Mechanical effects of ionic replacements in articular cartilage.: Part II:: Simulations of successive substitutions of NaCl and CaCl2

A three-phase multi-species electro-chemomechanical model of articular cartilage was developed in a companion paper, Loret and Sitnoes (in Biomech Model Mechanobiol, in press, DOI 10.1007/s10237-004-0062-7). The model can handle mechanical and chemical loadings and unloadings involving the two salts, NaCl and CaCl2. In order to reproduce experimental data, the shielding effects are made cation-dependent. In a tensile experiment, at constant axial strain, refreshment of the bath in contact with the cartilage is observed, and simulated, to induce a much different increase in tension depending on the order of the chemical sequence to which the cartilage is exposed. For example, the sequence dw (distilled water)-NaCl-dw-CaCl2-dw results in a decrease in tension. But the initial tension is recovered if the chemical sequence is pursued by NaCl-dw. Therefore, ionic replacements are essentially reversible, as evidenced when the chemical loading events respect a certain symmetry. Distinct shielding effects by cations sodium and calcium stem from two main features: (1) different free enthalpies of formation that represent different affinities of the proteoglyeans for these ions and that result in an equilibrium constant not equal to 1; (2) distinct valences but approximately the same diameter, which results in a more efficient shielding by cations calcium. The model accounts also: (1) for the anisotropy of the mechanical properties that are due to the strong orientation of collagen fibers; (2) for large deformations that occur during uniaxial traction with deionized water.