A fully three-dimensional model of interpenetrating collagen fibrillar networks for intervertebral disc mechanics

In this work, a fully three-dimensional model of the human intervertebral disc is proposed within a purely analytical framework in the final goal to create time and cost-efficient patient-specific models. The constitutive representation considers the deformation-induced damage along with the hydration effects on the regional disc mechanics. Special functions are introduced to generate versatile and anatomically accurate disc geometries taking into account morphology regional variation. The complex interpenetrating collagen fibrillar networks are explicitly introduced in the three-dimensional model considering the regional variation throughout the disc. A quantitative evaluation of the predictive capabilities of a human lumbar disc model shows a good agreement with compression and torsion experiments from the literature both for the overall disc stiffness and for the direct MRI kinematic fields. Model predictions are then performed and critically discussed on axially/torsionally loaded human lumbar discs.