Modeling and Control for Renal Anemia Treatment with Erythropoietin Using Physics-Informed Neural Network

Abstract

Patients with renal anemia are usually treated with recombinant human erythropoietin (EPO) because of insufficient renal EPO secretion. Clinically, this treatment process is labor intensive. It requires trained personnel to assess monthly Hgb levels, consider intra-patient variability and make adjustments every 2 or 4 weeks based on their experience. The purpose of this paper is to develop decision supporting tools to help medical personnel design optimal treatment plans. The establishment of a good hemoglobin (Hgb) response model is a necessary prerequisite for dose optimization design. First we apply physical-informed neural networks (PINN) to build the Hgb response model under EPO treatment. Neural network training is guided by the physiological model to avoid overfitting problems. During the training process, the parameters of the physiological model can be estimated simultaneously. To handle differential equations with impulse inputs and time delays, we propose approximate analytical expressions for the pharmacokinetic (PK) model and weighted formulations for the pharmacology (PD) model, respectively. The improved PK/PD model was incorporated into PINN for training. Tests on simulated data and clinical data show that the proposed method has better performance than the simple data-driven modeling method and the traditional physiological modeling based on the least squares method. But the original PINN does not allow control input, nor can it receive changing initial states, which indicates the original neural network architecture is not suited for the prediction model. In this context, we apply the new physics-informed neural networks for control (PINNC) which is enhanced with network input interfaces for control actions and initial states. This new structure enables the model predictive control (MPC) design for renal anemia treatment. The generated optimal EPO dosage value can be considered as a decision supporting information.