An open-source plugin for OpenSim® to model the non-linear behaviour of dense connective tissues of the human knee at variable strain rates

Abstract

The force-length characteristics of dense connective tissues (DCTs) vary non-linearly as a function of strain rate. However, there is no class of OpenSim® available to incorporate the effect of strain rate into the OpenSim® model. In this work, a new plugin for OpenSim® was developed to incorporate the non-linear strain rate behaviour of dense connective tissues (DCTs) of the human knee. Experimental force-length plots from the literature were used to extract the shape factor, scale factor, the coefficient of viscosity and elastic stiffness corresponding to specific strain rates. A new class object termed as NonLinearLigament was formulated using a customized plugin based on a structural constitutive model. A test platform was created to evaluate the force-length patterns at multiple strain rates ranging from 0.0001 s−1 to 100 s−1 for the DCT bundles. Knee kinematics of 25 DCT bundles were subjected to forward simulation at various strain rates. To understand the significance, the force-length characteristics of each of the DCTs were simulated as a function of strain rate for both existing Ligament class of OpenSim® and the proposed NonLinearLigament class. In the proposed ligament class, higher forces were observed with an increase of strain rate in DCTs. Existing Ligament class in OpenSim® was devoid of any changes at different strain rates. In summary, the developed plugin takes into account the short term viscoelastic behaviour of DCTs and hence, would help in accurate modelling of tissue behaviour specifically for dynamic situations.