Variable stiffness rheological model for interrelating creep and stress relaxation in ligaments

Creep and stress relaxation are two fundamental operational principles of joints that are significant for joint laxity. Modelling and relating creep and stress relaxation of ligaments is important if synthetic grafts (e.g., artificial ligaments) are to be developed and used for reconstructive surgery. This article discusses the use of rheological models to simulate creep and stress relaxation of ligaments. Modelling is performed using theory of linear viscoelasticity. Using principles of system identification, the parameters of constant and variable stiffness rheological models are determined considering experimentally measured stress relaxation of the medial collateral ligaments (MCL). The models are then tested to predict experimentally measured creep of the MCL. The proposed method proves the need to consider collagen fibre recruitment to interrelate creep and stress relaxation of ligaments. The results show that a rheological model with variable stiffness is capable of predicting creep from experimentally measured stress relaxation with a reasonable accuracy.