Développement d'un modèle analytique anisotrope non linéaire du disque intervertébral L5-S1

Abstract

Prevention of lumbar disc herniation requires that the failure mechanism of intervertebral discs be understood in clear details. The actual means for studying the mechanical behavior of intervertebral discs are experimental and finite element studies. Characterizing biological tissues is difficult due to ethical concerns, and specimens are generally limited in numbers. Therefore, inter-individual variations have considerable impacts in experimental studies. Numerical simulations are interesting to complement and support experimental studies. Literature shows that the finite element method is actually the only simulation tool for which the scientific community has given considerable efforts. The lack of methodological approaches make triangulation of results difficult to achieve. This study aims at developing an analytical model to predict the stresses anywhere in the anulus fibrosus of a healthy intervertebral disc, using the theories of pressure vessels and material composite materials. Modeling is organized in three phases. The first phase evaluates the ability of the thin shell theory to model multi-shell anulus fibrosus subjected to large deformations, in the case of uniaxial compression. This study shows a very good agreement between the stresses obtained analytically with those obtained with a simplified finite element model. This agreement gives confidence in the approach and allows continuing with model refinements. The second phase adds the effect of the Sharpey’s fibers anchoring the lamellae to the endplates, by using the theory of beam on elastic foundation. This characteristic allows the prediction of realistic deformation of the anulus fibrosus. A model refinement is provided to improve the deformed shape over the first idealized function used to represent the sagittal profile of the lamellae. Lamellae anisotropy is added in the third phase. Its role in reducing stresses is clearly demonstrated. With this level of details, the model predicts maximal stresses in the innermost lamella, and stress distribution in the anulus fibrosus is in agreement with finite element modeling. This study demonstrates the potential of the analytical approach to model intervertebral discs. It is expected that the model eventually helps validating the results of state-of-the-art finite element models. Meanwhile, future works should focus on adding material hyperelasticity, and improving the complex sagittal curvature of the lamellae occuring with large deformations. Geometrical, material and load asymmetry should also be investigated, including local structural defects. Considering elastic behavior of the endplates could be a further refinement. Finally, a suitable failure criterion would be necessary to predict lamellae tearing and delamination.

Date	9 Nov 2015
Original language	French
Awarding Institution	École de technologie supérieure
Supervisor	Hakim A. Bouzid (Supervisor) & Sylvie Nadeau (Co-supervisor)