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An equation for flow in the renal proximal tubule

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Abstract

Approximate equations for epithelial solute and water transport have been combined with the relations of mass conservation to yield a single differential equation representing volume flow along the proximal tubule. This flow equation is first order, quasilinear and may be integrated directly. For the steady state, the result is an implicit relation between volume flow and distance along the tubule. For two time-dependent problems (step change of tubule inlet velocity or osmolality) the trajectories (distance as a function of transit time) of a fluid element starting at the inlet are obtained. Differentiation of the steady-state relation with respect to the inlet velocity yields a first-order differential equation relating inlet and outlet velocity. This equation is considered in detail, particularly with regard to the influence of solute-linked water reabsorption. Model calculations with parameters representing rat proximal tubule indicate that it will be difficult to discern coupled water flux in this epithelium from only outlet and inlet flows. Calculations using lower transport rates and lower permeabilities suggest that this equation may be useful in quantifying coupled water flow in proximal tubules from other species.

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Authors and Affiliations

  1. Department of Physiology and Biophysics, Cornell University Medical College Rogosin Kidney Center, The New York Hospital, 10021, New York, NY, U.S.A.

    Alan M. Weinstein

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  1. Alan M. Weinstein
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Weinstein, A.M. An equation for flow in the renal proximal tubule. Bltn Mathcal Biology 48, 29–57 (1986). https://doi.org/10.1007/BF02460061

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  • DOI: https://doi.org/10.1007/BF02460061

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