Computer simulation of renal countercurrent systems

The history of mathematical modeling of renal countercurrent systems is briefly outlined. Several examples are cited and discussed. These include efforts at parameter estimation and experimental design with models. The goal of this work was the evaluation of hypotheses of hypertonic urine formation. The argument is made that computer simulation with reasonably isomorphic models can be used in a variety of ways, but that one indispensable role for this approach is to provide a test of the quantitative sufficiency of hypotheses. Hypotheses of hypertonic urine formation that do not consider active transport in thin ascending limbs do not pass this test. A new proposal is suggested in which the energy for NaCl reabsorption from thin ascending limbs is derived from dissipation of a urea gradient via an antiport.     

A model of NaCl and water flow through paracellular pathways of renal proximal tubules.

To explain how hydrostatic pressure differences between tubule lumen and interstitium modulate isotonic reabsorption rates, we developed a model of NaCl and water flow through paracellular pathways of the proximal tubule. Structural elements of the model are a tight junction membrane, an intercellular channel whose walls transport NaCl actively at a constant rate, and a basement membrane. Equations of change were derived for the channel, boundary conditions were formulated from irreversible thermodynamics, and a pressure-area relationship typical of thin-walled tubing was assumed. The boundary value problem was solved numerically. The principal conclusions are: 1) channel NaCl concentration must remain within a few mOsm of isotonic values for reabsorption rates to be modulated by transtubular pressure differences known to affect this system: 2) basement membrane and channel wall parameters determine reabsorbate tonicity; tight junction parameters affect the sensitivity of reabsorption to transmural pressure; 3) channel NaCl concentration varies inversely with transmural pressure difference; this concentration variation controls NaCl diffusion through the tight junction; 4) modulation of NaCl diffusion through the tight junction controls the rate of isotonic reabsorption; modulation of water flow can increase sensitivity to transmural pressure; 5) no pressure-induced change in permeability of the tight junction or basement membrane is needed for pressure to modulate reabsorption; and 6) system performance is indifferent to the distribution of active transport sites, to the numerical value of the compliance function, and to the relationship between lumen and cell pressures.