Derivation of the Partial Differential Equations utilized in a Model describing the Na Concentration Profile in the Renal Medulla

Abstract

THE purpose of this communication is to derive the partial differential equations and to clarify the mathematical details described in connexion with a model used to obtain the sodium concentration profile in the renal medulla¹. An elementary operating unit of the model is shown in Fig. 1. A generalized segment of a vascular or tubular channel is shown in the top half of Fig. 2. Consider the case where fluid moves in a direction from left to right, corresponding to motion in the descending limbs of the vas rectum or the Henle loop. The net change of sodium concentration ΔC(g/cm³) in the differential volume element of length ΔX shown is given by equation (1).