Mathematical Models for Peritoneal Transport Characteristics

Abstract

Four mathematical models and for the description of peritoneal transport of fluid solutes are reviewed. The membrane model is usually applied for (1) separation of transport components, (2) formulation of the relationship between flow components and their driving forces, and (3) estimation of transport parameters. The three-pore model provides correct relationships between various transport parameters and demonstrates that the peritoneal membrane should be considered heteroporous. The extended threepore model discriminates between heteroporous capillary wall and tissue layer, which are assumed to be arranged in series; the model improves and modifies the results of the three-pore model. The distributed model includes all parameters involved in peritoneal transport and takes into account the real structure of the tissue with capillaries distributed at various distances from the surface of the tissue. How the distributed model may be applied for the evaluation of the possible impact of perfusion rate on peritoneal transport, as recently discussed for clinical and experimental studies, is demonstrated. The distributed model should provide theoretical bases for the application of other models as approximate and simplified descriptions of peritoneal transport. However, an unsolved problem is the theoretical description of bi-directional fluid transport, which includes ultrafiltration to the peritoneal cavity owing to the osmotic pressure of dialysis fluid and absorption out of the peritoneal cavity owing to hydrostatic pressure.