Nonlinear Viscoelasticity of Native and Engineered Ligament and Tendon

Abstract

Ligaments and tendons are non-linear viscoelastic materials and their response functions are typically assessed using creep and stress relaxation tests. Non-linear viscoelastic models such as multiple Maxwell elements in parallel and the quasilinear viscoelastic model (QLV) used to capture the non-linear viscoelastic response of ligaments and tendons frequently employ multiple relaxation time constants determined from curve-fitting the entire available data set and generally lack a clear physiological relevance. Uniaxial load-unload tension tests on ligament and tendon also manifests the viscoelastic response and such experiments suggest that the bulk of the non-linearity in the response of these soft tissues is in the elasticity. We propose physiologically relevant nonlinear viscoelastic models in which the response of the main structural proteins in ligament and tendon (e.g. collagen and elastin) are described using non-linear elasticity. Our approach using a three-element, non-linear solid micromechanical model captures this viscoelastic response in load-unload, stress relaxation and creep with a limited number of physically meaningful parameters. Previous research also shows different viscoelastic responses between native tendon and ligaments. In our model, by varying the properties of the non-linear springs, we are able to capture the differences in the viscoelastic responses of ligaments verses tendon. We will demonstrate the capabilities of our model by comparing to the experimental results from testing native and engineered ligament and tendon.