Elsevier

Medical Engineering & Physics

Volume 35, Issue 9, September 2013, Pages 1266-1271
Medical Engineering & Physics

Biomechanical effects of spinal cord compression due to ossification of posterior longitudinal ligament and ligamentum flavum: A finite element analysis

https://doi.org/10.1016/j.medengphy.2013.01.006Get rights and content

Abstract

Ossification of the posterior longitudinal ligament (OPLL) and ossification of the ligamentum flavum (OLF) have been recognized as causes of myelopathy due to thickening of the ligaments resulting in narrowing of the spinal canal and compression of the spinal cord. However, few studies have focused on predicting stress distribution under conditions of OPLL and OLF based on clinical aspects such as the relationship between level of stress and severity of neurologic symptoms because direct in vivo measurement of stress is very restrictive. In this study, a three-dimensional finite element model of the spinal cord in T12-L1 was developed based on MR images. The von-Mises stresses in the cord and the cross-sectional area of the cord were investigated for various grades and shapes of spinal cord compression in OPLL and OLF. Substantial increases in maximum stresses resulting in the manifestation of spinal cord symptoms occurred when the cross-sectional area was reduced by 30–40% at 60% compression of the antero-posterior diameter of the cord in OPLL and at 4 mm compression in OLF. These results indicate that compression greater than these thresholds may induce spinal symptoms, which is consistent with clinical observations.

Introduction

Ossifications of the spinal ligaments such as the posterior longitudinal ligament and the ligamentum flavum have been recognized as causes of myelopathy due to spinal cord compression because thickened ligaments by calcification or ossification occupy the rest of spinal canal and result in clinical symptoms. Since ossification of the posterior longitudinal ligament (OPLL) was first reported in 1838 by Key [1] and ossification of the ligamentum flavum (OLF) was reported in 1920 by Polgär [2], it has been shown that OPLL occurs primarily in the cervical spine and rarely in the thoracic and lumbar spine, while OLF is more common in the thoracic and thoracolumbar region [3], [4]. Both OPLL and OLF are relatively common pathologies in Korea and Japan [3], although a few cases have also been reported in the European, African, Arab, and Chinese population [5].

CT myelography and MR imaging are used for diagnosis and pre-operative planning for the treatment of OPLL and OLF [3], [6]. The compression ratio, which is defined as the ratio of the sagittal diameter to the transverse diameter, and the reduction of the transverse area of the spinal cord have been analyzed according to the severity of pathological changes [7], [8]. In addition, the ratio of the antero-posterior diameter in the affected segment to the average diameter of the adjacent segment and the cross-sectional area of the cord have been investigated [9]. However, there are few studies regarding the influence of cord compression on biomechanical factors such as von-Mises stress or strain in the spinal cord, which are known to be related to clinical symptoms or injuries. Since direct in vivo measurements of stress and strain are very restrictive, a finite element model of the spinal cord is necessary to analyze the stress and strain in the cord during compression.

Recently, three-dimensional finite element models of the spinal cord including white and gray matter were developed and used to analyze mechanical features such as stresses and strains causing spinal cord injury situations, (e.g., traffic or falling accidents) [10], [11], [12], [13]. There have also been recent biomechanical modeling studies regarding spinal cord white matter. Using a pig spinal cord, correlations between tissue-level stresses and strains invoked during slow compression and white matter cellular injury were assessed [14]. A transversely isotropic constitutive model of spinal cord white matter was proposed [15], and the compression behavior of spinal cord white matter was investigated [16]. Recently, stress on the spinal cord was analyzed using finite element models. The effect of degree of static cord compression in OPLL on the stress placed on the cord has been investigated for a simple case [17]. The stress distribution on the spinal cord under three compression levels of thoracic OPLL with a beak type was investigated, and the local ossification angle was analyzed [18]. However, few studies have focused on predicting stress distribution under conditions of both OPLL and OLF based on clinical aspects such as the relationship between stress level and neurologic symptom severity. In this study, a three-dimensional finite element model of the spinal cord, including white and gray matter, was developed and validated. The grades and shapes of spinal cord compression were classified for both OPLL and OLF based on data from the clinical literature [6], [9], [19]. The von-Mises stresses in the cord and the cross-sectional areas of the cord were investigated for various grades and shapes of spinal cord compression in OPLL and OLF by finite element analysis.

Section snippets

Materials and methods

A three-dimensional CAD model of the human thoracolumbar spinal cord in T12-L1 was reconstructed based on sagittal MR images of a 75-year old male subject. The reconstructed model consisted of white matter and gray matter, and was assumed to be symmetric around the mid-sagittal plane. The finite element model was subsequently developed from the CAD model using FEMAP ver. 10.1.1 (UGS, Plano TX, USA). The finite element model consisted of 41,208 nodes and 37,400 elements (Figs. 1(a) and 2(a)).

Results

In the compression test for validation, deformation under 0.08 N was 1.59 mm as compared to 1.5 mm that was observed in a previous study [22]. In addition, the shape of the force–deformation curve for our model was consistent with that of a previous study [22] in which the relative differences in deformation under 0.02 N, 0.04 N, 0.06 N, and 0.08 N were 18.8%, 11.7%, 2.1%, and 6.0%, respectively, in comparison with the previous study (Fig. 3(a)). The stress–strain curve for the tensile test was

Discussion

A three-dimensional finite element model of the spinal cord in the T12-L1 was developed based on MR images in order to determine the effect of spinal cord compression due to OPLL and OLF on the stress distribution in the spinal cord. The model derived from a 75-year old male subject may be considered more reliable and applicable than models of young subjects with regard to geometrical aspects since both OPLL and OLF have higher incidences in the elderly population [3], [4], [5], especially

Conflict of interests

All authors, Yoon Hyuk Kim, Batbayar Khuyagbaatar, and Kyungsoo Kim, disclose that there are no financial and personal relationships with other people or organizations that could inappropriately influence (bias) our work.

Funding

This research was supported by 2009 National Agenda Project (NAP) funded by Korea Research Council of Fundamental Science & Technology (P-09-JC-LU63-C01) and Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0005167).

Ethical approval

Not required.

References (30)

  • M.J. Stevens

    Imaging of the spinal cord

    J Neurol Neurosurg Psychiatry

    (1995)
  • H. Ogino et al.

    Canal diameter, anteroposterior compression ratio, and spondylotic myelopathy of the cervical spine

    Spine

    (1983)
  • K. Fujiwara et al.

    Morphometry of the cervical spinal cord and its relation to pathology in cases with compression myelopathy

    Spine

    (1988)
  • S.H. Yoon et al.

    Clinical analysis of thoracic ossified ligamentum flavum without ventral compressive lesion

    Eur Spine J

    (2011)
  • C.Y. Greaves et al.

    A three-dimensional finite element model of the cervical spine with spinal cord: an investigation of three injury mechanisms

    Ann Biomed Eng

    (2008)
  • Cited by (26)

    • Biomechanical comparison of spinal cord compression types occurring in Degenerative Cervical Myelopathy

      2021, Clinical Biomechanics
      Citation Excerpt :

      Nishida et al. (2012) first studied the contribution of static and dynamic anterior cord compressions for three different patterns (central, lateral, diffuse). Kim et al. (2013) investigated the individual effects of different patterns of PLL and ligamentum flavum ossification. Nishida et al. (2015) then explored the static and dynamic effects of PLL ossification.

    • Numerical investigation of the relative effect of disc bulging and ligamentum flavum hypertrophy on the mechanism of central cord syndrome

      2020, Clinical Biomechanics
      Citation Excerpt :

      Hypertrophic ligamentum flavum and linear disc bulging idealized geometries (Fig. 1(b)) were defined based on MRI measurements of typical cases found in our institution database (Thompson et al., 2015), and were consistent with the literature (Muhle et al., 1998; Song et al., 2006; Tani et al., 1999; Yu et al., 1983). Geometrical representation of these features was made in accordance with the literature (Kim et al., 2013). These features were meshed with hexahedral (8 nodes) 3D elements and defined as rigid bodies.

    • A comprehensive finite element model of surgical treatment for cervical myelopathy

      2020, Clinical Biomechanics
      Citation Excerpt :

      Ethical reasons prevent invasive measurement techniques in humans, thus motivating researchers to explore alternative methods of investigating spinal cord mechanics. Finite element (FE) modeling has been a popular method of predicting the behavior of biologic tissues, and in the last fifteen years there has been increased use of this approach in the field of spinal cord mechanics (Bahramshahi et al., 2010; Heidari Pahlavian et al., 2014; Huang et al., 2014; Khuyagbaatar et al., 2014; Khuyagbaatar et al., 2016; Kim et al., 2013; Maikos et al., 2008; Nishida et al., 2014; Scifert et al., 2002; Sparrey et al., 2009). Each of these models has provided an important incremental step into understanding spinal cord mechanics and developing better, more comprehensive FE models of the spinal cord.

    View all citing articles on Scopus
    View full text