Analytical evaluation of stresses and displacements of an intervertebral disc

Abstract

Understanding the intervertebral disc response to mechanical loads is important to prevent back injuries. The experimental and the finite element methods are widely used for that purpose but methodological triangulation is deficient due to lack of a complementary method. This study aims at choosing theories and assumptions that could be used to develop an analytical model for stress analysis of intervertebral discs. Thin-shell and beam-onelastic-foundation theories are used in conjunction with an iterative method to account for large deformation of the disc. The model simulates an axial compression load acting on a simplified axisymmetric disc composed of a multi-shell linear and isotropic structure surrounding a pressurized cavity. The highly deformable lamellae are idealized by either circular or parabolic arches in the sagittal plane, and their effect on stress and strain response are compared. The circumferential and longitudinal stresses are compared to those of a simplified finite element model. The comparison shows that the analytical approach is promising and allows to identify improvements for future studies. The use of a parabolic profile is advantageous and allows to account for the interactive support of the lamellae near the endplates. The method should be adapted to improve bulge deformation obtained across the thickness of anulus fibrosus, and the model should include material anisotropy and hyperelasticity.