<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></abstract>

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.

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

Institute of Mathematics National Academy of Sciences of Ukraine, Tereshchenkivs’ka Street 3, 01601 Kyiv, Ukraine

School of Mathematical Sciences University of Nottingham, University Park, Nottingham, NG7 2RD, UK

Nałęcz Institute of Biocybernetics and Biomedical Engineering Polish Academy of Sciences, Ks. Trojdena 4, 02-109 Warsaw, Poland

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis"}

A mathematical model for fluid and solute transport in peritoneal dialysis is constructed. The model is based on a threecomponent nonlinear system of...

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

Published Online: Dec 20, 2014

Page range: 837 - 851

Received: Oct 07, 2013

DOI: https://doi.org/10.2478/amcs-2014-0062

© by Roman Cherniha

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.