A Constitutive Model for Swelling Pressure and Volumetric Behavior of Highly-Hydrated Connective Tissue

The fluid pressure within water-filled connective tissues such as cartilage, intervertebral disk and cornea facilitates a vital part of their functionality. Cartilage and intervertebral disk must resist compressive loading, and even the cornea uses fluid pressure loading to form its precise refractive geometry. The fluid pressure is composed of hydrostatic and swelling pressure components, with the latter deriving primarily from osmotic forces associated with ion concentrations. The tissues, like electrolyte gels in general, have a strong tendency to absorb water and swell. The goal of this work is to formulate an in vivo tissue theory from first principles and to arrive at the simplest possible model which captures the essential features of tissue charge effects and swelling behavior. The Gibbs free energy of the tissue, including elastic, hydrostatic, and electrostatic components, is characterized and equilibrium thermodynamics is employed to find explicit constitutive equations for the tissue osmotic pressure and osmotic compressibility over a unit cell. It is shown that the osmotic compressibility essentially defines the tissue macroscopic pressure-volume relationship at equilibrium. To illustrate the theory in detail, the human cornea is taken as a model tissue, and it is shown how the nanometer features of the glycosaminoglycan charge distribution can be modeled within the proposed theory. The cornea model is further extended to include the effects of the pump-leak hydration control mechanism based on active ion and passive water transport across the corneal endothelium. The model has been implemented in a standard finite element code and is shown to be capable of reproducing fundamental in vitro swelling experiments, including massive swelling, and typical in vivo swelling observed in disease states such as Fuch’s dystophy.