Linear and Nonlinear Biphasic Mechanical Properties of Goat IVDs Under Different Swelling Conditions in Confined Compression

To define technical specifications for artificial substitutes, it is necessary to model their mechanical behaviour. Here we studied the linear and nonlinear biphasic models for Nucleus Pulposus (NP) and Annulus Fibrosus (AF). The associated material parameters were obtained using confined compression stress relaxation tests on goat intervertebral disc (IVD) samples. The first parameter, aggregate modulus H_A0, which essentially describes load-bearing capacity of the solid phase, was larger for AF (H_A0 = 0.53 ± 0.06 MPa) than for NP (H_A0 = 0.26 ± 0.04 MPa). For hydraulic permeability, which quantifies the ability to transmit interstitial fluid, it was the opposite (k₀ = (0.20 ± 0.07) × 10^-15 m⁴/Ns for AF and k₀ = (0.67 ± 0.08)×10^-15 m⁴/Ns for NP). The values of nonlinearity coefficients, nonlinear stiffening coefficient β and non-dimensional nonlinear permeability coefficient M, reflected that these tissues had nonlinear elastic behaviour and permeability. Also, investigating the effect of swelling conditions in sample preparation showed that for both AF and NP, confined-swollen samples had higher aggregate modulus and lower permeability values compared to the free-swollen ones. The quantitative description of the nonlinear properties of AF and NP provided a better understanding of IVD behaviour as well as technical specifications for their artificial substitutes.