Determination and comparison of mechanical properties of articular cartilage using pro-hyper-viscoelastic models based on an unconfined stress relaxation

Abstract

Recently, the most common tool to compensate for various organ defects is tissue transplantation with several problems involved. These problems have led to the rapid growth of tissue engineering with a designed tissue approach or organ substitute in the last decade. For this purpose, it is important to determine the tissue mechanical properties. In this study, to obtain the cartilage structural parameters, isotropic Pro-Hyper-Viscoelastic Mooney-Rivlin and Neo-Hooke are used. These model coefficients are obtained by reverse engineering methods and using a coupled finite element-optimization algorithm utilized unconfined stress relaxation tests with root-mean-square error (RMSE)) less than 0.036, 0.033 for Neo-Hooke and Mooney-Rivlin respectively. Using Neo-Hooke and Mooney-Rivlin models, the modulus of elasticity was 0.47 MPa and 0.44 MPa, and the shear modulus was 0.188 MPa and 0.184 MPa, respectively. The predicted tissue mechanical response obtained by the finite element model showed that the Mooney-Rivlin model is more consistent with the stress relaxation experiments than Neo-Hooke one. The results showed that during the stress relaxation test, by applying a compressing load on the sample, initially the fluid pressurization in the matrix pores has the most contribution in the load-bearing (total stress). When time elapses, the fluid contribution in the load-bearing decreases, and the solid matrix contribution increases.

Keywords

• articular cartilage
• stress relaxation
• optimization algorithm
• viscoelastic
• finite element
• pro-hyper-viscoelastic