A model of the renal cortex and medulla

Abstract

Mathematical models of the renal cortex and medulla are developed. The glomerular filtration rate is treated as an input parameter. The differential equations for transfer of water and solutes are developed under the assumption that the primary driving forces are the osmotic effect of the plasma proteins and the active transport of one solute across the walls of the nephric tubules. The system of simultaneous ordinary differential equations obtained for the stationary state for constant inputs in the medulla present a multiple-point boundary-value problem of some complexity.In the course of developing the model a number of problems were unearthed. First, it became apparent that the commonly accepted countercurrent exchange model for the medullary capillaries is not supported by anatomical studies and that a distributed capillary bed model might give a truer picture. Second, it became obvious that the information available on the sodium pump is as yet insufficient to let us decide unambiguously whether the pump is reversible or irreversible.