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Finite element analysis of the lumbar destabilization following pedicle subtraction osteotomy
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Finite element analysis of the lumbar destabilization following pedicle subtraction osteotomy Claudia Ottardi a,∗, Fabio Galbusera b, Andrea Luca c, Liliana Prosdocimo a, Maurizio Sasso a, Marco Brayda-Bruno c, Tomaso Villa a,b a b c
Laboratory of Biological Structure Mechanics, Department of Chemistry, Materials and Chemical Engineering “G. Natta”, Politecnico di Milano, Milan, Italy IRCCS Istituto Ortopedico Galeazzi, Milan, Italy Department of Spine Surgery III, IRCCS Istituto Ortopedico Galeazzi, Milan, Italy
a r t i c l e
i n f o
Article history: Received 8 June 2015 Revised 18 January 2016 Accepted 6 February 2016 Available online xxx Keywords: Pedicle subtraction osteotomy Lumbar spine Osteotomy Finite elements Destabilization
a b s t r a c t This study aims to analyze the destabilization produced following a pedicle subtraction osteotomy (PSO), with a calibrated numerical model. A 30° resection was created on L3 and L4. Range of Motion (ROM) and the force acting on the vertebral body were calculated. Osteotomies consistently increased the ROMs. In the intact model, 87% of the compressive load was acting on the vertebral bodies whereas in the destabilized models all the load was on the fractured surface. Osteotomies at both levels induced a marked instability but the PSO at L4 seemed to have a greater influence on the ROM. Despite the significant deformity corrections which could be achieved with PSO, this technique needs further analyses. © 2016 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction
2. Material and methods
Spinal osteotomies are complex surgeries aimed at correcting a pathological spinal curvature. Different techniques were developed (e.g. Ponte osteotomy [1,2] and Smith–Petersen osteotomy [1-3]) all having a great correction power but also a high complications rate [1,2]. Pedicle subtraction osteotomy (PSO), which is mainly used for the treatment of fixed sagittal imbalance, is a posterior closing wedge technique that causes a high correction in a single level (up to 35°). PSO presupposes posterior fixation and the most frequent complications are neurological deficits and hardware failure, in particular rod breakage [1-4]. The aim of this work is to quantify the destabilization produced by a PSO, using a calibrated finite element model of the lumbar spine. This preliminary study is helpful to understand the mechanisms that can contribute to overload the spinal devices used to stabilize the osteotomies, therefore increasing the risk of rod breakage.
A non-linear finite element model of the intact lumbosacral spine (L1-S1) was created based on CT scans (512 × 512 pixels/slice, slice thickness 0.625 mm) of a 40 years old human male (CT scan taken due to kidney stones and not related to spinal pathologies). The position of each vertebra was readjusted mimicking the curvature of a subject having a low lumbar lordosis (35°), thus modeling a case needing surgical correction. Vertebral bodies and intervertebral discs were meshed with linear hexahedral elements whereas the posterior elements were meshed with linear tetrahedrons. Discs were divided in nucleus pulposus, annulus fibrosus and endplates and their heights were consistent with anatomical data [5]. In order to mimic the collagen fibers, four rebar layers were embedded in an isotropic solid matrix [6]. For each layer two bundles of tension-only linear elastic fibers were modeled with orientation of ±30° with respect to the horizontal plane. Moreover, a disc-nucleus volume ratio of about 50% [7,8] and a fiber cross-sectional area of 0.1 mm2 were assumed [9]. Ligaments were represented as tension-only linear spring elements while the facet joints were modeled with a cartilage layer of 0.2 mm and a gap of 0.6 mm [9]. Mechanical properties (Table 1) were taken from literature [9-12]. Trabecular bone was modeled with transverse isotropic properties. Regarding the ligaments, properties found in literature [13] were modified and adapted during the calibration process (see Supplementary Material). ICEM CFD 14.0 (ANSYS Inc,
∗ Corresponding author at: Laboratory of Biological Structure Mechanics, Department of Chemistry, Materials and Chemical Engineering “G. Natta”, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy. Tel.: +39 02 2399 4317; fax: +39 02 2399 4286. E-mail address: [email protected] (C. Ottardi).
http://dx.doi.org/10.1016/j.medengphy.2016.02.002 1350-4533/© 2016 IPEM. Published by Elsevier Ltd. All rights reserved.
Please cite this article as: C. Ottardi et al., Finite element analysis of the lumbar destabilization following pedicle subtraction osteotomy, Medical Engineering and Physics (2016), http://dx.doi.org/10.1016/j.medengphy.2016.02.002
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C. Ottardi et al. / Medical Engineering and Physics 000 (2016) 1–4 Table 2 ROMs and flexibility coefficients of each functional unit.
Table 1 Mechanical properties of the different structures of the model. Young modulus (MPa) Cortical bone Trabecular bone Posterior process Cartilage Anulus: fibers Anulus: ground substance Bony endplates Nucleus pulposus
12,0 0 0 140,140,200 2500 23.8 25 4.2 100 1
Flex
Ext
Left bend
Right bend
Left rot
Right rot
L1-L2 L2-L3 L3-L4 L4-L5 L5-S1 L1-L2
2.4 2.4 2.6 3.0 4.8 0.4
1.3 1.5 1.6 2.0 2.8 0.2
2.6 2.9 2.5 2.6 2.6 0.4
2.6 2.8 2.3 2.5 2.6 0.4
2.1 2.1 1.8 1.6 2.1 0.3
1.7 1.7 1.6 1.5 2.0 0.3
[14] L2-L3 [14] L3-L4 [14] L4-L5 [14] L5-S1 [14]
0.5 0.6 0.7 0.6 0.8 0.8 1.0 1.2 1.3
0.4 0.4 0.3 0.3 0.5 0.4 0.4 0.6 0.8
0.5 0.9 0.7 0.8 0.9 0.7 0.5 0.8 0.6
0.5 0.9 0.7 0.8 0.9 0.7 0.5 0.7 0.6
– 0.4 – 0.3 – 0.3 – 0.5 –
– 0.4 – 0.4 – 0.3 – 0.4 –
Poisson coefficient 0.3 0.45,0.325,0.315 0.25 0.4 0.3 0.5 0.4 0.449
ROM (°)
Flexibility coefficient (°/Nm)
Table 3 Variation of the ROM, at the osteotomy level, of the two destabilized models (OL3 and OL4). It must be noted that in one case the comparison is at L3-L4 level (model OL3) while the other one is at L4-L5 (model OL4). Fig. 1. Intact model of the lumbar spine (left) and osteotomy performed on L3 (middle) and L4 (right).
Canonsburg, PA, USA) was employed to create the mesh while Abaqus 6.12-3 (Dassault Systèmes, Simulia, Providence, RI, USA) was used for the numerical analysis. A mesh convergence study was conducted by monitoring the stresses on the endplates. The final mesh had 215.494 elements and 167.898 nodes. The model was loaded with a follower load of 500 N, by means of connector elements following the spinal curvature. An optimization of the position of the connectors was performed, ensuring a minimization of the rotations (<5%) along the three axes. Pure moments of ±7.5 Nm were applied in flexion-extension, lateral bending and axial rotation to simulate the standing condition, while the inferior part of the sacrum was totally constrained. All FSUs were calibrated by applying pure moments on the upper surface of the vertebrae, with the inferior endplate and the facets rigidly fixed. The moment/rotation curves as well as the overall Ranges of Motion (ROMs) were compared to literature data [14-21]. Two models were created to simulate the osteotomy on the L3 level (OL3) and on L4 (OL4) (Fig. 1). Since PSO may be used to obtain a correction up to 35° [3,4,22], a wedged shape resection of 30° was performed on the vertebral bodies, resulting in a lumbar lordosis of 65°. A surface-to-surface contact was defined along the fracture extremities with a friction coefficient of 0.46 [23]. To evaluate the influence of the destabilization following a PSO, the ROMs of the intact model (Fig. 3) were compared to the values obtained with OL3 and OL4. Due to the severe destabilization, the osteotomy models did not converge at 7.5 Nm so the comparison was done at the highest moment reached with OL4 (7.5 Nm in flexion, 4 Nm in bending and 3 Nm in extension and axial rotation). The percentage variation of the ROM at the osteotomy level was compared with the ROM of the same level of the intact model (Table 3). Moreover, the forces acting at the osteotomy level in the intact model and on the fractured surface following PSO were calculated after applying the follower load. 3. Results Comparing the results obtained with the intact model with literature data [15-21], it can be noted that the values of the
ROM variation (%)
OL3 vs intact
OL4 vs intact
Flexion/extension Lateral bending Axial rotation
74 38 61
143 327 277
total ROMs in flexion/extension, lateral bending and axial rotation (Table 2 and Fig. 2) are in good agreement. The calculated flexibility coefficients were similar to those found in a previous work [14], with an average error of 14% (Table 2). After both osteotomies, the global ROMs increased (Fig. 3). The largest variation can be noted in axial rotation (58% for OL3 and 45% for OL4) and lateral bending (43%) for OL4 but all the movements have significant changes (11–16% in flexion/extension). However, the variation of the ROM at the osteotomy site is even more pronounced (Table 3). Moreover, the load acting on L3 and L4 was 85% and 87% of the total follower load while in the osteotomy models (OL3 and OL4), as expected following the removal of the posterior structures of the spine, 500 N were insisting on the fracture. 4. Discussion This study, represents the first and key step to understand the behavioral changes in a spine subjected to PSO, and helps to compare the different fixation system and hardware constructs. Several osteotomy techniques are currently used but they are all technically demanding and imply a high rate of complications, which may be related to biomechanical factors [1-4,22,24]. Nevertheless, only few biomechanical studies are available in the literature. In a published study, Ponte osteotomy and discectomy were compared in terms of ROM and posterior translation of the vertebral segments with respect to the intact situation. The authors found that a Ponte osteotomy causes a 20% destabilization while a total discectomy is even more severe [25]. Hato et al. studied a closing-opening correction osteotomy with a numerical model of the thoraco-lumbar spine [26]. Several models were created, considering different grades of osteoporosis and varying the kyphotic angle but the results are not directly comparable with the present paper, due to the different surgical techniques investigated. Charosky et al. studied the PSO with a simplified computational model, reproducing three defect situations and studying loads and stresses arising in different configurations of spinal implants [27].
Please cite this article as: C. Ottardi et al., Finite element analysis of the lumbar destabilization following pedicle subtraction osteotomy, Medical Engineering and Physics (2016), http://dx.doi.org/10.1016/j.medengphy.2016.02.002
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3
Fig. 2. ROMs obtained with the finite element model of the single motion segments (FEM) compared with literature data.
Fig. 3. Comparison of the total ROM of the lumbar spine (L1-S1) obtained with the intact and osteotomy models (OL3 and OL4). The comparison is done considering the angle reached at 7.5 Nm in flexion, 4 Nm in bending and 3 Nm in extension and axial rotation.
One destabilization reported in this work is similar to the situation reproduced on OL4 with a 30° resection. However, the authors only studied the instrumented models, without considering the intact and destabilized conditions alone. Despite the differences concerning the modeling strategies, their results in terms of ROM express the same increasing trend going from an intact to a destabilized model. PSOs can be performed on different levels, depending on the patient and the type of deformity to be treated. However, the lower lumbar spine determines most of the lordosis of the whole region and thus many surgeries are reported on L4 [24]. In a clinical study, Bridwell et al. performed PSO on 78 patients, having the 56% and 17% of the surgeries on L3 and L4 respectively [3]. These data explain our decision of simulating with a finite element model a PSO on L3 and L4. Analyzing both cases and comparing the results with the intact model, it is clear that both osteotomies
induce a major destabilization of the lumbar spine. However, OL4 show a greater influence on the ROM (2 times more than OL3 in flexion-extension and more than 4 times in lateral bending and axial rotation, at the osteotomy level). Thus, an osteotomy on L3 may reduce the overload acting on the device. However, due to the morphology of the lumbar spine, a correction on L4 leads to a bigger variation of the lordosis and the same correction can be probably achieved removing a smaller wedge on L4 than L3. Although this would be the preferred approach, due to clinical factors is often not possible to perform the surgery on L4 and therefore L3 is operated. To ensure a comparability of the results, the simulation of the PSO was done removing a 30° wedge from the vertebral body in both cases. A smaller resection angle will probably cause a reduction of the stresses on the spinal instrumentation, independently from the osteotomy level. An interesting preliminary question before studying the PSO on instrumented models is therefore related to the determination of the optimal correction degree and the level in which it should be performed, since the high rate of failure of the fixation devices is well documented [1,3,4,28,29]. Based on the current results, the interplay of the considered factors (level of osteotomy, degree of correction) appears to be more complex than expected, and therefore a wider simulation campaign should be conducted before clinically relevant conclusions can be drawn. The evaluation of the load sharing between the anterior and posterior spines showed a similar distribution of the load for the two models (85% and 87% on the intact vertebral bodies of L3 and L4, respectively). A load sharing in the anterior column of about 75% was reported in a numerical study concerning the lumbar spine, imposing a follower load of 450 N and a pure flexion moment of 8 Nm [30]. Conversely, in the osteotomy models 100% of the imposed follower load was acting on the fractured surface. This can be explained considering the removal of the posterior elements and the ligaments at the osteotomy site. Due to the instability and the major loads acting on this interface, spinal instrumentation would therefore be highly stressed, in agreement with the high hardware failure rates reported in literature. In conclusion, PSO always induces a great instability but performing it at a lower level seems to be more severe. Therefore,
Please cite this article as: C. Ottardi et al., Finite element analysis of the lumbar destabilization following pedicle subtraction osteotomy, Medical Engineering and Physics (2016), http://dx.doi.org/10.1016/j.medengphy.2016.02.002
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despite the significant deformity corrections which could be achieved with PSO, this technique still needs to be analyzed in depth from a biomechanical point of view. Conflict of interest There are no actual or potential competing interests, of conflicts of interest, in relation to this article. Funding None. Ethical approval We deemed that an ethical approval was not required for this study. The patient, the CT data of whom were used to build the FE model, signed a letter of waiver in which he agreed that relevant clinical data may be used in the future for scientific purposes, according to the Italian regulations. The findings of the present study had no influence on the clinical treatment of the patient. Supplementary Materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.medengphy.2016.02. 002. References [1] Bergin PF, O’Brien JR, Matteini LE, Yu WD, Kebaish KM. The use of spinal osteotomy in the treatment of spinal deformity. Orthopedics 2010;33:586–94. [2] Dorward IG, Lenke LG. Osteotomies in the posterior-only treatment of complex adult spinal deformity: a comparative review. Neurosurg Focus 2010;28:E4. [3] Bridwell KH. Decision making regarding Smith-Petersen vs. pedicle subtraction osteotomy vs. vertebral column resection for spinal deformity. Spine (Phila Pa 1976) 2006;31:S171–8. [4] Luca A, Lovi A, Galbusera F, Brayda-Bruno M. Revision surgery after PSO failure with rod breakage: a comparison of different techniques. Eur Spine J 2014;23(Suppl 6):610–15. [5] Busscher I, Ploegmakers JJW, Verkerke GJ, Veldhuizen AG. Comparative anatomical dimensions of the complete human and porcine spine. Eur Spine J 2010;19(7):1104–14. [6] Dabirrahmani D, Becker S, Hogg M, Appleyard R, Baroud G, Gillies M. Mechanical variables affecting balloon kyphoplasty outcome–a finite element study. Comput Methods Biomech Biomed Eng 2012;15:211–20. [7] Violas P, Estivalezes E, Briot J, Sales de Gauzy J, Swider P. Objective quantification of intervertebral disc volume properties using MRI in idiopathic scoliosis surgery. Magn Reson Imaging 2007;25:386–91. [8] Boccaccio A, Vena P, Gastaldi D, Franzoso G, Pietrabissa R, Pappalettere C. Finite element analysis of cancellous bone failure in the vertebral body of healthy and osteoporotic subjects. Proc Inst Mech Eng H 2008;222(7):1023– 36.
[9] Galbusera F, Bellini C, Anasetti F, Ciavarro C, Lovi A, Brayda-Bruno M. Rigid and flexible spinal stabilization devices: a biomechanical comparison. Med Eng Phys 2011;33:490–6. [10] Lu YM, Hutton WC, Gharpuray VM. Can variations in intervertebral disc height affect the mechanical function of the disc? Spine 1996;21(19):2208–16. [11] Cowin SC. Bone mechanics. 2nd ed. Boca Raton, FL: CRC Press; 1991. p. 97–159. [12] Pitzen T, Geisler F, Matthis D, Müller-Storz H, Barbier D, Steudel WI, et al. A finite element model for predicting the biomechanical behaviour of the human lumbar spine. Control Eng Pract 2002;10:83–90. [13] Alizadeh M, Kadir MRA, Saldanha S. Biomechanical effects of short construct spine posterior fixation, in thoracolumbar region with L1 burst fracture. In: IEEE EMBS conference on biomedical engineering & sciences (IECBES 2010); 2010. [14] Guan Y, Yoganandan N, Moore J, Pintar FA, Zhang J, Maiman DJ, et al. Momentrotation responses of the human lumbosacral spinal column. J Biomech 2007;40:1975–80. [15] Wilke HJ, Geppert J, Kienle A. Biomechanical in vitro evaluation of the complete porcine spine in comparison with data of the human spine. Eur Spine J 2011;20:1859–68. [16] White A, Panjabi M. Clinical biomechanics of the spine. 2nd ed. Philadelphia: Lippincott Williams & Wilkins; 1990. [17] Dvorák J, Panjabi MM, Chang DG, Theiler R, Grob D. Functional radiographic diagnosis of the lumbar spine. Flexion-extension and lateral bending. Spine (Phila Pa 1976) 1991;16:562–71. [18] Hayes MA, Howard TC, Gruel CR, Kopta JA. Roentgenographic evaluation of lumbar spine flexion-extension in asymptomatic individuals. Spine (Phila Pa 1976) 1989;14:327–31. [19] Yamamoto I, Panjabi MM, Crisco T, Oxland T. Three-dimensional movements of the whole lumbar spine and lumbosacral joint. Spine (Phila Pa 1976) 1989;14:1256–60. [20] Pearcy M, Portek I, Shepherd J. Three-dimensional x-ray analysis of normal movement in the lumbar spine. Spine (Phila Pa 1976) 1984;9:294–7. [21] Pearcy MJ, Tibrewal SB. Axial rotation and lateral bending in the normal lumbar spine measured by three-dimensional radiography. Spine (Phila Pa 1976) 1984;9:582–7. [22] Bridwell KH, Lewis SJ, Lenke LG, Baldus C, Blanke K. Pedicle subtraction osteotomy for the treatment of fixed sagittal imbalance. J Bone Joint Surg Am 2003;85-A:454–63. [23] Goffin JM, Pankaj P, Simpson AH. A computational study on the effect of fracture intrusion distance in three- and four-part trochanteric fractures treated with Gamma nail and sliding hip screw. J Orthop Res 2014;32:39–45. [24] Berjano P, Aebi M. Pedicle subtraction osteotomies (PSO) in the lumbar spine for sagittal deformities. Eur Spine J 2015;24(Suppl 1):S49–57. [25] Wang C, Bell K, McClincy M, Jacobs L, Dede O, Roach J, et al. Biomechanical comparison of Ponte osteotomy and discectomy. Spine (Phila Pa 1976) 2015;40(3):E141–5. [26] Hato T, Kawahara N, Tomita K, Murakami H, Akamaru T, Tawara D, et al. Finiteelement analysis on closing-opening correction osteotomy for angular kyphosis of osteoporotic vertebral fractures. J Orthop Sci 2007;12:354–60. [27] Charosky S, Moreno P, Maxy P. Instability and instrumentation failures after a PSO: a finite element analysis. Eur Spine J 2014;23:2340–9. [28] Smith JS, Shaffrey CI, Ames CP, Demakakos J, Fu KM, Keshavarzi S, et al. Assessment of symptomatic rod fracture after posterior instrumented fusion for adult spinal deformity. Neurosurgery 2012;71:862–7. [29] Smith JS, Shaffrey E, Klineberg E, Shaffrey CI, Lafage V, Schwab FJ, et al. Prospective multicenter assessment of risk factors for rod fracture following surgery for adult spinal deformity. J Neurosurg Spine 2014;21:994–1003. [30] Gornet MF, Chan FW, Coleman JC, Murrell B, Nockels RP, Taylor BA, et al. Biomechanical assessment of a PEEK rod system for semi-rigid fixation of lumbar fusion constructs. J Biomech Eng 2011;133:081009.
Please cite this article as: C. Ottardi et al., Finite element analysis of the lumbar destabilization following pedicle subtraction osteotomy, Medical Engineering and Physics (2016), http://dx.doi.org/10.1016/j.medengphy.2016.02.002
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Medical Engineering and Physics 0 0 0 (2016) 1–4
Contents lists available at ScienceDirect
Medical Engineering and Physics journal homepage: www.elsevier.com/locate/medengphy
Communication
Finite element analysis of the lumbar destabilization following pedicle subtraction osteotomy Claudia Ottardi a,∗, Fabio Galbusera b, Andrea Luca c, Liliana Prosdocimo a, Maurizio Sasso a, Marco Brayda-Bruno c, Tomaso Villa a,b a b c
Laboratory of Biological Structure Mechanics, Department of Chemistry, Materials and Chemical Engineering “G. Natta”, Politecnico di Milano, Milan, Italy IRCCS Istituto Ortopedico Galeazzi, Milan, Italy Department of Spine Surgery III, IRCCS Istituto Ortopedico Galeazzi, Milan, Italy
a r t i c l e
i n f o
Article history: Received 8 June 2015 Revised 18 January 2016 Accepted 6 February 2016 Available online xxx Keywords: Pedicle subtraction osteotomy Lumbar spine Osteotomy Finite elements Destabilization
a b s t r a c t This study aims to analyze the destabilization produced following a pedicle subtraction osteotomy (PSO), with a calibrated numerical model. A 30° resection was created on L3 and L4. Range of Motion (ROM) and the force acting on the vertebral body were calculated. Osteotomies consistently increased the ROMs. In the intact model, 87% of the compressive load was acting on the vertebral bodies whereas in the destabilized models all the load was on the fractured surface. Osteotomies at both levels induced a marked instability but the PSO at L4 seemed to have a greater influence on the ROM. Despite the significant deformity corrections which could be achieved with PSO, this technique needs further analyses. © 2016 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction
2. Material and methods
Spinal osteotomies are complex surgeries aimed at correcting a pathological spinal curvature. Different techniques were developed (e.g. Ponte osteotomy [1,2] and Smith–Petersen osteotomy [1-3]) all having a great correction power but also a high complications rate [1,2]. Pedicle subtraction osteotomy (PSO), which is mainly used for the treatment of fixed sagittal imbalance, is a posterior closing wedge technique that causes a high correction in a single level (up to 35°). PSO presupposes posterior fixation and the most frequent complications are neurological deficits and hardware failure, in particular rod breakage [1-4]. The aim of this work is to quantify the destabilization produced by a PSO, using a calibrated finite element model of the lumbar spine. This preliminary study is helpful to understand the mechanisms that can contribute to overload the spinal devices used to stabilize the osteotomies, therefore increasing the risk of rod breakage.
A non-linear finite element model of the intact lumbosacral spine (L1-S1) was created based on CT scans (512 × 512 pixels/slice, slice thickness 0.625 mm) of a 40 years old human male (CT scan taken due to kidney stones and not related to spinal pathologies). The position of each vertebra was readjusted mimicking the curvature of a subject having a low lumbar lordosis (35°), thus modeling a case needing surgical correction. Vertebral bodies and intervertebral discs were meshed with linear hexahedral elements whereas the posterior elements were meshed with linear tetrahedrons. Discs were divided in nucleus pulposus, annulus fibrosus and endplates and their heights were consistent with anatomical data [5]. In order to mimic the collagen fibers, four rebar layers were embedded in an isotropic solid matrix [6]. For each layer two bundles of tension-only linear elastic fibers were modeled with orientation of ±30° with respect to the horizontal plane. Moreover, a disc-nucleus volume ratio of about 50% [7,8] and a fiber cross-sectional area of 0.1 mm2 were assumed [9]. Ligaments were represented as tension-only linear spring elements while the facet joints were modeled with a cartilage layer of 0.2 mm and a gap of 0.6 mm [9]. Mechanical properties (Table 1) were taken from literature [9-12]. Trabecular bone was modeled with transverse isotropic properties. Regarding the ligaments, properties found in literature [13] were modified and adapted during the calibration process (see Supplementary Material). ICEM CFD 14.0 (ANSYS Inc,
∗ Corresponding author at: Laboratory of Biological Structure Mechanics, Department of Chemistry, Materials and Chemical Engineering “G. Natta”, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy. Tel.: +39 02 2399 4317; fax: +39 02 2399 4286. E-mail address: [email protected] (C. Ottardi).
http://dx.doi.org/10.1016/j.medengphy.2016.02.002 1350-4533/© 2016 IPEM. Published by Elsevier Ltd. All rights reserved.
Please cite this article as: C. Ottardi et al., Finite element analysis of the lumbar destabilization following pedicle subtraction osteotomy, Medical Engineering and Physics (2016), http://dx.doi.org/10.1016/j.medengphy.2016.02.002
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C. Ottardi et al. / Medical Engineering and Physics 000 (2016) 1–4 Table 2 ROMs and flexibility coefficients of each functional unit.
Table 1 Mechanical properties of the different structures of the model. Young modulus (MPa) Cortical bone Trabecular bone Posterior process Cartilage Anulus: fibers Anulus: ground substance Bony endplates Nucleus pulposus
12,0 0 0 140,140,200 2500 23.8 25 4.2 100 1
Flex
Ext
Left bend
Right bend
Left rot
Right rot
L1-L2 L2-L3 L3-L4 L4-L5 L5-S1 L1-L2
2.4 2.4 2.6 3.0 4.8 0.4
1.3 1.5 1.6 2.0 2.8 0.2
2.6 2.9 2.5 2.6 2.6 0.4
2.6 2.8 2.3 2.5 2.6 0.4
2.1 2.1 1.8 1.6 2.1 0.3
1.7 1.7 1.6 1.5 2.0 0.3
[14] L2-L3 [14] L3-L4 [14] L4-L5 [14] L5-S1 [14]
0.5 0.6 0.7 0.6 0.8 0.8 1.0 1.2 1.3
0.4 0.4 0.3 0.3 0.5 0.4 0.4 0.6 0.8
0.5 0.9 0.7 0.8 0.9 0.7 0.5 0.8 0.6
0.5 0.9 0.7 0.8 0.9 0.7 0.5 0.7 0.6
– 0.4 – 0.3 – 0.3 – 0.5 –
– 0.4 – 0.4 – 0.3 – 0.4 –
Poisson coefficient 0.3 0.45,0.325,0.315 0.25 0.4 0.3 0.5 0.4 0.449
ROM (°)
Flexibility coefficient (°/Nm)
Table 3 Variation of the ROM, at the osteotomy level, of the two destabilized models (OL3 and OL4). It must be noted that in one case the comparison is at L3-L4 level (model OL3) while the other one is at L4-L5 (model OL4). Fig. 1. Intact model of the lumbar spine (left) and osteotomy performed on L3 (middle) and L4 (right).
Canonsburg, PA, USA) was employed to create the mesh while Abaqus 6.12-3 (Dassault Systèmes, Simulia, Providence, RI, USA) was used for the numerical analysis. A mesh convergence study was conducted by monitoring the stresses on the endplates. The final mesh had 215.494 elements and 167.898 nodes. The model was loaded with a follower load of 500 N, by means of connector elements following the spinal curvature. An optimization of the position of the connectors was performed, ensuring a minimization of the rotations (<5%) along the three axes. Pure moments of ±7.5 Nm were applied in flexion-extension, lateral bending and axial rotation to simulate the standing condition, while the inferior part of the sacrum was totally constrained. All FSUs were calibrated by applying pure moments on the upper surface of the vertebrae, with the inferior endplate and the facets rigidly fixed. The moment/rotation curves as well as the overall Ranges of Motion (ROMs) were compared to literature data [14-21]. Two models were created to simulate the osteotomy on the L3 level (OL3) and on L4 (OL4) (Fig. 1). Since PSO may be used to obtain a correction up to 35° [3,4,22], a wedged shape resection of 30° was performed on the vertebral bodies, resulting in a lumbar lordosis of 65°. A surface-to-surface contact was defined along the fracture extremities with a friction coefficient of 0.46 [23]. To evaluate the influence of the destabilization following a PSO, the ROMs of the intact model (Fig. 3) were compared to the values obtained with OL3 and OL4. Due to the severe destabilization, the osteotomy models did not converge at 7.5 Nm so the comparison was done at the highest moment reached with OL4 (7.5 Nm in flexion, 4 Nm in bending and 3 Nm in extension and axial rotation). The percentage variation of the ROM at the osteotomy level was compared with the ROM of the same level of the intact model (Table 3). Moreover, the forces acting at the osteotomy level in the intact model and on the fractured surface following PSO were calculated after applying the follower load. 3. Results Comparing the results obtained with the intact model with literature data [15-21], it can be noted that the values of the
ROM variation (%)
OL3 vs intact
OL4 vs intact
Flexion/extension Lateral bending Axial rotation
74 38 61
143 327 277
total ROMs in flexion/extension, lateral bending and axial rotation (Table 2 and Fig. 2) are in good agreement. The calculated flexibility coefficients were similar to those found in a previous work [14], with an average error of 14% (Table 2). After both osteotomies, the global ROMs increased (Fig. 3). The largest variation can be noted in axial rotation (58% for OL3 and 45% for OL4) and lateral bending (43%) for OL4 but all the movements have significant changes (11–16% in flexion/extension). However, the variation of the ROM at the osteotomy site is even more pronounced (Table 3). Moreover, the load acting on L3 and L4 was 85% and 87% of the total follower load while in the osteotomy models (OL3 and OL4), as expected following the removal of the posterior structures of the spine, 500 N were insisting on the fracture. 4. Discussion This study, represents the first and key step to understand the behavioral changes in a spine subjected to PSO, and helps to compare the different fixation system and hardware constructs. Several osteotomy techniques are currently used but they are all technically demanding and imply a high rate of complications, which may be related to biomechanical factors [1-4,22,24]. Nevertheless, only few biomechanical studies are available in the literature. In a published study, Ponte osteotomy and discectomy were compared in terms of ROM and posterior translation of the vertebral segments with respect to the intact situation. The authors found that a Ponte osteotomy causes a 20% destabilization while a total discectomy is even more severe [25]. Hato et al. studied a closing-opening correction osteotomy with a numerical model of the thoraco-lumbar spine [26]. Several models were created, considering different grades of osteoporosis and varying the kyphotic angle but the results are not directly comparable with the present paper, due to the different surgical techniques investigated. Charosky et al. studied the PSO with a simplified computational model, reproducing three defect situations and studying loads and stresses arising in different configurations of spinal implants [27].
Please cite this article as: C. Ottardi et al., Finite element analysis of the lumbar destabilization following pedicle subtraction osteotomy, Medical Engineering and Physics (2016), http://dx.doi.org/10.1016/j.medengphy.2016.02.002
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Fig. 2. ROMs obtained with the finite element model of the single motion segments (FEM) compared with literature data.
Fig. 3. Comparison of the total ROM of the lumbar spine (L1-S1) obtained with the intact and osteotomy models (OL3 and OL4). The comparison is done considering the angle reached at 7.5 Nm in flexion, 4 Nm in bending and 3 Nm in extension and axial rotation.
One destabilization reported in this work is similar to the situation reproduced on OL4 with a 30° resection. However, the authors only studied the instrumented models, without considering the intact and destabilized conditions alone. Despite the differences concerning the modeling strategies, their results in terms of ROM express the same increasing trend going from an intact to a destabilized model. PSOs can be performed on different levels, depending on the patient and the type of deformity to be treated. However, the lower lumbar spine determines most of the lordosis of the whole region and thus many surgeries are reported on L4 [24]. In a clinical study, Bridwell et al. performed PSO on 78 patients, having the 56% and 17% of the surgeries on L3 and L4 respectively [3]. These data explain our decision of simulating with a finite element model a PSO on L3 and L4. Analyzing both cases and comparing the results with the intact model, it is clear that both osteotomies
induce a major destabilization of the lumbar spine. However, OL4 show a greater influence on the ROM (2 times more than OL3 in flexion-extension and more than 4 times in lateral bending and axial rotation, at the osteotomy level). Thus, an osteotomy on L3 may reduce the overload acting on the device. However, due to the morphology of the lumbar spine, a correction on L4 leads to a bigger variation of the lordosis and the same correction can be probably achieved removing a smaller wedge on L4 than L3. Although this would be the preferred approach, due to clinical factors is often not possible to perform the surgery on L4 and therefore L3 is operated. To ensure a comparability of the results, the simulation of the PSO was done removing a 30° wedge from the vertebral body in both cases. A smaller resection angle will probably cause a reduction of the stresses on the spinal instrumentation, independently from the osteotomy level. An interesting preliminary question before studying the PSO on instrumented models is therefore related to the determination of the optimal correction degree and the level in which it should be performed, since the high rate of failure of the fixation devices is well documented [1,3,4,28,29]. Based on the current results, the interplay of the considered factors (level of osteotomy, degree of correction) appears to be more complex than expected, and therefore a wider simulation campaign should be conducted before clinically relevant conclusions can be drawn. The evaluation of the load sharing between the anterior and posterior spines showed a similar distribution of the load for the two models (85% and 87% on the intact vertebral bodies of L3 and L4, respectively). A load sharing in the anterior column of about 75% was reported in a numerical study concerning the lumbar spine, imposing a follower load of 450 N and a pure flexion moment of 8 Nm [30]. Conversely, in the osteotomy models 100% of the imposed follower load was acting on the fractured surface. This can be explained considering the removal of the posterior elements and the ligaments at the osteotomy site. Due to the instability and the major loads acting on this interface, spinal instrumentation would therefore be highly stressed, in agreement with the high hardware failure rates reported in literature. In conclusion, PSO always induces a great instability but performing it at a lower level seems to be more severe. Therefore,
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despite the significant deformity corrections which could be achieved with PSO, this technique still needs to be analyzed in depth from a biomechanical point of view. Conflict of interest There are no actual or potential competing interests, of conflicts of interest, in relation to this article. Funding None. Ethical approval We deemed that an ethical approval was not required for this study. The patient, the CT data of whom were used to build the FE model, signed a letter of waiver in which he agreed that relevant clinical data may be used in the future for scientific purposes, according to the Italian regulations. The findings of the present study had no influence on the clinical treatment of the patient. Supplementary Materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.medengphy.2016.02. 002. References [1] Bergin PF, O’Brien JR, Matteini LE, Yu WD, Kebaish KM. The use of spinal osteotomy in the treatment of spinal deformity. Orthopedics 2010;33:586–94. [2] Dorward IG, Lenke LG. Osteotomies in the posterior-only treatment of complex adult spinal deformity: a comparative review. Neurosurg Focus 2010;28:E4. [3] Bridwell KH. Decision making regarding Smith-Petersen vs. pedicle subtraction osteotomy vs. vertebral column resection for spinal deformity. Spine (Phila Pa 1976) 2006;31:S171–8. [4] Luca A, Lovi A, Galbusera F, Brayda-Bruno M. Revision surgery after PSO failure with rod breakage: a comparison of different techniques. Eur Spine J 2014;23(Suppl 6):610–15. [5] Busscher I, Ploegmakers JJW, Verkerke GJ, Veldhuizen AG. Comparative anatomical dimensions of the complete human and porcine spine. Eur Spine J 2010;19(7):1104–14. [6] Dabirrahmani D, Becker S, Hogg M, Appleyard R, Baroud G, Gillies M. Mechanical variables affecting balloon kyphoplasty outcome–a finite element study. Comput Methods Biomech Biomed Eng 2012;15:211–20. [7] Violas P, Estivalezes E, Briot J, Sales de Gauzy J, Swider P. Objective quantification of intervertebral disc volume properties using MRI in idiopathic scoliosis surgery. Magn Reson Imaging 2007;25:386–91. [8] Boccaccio A, Vena P, Gastaldi D, Franzoso G, Pietrabissa R, Pappalettere C. Finite element analysis of cancellous bone failure in the vertebral body of healthy and osteoporotic subjects. Proc Inst Mech Eng H 2008;222(7):1023– 36.
[9] Galbusera F, Bellini C, Anasetti F, Ciavarro C, Lovi A, Brayda-Bruno M. Rigid and flexible spinal stabilization devices: a biomechanical comparison. Med Eng Phys 2011;33:490–6. [10] Lu YM, Hutton WC, Gharpuray VM. Can variations in intervertebral disc height affect the mechanical function of the disc? Spine 1996;21(19):2208–16. [11] Cowin SC. Bone mechanics. 2nd ed. Boca Raton, FL: CRC Press; 1991. p. 97–159. [12] Pitzen T, Geisler F, Matthis D, Müller-Storz H, Barbier D, Steudel WI, et al. A finite element model for predicting the biomechanical behaviour of the human lumbar spine. Control Eng Pract 2002;10:83–90. [13] Alizadeh M, Kadir MRA, Saldanha S. Biomechanical effects of short construct spine posterior fixation, in thoracolumbar region with L1 burst fracture. In: IEEE EMBS conference on biomedical engineering & sciences (IECBES 2010); 2010. [14] Guan Y, Yoganandan N, Moore J, Pintar FA, Zhang J, Maiman DJ, et al. Momentrotation responses of the human lumbosacral spinal column. J Biomech 2007;40:1975–80. [15] Wilke HJ, Geppert J, Kienle A. Biomechanical in vitro evaluation of the complete porcine spine in comparison with data of the human spine. Eur Spine J 2011;20:1859–68. [16] White A, Panjabi M. Clinical biomechanics of the spine. 2nd ed. Philadelphia: Lippincott Williams & Wilkins; 1990. [17] Dvorák J, Panjabi MM, Chang DG, Theiler R, Grob D. Functional radiographic diagnosis of the lumbar spine. Flexion-extension and lateral bending. Spine (Phila Pa 1976) 1991;16:562–71. [18] Hayes MA, Howard TC, Gruel CR, Kopta JA. Roentgenographic evaluation of lumbar spine flexion-extension in asymptomatic individuals. Spine (Phila Pa 1976) 1989;14:327–31. [19] Yamamoto I, Panjabi MM, Crisco T, Oxland T. Three-dimensional movements of the whole lumbar spine and lumbosacral joint. Spine (Phila Pa 1976) 1989;14:1256–60. [20] Pearcy M, Portek I, Shepherd J. Three-dimensional x-ray analysis of normal movement in the lumbar spine. Spine (Phila Pa 1976) 1984;9:294–7. [21] Pearcy MJ, Tibrewal SB. Axial rotation and lateral bending in the normal lumbar spine measured by three-dimensional radiography. Spine (Phila Pa 1976) 1984;9:582–7. [22] Bridwell KH, Lewis SJ, Lenke LG, Baldus C, Blanke K. Pedicle subtraction osteotomy for the treatment of fixed sagittal imbalance. J Bone Joint Surg Am 2003;85-A:454–63. [23] Goffin JM, Pankaj P, Simpson AH. A computational study on the effect of fracture intrusion distance in three- and four-part trochanteric fractures treated with Gamma nail and sliding hip screw. J Orthop Res 2014;32:39–45. [24] Berjano P, Aebi M. Pedicle subtraction osteotomies (PSO) in the lumbar spine for sagittal deformities. Eur Spine J 2015;24(Suppl 1):S49–57. [25] Wang C, Bell K, McClincy M, Jacobs L, Dede O, Roach J, et al. Biomechanical comparison of Ponte osteotomy and discectomy. Spine (Phila Pa 1976) 2015;40(3):E141–5. [26] Hato T, Kawahara N, Tomita K, Murakami H, Akamaru T, Tawara D, et al. Finiteelement analysis on closing-opening correction osteotomy for angular kyphosis of osteoporotic vertebral fractures. J Orthop Sci 2007;12:354–60. [27] Charosky S, Moreno P, Maxy P. Instability and instrumentation failures after a PSO: a finite element analysis. Eur Spine J 2014;23:2340–9. [28] Smith JS, Shaffrey CI, Ames CP, Demakakos J, Fu KM, Keshavarzi S, et al. Assessment of symptomatic rod fracture after posterior instrumented fusion for adult spinal deformity. Neurosurgery 2012;71:862–7. [29] Smith JS, Shaffrey E, Klineberg E, Shaffrey CI, Lafage V, Schwab FJ, et al. Prospective multicenter assessment of risk factors for rod fracture following surgery for adult spinal deformity. J Neurosurg Spine 2014;21:994–1003. [30] Gornet MF, Chan FW, Coleman JC, Murrell B, Nockels RP, Taylor BA, et al. Biomechanical assessment of a PEEK rod system for semi-rigid fixation of lumbar fusion constructs. J Biomech Eng 2011;133:081009.
Please cite this article as: C. Ottardi et al., Finite element analysis of the lumbar destabilization following pedicle subtraction osteotomy, Medical Engineering and Physics (2016), http://dx.doi.org/10.1016/j.medengphy.2016.02.002