An accurate finite element model of the cervical spine under quasi-static loading

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Abstract

Cervical disc injury due to impact has been observed in clinical and biomechanical investigations; however, there is a lack of data that helps to elucidate the mechanisms of disc injury during these collisions. Therefore, it is necessary to understand the behavior of the cervical spine under different types of loading situations. A three dimensional finite element (FE) model for the multi-level cervical spine segment (C0–C7) was developed using computed tomography (CT) data and applied to study the internal stresses and strains of the intervertebral discs under quasi-static loading conditions. The intervertebral discs were treated as nonlinear, anisotropic and incompressible subjected to large deformations. The model accuracy was validated by comparing it with previously published experimental and numerical results for different movements. It was shown that the use of a fiber reinforced model to describe the behavior of the annulus of the discs would predict higher maximum shear strains than an isotropic one, being therefore important the use of complex constitutive models in order to be able to detect the appearance of injured zones, since those strains and stresses are supposed to be related with damage to soft tissues. Several movements were analyzed: flexion, extension and axial rotation, obtaining that the maximum shear stresses in the disc were higher for a flexo-extension movement.

Introduction

Damage to the cervical spine can be classified according to the neck movement and the mechanical loads. The most frequent consequence of traffic accidents consists in damage to the soft tissues, that means, intervertebral discs, ligaments and muscles. The intervertebral discs of the spine provide flexibility and absorb and transmit loads. The specialized structure of the intervertebral disc enables these highly demanding functions. As the spine is loaded in compression or bending, tensile loads are transmitted to the angled, lamellar collagen fiber structure of the annulus fibrosus. Clinical studies have documented acute intervertebral disc injury and accelerated disc degeneration in whiplash accidents, although there has not been any biomechanical investigation of the disc injury mechanisms (Panjabi et al., 2004). Although clinical studies can describe the kinematics, neither the actual force sustained by the spine nor the loads resisted by the spinal components (e.g. disc) can be directly obtained from these investigations. Biomechanical models, such as in vitro and finite element (FE) models, offer insights in understanding the underlying mechanisms of injury and dysfunction, leading to improved prevention, diagnosis, and treatment of cervical spine problems (Zhang et al., 2006).

FE analyses in this application may be broadly classified into two categories: specific dynamic and static analysis with different models for these studies, respectively. The models for dynamic studies generally consist of a series of vertebrae (treated as rigid bodies) connected by ligaments and discs that are modeled as springs (Stemper et al., 2006, Brolin and Halldin, 2004, Brolin et al., 2005). These models can effectively predict the gross intervertebral response under dynamic loads. However, they cannot predict accurately the response of the soft tissues of the cervical spine, specially the discs. In contrast, the models developed for static analyses are generally more detailed in the representation of the spinal materials and geometries (Kumaresan et al., 1999, Teo and Ng, 2001, Yoganandan et al., 2001, Ha, 2006). Thus, fiber-induced anisotropic models have been proposed to describe the behavior of the annulus fibrosus (Elliott and Setton, 2005, Goel et al., 1988, Natarajan et al., 1994, Klish and Lotz, 1999). Those models (Goel et al., 1988, Natarajan et al., 1994) that represent the fiber-induced anisotropy by using tension-only cable elements are limited by their dependence on model parameters that are difficult to determine (e.g. fiber modulus, matrix modulus, fiber volume fraction) (Elliott and Setton, 2001). On the other hand, several models relating the microstructure of the discs with actual material properties and involving the application of hyperelastic behavior with linear or exponential strain energy functions describing material orthotropy have been also developed (Klish and Lotz, 1999, Eberlein et al., 2001, Elliott and Setton, 2001). However, although these models could predict the internal stresses, strains and biomechanical complex loading conditions, presently they only mainly consist of either one or two spinal motion segments and therefore are not able to provide a realistic response of the physical multi-levels of the spinal column.

The goal of this work was to demonstrate that the introduction of a continuum model that incorporates the anisotropy induced by the collagen fibers is a good tool to predict the stresses and strains inside the intervertebral discs of the cervical spine and therefore to anticipate those zones that are more likely to be damaged. For that purpose, a three dimensional, anatomically accurate FE model of the complete human cervical spine validated with experimental data (Panjabi et al., 1994, Panjabi et al., 2001, Panjabi, 1998) was performed to investigate the biomechanical response of the spine under static conditions. In this model the intervertebral discs were treated as nonlinear, anisotropic and incompressible subjected to large deformations. In this paper, after a brief description of the models used, the stress and strain distributions in the discs as well as the predicted motion of the column are compared against published in vitro studies. Finally, a comparison between the stress undergone by the discs using an isotropic material or a fiber reinforced one for the annulus is also discussed.

Section snippets

Material and methods

To construct the FE model of the cervical spine, computerized tomographies of a 48-year old man were used. The vertebras were treated as rigid bodies, since the work was focused on the analysis of the soft tissues behavior and bones are much stiffer than the relevant soft tissues. Therefore, only the exterior surfaces of the bones were meshed using surface elements (triangles and quadrilaterals) (Fig. 1a).

The intervertebral discs were modeled as solid volumes (Fig. 1b). Their geometry was

Results

In first place the validation of the FE model was performed. The results for flexo-extension are shown in Fig. 7. During flexion, the biggest differences comparing with the results of Wheeldon et al. (2004) were obtained for the relative rotations coming from the highest moments (0.5 and 1 N m). The rotations were higher in the top of the spine (10), that means C2–C3. It can be seen that the curves are not symmetric, being the values smaller in extension than in flexion. It can be seen that the

Discussion

The purpose of the paper was to show the relevance of incorporating realistic constitutive models to accurately predict the internal stresses and strains undergone by the discs within the cervical spine through different loading scenarios. A special effort was done to describe the annulus fibrosus of the disc under a continuum model since this is an essential constituent of the intervertebral disc. Extreme stresses from excessive physical activities or accidents may result in a degenerated

Conflict of interest

There is not any financial and personal relationship with other people or organizations that could inappropriately influence this work.

Acknowledgments

The authors gratefully acknowledge the support of the Spanish Ministry of Education and Research through the research projects DPI2006-14669 and FIS2005-05020-C03-03.

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