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Paper details
Number 4 - December 2014
Volume 24 - 2014
A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis
Roman Cherniha, Joanna Stachowska-Piętka, Jacek Waniewski
Abstract
A mathematical model for fluid and solute transport in peritoneal dialysis is constructed. The model is based on a three-component 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.
Keywords
fluid transport, transport in peritoneal dialysis, nonlinear partial differential equation, ordinary differential equation, steady-state solution