The highly organized collagen network of human lumbar annulus fibrosus (AF) is fundamental to preserve the mechanical integrity of the intervertebral discs. In the healthy AF, fibres are embedded in a hydrated matrix and arranged in a criss-cross fashion, giving an anisotropic structure capable to undergo large strains. Quantitative anatomical examinations revealed particular fibre orientation patterns, possibly coming from regional adaptations of the AF mechanics. Based on such hypothesis, this study aimed to show that the regional differences in AF mechanical behaviour can be reproduced by considering only fibre orientation changes. Using the finite element (FE) method, AF matrix was modelled as a poro-hyperelastic material, where the porous solid was treated as a compressible continuum following a Neo-Hookean constitutive law. Strain-dependent permeability was assumed and all material parameters were taken from the literature. Fibre reinforcement was accounted for by adding an extra-term to the porous matrix strain energy density function, only active along the fibre directions. Through such term, fibre orientations were then adjusted, to reproduce AF tensile behaviours measured for four different regions: posterior outer (PO), anterior outer (AO), posterior inner (PI) and anterior inner (AI). Curve calibrations resulted in the following optimal angles, calculated with respect to the circumferential axis: 28º for PO, 23º for AO, 43º for PI and 31º for AI. In average, we obtained fibres 30% more transversal in the inner than in the outer AF against 38% as measured by Cassidy et al. (1989). Fibres more axial in the posterior than in the anterior AF were also measured by Holzapfel et al. (2005), with angle values comparable to our computed average values. Since all the hyperelastic and fluid-phase material parameters remained unchanged throughout the AF, calibration based only on fibre patterns variations may be an effective tool to calibrate the regional AF mechanics in a realistic way.
INTRODUCTIONA challenge for FE models of the intervertebral disc (IVD) AF is to capture its intricate structure and function. The concentric fibre-reinforced lamellae that build up the AF are strongly anisotropic, due to collagen fibre orientation patterns. At the same time the annulus presents significant regional differences in mechanical behaviour. For instance, under a moderate strain of 5-6%, specimens in the AO region of the AF experienced stresses about 10 times higher than those occurring in PI specimens 1 . Collagen fibres, embedded in a criss-cross pattern within the AF matrix are essential to properly