An analytical model of intervertebral disc mechanics

The intervertebral disc is a complex mechanical structure, and it is important to understand the loading of specific structures which might cause damage leading to failure or mechanical impairment. At present it is only possible to model such internal loadings owing to the extreme technical difficulties involved in experimental measurement. The simple analytical model described in this paper makes exact predictions of the loads carried by fibres and also their path within the annulus fibrosus, without pre-defining the fibre configuration. The disc is modelled as an axially symmetric structure comprising a fluid filled centre, retained by a thin, doubly curved, fibre-reinforced membrane under tensile stress. The annulus is taken to consist of two lamellae reinforced by oppositely oriented collagen fibres that are free to follow paths defined by one of two geometrical rules. The predictive power and possible uses of the model are illustrated using boundary conditions experimentally determined from a typical young disc. The model was used to calculate the shape of the membrane surface, fibre path, volume of disc, area of annulus, length of fibre bundle and tension at a point along length of fibre. Equatorial fibre angle could be approximately predicted (to about 5 degrees), since there was only a small range of valid solutions to the model. The predicted surface profiles, fibre loads and angles were found to be in reasonable agreement with published experimental studies. Two examples of how the static model might be used to calculate changes in disc morphology and loading are included to demonstrate how a wide range of experimental data and theoretical behavior might be incorporated. This analytical model is important since it enables exact solutions to be calculated for the forces acting at any point along a fibre, their paths and also the surface geometry, from a small number of physical measurements without the need to estimate the mechanical properties of individual areas of the disc. It facilitates the prediction of the behaviour of the disc under varying load by providing a framework that can be further developed using a wide range and combination of experimental conditions and theoretical relationships.