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. Its aim is to
model ultrafiltration of water combined with inflow of glucose to the tissue
and removal of albumin from the body during dialysis, and it does this by
finding the spatial distributions of glucose and albumin concentrations and
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 certain assumptions the model are simplified
with the aim of obtaining exact formulae for spatially non-uniform steady-state
solutions.
As the result, the exact formulae for the fluid fluxes from blood to 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.Comment: 28 pages, 8 figures. arXiv admin note: text overlap with
arXiv:1110.128
