Mathematical models of fluid and solute transport in peritoneal dialysis

Three types of mathematical models of peritoneal transport are reviewed: distributed models, membrane models, and pore models. The distributed model described the capillary bed distributed within the tissue with two sets of transport parameters for the capillary wall and for the tissue separately. The membrane and the three pore models consider blood as a compartment separated by a transport barrier from the dialysis fluid in the peritoneal cavity. The membrane model describes the barrier using "black box" transport parameters, whereas the three pore model assumes three types of pores across the barrier (large, small, and ultra small pores) and a mathematical theory of fluid and solute transport through the pore. Each model contributes its specific share to investigations of peritoneal transport. The basic features and specific areas of application of all three types of the models are discussed.