Distributed Models of Peritoneal Transport

Abstract

There are several methods to model the process of water and solute transport during peritoneal dialysis (PD). The characteristics of the phenomena and the purpose of modelling influence the choice of methodology. Among others, the phenomenological models are commonly used in clinical and laboratory research. In peritoneal dialysis, the compartmental approach is widely used (membrane model, three-pore model). These kinds of models are based on phenomenological parameters, sometimes called “lumped parameters”, because one parameter is used to describe the net result of several different processes that occur during dialysis. The main advantage of the compartmental approach is that it decreases substantially the number of parameters that have to be estimated, and therefore its application in clinical research is easier. However, in the compartmental approach, it is usually very difficult to connect the estimated parameters with the physiology and the local anatomy of the involved tissues. Therefore, these models have limited applications in the explanation of the changes that occur in the physiology of the peritoneal transport. For example, the membrane models describe exchange of fluid and solute between peritoneal cavity and plasma through the “peritoneal membrane”. However, this approach does not take into account the anatomy and physiology of the peritoneal transport system and cannot be used for the explanation of the processes that occur in the tissue during the treatment. Basic concepts and previous applications of distributed models are summarized in Section 2. A mathematical formulation of the distributed model for fluid and solute peritoneal transport is also presented in Section 2. The effective parameters, which characterize transport through the peritoneal transport system, PTS (i.e. the fluid and solute exchange between the peritoneal cavity and blood), can be estimated from the local physiological parameters of the distributed models. The comparisons between transport parameters applied in phenomenological description and those derived using a distributed approach, are presented in Sections 3 and 4 for fluid and solute transport, respectively. Typical distributed profiles of tissue hydration and solutes concentration in the tissue are presented in Section 5.