A cohesive interface approach to model the inter-lamellar behaviour of the intervertebral disc annulus fibrosus

INTRODUCTION - The method of representing the inter-lamellar behaviour in Finite Element (FE) models of the disc has been shown to affect the gross disc mechanics [1]. This study aim was to develop an approach to produce inter-lamellar models of the Annulus Fibrosus, i.e. constitutive models of interaction between lamellae. METHODS (Figure 1) - Mature ovine intervertebral discs were used in the present study as a model for the discs of the human lumbar spine. The annulus fibrosus was dissected and radial slices were subjected to mechanical tests. Images were taken under conventional and differential interference contrast (DIC) microscopy. The images before and during loading were used to produce 2D computational models of the annulus structural behaviour. The DIC images were analysed (ImageJ, U.S. N.I.H., USA) to extract the edges between lamellae and converted into quadrilateral FE meshes (ScanIP 5.1, Simpleware Ltd, UK, and Abaqus 6.12, Dassault Systèmes). Each lamella was modelled with Holzapfel’s anisotropic hyperelastic constitutive behaviour, with one fibre orientation per lamella. For this, model parameters were identified to fit to experimental data on the behaviour of tissue components (the proteoglycan matrix and the collagen fibres) [1]. Several modelling hypotheses were tested for the inter-lamellar behaviour: fully bonded conditions, simple frictionless behaviour, friction behaviour with a Coulomb contact, and delamination behaviour, with or without friction, through the use of a cohesive interface model. Displacement boundary conditions were applied reproducing the measured external displacement on the conventional microscopy images. Adequacy of the inter-lamellar behaviour model was assessed by comparing computational and experimental deformed geometries, specifically the change in lamellar interfaces.