Simplifications of Triphasic Mixture Theory for Articular Cartilage

*Lu, XL; *Guo, XE; +*Mow, VC +*Department of Biomedical Engineering, Columbia University, New York, NY [email protected] INTRODUCTION The triphasic mixture theories for articular cartilage [1] have been successfully used to describe the flow-dependent and flow-independent viscoelastic behaviors, swelling behaviors, and electrokinetic behaviors of charged-hydrated soft tissues in the last two decades. It is considered in the biomechanics literature as a unified theory for such materials. However, the mathematical complexity of this constitutive law has limited its applications in cartilage biomechanics studies, especially for those testing setups involving complicated loading conditions and deformation fields (e.g., indentation). The objective of this study is to develop three sets of new triphasic formulations that can greatly simplify the triphasic analysis for: 1) the tissue response at final steady state; 2) the transient response of cartilage under mechanical loading; and 3) the equilibrium response of the tissue under dynamic loadings. METHODS The correspondence principle for equilibrium response: By linearizing the triphasic constitutive equations with regular perturbation method [2], it is found that the deformational behavior of a charged-hydrated material at final steady state is identical to that of a pure elastic medium. The mechanical properties of this equivalent material can be correlated with the intrinsic elastic moduli, fixed charge density (FCD), and external solution concentration by following equations: