Regional annulus fibre orientations used as a tool for the calibration of lumbar intervertebral disc finite element models

Abstract

The highly organized collagen network of human lumbar a nnulus fibrosus (AF) is fundamental to preserve the mechanical inte grity of the interverte bral discs. In the healthy AF, fibres are embedded in a hydrated matrix and arranged in a criss-cross fashion, giving an anisotropic structure capab le to undergo large st rains. Quantitative anatomical examinations revealed particular fibre orientation patterns, possibly coming from regional adaptations of the AF mechan ics. Based on such hypothesis, this study aimed to show that the regional differen ces in AF mechanical behaviour can be reproduced by considering only fibre orientatio n changes. Using the finite element (FE) method, AF matrix was modelled as a poro-hy perelastic material, where the porous solid was treated as a comp ressible continuum following a Neo-Hookean constitutive law. Strain-dependent permeability was assumed and all material parameters were taken from the literature. Fibre reinforcement wa s accounted for by adding an extra-term to the porous matrix strain energy density func tion, only active along th e fibre directions. Through such term, fibre orientations were then adjusted, to reproduce AF tensile behaviours measured for four different regi ons: posterior outer (PO), anterior outer (AO), posterior inner (PI) and anterior inne r (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.