On the modeling of human intervertebral disc annulus fibrosus: Elastic, permanent deformation and failure responses

As a primary load-resisting component, annulus fibrosus (AF) maintains structural integrity of the entire intervertebral disc. Experiments have demonstrated that permanent deformation and damage take place in the tissue under mechanical loads. Development of an accurate model to capture the complex behaviour of AF tissue is hence crucial in disc model studies. We, therefore, aimed to develop a non-homogenous model to capture elastic, inelastic and failure responses of the AF tissue and the entire disc model under axial load. Our model estimations satisfactorily agreed with results of existing uniaxial (along fiber, circumferential and axial directions) and biaxial tissue-level tests. The model accurately predicted the failure of the tissue in various directions in uniaxial extension. Collagen fiber content, type and orientation substantially altered AF tissue responses in uni- and bi-axial tests. Although collagen fiber content and type mostly affected failure stress, fiber orientation significantly influenced the tissue failure strain. The entire L2-L3 disc model accurately replicated load-displacement as well as loading-unloading responses of the disc under compression-tension forces. Preconditioning of the disc-body unit substantially stiffened response. Poisson's ratio of both AF and nucleus considerably affected compression-displacement responses of the disc (173% increase in compression at 1.49 mm displacement when it was changed from 0.499 to 0.49999). Any AF constitutive model should be calibrated under various tissue-level loads and directions as well as the entire disc model responses since using a single tissue-level loading (e.g. uniaxial) for calibration can lead to unrealistic responses in other tests (e.g., biaxial). Special attentions should be given to the choice of Poisson's ratio and the realistic consideration of preconditioning load.