Nonlinear viscoelasticty plays an essential role in the functional behavior of spinal ligaments

Abstract

Despite the significant role ligament viscoelasticity plays in functional spinal biomechanics, relatively few studies have been performed to develop constitutive models that explicitly characterize this complex behavior. Unfortunately, the application and interpretation of these previous models are limited due to the use of simplified (quasi-linear) viscoelastic formulations or characterization techniques that have been shown to affect the predictive accuracy of the fitted coefficients. In order to surmount these previous limitations, the current study presents the application of a novel fitting technique (applied to stress relaxation experiments) and nonlinear viscoelastic constitutive formulation to human cervical spine anterior longitudinal ligament (ALL), posterior longitudinal ligament (PLL) and ligamentum flavum (LF). The fitted coefficients were validated by quantifying the ability of the constitutive equation to predict an independent cyclic data set across multiple physiologic strain amplitudes and frequencies. The resulting validated constitutive formulation indicated that the strain-dependent viscoelastic behavior of the longitudinal ligaments (ALL and PLL) was dominated by both the short-term (t=0.1s) and the steady-state (as t→∞) behavior. Conversely, the LF exhibited consistent relaxation behavior across the investigated temporal spectrum. From these data, it can be hypothesized that the unique strain-dependent temporal behavior of these spinal ligaments may be a functional adaptation that minimizes muscular expenditure during quasi-static postures while maximizing structural stability of the spine during transient loading events.