A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis

Roman Cherniha ; Joanna Stachowska-Piętka ; Jacek Waniewski

International Journal of Applied Mathematics and Computer Science, Tome 24 (2014), p. 837-851 / Harvested from The Polish Digital Mathematics Library

Résumé

A mathematical model for fluid and solute transport in peritoneal dialysis is constructed. The model is based on a threecomponent nonlinear system of two-dimensional partial differential equations for fluid, glucose and albumin transport with the relevant boundary and initial conditions. Our aim is to model ultrafiltration of water combined with inflow of glucose to the tissue and removal of albumin from the body during dialysis, by finding the spatial distributions of glucose and albumin concentrations as well as hydrostatic pressure. The model is developed in one spatial dimension approximation, and a governing equation for each of the variables is derived from physical principles. Under some assumptions the model can be simplified to obtain exact formulae for spatially non-uniform steady-state solutions. As a result, the exact formulae for fluid fluxes from blood to the tissue and across the tissue are constructed, together with two linear autonomous ODEs for glucose and albumin concentrations in the tissue. The obtained analytical results are checked for their applicability for the description of fluid-glucose-albumin transport during peritoneal dialysis.

Détail

Publié le : 2014-01-01

Zbl 1309.93022

EUDML-ID : urn:eudml:doc:271871

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