Mathematical modeling of fluid and solute transport in hemodialysis and peritoneal dialysis

Renal replacement therapy involves the control of body pools of water and electrolytes, and removal of small metabolites (urea, creatinine). The correct estimation of “the dose of therapy” and optimization of the procedure needs quantification of fluid and solute transport during dialysis as well as evaluation of the distribution and exchange of water and solutes within the body through a complex system of membranes. Mathematical models can combine the general physiological knowledge with information about individual patients yielded by clinical measurements. Many of these models (urea model, sodium model, models of peritoneal transport) have been presented to the community of clinical nephrologists in the form of computer programs often supplemented with on-line measuring devices. However, the debate about their meaning and the search for better methods of their application are still lively. In this brief review, current approaches to modeling of transport processes in dialysis, including alternative and complementary versions, are described and discussed.