An accurate finite element model of the cervical spine under quasi-static loading
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 , 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.
References (34)
- et al.
Degeneration affects the fiber orientation of human annulus fibrosus under tensile load
Journal of Biomechanics
(2006) Finite element modeling of multi level cervical spinal segments (C3–C6) and biomechanical analysis of an elastomer-type prosthetic disc
Medical Engineering & Physics
(2006)- et al.
Finite element modeling of the cervical spine: role of intervertebral disc under axial and eccentric loads
Medical Engineering & Physics
(1999) - et al.
Comparative strengths and structural properties of the upper and lower cervical spine in flexion and extension
Journal of Biomechanics
(2002) - et al.
Evaluation of the role of ligaments, facets and disc nucleus in lower cervical spine under compression and sagittal moments using finite element method
Medical Engineering & Physics
(2001) - et al.
Pathways of load induced cartilage damage causing cartilage degeneration in knee after meniscectomy
Journal of Biomechanics
(2003) - et al.
Biomechanics of the cervical spine Part 2. Cervical spine soft tissue responses and biomechanical modeling
Clinical Biomechanics
(2001) - et al.
Development of a finite element model of the upper cervical spine and a parameter study of ligament characteristics
Spine
(2004) - et al.
The effect of muscle activation on neck response
Traffic Injury Prevention
(2005) - et al.
Experimental flexibility measurements for the development of a computational head–neck model validated for near-vertex head impact
Tensile properties of nondegenerate human lumbar annulus fibrosus
Spine
An anisotropic model for annulus tissue and enhanced finite element analysis of intact lumbar disc bodies
Computer Methods in Biomechanics and Biomedical Engineering
Anisotropic and inhomogeneous tensile behaviour of the human annuls fibrosus: experimental measurement and material model prediction
Journal of Biomechanical Engineering
A linear material model for fiber-induced anisotropy of the annulus fibrosus
Journal of Biomechanical Engineering
A study of vertebra and disc geometric relations of the human cervical and lumbar spine
Spine
An analytical investigation of the mechanics of spinal instrumentation
Spine
Cited by (84)
Comparison of the biomechanical performance of three spinal implants for treating the wedge-shaped burst fractures
2022, Medicine in Novel Technology and DevicesA microstructure-based model for a full lamellar-interlamellar displacement and shear strain mapping inside human intervertebral disc core
2021, Computers in Biology and MedicineInfluence of nucleotomy on the load sharing in the spinal facet joint under the loading scenarios of different human postures
2021, Medical Engineering and PhysicsFebio finite element models of the human cervical spine
2020, Journal of BiomechanicsCitation Excerpt :By subdividing the spine in this way, these studies cannot accurately model the effects that boundary and loading conditions have on the full cervical spine. Additionally, even the FE studies that have included the entire cervical spine have only developed a single, subject-specific geometry (del Palomar et al., 2008; Leahy, 2007; Östh et al., 2016). In a study undertaken by Dreischarf et al., eight previously published FE models of the lumbar spine were compared (Dreischarf et al., 2010).