Application of dynamic optimisation for planning a haemodialysis process

BACKGROUND: The aim of the study is to show that optimization tools can be used in planning the haemodialysis process in order to obtain the most effective treatment aimed at removing both urea and phosphorus. To this end we use the IV–compartment model of phosphorus kinetics. METHODS: The use of the IV–compartment model of phosphorus kinetics forces us to apply new numerical tools which cope with a rebound phenomenon that can occur during haemodialysis. The proposed algorithm solves optimization problems with various constraints imposed on concentrations of urea and phosphorus. RESULTS: We show that the optimization tools are effective in planning haemodialysis processes aimed at achieving desired levels of urea and phosphorus concentrations at the end of these processes. One of the numerical experiments reported in the paper concerns patients data who experienced a rebound phenomenon during haemodialysis due to a low level of phosphorus concentration. CONCLUSION: In order to plan haemodialysis processes one should take into account the fact that these processes, in general, are described by different equations in different regions determined by phosphorus concentrations. This follows from the fact that mechanisms modelled by IV–compartment model are activated during dialysis. Therefore, advanced numerical tools have to be used in order to simulate and optimize these processes. The paper shows that these tools can be constructed and effectively applied in planning haemodialysis processes.