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 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

Quantitative Histomorphometry of the Healthy Peritoneum

The peritoneum plays an essential role in preventing abdominal frictions and adhesions and can be utilized as a dialysis membrane. Its physiological ultrastructure, however, has not yet been studied systematically. 106 standardized peritoneal and 69 omental specimens were obtained from 107 patients (0.1-60 years) undergoing surgery for disease not affecting the peritoneum for automated quantitative histomorphometry and immunohistochemistry. The mesothelial cell layer morphology and protein expression pattern is similar across all age groups. Infants below one year have a thinner submesothelium; inflammation, profibrotic activity and mesothelial cell translocation is largely absent in all age groups. Peritoneal blood capillaries, lymphatics and nerve fibers locate in three distinct submesothelial layers. Blood vessel density and endothelial surface area follow a U-shaped curve with highest values in infants below one year and lowest values in children aged 7-12 years. Lymphatic vessel density is much lower, and again highest in infants. Omental blood capillary density correlates with parietal peritoneal findings, whereas only few lymphatic vessels are present. The healthy peritoneum exhibits major thus far unknown particularities, pertaining to functionally relevant structures, and subject to substantial changes with age. The reference ranges established here provide a framework for future histomorphometric analyses and peritoneal transport modeling approaches. © 2016, EDP Science. All rights reserved