STRUCTURAL RESPONSE OF VISCOELASTIC CARTILAGE OF THE KNEE IN A CYCLE OF WALKING

Abstract

ABSTRACT: Finite element analysis (FEA) of the biomechanics of the knee joint requires nonlinear material models for cartilage in cases of knees with unicompartmental osteoarthritis (UOA). We present the FEA of two nonlinear material models to describe the mechanical behavior of cartilage in cases of knees with unicompartmental osteoarthritis (UOA). The selected non-linear material models consider finite deformations and nonlinear viscoelastic behavior over time. This work uses a generalized viscoelastic Maxwell model as well as hypo-type constitutive equations and a hyperelastic model of strain potential energy. Relaxation behavior is reproduced by using kernel functions for shear and volume relaxation, which are represented in terms of Prony series. The proposed material models are validated with experimental data of indentation tests of knee cartilage in cases of unicompartimental osteoarthritis, which were previously reported. For the reaction force the material models agree well in loading, relaxation and unloading for the viscohypoelastic (R2 = 0.974) and viscohyperelastic (R2 = 0.975) models. The viscohypoelastic cartilage versus linear elastic models are compared in a three-dimensional model of knee joint, results of this comparison showed a maximum difference up to 2.5 times for contact areas, 1.5 times for axial displacement and 1.6 times for von Mises stresses. Our findings suggest that viscoelastic behavior of cartilage in UOA can be well reproduced with a viscohypoelastic or a viscohyperelastic model. This nonlinear viscoelastic behavior modifies not only the structural response of cartilage but also can be useful in the design process of artificial unicompartmental prosthesis and to understand the degeneration and wear of the native cartilage left in the other compartment in cases of UOA. Keywords: Biomechanics, cartilage, viscoelasticity, finite element, knee joint.