Membrane Transport of Several Ions During Peritoneal Dialysis: Mathematical Modeling

Abstract

Peritoneal dialysis utilizes a complex mass exchange device created by natural permselective membranes of the visceral and abdominal muscle tissues. In mathematical modeling of solute transport during peritoneal dialysis, each solute is typically considered as a neutral, independent particle. However, such mathematical models cannot predict transport parameters for small ions. Therefore, the impact of the electrostatic interactions between ions on the estimated transport parameters needs to be investigated. In this study, transport of sodium, chloride, and a third ion through a permselective membrane with characteristics of the peritoneal transport barrier was described using two models: a model with the Nernst-Planck (NP) equations for a set of interacting ions and a model with combined diffusive and convective transport of each ion separately (DC). Transport parameters for the NP model were calculated using the pore theory, while the parameters for the DC model were estimated by fitting the model to the predictions from the NP model. Solute concentration profiles in the membrane obtained by computer simulations based on these two models were similar, whereas the transport parameters (diffusive mass transport parameters and sieving coefficients) were generally different. The presence of the third ion could substantially modify the values of diffusive mass parameter for sodium and chloride ions estimated using the DC model compared with those predicted by NP. The extent of this modification depended on the molecular mass and concentration of the third ion, and the rate of volumetric flow. Closed formulas for the transport parameters of the DC model in terms of the NP model parameters, ion concentration profiles in the membrane, and volumetric flow across the membrane were derived. Their reliable approximations, which include only boundary ion concentrations instead of spatial intramembrane concentration profiles, were formulated. The precision of this approximation was demonstrated by numerical simulations of the investigated three-ion system. Our modeling demonstrated that the fitted transport parameters depend not only on ion molecular weight but also on the characteristics and concentration of all other ions in the fluid as well as on the fluid flow rate through the membrane. Therefore, theoretical predictions of ion transport parameters need to take into account multi-ionic character of dialysis and body fluids. The transport parameters estimated using the DC model for one ion may vary with the ionic composition, ion concentrations in the fluids, and volumetric flow and may not reflect the theoretical description of diffusive and convective characteristics of single ion.

Quantifying citrate-enhanced phosphate root uptake using microdialysis

“…Constant root exudation could be realistic as a large electrochemical potential gradient exists between the root and soil which can drive citrate exudation even against a large external concentration (Jones 1998). This contrasts with the microdialysis probe where citrate exudation is solely driven by the strength of the diffusion gradient and associated ion sieving effects at the microdialysis probe-soil interface (Galach and Waniewski 2012). Our findings, however, suggest that a suitable concentration of citrate can be used in the perfusate so that the microdialysis probe exudes the same quantity of citrate as a model root in total, but fails to mimic the dynamic behaviour.…”

Artificial Organs 2012: A Year in Review

“…Magda Galach and Jacek Waniewski of the Nalecz Institute of Biocybernetics and Biomedical Engineering, PAS, Warsaw, Poland reported on a mathematical model of membrane transport of ions incorporating electrostatic interactions during peritoneal dialysis. The fitted transport parameters were shown to depend not only on ion molecular weight but also on the characteristics and concentration of all other ions in the fluid, as well as on the fluid flow rate through the membrane, thus the multi‐ionic character of dialysis and body fluids.…”

Kinetics simulation of transmembrane transport of ions and molecules through a semipermeable membrane

“…In the literature, it is possible to find reviews on the application of various models in the description of the most important industrial membrane processes, such as, for example, nanofiltration (Palmeri and Lefebvre 2006;Kumaran and Bajpai 2015), reverse osmosis (Sobana and Panda 2011;Wang et al 2014;Al-Obaidi et al 2017), and Donnan dialysis (Pyrzynska 2006) and electrodialysis (Rohman and Aziz 2008). The models based on the Nernst-Planck equation (Gimmi and Alt-Epping 2018;Fridman-Bishop et al 2018;Galach and Waniewski 2012;Kozmai et al 2017;Prado-Rubio et al 2010), extended Nernst-Planck equation (Moshtari et al 2017;Kumaran and Bajpai 2015;Deon et al 2013), Kedem-Katchalsky equation (Shu et al 2016;Kim et al 2010;Tanaka 2012), and also the solution-diffusion model (Yaroshchuk et al 2011) are considered the most suitable for describing the process of ion separation.…”