Modeling of human intervertebral disc annulus fibrosus with complex multi-fiber networks

Collagen fibers within the annulus fibrosus (AF) lamellae are unidirectionally aligned with alternating orientations between adjacent layers. AF constitutive models often combine two adjacent lamellae into a single equivalent layer containing two fiber networks with a crisscross pattern. Additionally, AF models overlook the inter-lamellar matrix (ILM) as well as elastic fiber networks in between lamellae. We developed a nonhomogenous micromechanical model as well as two coarser homogenous hyperelastic and microplane models of the human AF, and compared their performances against measurements (tissue level uniaxial and biaxial tests as well as whole disc experiments) and seven published hyperelastic models. The micromechanical model had a realistic non-homogenous distribution of collagen fiber networks within each lamella and elastic fiber network in the ILM. For small matrix linear moduli (<0.2 MPa), the ILM showed substantial anisotropy (>10%) due to the elastic fiber network. However, at moduli >0.2 MPa, the effects of the elastic fiber network on differences in stress-strain responses at different directions disappeared (<10%). Variations in sample geometry and boundary conditions (due to uncertainty) markedly affected stress-strain responses of the tissue in uniaxial and biaxial tests (up to 16 times). In tissue level tests, therefore, simulations should represent testing conditions (e.g., boundary conditions, specimen geometry, preloads) as closely as possible. Stress/strain fields estimated from the single equivalent layer approach (conventional method) yielded different results from those predicted by the anatomically more accurate apparoach (i.e., layerwise). In addition, in a disc under a compressive force (symmetric loading), asymmetric stress-strain distributions were computed when using a layerwise simulation. Although all developed and selected published AF models predicted gross compression-displacement responses of the whole disc within the range of measured data, some showed excessively stiff or compliant responses under tissue-level uniaxial/biaxial tests. This study emphasizes, when constructing and validating constitutive models of AF, the importance of the proper simulation of individual lamellae as distinct layers, and testing parameters (sample geometric dimensions/loading/boundary conditions). Statement of significance Annulus fibrosus (AF) of human intervertebral discs has complex and highly organized networks of collagen and elastic fibers. Model studies, however, often do not fully account for such networks and use instead rather simplified representations. In this study, we have proposed three novel models of the human AF with complex collagen and elastic fiber networks, and then compared their performances along with seven published models versus available tissue-level and whole disc tests. We have demonstrated that some popular techniques in AF modeling (such as combining two adjacent lamellae into a single layer as well as using planes of symmetry in disc models) should be used with caution since those assumptions may no more be valid. Contrary to commonly used approaches, the thorough validation of constitutive models should be carried out under multiple tissue-level (at different directions/loadings) and whole disc tests as the consideration of a single loading condition/direction can lead to unrealistic responses in other conditions/directions. In tissue-level tests, furthermore, variations in the sample geometry and boundary conditions can markedly affect stress-strain responses (e.g., uniaxial, biaxial); therefore, model studies should replicate experimental conditions as closely as possible. In addition, experimental studies should report essential parameters (e.g. geometry, boundary conditions, stress/strain measures) in sufficient details. (C) 2021 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Automated summary

The study developed three novel models of human AF with complex collagen and elastic fiber networks and compared their performance with seven published models. The importance of accurately simulating individual lamellae as distinct layers, and testing parameters in constructing and validating AF constitutive models was emphasized. Variations in sample geometry and boundary conditions significantly affected stress-strain responses in tissue-level tests, indicating the need to replicate experimental conditions closely in model studies.