Bulging intervertebral disc: an asymptotic elasticity solution

A bulging intervertebral disc (IVD) occurs when pressure on a spinal disc damages the once healthy disc, causing it to compress or change its normal shape. In medicine, most attention has been paid clinically to diagnosis of and treatment for such problems, which little effect has been made to understand such issues from a mechanics perspective, i.e., the bulging deformation of the soft IVD induced by excessive compressive load. We report herein a simple elasticity solution to understand the bulging disc issue. For simplicity, the soft IVD is modeled as an incompressible circular composite layer consisting of an inner nucleus and outer annulus, sandwiched between two vertebral segments which are much stiffer than the IVD and can be treated as rigid bodies. Without adopting any assumptions regarding prescribed displacements or stresses, we obtained the stress and displacement fields within the composite layer when a certain compressive stain is applied via an asymptotic approach. This asymptotic approach is very simple and accurate enough for prediction of the bugling profile of the IVD. We also performed finite-element modeling (FEM) to validate our solutions; the predicted stress and displacement fields inside the composite are in good agreement with the FEM results.