Letter | Published:

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

Nature volume 204, pages 689690 (14 November 1964) | Download Citation



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).

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  1. 1.

    , and , Nature, 200, 955 (1963).

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    • G. G. PINTER

    Holder of U.S. Public Health Service career and development award 5K3–GM–14794–04.


  1. Department of Electrical Engineering, The Johns Hopkins University, Baltimore, Maryland.

    • J. L. SHOHET
  2. Department of Physiology, School of Medicine, University of Maryland, Baltimore, Maryland.

    • G. G. PINTER


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