Mathematical models for evaluation, optimization, and control of artificial kidney therapy

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 optimisation 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. 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 vivid.