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Open AccessArticle

Exact and Numerical Solutions of a Spatially-Distributed Mathematical Model for Fluid and Solute Transport in Peritoneal Dialysis

1
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka Street, Kyiv 01004, Ukraine
2
Institute of Biocybernetics and Biomedical Engineering, PAS, Ks. Trojdena 4, 02 796 Warszawa, Poland
*
Author to whom correspondence should be addressed.
Academic Editor: Ka Lok Man
Symmetry 2016, 8(6), 50; https://doi.org/10.3390/sym8060050
Received: 18 April 2016 / Revised: 27 May 2016 / Accepted: 4 June 2016 / Published: 16 June 2016
(This article belongs to the Special Issue Symmetry in Systems Design and Analysis)
The nonlinear mathematical model for solute and fluid transport induced by the osmotic pressure of glucose and albumin with the dependence of several parameters on the hydrostatic pressure is described. In particular, the fractional space available for macromolecules (albumin was used as a typical example) and fractional fluid void volume were assumed to be different functions of hydrostatic pressure. In order to find non-uniform steady-state solutions analytically, some mathematical restrictions on the model parameters were applied. Exact formulae (involving hypergeometric functions) for the density of fluid flux from blood to tissue and the fluid flux across tissues were constructed. In order to justify the applicability of the analytical results obtained, a wide range of numerical simulations were performed. It was found that the analytical formulae can describe with good approximation the fluid and solute transport (especially the rate of ultrafiltration) for a wide range of values of the model parameters. View Full-Text
Keywords: nonlinear differential equation; fluid and solute transport; transport in peritoneal dialysis; steady-state solution; hypergeometric function; 35K61; 34A05; 35Q92; 92C50 nonlinear differential equation; fluid and solute transport; transport in peritoneal dialysis; steady-state solution; hypergeometric function; 35K61; 34A05; 35Q92; 92C50
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Cherniha, R.; Gozak, K.; Waniewski, J. Exact and Numerical Solutions of a Spatially-Distributed Mathematical Model for Fluid and Solute Transport in Peritoneal Dialysis. Symmetry 2016, 8, 50.

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