New formulation of water and macromolecular flux which corrects for non-ideality: Theory and derivation, predictions, and experimental results

Abstract

Classic irreversible formulation of coupled water and macromolecular transport across capillaries by Kedem & Katchalsky (1958), even with subsequent refinements (Spiegler & Kedem, 1966), assumes explicitly that colloid osmotic pressure (pi) is linearly related to macromolecular concentration. It is known, however, that pi is related to concentration by an accelerating function empirically expressed as a cubic equation (Landis & Pappenheimer, 1963). Using only basic rules of irreversible thermodynamics (Onsager, 1931), we rederived the coupled flux equations in exact form. To render them approximately solvable, we assumed mathematical continuity across the membrane and incorporated the Landis-Pappenheimer relationship. Results yielded equations giving different membrane descriptors from the classic formulation (CF). Instead of a sieving coefficient (1 - sigma), the new formulation (NF) gives a parameter A which is solute flux per unit volume flux when oncotic gradient is zero. Instead of a permeability-surface area product (PS), the NF gives a parameter phi which is solute flux per unit "solute pressure" at zero water flow. Relationships between sigma, PS, A, and phi are shown whereby differences between CF and NF can be investigated. Predictions were made comparing values expected from experiment for a variety of membrane descriptors and variables using either CF or NF. Predictions show that for any sets of lymph flux and lymph/protein concentration ratio, a number of inequalities are expected: For reflection coefficient, sigma NF greater than sigma CF; for PS, PSNF greater than PSCF; for mean relative membrane protein concentration, C/C p(NF) less than C/C p(CF); and for fraction of protein transport carried by permeative processes, Fr DNF greater than Fr DCF. In venous pressure perturbation experiments in the hindquarters of 21 dogs, the predictions were upheld. Moreover, CF values were not closely predictive of NF values. As others have noted, CF values of sigma and PS are correlated with capillary pressure or filtration; and this relationship is not obliterated by NF treatment, possibly indicating a true pressure or flow dependency of membrane descriptors.