Improving Predictive Models of Annulus Fibrosus Mechanics Through New Biaxial Compressive–Tensile Testing and Constitutive Modeling

The annulus fibrosus (AF) is subjected to complex, multi-axial loading in the spine. Developing accurate constitutive models to predict the AF mechanical response to load is critical to understanding load-induced degeneration and pain. Prior work has performed uniaxial tension, uniaxial compression, and biaxial tensile experiments, but no multi-axial compressive-tensile experiments have ever been performed on the AF. Additionally, based on prior comparisons between uniaxial and biaxial optimization of current constitutive models, current coefficients may be unable to accurately explain AF mechanics. To address these limitations, this study established a novel multi-axial compressive and tensile experiment and evaluated whether existing constitutive models can accurately predict multi-axial compressive and tensile mechanics. Porcine AF samples were preconditioned and then tested in uniaxial tension or biaxial compressive-tensile loading. Constitutive models included a fiber matrix (FM) model and a fiber matrix interaction (FMI) model. These models consisted of a Holmes-Mow matrix component, an exponential fiber component, and a shear term to capture interlamellar "scissoring." Compression reduced stiffness in the tensile direction and decreased the fiber angle. Coefficients fit to tensile-only data were unable to accurately explain biaxial loading, whereas biaxial coefficients improved model fits. These biaxial optimizations further improved when the fiber angle was manually adjusted to 17.0 deg to account for compressive loading-induced fiber reorientation. These findings underscore the importance of incorporating fiber reorientation and interlamellar interactions to ensure model accuracy. This framework and dataset enable more predictive constitutive models of AF mechanics for spine biomechanics and translational disc repair applications.