Mathematical models of tubular transport.

Abstract

Mathematical models of the renal tubule are classified as epithelial, tubular, or multitubular. The simplest epithelial models are single equations that represent the overall transepitheiiai solute and water fluxes as functions of the luminal and peritubular bath conditions. More detailed models represent both luminal and peritubular cell membranes, in parallel with a tight junction, all in series with an epithelial basement membrane. In these models, the presence of transport components in series renders the cell and interspace concentrations unknown variables that must be determined via solution of a set of conservation equations. The tubular models allow prediction of the effect of epithelial transport to modify the luminal solution and, conversely, the effect of altered luminal composition on transepithelial fluxes. Here the conservation equations constitute a set of ordinary differential equations, with initial data that must be integrated along the tubule length. The lining epithelium may be represented by single flux equations, or by a compart­ )