a finite element study of the stress redistribution of the ... · 第十四屆2009 abaqus taiwan...

第十四屆 2009 Abaqus Taiwan Users’ Conference

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A Finite Element Study of the Stress Redistribution of the Lumbar

Spine after Posterior Lumbar Interbody Fusion Surgery

Hsuan-Teh Hu1, Kuo-Yuan Huang2,3, Che-Jung Liu1, Ching-Sung Kuo1,4

1 Department of Civil Engineering, National Cheng Kung University 2 Institute of Clinical Medicine, College of Medicine, National Cheng Kung University

3Department of Orthopedics, National Cheng Kung University Hospital 4 Center for General Education, Nan Jeon Institute of Technology

ABSTRACT

In this study we focused on the effect of the Posterior Lumbar Interbody Fusion(PLIF) surgery

on the adjacent discs. By using the Finite Element(FE) method, we investigated separately the responses of bone graft fusion and screw fixed system to various loading modes from different models divided into seven types: intact lumbar, (PLIF,L4-5), (PI,L4-5), (PLIF+PI,L4-5), (PLIF,L3- 5), (PI,L3-5), and (PLIF+PI, L3-5). In addition to approaches to the discrepancy between bone graft fusion and screw fixed system about the stress changes under separate loading conditions: preload, extension, flexion, lateral bending, and axial rotation, we compared the variation of relative angle of the endplates, changes of the von Mises stress and strain energy after PLIF surgery.

The results showed that the pedicle screw played an important role in raising the maximum von Mises stress to the adjacent discs: (1)In extension and one-level model, von Mises stress increment was about 4-8% raised in the adjacent discs, while in two-level model the increment was 11-18% in the upper disc adjacent to the fusion and 6-10% in the lower one. (2)In flexion, the increment was about 3-14% raised in the upper disc in one-level model, but decreased in two-level model with bone graft fusion. (3)In lateral bending, the increment decreased in one-level model in the upper disc but increased about 1-4% in the lower one. In tow-level model the increment was around 2% in the adjacent discs.

The numerical results also indicated that bone graft fusion would increase the strain energy percentage of the adjacent discs, and all the models with screw fixed system had higher increment in the adjacent discs than with bone graft fusion.

Keywords: Posterior Lumbar Interbody Fusion(PLIF), bone graft fusion, screw fixed system, von

Mises stress, strain energy.

1. Introduction The spinal disorders usually occur in the

lumbar region because of the wide physical movement and frequent loading caused from the daily activity of the body [1].

There were about 80% of adults suffer- ing from the back pain [2] due to the illness of the lumbar spine. Most of them would recover after conservative treatment, but few of them still had to take a surgical treatment due to severe symptoms resulting from the compre- ssion on the nerves. There were many types of surgery for treating different spinal disorders, the lumbar interbody fusion was one of the

surgery techniques chosen. The purpose of the lumbar fusion surgery

was to fuse two or more segments together after the damaged parts of the lumbar spine were removed. Generally, the screw fixed system would be implanted to maintain strength of the initial stage of the lumbar spine after surgery, and to ensure the bone graft fusion rate higher. However, some accelerated degeneration problems would occur in the adjacent regions of the fused segment after surgery. These accelerated degeneration phenomena were considered to be originating from the segment stiffened by


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the fusion or screw fixed system. It changed the transmission of stress, and induced some stress concentrations in the adjacent parts, but the roles of the bone graft fusion and screw fixed system were still not confirmed.

In PLIF surgery the surgeon cut off some lamina or facet joint to excise the damaged part through the low back incision, and then some bone graft or other spacer was put into to fill the space [3].

In recent years, some clinical researches reported that the adjacent parts of fused vertebra segment would degenerate faster, and the reason was directed to the more stiffened segment of the interbody fusion [4]. However, some researches argued that the weakness of the damaged segment could induce more ex- ertion to the adjacent parts before surgery [5].

The purpose of this study was to figure out the difference between the pedicle screw and bone graft fusion appearing after the PLIF surgery. Although the objective of the PLIF surgery was bone fusion, the screw fixed system influencing the transmission of the stress could not be ignored in the viewpoint of mechanics.

2. Methods 2.1 FE Models

We constructed the mesh of the lumbar spine model by getting the vertebral bound- aries from the DICOM files scanned by Computed Tomography(CT), and retouched each CT slice to make the boundary line more smooth in 3D-Doctor software, and then stacked each boundary line to form the 3D surface model(STL formatted file). After we imported the STL file into Msc.Patran for the preprocessing of the model, a converted input file was exported to ABAQUS for execution and post-processing. The detailed steps adopted in this study are shown in Table 1.

There were seven models corresponding to the specific surgery conditions whose notation is listed in Table 2. The purpose of this setting was to separate the influence of the pedicle screw and the bone graft fusion, we would observe the variations in relative angle of the endplate (the angle between two vertebrae), maximum von Mises stress and strain energy in the adjacent discs after surgery, because the last two physical quantities were related to the fracture.

2.2 Materials The spine consists of 33 vertebrae and is

generally divided into five regions: cervical, thoracic, lumbar, sacrum, and coccyx, as shown in Fig. 1 [6]. Each vertebra (Fig. 2) is composed of cancellous bone, cortical shell, posterior bone, and endplates. A disc, shown in Fig. 3 [7], is composed of nucleus pulposus, annulus fibrosus, and annulus ground substance. This study adopted linear and isotropic material properties for most spinal components such as the cancellous bone, cortical shell, posterior bone, endplate, annulus ground substance, and nucleus pulposus, whereas spinal ligaments, shown in Fig. 4 [7], were modeled as tension-only resistance hyperelastic materials, and annulus fiber layer as composite ones, the material parameters and section properties used for each part of the lumbar spine are listed in detail in Table 3, referring to Chen’s study [8]. 2.3 Loading and Boundary Conditions

The loading case for each posture is shown in Fig. 5, we hypothesized that the real lumbar spine should sustain little shear force because almost of the muscles are in the frontal plane of the body. For each model, the forces were exerted on the same place.

The boundary condition was set with all nodes of the upper endplate of S1 constrained in all directions. 2.4 Validation of the Model

To verify the rationality of this FEM model, we compared the results with the experimental data in Yamamoto’s study [9] and Chen’s study [10]. Under the same loading condition with 150N applying on the upper endplate of L1,and with 10Nm moment on the lumbar spine in various postures: flexion, extension, lateral bending, and axial rotation, the results are plotted in Fig. 6.

3. Results 3.1 Relative angle of endplate increment

The relative angle of endplates was defined by the angle between two consecutive endplates corresponding to the same location of the vertebrae, and was compared to the original model to derive the increment percentage, which could lead us to know how the fusion and screw fixed system influenced the stiffness of the lumbar spine (Fig. 7).

Doubtlessly, the fused segments or screw


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fixed segments got stiffer, and had some effects to the adjacent discs, especially for the upper disc adjacent to the fusion, more relative angle increment would be induced at the lower side, and the largest angle increment occurred in extension. 3.2 Maximum von Mises stress

The maximum von Mises stress in the adjacent discs was observed and compared to the original model, the expression defined below,

(σ-σo) × 100/σo (1) was calculated, where σ is the maximum von Mises stress at each model, and σo denotes the original model(Fig. 8).

In preload and one-level models the maximum von Mises stress had about 1.7% increment in the upper disc adjacent to the fusion, less than 1% in the lower disc. In two-level models, the maximum von Mises stress decreased in models with screw fixed system.

In extension, 4-8% increment occurred in the adjacent discs in one-level models. For two-level models, stress increment was about 11-18% in the upper disc and 6-10% in the lower one.

In flexion, it was about 3-14% increment raised in the upper disc in one-level models, however, it decreased in two-level models with bone fusion.

In lateral bending, it decreased in one- level model in the upper disc and increased about 1-4% in the lower one, as for the tow- level models, the increment was around 2%.

In axial rotation, the variation was less than 1% in the adjacent discs in one-level models. While in two-level models, it decreased in the lower disc about 2% for models with screw implanted.

The data showed that the pedicle screw was one of the influencing factors to raise the maximum von Mises stress in the adjacent discs in extension, flexion,and lateral bending. In preload, the bone graft fusion was the important factor; however, in axial rotation, the trend was not obvious. 3.3 strain energy

The strain energy of the adjacent discs for each model was recorded and compared to the original model (Fig. 9). The strain energy increment was defined as [ (strain energy of disc) / (strain energy of the whole model) －

(strain energy of disc of intact model) / (strain energy of the whole intact model) ] × 100.

Choosing the quantity to exhibit the trend was from the fact that different models in the same posture would not have the same strain energy in the whole model (Fig.10). It was not enough to represent the model with such data if we only used the values of the strain energy in the adjacent discs for study.

By observation of the figures, we could identify that the bone graft fusion was an important factor to raise the strain energy of the adjacent discs, especially in extension, lateral bending, and axial rotation.

4. Discussion The purpose of surveying these three

physical quantities, relative angle, von Mises stress, and strain energy, was to find out the way to measure the degeneration of the discs from the point of view of mechanics. We hypothesized the phenomenon of accelerated degeneration problem in the discs adjacent to the fusion was related to the mechanical changes of the lumbar spine. In this study, we were devoted to the mechanical quantities associated with the deformation, and other field variables would not be considered here. 4.1 Relative angle of endplates

In the changes of relative angle of endplates, we concluded that the bone graft fusion was an important factor to constrain the movement of the vertebrae, especially in axial rotation and lateral bending. By inference, relative angle would be induced by the larger moment of inertia along the axis of rotation and the bigger size of the vertebral body in transverse direction. 4.2 Maximum von Mises stress

The elevated von Mises stress increment appeared in most of the different postures and models, and the screw fixed system was also a governing cause of the rising of the stress increment in extension, flexion, lateral bending, and axial rotation. In extension and axial rotation, the increment occurred more in two-level models (L3-L4, L4-L5). In lateral bending posture, von Mises stress increment would be higher in the lower disc adjacent to the fusion. The reason of increasing stress increment might result from the more stiffness of the screw which shared more loading owing to its geometric shape.


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In this study, we selected von Mises stress as the stress criterion due to the ductile fracture model used as well as the discs were soft tissues compared to the whole spine column. These maximum von Mises stresses were all located in the annulus laminates. 4.3 Strain Energy

After PLIF surgery, the adjacent discs would store more strain energy. In extension, lateral bending, and axial rotation, the upper disc had more energy increment than in other postures, and the bone fusion was the major factor to raise the increment, especially in axial rotation.

The effect of bone fusion on the lower disc adjacent to the fusion was very obvious, and for the axial rotation case the effect was apparent, as the peak value shown in Fig. 9.

5. Conclusions We took these three physical quantities, relative angle of endplates, von Mises stress, and strain energy for making a study on the problem of stress shielding, and tried to find out the way to improve the accelerated degeneration problem encountered.

The screw fixed system was a significant factor causing higher von Mises stress in the discs adjacent to fusion in extension and flexion, and patients should prevent from excessive movement exceeding the normal range of activity after operation. On the other hand, the strain energy was also another important factor leading to the degeneration phenomenon, and the bone graft fusion played a key role in the increasing strain energy percentage of the adjacent discs.

If we could confirm the real fracture mode of the discs, our conclusion would be an important reference when designing the screw fixed system or an artificial disc implant.

6. Acknowledgements The CT image scans for the FE model were acquired with the support of the faculty of the Department of Diagnostic Radiology, National Cheng Kung University Medical Center. The authors would like to express their sincere gratitude for this assistance.

7. References [1]Nordin, M., and Frankel, V. H. : Basic

Biomechanics of the Musculoskeletal System. Lippincott Williams and Wilkins,

Baltimore, 2001 [2]Huang, K. Y., Lee, C. H. and Chen, P. Q.

“ Basic Research and Future Treatment of Intervertebral Disc Disorder ”, Formosan Journal of Medicine, Vol. 7, No. 5, 2003

[3]Andrea Strayer,” Lumbar Spine Surgery-A Guide to Preoperative and Postoperative Patient Care ”, AANN Reference Series for Clinical Practice, 4700 W. Lake Avenue, Glenview, IL60025-1485

[4]Lee, C. K., “ Accelerated degeneration of the segment adjacent to a lumbar fusion ”, Spine, Vol. 13, pp. 375–7, 1988

[5]Lin, R. M., Huang, K. Y., Lee, Y. L. and Li, J.D.,” Factors affecting disability and physical function in degenerative lumbar spondylolisthesis of L4–5: evaluation with axially loaded MRI ”, European Spine Journal, Published online: 14 June 2009.

[6]Gray Henry, “Grey's Anatomy”, New York, 1917.

[7]White III, A.A. and Panjabi, M.M., “ Clinical biomechanics of the spine ”, second edition, J.B. Lippincott Company, Philadelphia, 1990.

[8]Chen, C.H., “ A Finite Element study of the Biomechanical Behavior of the Nonli- near Ligamentous Thoracic and Lumbar Spine ”, National Cheng Kung University, Department of Civil Engineering, Dissertation of Master Degree, June 2007.

[9]Yamamoto, I., Panjabi, M. M., Crisco, T. and Oxland, T., “ Three-Dimensional Movements of the Whole Lumbar Spine and Lumbosacral Joint ”, Spine, Vol. 14, No.11, pp.1256-1260.

[10]Chen, C. S. , Cheng, C. K., Liu, C. L. and Lo, W. H., “ Stress analysis of the disc adjacent to interbody fusion in lumbar ”, Medical Engineering & Physics, Vol. 23, pp.483– 491, 2001.

8. Tables

Table 1


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Model name Medical terms

Pedicle screw Bone graft fusion

ORG Intact lumbar No No

ORG-45B PLIF, L4-5 No Implanted

SCR-45NC PI, L4-5 Implanted No

SCR-45B PLIF, L4-5 + PI, L4-5 Implanted Implanted

ORG-345B PLIF, L3-5 No Implanted

SCR-345NC PI, L3-5 Implanted No

SCR-345B PLIF, L3-5 + PI, L3-5 Implanted Implanted

ORG=Original model、SCR=Screwed model

Table 2 Seven models for different cases

Parts Elastic Modulus E (MPa) Poisson’s Ratio ν

Annulus Fiber laminate: side laminate : inner ply (±30°) Inside laminate : middle ply (In±30°) Inside laminate : outer ply (±30°) Outside laminate : inner ply (±30°) Outside laminate : middle ply (±30°) Outside laminate : outer ply (±30°)

E1/E2

360/4.2 385/4.2 420/4.2 440/4.2 495/4.2 550/4.2

0.30 0.30 0.30 0.30 0.30 0.30

Annulus Ground Substance 4.2 0.45

Cancellous Bone 100 0.20 Cortical Bone、Endplate 12000 0.30

Nucleus Pulposus 1 0.4999

Posterior Bone、Bone graft、PEEK Cage 3500 0.25

Titanium Screw&Rod 110000 0.3

Anterior Longitudinal Ligament Hyperelastic 7.80~20.0 (MPa)

Posterior Longitudinal Ligament Hyperelastic 10.0~20.0 (MPa)

Ligamentum Flavum Hyperelastic 15.0~19.5 (MPa)

Transverse Ligament Hyperelastic 10.0~58.7 (MPa)

Inter-Spinous Ligament Hyperelastic 10.0~11.6 (MPa)

Supra-Spinous Ligament Hyperelastic 8.00~15.0 (MPa)

Table 3 Material properties


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Element Parts Section Type Section Area Thickness ABAQUS Type

Annulus Fiber Laminate Membrane [email protected] M3D3 Annulus Ground Substance、Cancellous Bone、Nucleus pulposus、Posterior Bone、Cage、Bone Graft

Solid - C3D4

Cortical Bone Shell 0.35 mm S3R

Endplate Shell 0.5 mm S3R

Facets joint Truss 5@20mm2 Gapuni

Anterior Longitudinal Ligament Truss [email protected] mm2 T3D2

Posterior Longitudinal Ligament Truss [email protected] mm2 T3D2

Ligamentum Flavum Truss [email protected] mm2 T3D2

Transverse Ligament Truss [email protected] mm2 T3D2

Inter-Spinous Ligament Truss [email protected] mm2 T3D2

Supra-Spinous Ligament Truss [email protected] mm2 T3D2 Table 4 Material section types

9. Figures

Figure 1 Five regions of the spine

Cervical (7)

Thoracic (12)

Lumbar (5)

Sacrum (5, fused)

Coccyx (4, fused)


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Figure 2 Each part of the vertebra

Figure 3 Intervertebral disc

Fig. 4 Spinal Ligaments

Spinal canal

Articular processes (Facet)

Spinal process

Transverse processes

Pedicle arch

Posterior bone

Vertebral body Cancellous bone

Cortical bone

Nucleus pulposus

Annulus laminates


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Figure 5 loading case for different postures (a)extension (b)flexion (c)lateral bending (d)axial rotation

(a) (b) (c) (d)


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Figure 6 Validation for each posture


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Figure 7 Relative angle of endplate increment (%)

ORG Intact lumbar

ORG‐45B PLIF, L4-5

SCR‐45NC PI, L4-5

SCR‐45B PLIF, L4-5 + PI, L4-5

ORG‐345B PLIF, L3-5

SCR‐345NC PI, L3-5

SCR‐345B PLIF, L3-5 + PI, L3-5


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Figure 8 Maximum von Mises stress increment in the adjacent discs compared to the intact model(%)


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Figure 9 The strain energy increment in the adjacent discs compared to the intact model (%)

Figure 10 The whole strain energy for each model

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