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

Anemia management with erythropoiesis stimulating agents is a difficult task in hemodialysis patients since their response to treatment varies highly. The aim is to stabilize hemoglobin levels within a narrow target window while keeping drug doses low to mitigate side effects and further reduce costs. Based on a model of erythropoiesis, which contains a number of personalized parameters, we present a non-linear model predictive control (NMPC) algorithm for the individualized optimization of epoetin alfa (EPO) doses. The optimal control problem is formulated for a continuous drug administration at a daily or multiple-day constant rate. In each step of the NMPC method the open-loop problem is solved with a projected quasi-Newton method. The controller is successfully tested on various patient data sets and it satisfactorily handles the following challenging problems: bleedings, missed treatments and dosing errors. Moreover, we analyze the effect of restricting EPO administration rates to be constant over a number of weeks.