral fixation alone, withinterbody cages adjacent to PSO level and supplementary accessory rods. Lumbar spine segments
were loaded in vitro under flexion–extension, lateral bending, and torsion using an establishedspine tester. Digital image correlation (DIC) and strain-gauge (SG) analyses measured, respectively,
the full-field strain distribution on the ventral surface of the spine and the local strain on posterior
primary rods. Ventral strains considerably decreased following PSO and instrumentation, confirming
the effectiveness of posterior load-sharing. Supplemental accessory rods considerably reduced theposterior rod strains only with interbody cages, but the ventral strains were unaffected: this indicatesthat the load transfer across the osteotomy could be promoted, thus explaining the higher fusion ratewith decreased rod fracture risk reported in clinical literature.
Pedicle subtraction osteotomy (PSO) is a challenging surgical technique performed through a posterior approach,resecting major parts of the vertebral body (VB), pedicles, and bony structures to restore a well-balanced sagittal­profile1. Posterior fixation with pedicle screws and spinal rods is always required to stabilize the spine and toachieve long-term fusion. PSO is also accompanied by a high rate of post-operative complications mainly related
to rod fracture (16–39%) and malunion or pseudarthrosis (12–31%) at the treated l­ evel2–9.
The recent literature contributed in better understanding of the basic biomechanics behind PSO fixation.
Clinical studies reported lower pseudarthrosis and implant failure rates with multi-rod constructs and interbody cages i­ mplantation2–5,10. Previous in vitro studies demonstrated the effectiveness of accessory and satellite
rods supplemented with adjacent cages in providing adequate motion restriction or primary ­stability11–17, while
reducing the strains on the spinal ­rods11–13. Computational studies based on finite element analysis also reported
similar ­findings18,19.
The past literature did not address how the load are transferred through the anterior column. Well-establishedintradiscal pressure (IDP) measurements have often been used as an index of the loads transferred through theanterior column of intact and instrumented spine segments, following a destabilization of one or more functional
spine units (FSUs) due to damage of the soft tissues (e.g. nucleotomy, ligaments resections), bony structures (e.g.
VB fracture) or both (e.g. laminectomy)20–22, however neglecting the biomechanical contribution of the remaining
bony structures and ligaments. Other studies relied on strain gauges (SG) to investigate how the cortical shell of
the vertebra is shielded by posterior ­instrumentation23, thus neglecting the surrounding soft tissues and providing only pointwise measurement on bone. The load transfer between the column and the posterior fixation is ofgreat interest in the setting of PSO fixation and fusion, where the integrity of the anterior longitudinal ligament(ALL) and the anterior “bony bridge” is preserved to intraoperatively guide osteotomy closure in order to postoperatively stabilize the anterior spine and to promote fusion early after surgery, but the current measurements
1

Laboratory of Biological Structure Mechanics, Department of Chemistry, Materials and Chemical Engineering“G. Natta”, Politecnico Di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy. 2Institute of Orthopaedic
Research and Biomechanics, Trauma Research Center Ulm, Ulm University, Ulm, Germany. 3Department ofIndustrial Engineering, School of Engineering and Architecture, Alma Mater Studiorum, Università Di Bologna,
Bologna, Italy. 4Department of Spine Surgery III, IRCCS Istituto Ortopedico Galeazzi, Milan, Italy. 5IRCCS Istituto
Ortopedico Galeazzi, Milan, Italy. *email: luigi.labarbera@polimi.it
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Height (cm)Weight (kg)

BMD (mg/cm )Intervertebral
Lumbar lordosis disc­degeneration29(°)

Specimen

Segment

Sex

Age at death(years)#1

T11-S1

M

66

183

141

82.5 ± 2.3

39Grade 1 (milddegeneration)#2

T11-S1

M

62

178

164

94.4 ± 3.6

39Grade 2 (moderate degeneration)#3

T11-S1

F

60

163

114

122.6 ± 7.4

38Grade 2 (moderate degeneration)

3

Table 1.  Specimen data.

Figure 1.  Sagittal X-ray scans of a representative specimen reporting the three steps of instrumentation.
are not able to fully appreciate this process. In this context, an experimental approach based on Digital Image
Correlation (DIC) could offer the potential to measure the superficial full-field strain distribution on hard andsoft-tissue, both on the treated vertebral body (VB), the adjacent intervertebral disc (IVD), as well as the ligamentous structures. The potential of such an approach has been recently demonstrated for intact ­porcine24,25
and ­human26,27 poly-segmental spine specimens.
No prior study ever investigated the strain distribution on the anterior column of an instrumented spine
following PSO, nor how the strain is related to the usage of posterior fixation and anterior interbody fusion.
We hypothesized that the load-sharing mechanism, well-accepted for an instrumented spine ­segment28, may
play a decisive role also in the setting of PSO instrumentation: the loads on the anterior column may promotebone remodelling and fusion of the osteotomy rims, while the loads shielded by the posterior instrumentation
may be responsible of posterior rod breakage due to cyclic loads. Therefore, the aim of the current study was toquantify how the load supported by the ventral spinal structures and the posterior instrumentation is affectedboth by the number of rods and the implantation of anterior supports adjacent to PSO. In particular, the present
study focused on the variations in biomechanics due to alternative instrumentation techniques (simple bilateral
fixation, additional interbody cage implantation, and usage of supplementary accessory rods) following PSO
through in vitro flexibility tests integrated with DIC strain measurement on the ventral spine and using strain
gauge analysis on the posterior primary rods.

Material and methods

Specimens. Three fresh-frozen human spine specimens were collected via an ethically approved donation
program (Science Care Inc., Phoenix, AZ). The study was approved by the Institutional Review Board (Ethikkommission) of Ulm University (Document of approval Nr. 307/17).
All specimens underwent sagittal X-rays (Faxitron 43,805 N, Hewlett Packard, Palo Alto, USA) and clinicalCT-scans (Philips Brilliance 64, Philips Healthcare, Cleveland, USA) to assess the bone mineral density (BMD)
and to exclude any defect, tumour or severe degeneration (Table 1). Specimens, stored at − 20 °C, were thawed
at 6 °C for about 10 h prior to preparation, including muscle and fat tissue removal, and testing, both performed
within 20 h to avoid degradation in terms of mechanical response. Half of the cranial and the caudal vertebrae
were embedded in bone cement (Technovit 3040, Heraeus Kulzer, Werheim, Germany).
Surgical constructs. The intact specimens underwent the following three steps of instrumentation (Fig. 1):• “PSO-2”: the PSO (Fig. 1) was performed at L4, setting a target lordosis of 60°, followed by bilateral fixation
with pedicle screws (Expedium polyaxial screw system 5.5–6.5 × 40–45 mm, DePuy Synthes, Raynham, MA,
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USA; CD Horizon Legacy 5.5–6.5 × 40-45 mm, Medtronic Sofamor Danek, Minneapolis, MN, USA) and5.5 mm CoCr spinal rods (Medtronic, Minneapolis, MN, USA) from L2 to S1;• “PSO-2 + Cages”: two 10° XLIF cages (8/10 × 22x55 mm, NuVasive, San Diego, CA) were introduced adjacentto PSO level following lateral excision of L3-L4 and L4-L5 IVDs. The accurate preparation of the disc space,which was best fitted with the appropriate cage size ensured a wide footprint on the outer margins of theendplates;• “PSO-4 + Cages”: the construct was instrumented with a pair of supplementary accessory rods fixed withdominos (Medtronic, Minneapolis, MN, USA) to the primary ones.
The two experienced surgeons participating in the study (MBB, AL) took care of specimens’ preparation andimplants’ selection according to their routine surgical practice. Each instrumentation step was followed by abiomechanical test as described below.

Flexibility tests.

Quasi-static loading was applied using a well-established spine t­ester30, equipped withthree stepper motors (Isel 3450, Isert-electronic, Eiterfeld, Germany) and a 6-DOF load cell (FT1500/40, Schunk
GmbH &Co.KG, Lauffen/Neckar, Germany). The caudal end of the specimen was fixed to the testing apparatus,
while the cranial end was loaded for 3.5 cycles under pure bending moments up to ± 7.5 Nm in flexion/extension (FE), right/left lateral bending (LB), and right/left (or clockwise/counter-clockwise) axial torsion (AT), at aconstant angular velocity (1.0°/s in FE and LB, 0.5°/s in AT). To avoid viscoelastic effects, the third loading cycle
served for data ­analysis31.
For motion analysis, three reflective markers were screwed on each vertebra. The kinematics of each vertebra was captured using a motion tracking device based on six Vicon MX13 cameras (Vicon Motion Systems
Ltd., Oxford, UK). The error on angle measurement was < 0.1°32. The kinematics of each functional spine unit
was matched with the moment data to determine the resulting moment–angle curve and to calculate the local(L3–L5) range of motion (RoM) and neutral zone (NZ) using a script in MATLAB R2014b (MathWorks, Natick,
MA, USA).

DIC on the ventral spine. To measure the full-field strain distribution with the DIC on the ventral aspectof the spine, flexibility tests were repeated. The DIC system (Q400, Dantec Dynamics, Denmark) based on two 5
Mpixel cameras (2440 × 2050, 8-bit, black-and-white) with high-quality metrology standard 17 mm lens (Xenoplan, Schneider-Kreuznach, Germany; 35 mm equivalent focal length of 65 mm), allowing to acquire images ofthe specimens through a stereoscopic vision.
The specimens were placed at a distance of 540 mm from the cameras, which were vertically aligned to include
L4 vertebra and the adjacent IVDs (L3–L4 and L4–L5) within the region of interest (ROI). In this configuration, the field of view was of about 120–160 mm (depending on the specific specimen), resulting in a pixel sizeof about 0.08 mm, and a depth of field of 70 mm with the aperture adopted (f/22). ROI images were acquired
at five frames per second. Lighting of the specimen was carried out with a directional custom system of LEDs
(10,000 lm in total).
To allow stereoscopic reconstruction and to minimize the distortion of the lenses, a calibration was performed
before each test using a calibration target (Al4-BMB-9 × 9, Dantec Dynamics). Proprietary software Istra 4D(v4.3.1, Dantec Dynamics, Denmark) was used to measure the 3D displacement field and to calculate the strains.
The maximum (ε1) and minimum (ε2) engineering principal strains and their direction were computed keeping
consistent software parameters (facet size: 39–59 pixels; grid spacing: 4 pixels; contour smoothing: kernel size
5 × 5), obtained by former validation and o­ ptimization27,33,34.
To estimate the measurement uncertainties, a couple of images for each specimen in the unloaded condition
were taken before each test. The systematic and random errors were evaluated in terms of mean and standard
deviation of the components of strain over the entire ROI.
The full-field strains were computed by the DIC during all cycles, considering only the third one fordata ­analysis31. For a qualitative analysis, the strain maps, from L4 VB to L4-L5 IVD, were reported for eachloading mode (F/E, right/left LB, right/left AT) and for each surgery step (Intact, “PSO-2”, “PSO-2 + Cages”,“PSO-4 + Cages”) at maximum and minimum load.
Quantitative analysis was performed at full load using a MATLAB script (R2019b, MathWorks, Natick, USA),extracting the median strain value on specific sub-regions of interest (sub-ROIs, Fig. 2), then normalized withrespect to “Intact” condition. Being the load symmetric in flexion–extension on both sides of the specimen, one
sub-ROI in front of L4 vertebra and another on L4–L5 IVD were considered, resulting in 3 median strain values(one per specimen) for each loading condition. Being the load asymmetric in lateral bending and axial torsion,
to discriminate the difference in strain distribution arising on each side of the specimen, the sub-ROIs were
furtherly divided in two symmetrical regions, resulting in 6 median strain values for each loading condition.

Strain gauge analysis on primary rods. During the flexibility tests, the primary rods at PSO level wereposteriorly instrumented with rectangular strain gauge (SGs) rosettes (KFG-2-120-D17-11L1M2S; Kyowa
Electronic Instruments Co. Ltd, Tokyo, Japan) on the most posterior part of the ­rods11,12,35,36. Compensation ofthermal effects was achieved connecting each SG to a dummy compensator in a half-bridge configuration to a
MX840B (HBM, Darmstadt, Germany) amplifier. Strain signals were zeroed before testing and then sampled at
10 Hz. The strains on each rosette were combined to calculate the maximum (tensile) and minimum (compressive) principal strains on all loading cycles in every motion direction for each rod, considering only the third one
for data analysis. Primary rod strains collected on both SG rosettes were considered as independent, resulting in

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Figure 2.  Identification of sub-regions of interest (sub-ROIs) used for median strain values extraction ona representative specimen (Specimen #2, anterior view) and schematic drawing of corresponding spinal
structures. One unique sub-ROI was used in flexion–extension (left) in correspondence of the L4 VB (PSO
level) and another of the L4-L5 IVD, while two sub-ROIs were used in lateral bending and torsion (right).
The DIC strain maps have been obtained using the proprietary software Istra 4D (v4.3.1, Dantec Dynamics,
Denmark; URL: https​://www.dante​cdyna​mics.com/).

IntactFlexion/extension

Lateral Bending

RoM (°)NZ (°)RoM (°)NZ (°)RoM (°)

Axial Torsion
NZ (°)

12.0 [9.7; 14.5]

3.7 [1.9; 5.5]

12.8 [12.4; 13.6]

4.4 [3.7; 5.3]

7.8 [5.4; 8.5]

0.8 [0.8; 1.8]

PSO-2

0.5 [0.0; 0.6]

0.0 [− 0.1; 0.1]

− 0.1 [− 0.3; 0.0]

0.0 [0.0; 0.0]

1.5 [1.4; 1.7]

0.1 [0.1; 0.1]

PSO-2 + Cages

0.3 [− 0.5; 0.3]

0.1 [0.1; 0.1]

0.0 [0.0; 0.0]

0.0 [0.0; 0.1]

1.5 [1.5; 1.5]

0.2 [0.0; 0.2]

PSO-4 + Cages

0.2 [− 0.4; 0.4]

− 0.1 [0.0; − 0.1]

0.0 [0.0; 0.0]

0.0 [0.0; 0.1]

1.4 [1.2; 1.4]

0.1 [0.1; 0.2]

Table 2.  Median [min; max] local (L3–L5) range of motion (RoM) and neutral zone (NZ) values for each
instrumentation step. Data for each specimen provided as Supplementary Table 1.

2 values per specimen for each loading condition either at maximum and minimum load. Data were normalized
to “PSO-2” condition. Only tensile values, considered to be more critical, will be discussed herein.

Data analysis and statistics. Statistical differences on strain variance due to each instrumentation step(“PSO-2”, “PSO-2 + Cages”, “PSO-4 + Cages”), were calculated in Statistica (v13, TIBCO software Inc, Tulsa, OK)
using a non-parametric Kruskal–Wallis test and Dunn post-hoc correction of the significance level p* = 2p/(K(K − 1), with K = number of multiple comparisons and p = 0.05.
To discriminate asymmetric loading conditions, strain data were grouped as “ipsilateral”, with the load
directed on the same side where the sub-ROI and the SG rosette were located (e.g. left sub-ROIs and left primary rod are ipsilateral in left LB), and “contralateral”, with the load directed on the opposite side compared towhere the sub-ROI and the SG rosette were located (e.g. right sub-ROIs and right primary rod are contralateralin left AT).

Results

Flexibility tests. The RoM was consistent for all intact specimens with higher values in flexion–extension and lateral bending compared to torsion (Table 2, Supplementary Table 1). Following PSO and bilateral
instrumentation (“PSO-2”), the RoM approached the error of measurement (0.1°) without relevant differencescompared to cages implantation (“PSO-2 + Cages”) and addition of supplementary rods (“PSO-4 + Cages”) bothin flexion/extension and lateral bending (below 4% of the intact condition), while torsional values were relatively
higher (about 20% of intact). The neutral zone (NZ) followed the same qualitative trend of RoM, with lower
initial values (Table 2, Supplementary Table 1).
General trends—Strain distribution on the ventral spine and on primary rods. The systematicand random errors over the entire ROI were, respectively, lower than 20 and 60 µstrains.
The spine segments demonstrated highly inhomogeneous ventral strain distribution in the intact condition, with lower values on L4 than on the L4-L5 IVD (Figs. 3, 5, 7, strain maps of every specimen provided as
Supplementary Figures, strain data provided as Supplementary Table 2). Following PSO, a general decrease inventral strains was noticed compared to the intact condition in all loading directions, while lower changes wereobserved among PSO configurations.

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Figure 3.  Flexion (a) and extension (b): tensile (ε1) and compressive (ε2) strain maps measured on the “Intact”
condition and following PSO at L4 and posterior instrumentation with 2 primary-rods (“PSO-2”), with 2
rods and supplementary intervertebral cages (“PSO-2 + Cages”), and with supplementary accessory rods andintervertebral cages (“PSO-4 + Cages”). A picture of the specimen with the correlated areas are reported on theleft, indicating the treated level (L4) and the caudal IVD. A representative specimen (#2) is shown here (strain
maps for every specimen provided as Supplementary Figures). The DIC strain maps have been obtained using
the proprietary software Istra 4D (v4.3.1, Dantec Dynamics, Denmark; URL: https​://www.dante​cdyna​mics.
com/).
Flexion. In the intact condition, compressive strains were directed in axial direction (Fig. 3a) and they werehigher on the L4-L5 IVD (− 23,000 µstrains), while being lower on the L4 VB (− 15,300 µstrains); tensile strains
were directed transversally and they were comparable on the IVD (18,600 µstrains), but much lower on the VB(4400 µstrains). Following PSO, median tensile and compressive strains significantly decreased compared to theintact condition (p = 0.014), respectively, to 30% and 16% on the VB, and to 12% and 10% on the IVD (Fig. 4a,b).
No significant differences were noticed among different instrumentation steps.
The posterior side of the primary rods underwent longitudinal tension, with median rod strains being thehighest (400 µstrains) for simple bilateral stabilization. Strains normalized to “PSO-2” decreased to 81% after
cage insertion and to 50% with supplemental accessory rods (Fig. 4c,d). Significant variations were found for“PSO-4 + Cages” compared to “PSO-2” (p = 0.004).
Extension. In the intact condition, tensile strains were directed axially (Figs. 3.b) on the L4-L5 IVD (21,000µstrains), while they were lower on the L4 VB (11,800 µstrains); transverse compressive strains were comparable
on the VB (− 10,500 µstrains), but much lower on the IVD (− 8300 µstrains). Following PSO, median tensile andcompressive strains significantly decreased compared to the intact condition (p = 0.037), respectively, to 17%
and 10% at PSO level, and to 9% and 17% on the IVD (Fig. 4a,b). No significant differences were noticed among
different instrumentation steps.
The posterior side of the primary rods underwent longitudinal compression, with median strains being
lower than in flexion (110 µstrains) for simple bilateral stabilization. Normalized strains decreased to 88% after
cage insertion and to 60% with supplemental accessory rods (Fig. 4c,d). Significant variations were found for“PSO-4 + Cages” compared to “PSO-2” (p = 0.011).
Lateral bending. In the intact condition, the median tensile and compressive strains were both comparable on
the IVD (12,000 vs. − 11,000 µstrains) and higher than on the VB (5400 vs. − 7700 µstrains). Specimens underwent axial compression on the ipsilateral side with circumferential stretching on the IVD (Fig. 5), while thecontralateral side underwent axial stretching and circumferential compression. Following PSO, ipsilateral tensileand compressive strains significantly decreased compared to the intact condition (p ≤ 0.002), respectively, to 18%
and 13% at PSO level, and to about 17% and 15% on the IVD (Fig. 6a–d). On the contralateral side, tensile andcompressive strains decreased to 14% and 29% at PSO level, and to about 17% and 20% on the IVD. Variations

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Figure 4.  Flexion/extension: Normalized strain values on the regions of interest (ROI) on L4 VB (a) and on theL4–L5 IVD (b) and normalized primary rods strains both on the left (c) and right (d) rods following PSO at L4
and posterior instrumentation with 2 primary-rods (“PSO-2”), with 2 rods and supplementary intervertebral
cages (“PSO-2 + Cages”) and with supplementary accessory rods and intervertebral cages (“PSO-4 + Cages”).
Supplementary Tables provide quantitative strain data either for each specimen both anteriorly and posteriorly.

Figure 5.  Lateral bending (LB) left (a) and right (b): tensile (ε1) and compressive (ε2) strain maps measured
in the “Intact” condition and following PSO at L4 and posterior instrumentation with 2 primary-rods (“PSO2”), with 2 rods and supplementary intervertebral cages (“PSO-2 + Cages”) and with supplementary accessory
rods and intervertebral cages (“PSO-4 + Cages”). A picture of the specimen with the correlated areas is reported
on the left, indicating the treated level (L4) and the caudal IVD. A representative specimen (#3) is shown here
(strain maps for every specimen provided as Supplementary Figures). The DIC strain maps have been obtainedusing the proprietary software Istra 4D (v4.3.1, Dantec Dynamics, Denmark; URL: https​://www.dante​cdyna​
mics.com/).
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Figure 6.  Lateral bending (LB): Normalized strain values on the sub-regions of interest (subROI) on L4
VB (a right subROI; b left subROI) and on the L4-L5 IVD (c: right subROI; d left subROI) and normalized
primary rods strains both on the left (e) and right (f) rods following PSO at L4 and posterior instrumentation
with 2 primary-rods (“PSO-2”), with 2 rods and supplementary intervertebral cages (“PSO-2 + Cages”) andwith supplementary accessory rods and intervertebral cages (“PSO-4 + Cages”). Supplementary Tables provide
quantitative strain data either for each specimen and grouped by ipsi-/contra-lateral sides both anteriorly andposteriorly.
were significant in all cases (p ≤ 0.016), except on the contralateral compressive side of the VB. Significant variations were noticed on the ipsilateral compressive strains on the IVD for “PSO-2” and “PSO-4 + Cages” (p = 0.009)
and on the contralateral tensile strains on the VB for “PSO-2” (p = 0.013). When grouping by number of rods (2rods, 4 rods) and cage use, significant differences compared to intact were found (p ≤ 0.010).
The tensile and compressive rod strains were, respectively, higher on the ipsi- than the contralateral rod (185vs. 66 µstrains) and lower on the contra- compared to the ipsi-lateral rod (− 230 vs- − 80 µstrains) in “PSO-2”
configuration. Normalized tensile strains slightly decreased to 95% and 97%, respectively, on the ipsi- andcontra-lateral rods after cage implantation and to 84% and 80% with supplemental accessory rods (Fig. 6e,f).
Axial torsion. Torsion induced the highest tensile and compressive strains (about 27,300 and -30,300 µstrains,respectively) on the IVD of the intact specimens, while on the VB they were relatively lower (8300 and − 6600
µstrains). Tensile and compressive strains were oriented in the direction of load at about + 45° and − 45° (Fig. 7).
Following PSO, ipsilateral tensile and compressive strains significantly decreased compared to the intact condition (p ≤ 0.011), respectively, to 35% and 31% at PSO level, to about 21% and 18% on the IVD (Fig. 8a–d); on thecontralateral side, tensile and compressive strains significantly decreased to 34% and 49% at PSO level, to about
22% and 25% on the IVD (p ≤ 0.003). Significant variations were noticed for “PSO-4 + Cages” in the ipsilateralcompressive strains on the IVD (p = 0.001) and in the contralateral tensile strains both at PSO level and on the
IVD (p = 0.007).When grouping, significant differences compared to the intact condition were found when using
4 rods and cages (p ≤ 0.010).
The median tensile rod strains were slightly higher on ipsilateral rods, while the compressive strains wereslightly higher on contralateral rods for simple bilateral stabilization. Normalized tensile strains kept rather
constant both on the ipsi- and contra-lateral rods after cages implantation, but decreased, respectively, to 67%
and 57% with supplemental accessory rods (Fig. 8e,f). Significant variations were found on the ipsilateral rod
for “PSO-4 + Cages” compared to “PSO-2” (p = 0.015) and “PSO-2 + Cages” (p = 0.012).

Specimen‑specific analysis—strain distribution on the ventral spine and on primary rods. Eachspecimen demonstrated specific properties, both related to its size, BMD, lumbar lordosis before/after PSO procedure and the presence of mild to moderate degenerative signs (Table 1, Fig. 9). The strain maps of every specimen are provided as Supplementary Figs. 1–9, strain values as Supplementary Tables 2, 3.

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Figure 7.  Axial torsion (AT) right (a) and left (b): tensile (ε1) and compressive (ε2) strain maps measured on the“Intact” condition and following PSO at L4 and posterior instrumentation with 2 primary-rods (“PSO-2”), with
2 rods and supplementary intervertebral cages (“PSO-2 + Cages”), and with supplementary accessory rods andintervertebral cages (“PSO-4 + Cages”). A picture of the specimen with the correlated areas is reported on theleft, indicating the treated level (L4) and the caudal IVD. A representative specimen (#1) is shown here (strain
maps for every specimen provided as Supplementary Figures). The DIC strain maps have been obtained using
the proprietary software Istra 4D (v4.3.1, Dantec Dynamics, Denmark; URL: https​://www.dante​cdyna​mics.
com/).
Specimen #1. It exhibited mild degeneration (grade 1) with diffused osteophyte formations, which were more
pronounced on the left inferior margin of L4-L5 IVD (Table 1, Fig. 9). Lumbar lordosis improved to 48° after
PSO and posterior fixation. Although median strains were in line with the trends reported for other specimen,
asymmetric loading was noticed particularly in torsion (Fig. 7), where the strains kept rather high even withcages and supplementary rods (Supplementary Figs. 1–3). Variability on normalized strains was rather high inspecific cases across PSO configurations (Figs. 4, 6, 8). Following PSO, a general strain decrease was noticed on
the IVD and at PSO level. IVD strains kept rather comparable in extension, lateral bending and torsion acrossdifferent instrumentation steps. After cages insertion, a slightly decreasing trend on tensile strains was noticed
in flexion both on the IVD (from 20% in “PSO-2” to 10% in “PSO-4 + Cages”) and on the VB (from 24 to 19%).
Specimen #2. It showed moderate degeneration (grade 2) with osteophytes on both sides of the IVD (Table 1,
Fig. 9). Lumbar lordosis increased to 60° with PSO and posterior fixation. Strains higher than the median values
reported for the other specimens were noticed in flexion/extension (Figs. 3, 4), with a symmetric map in torsion(Fig. 9, Supplementary Figs. 4–6). Normalized strains were higher than for other specimens in most loading
conditions (Figs. 4, 6, 8). Normalized strains were comparable or slightly lower on the IVD than at PSO level in“PSO-2” configuration in flexion and torsion. A decreasing trend was noticed on the IVD following cages insertion (from 14–68% in “PSO-2” to 10% in “PSO-4 + Cages”), while normalized strains remained rather constanton the VB.
Specimen #3. It exhibited moderate degeneration (grade 2, Table 1, Fig. 9). Lumbar lordosis improved to 67°
with PSO and posterior fixation. Osteophytes were more pronounced on the left inferior margin (grade 2–3)
than on the right one (grade 1–2) of the IVD. High local asymmetric strain (even beyond ± 7800 µstrains) bothin lateral bending and torsion were noticed (Figs. 5, 9, Supplementary Figs. 7–9), with relatively high variability
on normalized strain values across PSO configurations (Figs. 4, 6, 8). Some similarities among the ventral strain
maps in lateral bending and torsion were noticed (Fig. 9).
Following PSO, a consistent normalized strain decrease was noticed on the IVD in flexion and extension,
with similar trends also at PSO level. Switching from “PSO-2” to “PSO-2 + Cages”, a relevant strain variation,
more relevant for the IVD than for the VB, was noticed in compressive values in lateral bending and in torsion.

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Figure 8.  Axial torsion (AT): Normalized strain values on the sub-regions of interest (subROI) on L4 VB(a: right subROI; b: left subROI) and on the L4–L5 IVD (c: right subROI; d: left subROI) and normalized
primary rods strains both on the left (e) and right (f) rods following PSO at L4 and posterior instrumentation
with 2 primary-rods (“PSO-2”), with 2 rods and supplementary intervertebral cages (“PSO-2 + Cages”), andwith supplementary accessory rods and intervertebral cages (“PSO-4 + Cages”). Supplementary Tables provide
quantitative strain data either for each specimen and grouped by ipsi-/contra-lateral sides both anteriorly andposteriorly.

Discussion

PSO is an invasive surgical technique allowing the restoration of a well-balanced profile in patients with severe
sagittal ­imbalance1. PSO procedure is often accompanied by a high risk of rod breakage and pseudarthrosis at
the osteotomy level due to the extensive resection through posterior, middle and anterior bony and ligamentous
structures, featuring unique biomechanical c­ hallenges2–9.
Previous biomechanical studies demonstrated improved primary stability and reduced instrumentationloads using multi-rod constructs and additional interbody ­spacers11–19. However, they focused on the load
supported by the posterior instrumentation in relation to rod breakage, neglecting the load supported by theanterior column, which is fundamental to promote fusion across the osteotomy early after surgery. While IDP­measurements20–22 and SG ­techniques23 may offer a limited description on the actual loads on a specific structure,
new DIC ­techniques24–27 can investigate the superficial full-field load (i.e. strain) distribution both on the VB
treated with PSO and the adjacent IVDs, as well as the ALL running on the ventral spine. The present study aimed
to quantify the load-sharing occurring across the ventral spinal structures and the posterior instrumentation, as
affected by simple bilateral fixation with and without cages and additional supplementary rods. To achieve this,conventional in vitro flexibility tests were integrated with DIC strain measurements on the ventral spine andwith SG analysis on posterior primary rods.
Flexibility tests demonstrated that a posterior bilateral fixation is effective in reducing the RoM and the NZ
to negligible values in all motion directions (beyond 98% compared to the intact), except for axial torsion, wherea residual instability remained. These trends, consistent for all specimens, were independent on the type of
instrumentation considered, in agreement with previous in vitro data on a larger sample s­ ize11–15. Compared toother studies on degenerative cases without any osteotomy, where XLIF cages were found to provide superior orcomparable primary stability characteristics also as a standalone technique in comparison to other cage design(i.e. ALIF)37,38, our results may indicate that, despite the preservation of the anterior longitudinal ligament,
additional stabilizing features (i.e. anchoring screws, plates) could help achieving superior primary stability alsoin challenging PSO cases.
Several studies reported that using multi-rod constructs and/or implantation of cages allows to reduce rod
strains, which are directly associated to the risk of rod ­breakage11–15,18,19. It is important to remark that, althougha cause-effect relationship between the measured strains and the actual loads is quite reasonable, the strain
data herein reported should be read as an indirect measure of load effects both on the ventral spine and on theposterior instrumentation. Our strain analysis on primary rods confirmed that usage of interbody cages andsupplementary accessory rods is the best strategy to achieve adequate primary stability and to reduce rod strains
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Figure 9.  Specimen-specific analysis of maximum (ε1) and minimum (ε2) strain maps vs. osteophyte grade
for cases “PSO-2” at full load for all loading conditions. CT reconstruction of each specimen (left) was used tograde osteophytes f­ ormations26. The asterisks (*) indicate the presence of strain intensification effects. The DIC
strain maps have been obtained using the proprietary software Istra 4D (v4.3.1, Dantec Dynamics, Denmark;
URL: https​://www.dante​cdyna​mics.com/).
early after surgery. This is in line with the biomechanical literature, reporting significant differences with supplemental accessory rods and interbody cages compared to the intact condition both in vitro11–13 and in s­ ilico18,19.
Movements in the sagittal plane induced a common and consistent strain pattern for all treated specimens
both in flexion and extension, where the anterior spine undergoes axial compression and traction, respectively,
while the posterior instrumentation undergoes tension and compression. A similar qualitative response characterized by lower absolute values was observed in lateral bending: the axial compressive strains observed on thecompressed (ipsilateral) side of the ventral spine were associated with compression on the posterior contralateralrod and tension on the ipsilateral one because of coupled loading components introduced by the specimens’
enhanced sagittal profile after ­PSO39. In axial torsion, the ventral strains were relatively high and aligned atroughly 45°, with both primary rods experiencing rather comparable strains. These observations relate well withthe hypothesized load-sharing effect, where the posterior fixation shielded the whole ventral spine (treated VB
and IVD) from reaching the higher strains observed in the intact c­ ondition28. This was supported by a generalsignificant reduction of ventral strains following PSO in flexion (IVD: about − 88% vs. Intact; PSO level: − 77%),
extension (about − 87% and − 86%), lateral bending (− 83% and − 83%) and torsion (− 79% and − 63%), with
only specific trends related to the adopted instrumentation.
The strains were higher on the IVD than on the VB, where the presence of mild/moderate osteophytes produced an expected strain-intensification e­ ffect26. This may indicate that the ventral aspect of the treated vertebra(PSO level) could be more stable, probably because shielded by the posterior instrumentation or by adequate
osteotomy closure, thus increasing the load transferred to the anterior column through the intact adjacent discs.
Although the mechanical function of the anterior longitudinal ligament (ALL) may be altered following PSO
closure, the relatively higher strains noticed on the IVDs adjacent to PSO level may indicate that some residualload is transferred ventrally to the treated vertebra. These mechanisms, coupled to the residual instability measured in t­ orsion11–17 may indicate that micromotions could potentially arise on the osteotomy rims if the loads
transmitted to the osteotomized vertebra, “floating” among two intact IVDs and “pulled” by the ALL, are sufficiently high. Such an interpretation, supported by our analysis, seems to explain the high rate of revision due
to pseudarthrosis as reported by several clinical studies with simple bilateral i­ nstrumentation2–9,40.
The implantation of cages adjacent to PSO (“PSO-2 + Cages”) did not remarkably affect the ventral strains
nor the posterior primary rod strains compared to simple bilateral stabilization. Anyway, the normalized strain
on the IVD of specimens #1 and #2 demonstrated a decreasing trend in flexion and in torsion, accompanied bya parallel slight decrease of primary rods strains. This may be attributed to a promoted anterior load-transfer
through the stiff intervertebral cages, thus reducing the load on the remaining ventral aspects of the treated
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disc. The rather constant strains observed at PSO level may indicate that the ventral portion of the treated VB isalready shielded by the posterior instrumentation and/or adequate load transfer through the anterior column.
Even if not differentiating between the superficial ventral aspect of the spine and the anterior column, a previous computational study reported an improved anterior axial load transfer using interbody ­cages18,19. Although
not significant, these mechanisms may relate to the slightly higher fusion rate reported using interbody spacers, graft or cages implanted immediately above and/or below PSO ­level6,40. Even if primary rod strains wereslightly reduced in flexion and extension after cages insertion (− 17%, − 13% for “PSO-2 + Cages” vs. “PSO-2”,
respectively), variations were not significant. These results may contribute to explain the marginal positive effectreported in previous clinical literature in preventing rod failure with simple bilateral fixation with c­ ages6,40.
The addition of supplementary accessory rods (“PSO-4 + Cages”) significantly decreased primary rods strains
compared to simple bilateral fixation (“PSO-2”) both in flexion (− 50%), extension (− 40%) and axial rotation(about − 40%). Significant rod strain reduction (about − 44%) was also found in “PSO-4 + Cages” compared
to “PSO-2 + Cages” in torsion. Although we expected that increased stiffness of the posterior instrumentation
could have further shielded the ventral spine, this was not observed. This indicates that usage of accessory rods
may be more effective than simple bilateral instrumentation with/without adjacent cages in reducing the risk ofrod failure, rather than affecting the ventral spine or promoting load transmission through the anterior column.
The current in vitro study is affected by specific limitations. The adopted quasi-static protocol based on
unconstrained pure moments up to ± 7.5 Nm is considered reliable for comparative ­purposes43, although it may
not closely describe the complex in vivo loading condition of severely unbalanced patients. Indeed, the current
approach is considered highly reproducible and suitable to describe the early post-operative time while controlling the boundary conditions.
The relatively low posterior primary rod strains measured with SG technique on the most critical configuration (“PSO-2”) resulted to be in the linear elastic regime, therefore not describing inelastic effects occurring
during spinal rods contouring or long-term fatigue ­failure41,42.
Due to time constraints involved in the preparation of each instrumentation step and the time required forflexibility test repetition, SG analysis, optimal DIC data collection, and postprocessing, three specimens wereanalysed. Given the consistency between the results herein discussed and the previous literature on a higher
sample ­size11–15, the present study could be seen as an original extension of the previous study on i­ ntact26,27 andPSO-treated11,12 spine segments, where the detailed information about the strain distribution on the ventral spine,once integrated with SG analysis on posterior primary rods, successfully elucidated the load-sharing mechanism
among different constructs for fixation and fusion following PSO procedure. The same approach could be easily
adapted to investigate the biomechanics of other spinal disease (i.e. aetiology of degenerative disc disease) or toeither more conservative spinal treatments or surgical procedure.

Conclusion

The present study demonstrated how the ventral strains, specifically affected by the loading condition and thepresence of local osteophytes, considerably decreased following PSO and instrumentation, confirming the effectiveness of posterior load-sharing. Supplemental accessory rods considerably reduced the posterior rod strains
only with interbody cages, but the ventral strains were unaffected: this indicates that the load transfer across theosteotomy could be promoted, while explaining the higher fusion rate with decreased rod fracture risk reported
in clinical literature.

Data availability

All data generated or analysed during this study are included in the published article and the Supplementary
Information files.
Received: 29 May 2020; Accepted: 23 December 2020

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Acknowledgements

The specimens considered in the present study were obtained through a New Investigator Grant awarded to
the first author (L.L.B.) by the Scoliosis Research Society. The authors gratefully acknowledge Gloria Casaroli
Ph.D., Lisa Flachmüller, and Theodor Di Pauli von Treuheim for their assistance during specimens’ preparation
and Prof. Tomaso Villa and Tito Bassani Ph.D. for the hints provided during the first steps of the present study.

Author contributions

Conceptualization, study design: L.L.B., H.J.W., M.B.B., F.G., L.C. Methodology: L.L.B., H.J.W., L.C. Formal
analysis, data curation: M.L.R., M.P., C.L., L.L.B. Writing original draft: L.L.B. Review and editing: all authors.
Funding acquisition, project management: L.L.B. H.J.W and L.L.B. contributed as co-first authors. All authors
have read and agreed to the published version of the manuscript.
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Competing interests

The authors declare no competing interests.

Additional information

Supplementary Information The online version contains supplementary material available at https​://doi.
org/10.1038/s4159​8-021-83251​-8.
Correspondence and requests for materials should be addressed to L.L.B.
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