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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 HA0, which essentially describes load-bearing capacity of the solid phase, was larger for AF (HA0 = 0.53 ± 0.06 MPa) than for NP (HA0 = 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.

Background Linear elastic, hyperelastic, and multiphasic material constitutive models are frequently used for spinal intervertebral disc simulations. While the characteristics of each model are known, their effect on spine mechanical response requires a careful investigation. The use of advanced material models may not be applicable when material constants are not available, model convergence is unlikely, and computational time is a concern. On the other hand, poor estimations of tissue’s mechanical response are likely if the spine model is oversimplified. In this study, discrepancies in load response introduced by material models will be investigated. Methods Three fiber-reinforced C2-C3 disc models were developed with linear elastic, hyperelastic, and biphasic behaviors. Three different loading modes were investigated: compression, flexion and extension in quasi-static and dynamic conditions. The deformed disc height, disc fluid pressure, range of motion, and stresses were compared. Results Results indicated that the intervertebral disc material model has a strong effect on load-sharing and disc height change when compression and flexion were applied. The predicted mechanical response of three models under extension had less discrepancy than its counterparts under flexion and compression. The fluid-solid interaction showed more relevance in dynamic than quasi-static loading conditions. The fiber-reinforced linear elastic and hyperelastic material models underestimated the load-sharing of the intervertebral disc annular collagen fibers. Conclusion This study confirmed the central role of the disc fluid pressure in spinal load-sharing and highlighted loading conditions where linear elastic and hyperelastic models predicted energy distribution different than that of the biphasic model.

Lower limb tissue stiffness is contingent on various factors, including location, tissue composition, loading rates, and the geometry of the indenting object. Previous studies demonstrated that tissue stiffness varies greatly between individuals and between locations on an individual. Additionally, some studies have shown that activation of underlying muscle tissue increases bulk soft tissue stiffness. Yet, few studies have simultaneously considered both location and activation; this could be particularly important for measuring and predicting the function of devices such as prostheses and exoskeletons that interact with limbs at various locations during dynamic movement. In the present study, a custom handheld indentation device was used to explore changes in bulk leg tissue stiffness at rest and during isometric contractions. The indentation force-displacement curves were modelled using a Hertz model. At each level of activation (active/inactive), the shank had dramatically (∼150%) greater tissue stiffness than the thigh (p < 0.001). However, results suggested location independence for stiffness ratio (active/inactive, p = 0.42); for either location, stiffness was approximately 2x greater for active vs inactive muscle. These results should be considered during the development of biomechanical models to simulate human tissue indentation stiffness across a range of activation states and locations.