Sébastien Demers

On the Modeling of an Intervertebral Disc Using a Novel Large Deformation Multi-Shell Approach

The objective of this study is to develop an analytical model to predict the stresses and displacements in the lamellae of the intervertebral disc subjected to a compressive force. This is achieved by developing a model based on membrane theory combined to large deformation multishell structural behavior. Equations for longitudinal and circumferential stresses are formulated for each lamella of the anulus fibrosus. Multilamellae interaction is a statically indeterminate problem, which requires equations of compatibility of the displacements of adjacent lamellae to be resolved. The large deformation inherent to soft tissue is considered and the solution is obtained using an iterative process. Elastic interactions with a large deformation is a novelty in analytical modeling of soft tissues. This provides model realism and offers the possibility for new and in-depth investigations. Results are given for longitudinal and circumferential stresses and displacements as well as contact pressures for every lamella of the anulus fibrosus. The analytical results are compared to those of two finite element models. The results suggest that the most highly stressed zone is located on the innermost lamella. Stresses decrease through disc thickness and are at a maximum at the innermost lamella. Circumferential stress is predominant and the difference is less than 5% at any point of the anulus fibrosus when the analytical model is compared to the finite element model using coupled degrees of freedom at the lamellae interface. When compared to the finite element model using contact elements, the difference is below 11%. Contact pressures from the inside to the outside of the anulus fibrosus are shown to decrease nonlinearly. The model presented in this study has demonstrated that it is possible to analytically simulate the complex mechanical behavior of a multishell intervertebral disc subjected to compression, provided some simplifications. Further improvements are suggested to increase model realism and recommendations are given for future experimentation necessary to support both the analytical and numerical models.

Anisotropic multishell analytical modeling of an intervertebral disk subjected to axial compression

Studies on intervertebral disk (IVD) response to various loads and postures are essential to understand disks mechanical functions and to suggest preventive and corrective actions in the workplace. The experimental and finite-element (FE) approaches are well-suited for these studies, but validating their findings is difficult, partly due to the lack of alternative methods. Analytical modeling could allow methodological triangulation and help validation of FE models. This paper presents an analytical method based on thin-shell, beam-on-elastic-foundation and composite materials theories to evaluate the stresses in the anulus fibrosus (AF) of an axisymmetric disk composed of multiple thin lamellae. Large deformations of the soft tissues are accounted for using an iterative method and the anisotropic material properties are derived from a published biaxial experiment. The results are compared to those obtained by FE modeling. The results demonstrate the capability of the analytical model to evaluate the stresses at any location of the simplified AF. It also demonstrates that anisotropy reduces stresses in the lamellae. This novel model is a preliminary step in developing valuable analytical models of IVDs, and represents a distinctive groundwork that is able to sustain future refinements. This paper suggests important features that may be included to improve model realism.

Analytical Anisotropic Multi-Shell Model of a Simplified Intervertebral Disc Subjected to Axial Compression

The nucleus pulposus (NP) and the anulus fibrosus (AF) are the two main components of the intervertebral discs. At low deformation rates, in young and healthy adults, the NP reacts like an inviscid and incompressible fluid. Its internal pressure varies depending on the external forces acting on it. The AF surrounds the NP and, together with the vertebral endplates, they form a pressurized vessel.© 2013 ASME

Analytical and finite element multi-shell modelling of an intervertebral disc

The objective of this study is to develop an analytical model of an intervertebral disc capable of predicting stresses and deformations in the anulus fibrosus. The anulus fibrosus is treated as a multi-shell structure for which membrane theory applies and the junction with the end plates assumed rigid is treated with beam on elastic foundation theory. The displacements and stresses of the anulus fibrosus, when the disc is subjected to a compressive force are investigated. The discontinuity stresses are superimposed to those of the membrane stresses to estimate the stress state of the anulus fibrosus. The analytical results are compared to those of a finite element model for validation. The analytical and the finite element models show the same general trend, but their relative difference in estimating the stresses is rather high. However, both models show that the highest circumferential stress is located on the innermost lamella at the transverse plane. Furthermore, the stresses decrease through the disc thickness and at the vicinity of the endplates. These results allow to indicate, analytically, the location for maximal principal stresses in the anulus fibrosus.Copyright