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The Journal of Spinal Cord Medicine logoLink to The Journal of Spinal Cord Medicine
. 2015 Sep;38(5):593–598. doi: 10.1179/2045772314Y.0000000221

Cervical ossification of the posterior longitudinal ligament: Biomechanical analysis of the influence of static and dynamic factors

Norihiro Nishida 1,✉, Tsukasa Kanchiku 1, Yoshihiko Kato 1, Yasuaki Imajo 1, Yuichiro Yoshida 1, Syunichi Kawano 1, Toshihiko Taguchi 1
PMCID: PMC4535801  PMID: 24964955

Abstract

Objective

Cervical myelopathy due to ossification of the posterior longitudinal ligament (OPLL) is induced by static factors, dynamic factors, or a combination of both. We used a three-dimensional finite element method (3D-FEM) to analyze the stress distributions in the cervical spinal cord under static compression, dynamic compression, or a combination of both in the context of OPLL.

Methods

Experimental conditions were established for the 3D-FEM spinal cord, lamina, and hill-shaped OPLL. To simulate static compression of the spinal cord, anterior compression at 10, 20, and 30% of the anterior–posterior diameter of the spinal cord was applied by the OPLL. To simulate dynamic compression, the OPLL was rotated 5°, 10°, and 15° in the flexion direction. To simulate combined static and dynamic compression under 10 and 20% anterior static compression, the OPLL was rotated 5°, 10°, and 15° in the flexion direction.

Results

The stress distribution in the spinal cord increased following static and dynamic compression by cervical OPLL. However, the stress distribution did not increase throughout the entire spinal cord. For combined static and dynamic compression, the stress distribution increased as the static compression increased, even for a mild range of motion (ROM).

Conclusion

Symptoms may appear under static or dynamic compression only. However, under static compression, the stress distribution increases with the ROM of the responsible level and this makes it very likely that symptoms will worsen. We conclude that cervical OPLL myelopathy is induced by static factors, dynamic factors, and a combination of both.

Keywords: Cervical myelopathy, Dynamic factor, Finite element method, Static factor, Ossification of the posterior longitudinal ligament

Introduction

Cervical ossification of the posterior longitudinal ligament (C-OPLL) is recognized as a common clinical entity that causes complicated myelopathy of the cervical spinal cord. It is believed that myelopathy develops due to compression of the spine by C-OPLL. However, some patients with little ossification exhibit myelopathy, whereas others with marked ossification do not. Thus, static factors alone cannot account for myelopathy.1 Dynamic factors such as mobility of the spinal column are also important in the development of cervical myelopathy.1–4 However, the contribution of dynamic factors to the development of myelopathy in C-OPLL patients has not been fully determined.5 C-OPLL myelopathy is therefore likely to be induced by static factors, dynamic factors, or a combination of both.6,7

In the present study, we used a three-dimensional finite element method (3D-FEM) to analyze the stress distributions of cervical spinal cord under static compression, dynamic compression, and a combination of both in the context of OPLL.

Material and methods

The ABAQUS 6.11 (Dassault Systèmes, Simulia Corporation, Valley Street, Providence, RI, USA) finite element package was used for FEM simulation. The 3D-FEM spinal cord model used in this study consisted of gray matter, white matter, and pia mater (Fig. 1). In order to simplify calculation in the model, the denticulate ligament, dura, and nerve root sheaths were not included. The pia mater was included since it has been demonstrated that spinal cord with and without this component shows significantly different mechanical behavior.8 The spinal cord was assumed to be symmetrical about the mid-sagittal plane, such that only half the spinal cord required reconstruction and the whole model could be integrated by mirror image. The vertical length of spinal cord for computerized tomographic myelography (CTM) measurement was two vertebral bodies (about 40 mm).

Figure 1 .

Figure 1 

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The 3D-FEM model of the spinal cord consists of gray matter, white matter, and pia mater.

Iwasaki et al. reported that neurological outcomes following laminoplasty for C-OPLL were only poor or fair in patients with an occupying ratio >60% and/or hill-shaped ossification.9 The rigid, hill-shaped body with a slope of 30° was used to simulate C-OPLL by measuring paper (Fig. 2).9 To assume a segmental range of motion (ROM) at the level of maximum cord compression, the center of hill-shaped OPLL was established discontinuity. In addition, upper and lower edges of the hill-shaped OPLL were matched to the posterior upper and lower edges of the vertebral body (Fig. 2).

Figure 2 .

Figure 2 

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A rigid, hill-shaped body with a slope of 30° was used to simulate C-OPLL. The center of the hill-shaped OPLL established discontinuity. In addition, the upper and lower edges of the hill-shaped OPLL were set to match the posterior upper and lower edges of the vertebral body.

The lamina model was established by measuring CTM, magnetic resonance imaging, and simulated C-OPLL (Fig. 3).

Figure 3 .

Figure 3 

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The lamina model was established at the rear of the spinal cord.

The spinal cord consists of three distinct materials referred to as white matter, gray matter, and pia mater. The mechanical properties (Young's modulus and Poisson's ratio) of the gray and white matter were determined using data obtained by the tensile stress–strain curve and stress relaxation under various strain rates.10,11 The mechanical properties of pia mater were obtained from the literature.12 The mechanical properties of hill-shaped ossification and lamina were stiff enough for the spinal cord to be pressed. Based on the assumption that no slippage occurs at the interfaces of white matter, gray matter, and pia mater, these interfaces were glued together. Since there are no data on the friction coefficient between lamina and spinal cord, this was assumed to be frictionless. Similarly, the coefficient of friction between the hill-shaped ossification and spinal cord was assumed to be frictionless at the contact interfaces.

The spinal cord, hill-shaped ossification, and lamina model were symmetrically meshed with 15- or 20-node elements. The total number of elements was 11 438 and the total number of nodes was 67 434.

For the static compression model, compression was simulated by C-OPLL with a hill-shaped ossification. The top and bottom of the spinal cord and the lamina were fixed in all directions and then anterior static compression at 10, 20, and 30% of the anterior–posterior (AP) diameter of the spinal cord was applied by the OPLL (Fig. 4A).

Figure 4 .

Figure 4 

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For the static model, anterior static compression at 10, 20, and 30% of the AP diameter of the spinal cord was applied to the spinal cord by the OPLL (A). For the dynamic compression model, the lower and upper edges of OPLL were rotated at 2.5° (total 5°), 5° (total 10°), and 7.5° (total 15°) to the flexion direction as the ROM (B). For the combined static and dynamic model, anterior static compression was 10 and 20% of the AP diameter of the spinal cord and the lower and upper edges of OPLL were rotated at 2.5° (total 5°), 5° (total 10°), and 7.5° (total 15°) to the flexion direction as the ROM (C).

For the dynamic compression model, the top and bottom of the spinal cord as well as the lamina were fixed. The lower and upper edges of the OPLL were rotated 2.5° (total 5°), 5° (total 10°), and 7.5° (total 15°) to the flexion direction as a segmental ROM to match the movement of the vertebral body without anterior static compression by OPLL (Fig. 4B).

For the combined static (10%) and dynamic compression model, the top and bottom of the spinal cord as well as the lamina were fixed. Static compression to the spinal cord of 10% of the AP diameter of the spinal cord was applied by OPLL. In this state of compression, the lower and upper edges were rotated 2.5° (total 5°), 5° (total 10°), and 7.5° (total 15°) to the flexion direction as ROM (Fig. 4C).

For the combined static (20%) and dynamic compression model, the top and bottom of the spinal cord as well as the lamina were fixed. Static compression to the spinal cord of 20% of the AP diameter of the spinal cord was applied by OPLL. In this state of compression, the lower and upper edges were rotated 2.5° (total 5°), 5° (total 10°), and 7.5° (total 15°) to the flexion direction as ROM (Fig. 4C).

In total, 12 different compression combinations were evaluated and the average von Mises stress was recorded for each cross section.

Results

In the static compression model, stresses were very low under the condition of 10% compression of the AP diameter of the spinal cord. At 20% compression, the stress distributions were confined to gray matter and the anterior funiculus. At 30% compression, the stresses on gray matter, anterior funiculus, lateral funiculus, and posterior funiculus were all increased (Fig. 5A).

Figure 5 .

Figure 5 

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Stress distributions in proximal and central area of compression by C-OPLL are shown for the static compression model (A), the dynamic compression model (B), the combined static (10%) and dynamic compression model (C), and the combined static (20%) and dynamic compression model (D).

For the dynamic compression model with 5° ROM, stresses on the spinal cord were very low. A 5° ROM corresponds to ∼9% compression of the AP diameter of the spinal cord at the maximal compression site. At 10° ROM, stress distributions were confined to the gray matter and the anterior funiculus. A 10° ROM corresponds to about 16% compression of the AP diameter of the spinal cord at the maximal compression site. The stresses increased at 15° ROM, which corresponds to about 25% compression of the AP diameter of the spinal cord at the maximal compression site (Fig. 5B).

For the combined static (10%) and dynamic compression model, at 5° ROM, the stress distributions were higher than for 10% static compression alone, but were still quite low. This corresponded to about 19% compression of the AP diameter of the spinal cord at the maximal compression site. At 10° ROM, stress appeared in the gray matter and anterior funiculus, while at 15° ROM the stresses on gray matter, anterior funiculus, lateral funiculus, and posterior funiculus all increased. A 10° ROM corresponds to 26% compression of the AP diameter of the spinal cord at the maximal compression site while a 15° ROM corresponds to about 35% compression (Fig. 5C).

For the combined static (20%) and dynamic compression model, at 5° ROM, the stress distributions were higher than for 20% static compression alone. At 10° ROM, stresses appeared in the spinal cord and increased further at 15° ROM (Fig. 5D). A 5° ROM corresponds to about 29% compression of the AP diameter of the spinal cord at the maximal compression site, 10° ROM corresponds to about 36% compression, and 15° ROM corresponds to about 45% compression.

Discussion

The development of myelopathy significantly affects the prognosis of patients with OPLL in the cervical spine. Matsunaga et al.1 reported that when the space available for the spinal cord (SAC, static compression factor) was <6 mm, this could induce myelopathy of the cervical spine. Koyanagi et al.13 reported that the proportion of patients showing motor deficits of the lower extremities increased significantly when the sagittal canal diameter of computerized tomography (CT) was narrowed to <8 mm. Matsunaga et al.7 further reported that all patients with >60% spinal canal stenosis due to OPLL exhibited myelopathy. These findings indicate that static compression is an important factor in myelopathy associated with C-OPLL and that pathologic compression beyond a certain critical point may indeed be the most significant causal factor. Prior to these studies, it was believed that dynamic factors were largely responsible for the development of myelopathy associated with C-OPLL. Matsunaga et al.1 found that ROM of the cervical spine was significantly greater in patients with myelopathy and whose SAC diameter was >6 mm. Azuma et al. concluded that C-OPLL myelopathy was induced by static factors, dynamic factors, or a combination of both. To evaluate the contribution of each factor and the responsible level, they measured SAC and ROM at each vertebral and intervertebral level and determined the responsible level by spinal cord-evoked potentials.6 Fujiyoshi et al.5 reported that patients with massive OPLL did not develop myelopathy and the mobility of their cervical spine was highly restricted. These workers concluded that dynamic factors such as segmental ROM preferentially contributed to the development of myelopathy in patients with C-OPLL.

Using this prior knowledge, we investigated whether static factors and segmental ROM of the responsible level (dynamic factor) in C-OPLL were associated with stresses in the spinal cord. Our first goal was to develop a 3D-FEM spinal cord model that simulates the clinical situation, while our second goal was to analyze the clinical condition of patients. Similar to previous studies by Kato et al.,14–16 Li and Dai,17,18 and Nishida et al.,19–21 bovine spinal cord was used in the current analytical model since it was impossible to obtain fresh human spinal cord. The mechanical properties of the spinal cord used in our study were similar to earlier reports.15–21 Li et al. noted that it was reasonable to use the mechanical properties of bovine spinal cord because the brain and spinal cord of cattle and humans show similar injury-induced changes.17 For the purpose of this study, we therefore assumed that the mechanical properties of spinal cord from these two species were similar. Cecilia et al.8 reported on the division of spinal cord into pia mater and white and gray matter. These workers showed that the presence of pia mater had a significant effect on spinal cord deformation. Pia mater was therefore included in our model in order to accurately simulate the clinical situation.

Our study was limited to the investigation of stress distribution caused by compression. The amount of compression of the spinal cord does not appear to correlate directly with myelopathy. Furthermore, morphological evidence of apoptosis and molecular changes in the gray and white matter did not correlate with the amount and time of compression. There is currently a dearth of information in the literature on the relationship between myelopathy and the amount and time of compression. Other causal factors that could contribute to C-OPLL include ischemia, congestion, and spinal cord stretch injury.22 Blood flow and a possible influence of the ligamentum flavum via neck extension were not factored into our FEM analysis and only one movement (neck flexion) was investigated as dynamic factor in C-OPLL. Discontinuity of OPLL was set in the center of OPLL. Long-term compression and apoptotic factors were not considered in the FEM analysis. Moreover, the FEM model used here was simplified in order to facilitate the calculations. Analysis errors were reduced by using a FEM mesh, by assuming the spinal cord was symmetric, by not including the denticulate ligament, dura, and nerve root sheaths, and by setting a close distance between the spinal cord and lamina and between the spinal cord and OPLL. The results for stress distributions may vary if the denticulate ligament is included, since traction is also applied to the spinal cord. Furthermore, because compression is applied in the OPLL model, results may differ in the presence of osteophytes. The ligamentum flavum has a pincer-like movement mechanism that could also influence the results. However, to date there are no published papers on the relationships between osteophytes, ligamentum flavum, and discontinuity of OPLL on the compression of the spinal cord.

In pathology-based studies, Ono et al.23 and Ogino et al.24 described how patients with severe myelopathy showed spinal cord atrophy and presented with extensive degeneration and infarction of the entire gray matter and white columns, except for the anterior funiculus. In the present analysis, stress distributions in the anterior funiculus also increased. However, this increase was not associated with clinical symptoms or with apoptosis; hence, the current results merely provide an estimate for the possible range of increased stress distribution at this site. Nevertheless, the observed stress distribution of OPLL under dynamic motion was similar to a prior clinical report and therefore our results may be applicable to the clinical situation. More complex materials and structural characteristics of the spinal cord model should be included in future investigations.

In the present study, the stress distribution in the spinal cord increased following static compression and dynamic compression by C-OPLL with hill-shaped ossification. However, the stress distribution did not increase throughout the entire spinal cord. Under combined static and dynamic compression, the stress distribution increased in the entire spinal cord at a ROM of >10° even at a static compression of 10% of the AP diameter of the spinal cord. Stress increased in the entire spinal cord under static compression of 20% and dynamic compression at a ROM of >5°. As static compression increases, the stress distribution increases, even with a mild ROM. Thus, when both static compression and dynamic compression such as segmental ROM occur, damage to the spinal cord and the progression of symptoms are likely to arise.

Conclusion

We conducted stress analyses in a static compression model, dynamic compression model, and combination static and dynamic compression model of C-OPLL with hill-shaped ossification.

It is possible that symptoms occur under static compression only or under dynamic compression only. However, under static compression, the stress distribution increases with the ROM at the responsible level and this makes it very likely that symptoms will worsen. We conclude that C-OPLL myelopathy is induced by static factors, dynamic factors, and a combination of both. When ROM is large, careful attention must be paid in case the symptoms worsen, even if static compression is small.

Disclaimer statements

Contributors TK, YK, SK and TT played role of guidance and modification of research. YY and YI were cooperators in research.

Conflicts of interest None.

Ethics approval This report does not need ethical approval.

Funding None.

References

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