Human cervical spine ligaments exhibit fully nonlinear viscoelastic behavior

Spinal ligaments provide stability and contribute to spinal motion patterns. These hydrated tissues exhibit time-dependent behavior during both static and dynamic loading regimes. Therefore, accurate viscoelastic characterization of these ligaments is requisite for development of computational analogues that model and predict time-dependent spine behavior. The development of accurate viscoelastic models must be preceded by rigorous, empirical evidence of linear viscoelastic, quasi-linear viscoelastic (QLV) or fully nonlinear viscoelastic behavior. This study utilized multiple physiological loading rates (frequencies) and strain amplitudes via cyclic loading and stress relaxation experiments in order to determine the viscoelastic behavior of the human lower cervical spine anterior longitudinal ligament, the posterior longitudinal ligament and the ligamentum flavum. The results indicated that the cyclic material properties of these ligaments were dependent on both strain amplitude and frequency. This strain amplitude-dependent behavior cannot be described using a linear viscoelastic formulation. Stress relaxation experiments at multiple strain magnitudes indicated that the shape of the relaxation curve was strongly dependent on strain magnitude, suggesting that a QLV formulation cannot adequately describe the comprehensive viscoelastic response of these ligaments. Therefore, a fully nonlinear viscoelastic formulation is requisite to model these lower cervical spine ligaments during activities of daily living.