Optimal EPO dosing in hemodialysis patients using a non-linear model predictive control approach

Anemia management with erythropoiesis stimulating agents is a challenging task in hemodialysis patients since their response to treatment varies highly. In general, it is difficult to achieve and maintain the predefined hemoglobin (Hgb) target levels in clinical practice. The aim of this study is to develop a fully personalizable controller scheme to stabilize Hgb levels within a narrow target window while keeping drug doses low to mitigate side effects. First in-silico results of this framework are presented in this paper. Based on a model of erythropoiesis we formulate a non-linear model predictive control (NMPC) algorithm for the individualized optimization of epoetin alfa (EPO) doses. Previous to this work, model parameters were estimated for individual patients using clinical data. The optimal control problem is formulated for a continuous drug administration. This is currently a hypothetical form of drug administration for EPO as it would require a programmable EPO pump similar to insulin pumps used to treat patients with diabetes mellitus. In each step of the NMPC method the open-loop problem is solved with a projected quasi-Newton method. The controller is successfully tested in-silico on several patient parameter sets. An appropriate control is feasible in the tested patients under the assumption that the controlled quantity is measured regularly and that continuous EPO administration is adjusted on a daily, weekly or monthly basis. Further, the controller satisfactorily handles the following challenging problems in simulations: bleedings, missed administrations and dosing errors.