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

TL;DR

This paper develops a new mathematical model using nonlinear PDEs to describe fluid, glucose, and albumin transport in peritoneal dialysis, providing exact solutions and analyzing parameter restrictions for better understanding of the process.

Contribution

It introduces a novel nonlinear PDE model with exact steady-state solutions for fluid, glucose, and albumin transport in peritoneal dialysis.

Findings

Derived exact formulas for fluid fluxes in dialysis.

Established parameter restrictions for model validity.

Validated analytical results against dialysis transport data.

Abstract

A mathematical model for fluid 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. Non-constant steady-state solutions of the model are studied. The restrictions on the parameters arising in the model are established with the aim to obtain exact formulae for the non-constant steady-state solutions. As the result, the exact formulae for the fluid fluxes from blood to tissue and across the tissue were constructed together with two linear autonomous ODEs for glucose and albumin concentrations. The analytical results were checked for their applicability for the description of fluid-glucose-albumin transport during peritoneal dialysis.