Modeling the effects of hydration on viscoelastic properties of nucleus pulposus tissue in shear using the fractional Zener model

Abstract

Nucleus pulposus (NP) tissue in the intervertebral disc (IVD) is a viscoelastic material exhibiting both solid- and fluid-like mechanical behaviors. Advances in viscoelastic models incorporating fractional calculus, such as the Fractional Zener (FZ) model, have potential to describe viscoelastic behaviors. The objectives of this study were to determine whether the FZ model can accurately describe the shear viscoelastic properties of NP tissue and determine if the fractional order (α) is related to tissue hydration. 30 caudal IVDs underwent equilibrium dialysis in 5% or 25% polyethylene glycol solutions to alter tissue hydration. Excised NP tissue underwent stress relaxation testing in shear and unconfined compression. Stress relaxation data was fitted to the FZ model to obtain viscoelastic properties. In both loading modes, the initial modulus was greater for the less hydrated 25% equilibrated samples compared to 5% with no change in the equilibrium modulus. Samples with lower water content (25% samples) had shorter relaxation times in shear and longer time constants in compression, highlighting the different interactions between the fluid and solid matrix in loading modes. Samples with lower water content had α values closer to 0, indicating that less hydrated samples behaved more solid-like on the viscoelastic spectrum. Tissue hydration correlated with α values for 25% samples in shear. This study demonstrates that the FZ model may be used to describe IVD tissue behavior under both loading modes; however, the greatest utility of the FZ model is in describing flow-independent shear behaviors, and α may inform tissue hydration in shear.

Keywords: Fractional Zener model; Intervertebral disc; Viscoelastic properties.