Fixed negative charges modulate mechanical behaviours and electrical signals in articular cartilage under unconfined compression — a triphasic paradigm

The unconfined compression test has been frequently used to study the mechanical behaviour of articular cartilage. Recently, it has also been used in explant and gel-cell-complex studies in tissue engineering. Mechanical responses in these experiments have been analyzed using the biphasic theory as well as fibril reinforced poroelastic theory (Armstrong et al. [1], Brown and Singerman [5], Spilker et al. [45, 46], Soulhat et al. [44], Li et al. [30, 31], Fortin et al. [12], DiSilvestro et al. [10, 11]). Using an optical technique and testing cartilage samples in unconfined compression, the apparent Poisson’s ratio of articular cartilage has also been determined (Jurvelin et al. [23]). In the biphasic and poroelastic theory, the effect of fixed charges is embodied in the apparent compressive Young’s modulus and Poisson’s ratio of the tissue, and the fluid pressure is considered to be that which is over and above the osmotic pressure. In order to understand the effects of fixed charges on the mechanical behaviours of articular cartilage, and in order to predict the osmotic pressure and electric fields inside the tissue in this experimental configuration, it is necessary to use a model that explicitly takes into account the charged nature of the tissue and ion flow. In this paper, the triphasic theory is used to study how the fixed charges within a porous-permeable soft tissue modulate its mechanical and electrochemical responses under a step displacement load. The results showed that: 1) A charged tissue always supports a larger load than an uncharged tissue of the same intrinsic elastic moduli. 2) The apparent Young’s modulus (ratio of equilibrium axial stress to axial strain) is always more than the intrinsic Young’s modulus of an uncharged tissue. 3) The apparent Poisson’s ratio (negative ratio of lateral strain to axial strain) is always larger than the intrinsic Poisson’s ratio of an uncharged tissue. 4) Load support derives from three sources: intrinsic matrix stiffness, hydraulic pressure and osmotic pressure. Under unconfined compression, the Donnan osmotic pressure can constitute between 13–22% of the total load support at equilibrium. 5) During the stress-relaxation and recoiling processes following the initial instant of loading, diffusion potential (due to the gradient of the fixed charge density or FCD, and the gradient of ion concentrations) and streaming potential (due to fluid pressure gradient) compete against each other. Within physiological range of material parameters, the polarity of the electric potential depends on both the mechanical properties and FCD of the tissue. For softer tissue, the diffusion potential dominates while the streaming potential dominates in a stiffer tissue. 6) Fixed charges do not affect the instantaneous strain field relative to the initial equilibrium state. However, there is a sudden increase in the fluid pressure above the initial equilibrium state. These new findings are relevant and necessary for the understanding of cartilage mechanics, cartilage biosynthesis, electromechanical signal transduction by chondrocytes, and tissue engineering.