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An exact analysis for a solute transport, due to simultaneous dialysis and ultrafiltration, in a hollow-fibre artificial kidney

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Abstract

Transport of a uremic solute effected by a combined dialysis and ultrafiltration procedure in a hollow-fibre artificial kidney, is investigated theoretically under standard assumptions. An exact analytical solution for the concentration profile in a blood channel is obtained by using the method of separation of variables. The necessary requirement that the solution must tend to that of pure dialysis, in the limit ultrafiltration tending to zero, is fulfilled. Exact analytical expressions are derived for the eigenconstants of the solution. In using the solution, the solute clearance is emphasized. Diffusive and ultrafiltration components of the solute clearance are defined and studied. The combined procedure is examined for middle versus small molecules and for polyacrylonitrile versus cuprophan hollow-fibres.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, 400 076, Bombay, Powai, India

    V. P. Tyagi

  2. Department of Computer Science and Engineering, Indian Institute of Technology, 400 076, Bombay, Powai, India

    M. Abbas

Authors
  1. V. P. Tyagi
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  2. M. Abbas
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Tyagi, V.P., Abbas, M. An exact analysis for a solute transport, due to simultaneous dialysis and ultrafiltration, in a hollow-fibre artificial kidney. Bltn Mathcal Biology 49, 697–717 (1987). https://doi.org/10.1007/BF02481768

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  • DOI: https://doi.org/10.1007/BF02481768

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