The Incorporation of Gel Pressure into the Irreversible Thermodynamic Equation of Fluid Flow in Order to Explain Biological Tissue Swelling

After the Donnan osmotic potential derived theory of corneal stromal swelling was suggested (Hodson, 1971) it later was proposed, and verified experimentally, (Elliott et al., 1980) that the theory could be applied even in situations where there were no bounding cellular membranes attached to the corneal stroma. This was a paradox. The central problem with swelling in the absence of membranes (i.e. with a gel boundary whose reflexion coefficient is essentially zero) is that the driving force is not readily understandable as osmotic (but see Oster & Peskin, 1992) and yet the magnitude of the swelling fitted quantitatively with Donnan theory. We believe that we have resolved this paradox with a new and expanded irreversible thermodynamic relationship for fluid flows into and across biological tissues. In the course of the derivation, fresh concepts arise: for example the relationship of salt disparity is described which forbids diffusible salt-generated chemical and osmotic potentials to be simultaneously at equilibrium in the presence of ionised macromolecules and this relationship is developed to generate a new intrinsic thermodynamic property which is termed gel pressure and which drives fluid flow. Gel pressure provides a theoretical basis for biological tissue swelling. Microscopically, gel pressure is identified as the electrostatic potential developed by the mutual repulsion of the fixed matrix charges.