J Orthop Sci (2003) 8:577–584 DOI 10.1007/s00776-003-0675-1
Effects of lumbar spinal fusion on the other lumbar intervertebral levels (three-dimensional finite element analysis) Keisuke Goto1, Naoya Tajima1, Etsuo Chosa1, Koji Totoribe1, Shinichiro Kubo1, Hiroshi Kuroki1, and Takashi Arai2 1 2
Department of Orthopaedic Surgery, Miyazaki Medical College, 5200 Kihara, Kiyotake, Miyazaki 889-1692, Japan Yokogawa Technical Information, Funabashi, Japan
Abstract The risk of accelerating the degeneration of adjacent disc levels after lumbar spinal fusion is a controversial issue. A finite element model consisting of L1 to L5 lumbar spines was used to assess the effect on adjacent disc level after lumbar spinal fusion. We compared intact, L4/5 posterior interbody fusion (PLF), and L4/5 posterior lumbar interbody fusion (PLIF) models. The loading conditions applied were compressive force, compressive force plus flexion moment, and compressive force plus extension moment. Evaluations were made for von Mises stress on each vertebral end-plate, Tresca stress of all the annulus fibrosus, and Tresca stress of the annulus fibrosus from the posterior surface of the disc to the neural foramen. As the result, the von Mises stress adjacent to the fusion level was higher than the other nonfusion levels; it was higher under conditions of flexion moment loading plus compression loading [112% (2.59 PMa) in the PLF model and 117% (2.72 Mpa) in the PLIF model] than in the intact model. The Tresca stress of all the annulus fibrosus adjacent to the fusion level was higher than that on other nonfusion intervertebral levels; it was higher under conditions of flexion moment loading plus compression loading [127% (0.57 PMa) in the PLF model and 209% (0.89 Mpa) in the PLIF model] than in the intact model. The Tresca stress of the annulus fibrosus from the posterior surface of the disc to the neural foramen adjacent to the fusion level was higher than that on other nonfusion intervertebral levels; and it was higher under conditions of flexion moment loading plus compression loading [107% (1.48 PMa) in the PLF model and 112% (1.54 Mpa) in the PLIF model] than in the intact model. These findings demonstrate that with lumbar fusion, stresses on the vertebral end-plate and the annulus fibrosus were high adjacent to the fusion level; furthermore, stresses were higher in the PLIF model than in the PLF model. These results suggested that lumbar spinal fusion might bring with it a risk of damage to the annulus fibrosus and the vertebral end-plate adjacent to the fusion level.
Offprint requests to: K. Goto Received: July 3, 2002 / Accepted: April 9, 2003
Key words Finite-element method · Adjacent segment · Posterolateral lumbar fusion (PLF) · Posterior lumbar interbody fusion (PLIF)
Introduction Various fusion techniques are undertaken for unstable lumbar spines. Spinal fusion has been suggested to have the risk of promoting degeneration at the other intervertebral levels due to the rigidity of the fusion area.12 Seitsalo et al.,15 however, reported that spinal fusion did not accelerate adjacent-segment degeneration. Several reports regarding the influence on the motion of adjacent segments after in vivo spinal fusion in humans,3,8,9 but no in vivo studies have detailed stress changes in relation to the annulus fibrosus. There are some in vitro studies regarding the influence on adjacent motion segments in fusion models17,21 using an instrument that makes the initial fusion more rigid than can be obtained by autogenous bone fusion. No reports have been presented about the influence of autogenous bone fusion on the adjacent motion segments. This could be because evaluations of such influences in a bone-fused state are difficult in cadaver experiments. If a model in a bone-fused state after lumbar spinal fusion could be produced by the three-dimensional finite element method, however, numerical analysis would be possible. Data on the material constants of the vertebral body are indispensable for producing models for finite element analysis, but, there are no measurement values that give accurate material constants for the intact nucleus pulposus. Given this, an accurate model of the intervertebral disc could not be made. In previous studies, models of the intervertebral disc have been produced by conferring viscoelastic20 or
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poroelastic18,23 characteristics on the elements of the disc, with analyses performed using virtual intervertebral disc models. In a previous study, we did not venture to express the nucleus pulposus in terms of elements and so produced a lumbar spine model by directly inputting the intradiscal pressure of the lumbar spine with no abnormalities of the nucleus pulposus. We then analyzed changes in stress on the disc utilizing the three-dimensional finite element method.5 In the present study, a model of the entire lumbar spine (L1L5) has been produced by this method, and the influence of L4/5 fusion on the vertebral end-plate and the annulus fibrosus of the intervertebral disc at the other intervertebral levels has been evaluated by threedimensional finite element analysis.
Material and methods We performed finite element analysis to investigate biomechanical changes induced by posterolateral interbody fusion (PLF) and posterior lumbar interbody fusion (PLIF). Three finite element models (FEMs) of the lumbar spine consisting of the five vertebral bodies and the four discs from L1 to L5 were established. A commercially available finite element program, COSMOS/M 2.5 (Structural Research and Analysis Corporation, Los Angeles, CA, USA), was used to model the spinal segments. The models and the loading and boundary conditions are described here.
a
b
Intact model For the analytical model (Fig. 1a) computed tomography (CT) scanning was performed at slice widths of 2 mm in a 29-year-old man with no clinical or roentgenological abnormalities. This model contains elements of cortical and cancellous bone, annulus fibrosus, and anterior longitudinal, posterior longitudinal, supraspinous, interspinous, and intertransverse ligaments. A three-dimensional isotropic eight-nodal solid element was used for modeling the cortical and cancellous bones, the end-plate, and ground substance of the disc. The material properties of each element were determined according to the literature (Table 1).1,2,4,7,10,11,13,16,19,22 When modeling the disc, the annulus was regarded as composite material consisting of fiber embedded in the ground substance. Annular fibers were modeled using a three-dimensional cable element with pure tensile force. The facet joints (L1/2, L2/3, L3/4, L4/5) were treated as in three-dimensional contact with a total of 139 individual gap elements. This model was symmetrical in the sagittal plane and was separated into 31 948 total elements and 33 035 total nodal points, as shown in Fig. 1. Posterolateral lumbar fusion model For PLF, bone graft was placed between the transverse process of the adjacent two vertebrae. The PLF model (Fig. 1b) consisted of the bone graft and the intact
c
Fig. 1. Finite element models. a Intact model. b Posterolateral lumbar fusion model. c Posterior lumbar interbody fusion model. b In the encircled part, the graft bone is crosslinked with the transverse process at L4/5 and subjected to posterolateral fusion. c In the encircled part, intervertebral tissues are converted to the material characteristic values of cortical bone and are subjected to interbody fusion
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Table 1. Material properties/values and element types Position Parameter
Element type
Material Cortical bone Cancellous bone End-plate Annulus ground
8–Node solid 8–Node solid 8–Node solid 8–Node solid
Annulus fiber Ligaments Anterior long Posterior long Interspinous Supraspinous Intertransverse Facet Intradiscal pressure Flexion Upright Extension
Young’s modulus (E : MPa)
Poisson’s ratio (ν)
L1/2
L2/3
L3/4
L4/5
1.19 0.49 0.53
1.23 0.5 0.55
1.28 0.52 0.56
1.32 0.54 0.59
12 000 0.3 100 0.2 23.8 0.4 4.2 0.45 Cross section (mm2) Nonlinear 0.22015 Nonlinear 75.9 51.8 36.3 75.7 2.0
2–Node cable 2–Node cable
Gap element
lumbar spine; it contained 32 023 nodes and 32 149 elements. Posterior lumbar interbody fusion model The intact FEM model described above was modified to simulate posterior lumbar interbody fusion (Fig. 1c). To mimic interbody fusion, the disc was totally replaced by the interbody bone graft. The assumption of the study was that patients would have gained solid fusion, so the stress distribution within the model was determined by assuming that the bone grafts would be able to transmit loads in compression as well as in tension. Stress distribution can be evaluated differently depending on kinetic behavior when loads are given. Evaluation methods16 for Tresca stress (shear stress) or von Mises stress (shear strain energy) are applicable to ductile materials such as ligaments and vertebrae undergoing nonelastic deformation. In this study, the annulus fibrosus could be evaluated for Tresca stress because uniaxial truss elements are made up of twodimensional lines,16 and vertebral end-plates could be evaluated for von Mises stress because they are made up of eight-nodal hexagonal elements.4,16 The respective stress formulas are as follows. Tresca stress: Tresca stress 1/2 (σ1 σ3) 2
2
Mises stress: 2(Mises stress) (σ1 σ2) 2 2 (σ2 σ3) (σ3 σ1) The respective stresses of σ1, σ2, and σ3 are σ1 σ2 σ3.
Because loads in different directions caused stress accumulation in the fused lumbar spine, this study estimated both the maximum von Mises stress of the vertebral end-plate and the maximum Tresca stress of annulus fibers to evaluate the difference between the two fusion procedures. Von Mises stress of the vertebral end-plate was the mean stress of the upper and lower vertebral end-plate. After modification of the models, this study simulated posterolateral fusion and interbody fusion at the L4/5 level to determine the influence on the other annulus fibers and the vertebral end-plate stress. The annulus fibers and vertebral end-plate stress from these flexion, standing, and extension models were examined comparatively.
Boundary and loading condition The following can be used to assess the validity of the results from the finite element method (1) using knowledge of the strength of the materials, (2) referring to similar calculations, or (3) referring to observed values. In our model, the results cannot be judged for validity by either method (1) or (2) because our model is based on the human lumbar spine, and there have been no reports of the whole lumbar spine that have dealt with finely divided validity indexes. Method (3) can be evaluated by comparing our data with in vivo or cadaveric measurements. We did not simulate the neuromuscular control of the lumbar spine, but our model does not include data on these muscles and so is not appropriate for comparison with in vivo data.
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Therefore, in this study, we referred to a report24 on stress evaluation of the cadaveric lumbar spine, confirming the validity of our model through a comparison with that report. The data also included in our model allowed us to analyze the model using the same values as the stress loads of the cadaveric lumbar spine. Compressive loading was performed in 10 steps to 265 N by the loading increment method. Then loading of flexion and extension loads of 10 Nm2 imposed on the L1 vertebral body was performed in 15 steps for the flexion and extension models. Boundary conditions were such that symmetrical conditions were set for the sagittal plane, and the inferior surface of the L5 vertebral body was not allowed to move in any direction. The selection of these loads simulated situations that were analyzed in an experimental in vitro study.24 This allowed validation of the output of the intact FEMs. Based on a preliminary study, these loads were judged to be sufficient to produce physiological motion.
Results Model validation To evaluate the validity of our model, the results were compared with those of a previous experiment using cadavers. Yamamoto et al.24 performed a study using lumbar spines of cadavers. The flexion/extension range in the FEM model in this study was 6.7° at L1/2, 8.1° at L2/3, 8.6° at L3/4, and 12.2° at L4/5, being greater at the caudal intervertebral level. The data reported by Yamamoto et al. were consistent with ours, including the greater range of motion at L4/5 than at the other three, higher intervertebral levels (Fig. 2).
PLF and PLIF The range of motion at L4/5 was 1.79° in the PLF model and 0.33° in the PLIF model. These are marked decreases compared with that of the intact model (12.2°) (Fig. 2). Stress on the vertebral end-plate Compressive load alone The mean von Mises stress on the upper and lower vertebral end-plate at the nonfusion intervertebral level, especially in L1/2 and L2/3, was similar among the intact, PLF, and PLIF models. In each model, the stress on the vertebral end-plate was lower at the cranial intervertebral level. In the fusion models, the von Mises stress adjacent to the fusion level was higher than other nonfusion intervertebral levels. The von Mises stress on the vertebral end-plate at L4/5 in the PLF model decreased to 33% (0.56 MPa) of that in the intact model (Fig. 3). Compressive force and flexion moment The mean von Mises stress on the upper and lower vertebral end-plates at the nonfusion intervertebral level was lower at cranial intervertebral levels in the intact, PLF, and PLIF models. At each nonfusion intervertebral level, the von Mises stress on the vertebral end-plate in the PLIF model was higher than those in the other models. In the fusion models, the von Mises stress adjacent to the fusion level was higher than at other nonfusion intervertebral levels. In particular, the stress at L3/4 in the PLIF model was 117% (2.72 MPa) of that in the intact model. The stress on the vertebral end-plate at the fusion level (L4/5) in the PLF model was 29% (0.79 MPa) of that in the intact model (Fig. 4). Compressive force and extension moment The mean von Mises stress on the upper and lower vertebral end-plates at the nonfusion intervertebral level was lower at cranial intervertebral levels in the
(degree) 14 12 10
(MPa)
Yamamoto
6
PLF
1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0
PLIF 4 2 0 L1/2
L2/3
L3/4
L4/5 (Disc level)
von Mises stress
Intact 8
Intact PLF PLIF
L1/2
Fig. 2. Finite element models and the intervertebral range of motion in an in vitro study (10 Nm moment). PLF, posterior interbody fusion; PLIF, posterior lumbar interbody fusion
L2/3
L3/4
L4/5 (Disc level)
Fig. 3. von Mises stress on the vertebral end-plate under a compressive load
K. Goto et al.: Mechanical analysis of lumbar spinal fusion
581 (MPa) 0.25
3 2.5 2 1.5 1 0.5 0
Intact PLF PLIF
Tresca stress
von Mises stress
(MPa)
0.2 Intact PLF PLIF
0.15 0.1 0.05
L1/2
L2/3
L3/4
L4/5
(Disc level)
0 L1/2
Fig. 4. von Mises stress on the vertebral end-plate under a compressive load plus a flexion moment load
L3/4
L4/5 (Disc level)
Fig. 6. Tresca stress on all annulus fibers under a compressive load (MPa)
(MPa)
1 Intact PLF PLIF
1.5 1 0.5
Tresca stress
2
von Mises stress
L2/3
0.8 0.6
Intact PLF PLIF
0.4 0.2
0 L1/2
L2/3
L3/4
L4/5 (Disc level)
Fig. 5. von Mises stress on the vertebral end-plate under a compressive load plus an extension moment load
intact, PLF, and PLIF models. At each nonfusion intervertebral level, the von Mises stress on the vertebral end-plate in the PLIF model was higher than those in the other models. In the fusion models, the von Mises stress adjacent to the fusion level was higher than that at other nonfusion intervertebral levels. The stress on the vertebral end-plate at the fusion level (L4/5) in the PLF model was 32% (0.56 MPa) of that in the intact model (Fig. 5). Stress on all the annulus fibers Compressive load alone The mean Tresca stress of annulus fibers at the nonfusion intervertebral level was lower at cranial intervertebral levels in the intact, PLF, and PLIF models. At each nonfusion intervertebral level, the Tresca stress of annulus fibers in the PLIF model was higher than those in the other models. In the fusion models, the Tresca stress adjacent to the fusion level was higher than that at other nonfusion intervertebral levels. In particular, the Tresca stress of the annulus fibers at L3/4 in the PLIF model was 182% (0.22 MPa) of that in the intact model. At the fusion intervertebral level (L4/5), the stress on annulus fibers in the PLF model was 17% (0.03 MPa) of that in the intact model (Fig. 6). Compressive force and flexion moment The mean Tresca stress of the annulus fibers at the nonfusion intervertebral level was lower at cranial
0 L1/2
L2/3
L3/4
L4/5 (Disc level)
Fig. 7. Tresca stress on all annulus fibers under a compressive load plus a flexion moment load
intervertebral levels in the intact, PLF, and PLIF models. At each nonfusion intervertebral level, the Tresca stress of the annulus fibers in the PLIF model was higher than those in the other models. In the fusion models, the Tresca stress adjacent to the fusion level was higher than at other nonfusion intervertebral levels. In particular, the Tresca stress at L3/4 in the PLIF model was 209% (0.89 MPa) of that in the intact model. At the fusion level (L4/5), the stress on annulus fibers in the PLF model was 6% (0.04 MPa) of that in the intact model (Fig. 7). Compressive force and extension moment The mean Tresca stress of the annulus fibers at the nonfusion intervertebral level was lower at cranial intervertebral levels in the intact, PLF, and PLIF models. At each nonfusion level, the Tresca stress of the annulus fibers in the PLIF model was higher than those in the other models. In the fusion models, the Tresca stress according to the nonfusion levels was the highest at L3/4, adjacent to the fusion level. At the fusion level (L4/5), the stress on annulus fibers in the PLF model was 13% (0.02 MPa) of that in the intact model (Fig. 8). Stress on the annulus fibers (from the posterior surface of the disc to the neural foramen) Compressive load alone The mean Tresca stress of the annulus fibers from the posterior surface of the disc to the neural foramen
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(MPa)
2
0.15 Intact PLF PLIF
0.1 0.05
Tresca stress
Tresca stress
0.2
1.5 Intact PLF PLIF
1 0.5 0
0 L1/2
L2/3
L3/4
L1/2
L4/5 (Disc level)
Fig. 8. Tresca stress on all annulus fibers under compressive plus extension moment loads
L2/3
L3/4
L4/5 (Disc level)
Fig. 10. Tresca stress on annulus fibers from the posterior surface of the disc to the neural foramen under compressive plus flexion moment loads
(MPa)
(MPa)
0.6
Intact PLF PLIF
0.4 0.2 0 L1/2
L2/3
L3/4
L4/5 (Disc level)
Fig. 9. Tresca stress on annulus fibers from the posterior surface of the disc to the neural foramen under a compressive load
showed a pattern similar to that of the Tresca stress of all annulus fibers under a compressive load alone. At L3/4, adjacent to the fusion level, the Tresca stresses in the PLIF and PLF models were 171% (0.92 MPa) and 109% (0.58 MPa), respectively, of the stress in the intact model. At the fusion level (L4/5), the stress on annulus fibers in the PLF model was only 8% (0.07 MPa) of that in the intact model (Fig. 9). Compressive force and flexion moment Changes in the Tresca stress of annulus fibers from the posterior surface of the disc to the neural foramen were higher than changes in the Tresca stress of all annulus fibers. The Tresca stress at the nonfusion intervertebral levels was lower at the cranial intervertebral level. In the fusion models, the Tresca stress adjacent to the fusion level was higher than those at other nonfusion intervertebral levels. The Tresca stress at the nonfusion level was highest in the PLIF model followed, in order, by the PLF and intact models. At the fusion level (L4/ 5), the Tresca stress of annulus fibers in the PLF model was 9% (0.16 MPa) of that in the intact model (Fig. 10). Compressive force and extension moment The mean Tresca stress of annulus fibers from the posterior surface of the disc to the neural foramen showed a pattern similar to that of the Tresca stress of all annulus fibers under a compressive load alone. At L3/4, adjacent to the fusion level, the Tresca stresses in the PLIF and PLF models were 192% (0.64 MPa) and
Tresca stress
Tresca stress
1 0.8
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
Intact PLF PLIF
L1/2
L2/3
L3/4
L4/5 (Disc level)
Fig. 11. Tresca stress on annulus fibers from the posterior surface of the disc to the neural foramen under compressive plus extension moment loads
178% (0.59 MPa), respectively, of the stress in the intact model. At the fusion level (L4/5), the stress on annulus fibers in the PLF model was only 9% (0.07 MPa) of that in the intact model (Fig. 11).
Discussion To evaluate the influence of lumbar spinal fusion on the other lumbar intervertebral levels, we produced a three-dimensional model of the entire lumbar spine and performed finite element analysis. This method is a highly accurate simulation technique that is useful for clarifying mechanisms of the lumbar spine. Models that accurately reproduce the vertebral body are important for this analysis. Data on the material constants of the vertebral body are indispensable for the production of models. However, the nucleus pulposus is not uniform, and resected nucleus pulposus rapidly degenerates. At present, there are no accurate measurement values of the material constant for normal nucleus pulposus. Thus, production of an accurate model of the intervertebral disc appears impossible. Various investigators have made disc models by conferring viscoelastic20 or poroelastic18,23 characteristics on disc elements and performed analyses using virtual
K. Goto et al.: Mechanical analysis of lumbar spinal fusion
disc models. In a previous study, we did not venture to express the nucleus pulposus as elements and so directly input data on the intradiscal pressure of normal people into the nucleus pulposus area; we then performed analyses utilizing the three-dimensional finite element method.5 In this study, a model of L1-L5 was produced by the same method. Yamamoto et al.24 reported data obtained from experiments in cadavers. To evaluate the validity of our model, a 10-Nm flexion/extension moment load, which was used in their study, was applied to our model, and the rotation angles were compared. A black box of the infinite element program was made, so that when data are input results can be extracted. However, the analysis method must be carefully selected. The von Mises stress can be applied to the stress analysis of the entire annulus fibrosus of the intervertebral disc but not that of annulus fiber. This is because our model, as well as the model reported by Shirazi-Adl et al.,16 was a complex in which the volume of annulus fibrosus of the intervertebral disc elements consists of 16% annulus fibers and 84% annulus fibrosus elements. When rupture of annulus fibers is discussed, stress analysis in the axial direction of fibers is necessary. There have been FEM analyses of the intervertebral discs at levels adjacent to the fusion level5 but no studies of stress analysis of the annulus fibers themselves. The present study is the first attempt. In all models, the mean Tresca stress of annulus fibers from the posterior surface of the disc to the neural foramen was higher than that on all annulus fibers, being especially high after under a compression force and flexion moment (Fig. 10). These results are consistent with increased stress in areas frequently affected by intervertebral disc herniation, as in our earlier study.10 Under all loading conditions, the Tresca stress of annulus fibers was lower at higher intervertebral levels. The Tresca stress of annulus fibers at nonfusion intervertebral levels was highest in the PLIF model, followed in order by the PLF and intact models. In the fusion models, the Tresca stress was high at L3/4, adjacent to the fusion level. In particular, the Tresca stress of annulus fibers (from the posterior surface of the disc to the neural foramen) at L3/4 in the PLIF model under a compression force and flexion moment was highest (1.54 MPa), being 3.2 times that of the Tresca stress of all annulus fibers in the intact model. At the fusion intervertebral level, the Tresca stress of annulus fibers in the PLF model was markedly lower (6%–17% of that in the intact model) under each loading condition. These results suggest that annulus fiber rupture tends to be induced in the compression force and flexion moment model. In particular, stress on the posterior area of the annulus fibers to the neural foramen increases at L3/4, a level adjacent to the fusion level.
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The von Mises stress on the vertebral end-plate was lower at cranial intervertebral levels under all loading conditions. In the fusion models, the von Mises stress on the vertebral end-plate at L3/4, a level adjacent to the fusion level, was highest among the nonfusion intervertebral levels. In particular, von Mises stress on the vertebral end-plate at L3/4 under a compressive force and flexion moment in the PLIF model was highest (2.72 MPa), being 117% of that at L3/4 in the intact model. The von Mises stress on the vertebral endplate at the fusion intervertebral level in the PLF model was 29%–33% of that in the intact model. These results suggest that lumbar spinal fusion induces end-plate damage, particularly at the adjacent intervertebral level (L3/4), in a compressive force and flexion moment model. The intervertebral range of motion at level L3/4, adjacent to the fusion level, in the PLIF model (10.4°) was 120% of that in the intact model (8.6°). This also suggests an increase in the rotation angle and resulting intervertebral disc degeneration.6,14 The intervertebral range of motion, the von Mises stress on the vertebral end-plate, and the Tresca stress of the annulus fibers were higher at the level adjacent to the fusion level (L3/4) in the PLIF model, but these changes remained within the normal range. Clinical degeneration at the intervertebral level adjacent to the fusion level may be induced by a combination of factors. Aging and long-term continuous loading on the vertebrae adjacent to the fusion may reduce the fracture coefficient on the vertebral end-plate and annulus fibers, which may promote degeneration in the annulus fibrosus of the intervertebral disc and the vertebral end-plate damage, resulting in damage in the annulus fibrosus. The finite element method makes it possible to carry out stress tests after graft bones have been assimilated and to make analyses of intact and modified models, depending on what kind of material constants are input. In this instance, the finite element method is superior to the use of cadavers for vitro experiments. However, because there are limitations on analysis performances of computers and analysis software abilities, and as all the in vivo material constants are not always clarified in the finite element method, it is impossible to create a full simulation based on in vivo data. In our model, data on the lumbar spine and supporting ligaments are included, but data on abdominal pressure derived from the paravertebral muscle and the abdominal organs and muscles are not included. As described above, our model is incomplete and has problems concerning its validity. Therefore, because all the in vivo data are not necessarily included in our model, we must compare the model with data obtained from cadaver experiments under similar conditions. The above findings confirmed
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an increased tendency for stress to the fixed area adjacent to the fusion level (the annulus fibrosus and the vertebral end-plate) by lumbar spinal fusion. They also suggest possible changes in the degree of such increases depending on the conditions.
Conclusions We produced an intact model consisting of L1-L5 from which PLF and PLIF models were constructed. Threedimensional finite element analyses were performed using each model. Compressive force, compressive force plus flexion moment, and compressive force plus extension moment were applied to each model; the flexion/extension angle, Tresca stress of annulus fibers, and von Mises stress on the vertebral end-plate at each intervertebral level were then evaluated. The flexion/extension angle and stress values on the vertebral end-plate and annulus fibers were highest at the intervertebral level adjacent to the fusion level. Comparisons between the PLF and PLIF models showed higher stress on the vertebral end-plate and annulus fibers in the PLIF model than in the PLF model at each nonfusion intervertebral level.
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