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 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

Modelling the Influence of Heterogeneous Annulus Material Property Distribution on Intervertebral Disk Mechanics

“…Nonlinear models with a discretization grid resolving the single fibers would be computationally prohibitive, whereas heterogeneous phenomenological models need to be calibrated carefully, and may have too many valid parameter combinations which are then difficult to relate to specific characteristic of the tissue. 40 Models describing purely the structural organization of the tissue components 13,31 do not consider the change in mechanical properties due to the tissue composition, which is relevant when considering tissue aging and remodeling. The outcome of the numerical analysis suggests that investigation of the link between the collagen type and the local lamellae mechanical response, with a particular focus on the effect of age, would provide valuable information on natural disk function or even guidance for future tissue engineering applications.…”

“…1a). Although numerical models have demonstrated that the local fiber orientation may partially explain the regional differences of stiffness, 13,31 an approach focused only on fiber orientation fails to explain and incorporate the variable response of single lamellae when stretched along the fiber direction. 26 In general, this could be explained by the heterogeneous distribution of the collagen content itself, which has been found to vary radially.…”

Automated finite element meshing of the lumbar spine: Verification and validation with 18 specimen-specific models

“…The annulus fibrosis properties were divided into anterior, lateral, and posterior regions (Rao, 2012). A different fiber stiffness was defined in each region (Eberlein et al, 2001(Eberlein et al, , 2004Malandrino et al, 2013) and the fiber angle was based on the average angle for each region in a regression model (Holzapfel et al, 2005). The generalized material parameters are summarized in Table 1.…”

Challenges and strategies in the repair of ruptured annulus fibrosus

“…These data were incorporated into the validation of the intrinsic material properties of the annulus in simulation models (Schmidt et al ., 2006), where only one unique combination of ground substance and fibre properties was valid for all loading directions and magnitudes, which provides a potential design target for AF repair materials. In a bottom-up approach, starting with known individual fibre properties (Malandrino et al ., 2012), the predicted optimal region-specific fibre orientation for normal annulus function is consistent with previous anatomical and biomechanical descriptions (Schmidt et al ., 2007). …”