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

Cherniha R., Stachowska-Piętka J., Waniewski J.

International Journal of Applied Mathematics and Computer Science

2014

Vol. 24, no. 4

837--851

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.

Distributed modeling of osmotic fluid flow during single exchange with hypertonic glucose solution

Stachowska-Piętka J., Waniewski J.

Biocybernetics and Biomedical Engineering

2011

Vol. 31, no. 1

39-50

The aim of the study was to model fluid and solute peritoneal transport inside the tissue together with the kinetics in peritoneal cavity during single exchange with hypertonic glucose 3.86% solution. The distributed model of osmotic flow and glucose transport was formulated and applied for computer simulations assuming 1 cm width of tissue layer. The simulated kinetics of intraperitoneal volume and glucose concentration were in good agreement with clinical data. The predicted intratissue profiles of glucose concentration and hydrostatic pressure of the interstitial fluid demonstrated a restricted penetration of glucose (0.1 cm) and water (0.25 cm) into the interstitium at the end of dwell time, in agreement with animal data. The proposed model was able to describe correctly the basic kinetics of peritoneal dialysis as investigated in clinical studies and intratissue profiles known from animal studies.