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Optimal EPO dosing in hemodialysis patients using a non-linear model predictive control approach. (English) Zbl 1430.92039

A mathematical model of erythropoiesis predicts the erythropoietic response of patients. The authors use this model to develop a feedback controller. The successful use of control algorithms for drug dosing has been shown previously, but in connection with insulin dosing in a closed cycle. The management strategy developed by the authors is based on the predictive control model (MPC). Other models differ from the proposed approach in that their predictive model is based on the concept of artificial neural networks. In this case, neural networks cannot be used because they require large size training samples. But the aim of this work is to develop a controller circuit that is fully personalized. Note that the insufficient availability of iron is clearly not modeled, but some parameters of the bone marrow model of erythropoiesis, which depend on the presence of iron, are evaluated at the patient level. The authors’ feedback controller is tested on various sets of patient parameters. This approach is chosen because it provides continuous monitoring, which provides the best situation for stabilizing the system. After developing a functional diagram of the controller, it can be adapted to the actual dosing regimens and analyze the effect of reducing the dosing frequency on the achieved stability. Model equations are related hyperbolic partial differential equations (PDEs), and the control variable enters into these equations nonlinearly. With a nonlinear model, MPC is called nonlinear MPC (NMPC). The basic principle of the MPC is to repeatedly solve the problems of optimal control with an open circuit. At each stage, the open loop problem is solved and only the first component of the obtained optimal control is applied, and the optimization horizon is shifted. This allows you to enable measurements and respond to unforeseen violations or complications. The model imitates (gastrointestinal) bleeding, which is a frequent complication, given the malfunction of the pump. In addition, various frequencies of speed change of the pump is modeled. To obtain the differentiability required for the numerical solution of the optimal control problem using first-order optimality conditions, the model equation of red blood cells is ordered. The optimal control problem is formulated and the NMPC algorithm is described. The numerical results of the following in-silico experiments are given: bleeding, missed or improperly administered doses, and limiting the constant rates of EPO administration for several weeks.

MSC:

92C50 Medical applications (general)
93B45 Model predictive control
93C10 Nonlinear systems in control theory
35Q92 PDEs in connection with biology, chemistry and other natural sciences
49K20 Optimality conditions for problems involving partial differential equations

Software:

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References:

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