In this work we present a data-driven modeling of the insulin dynamics in different in silico patients using a recurrent neural network with output feedback. The inputs for the identification is the rate of insulin (microU/dl/min) applied to the patient, and blood glucose concentration. The output is insulin concentration (microU/ml) present in the blood stream. Once completed the off-line modeling, this model could be used for on-line monitoring of the insulin concentration for a better treatment. The learning law of the recurrent neural network is inspired by adaptive observer theory, and proven to be convergent in the parameters and stable in the Lyapunov sense, even with only 13 samples available. Simulation results are shown to validate the presented modeling.

This paper analyzes two glucose-insulin models for diabetic patients: by Bergman and by Hovorka. Bergman's Model is nonlinear, and has relative degree three. It offers a good approximation of the system, but omits several important physiological functions, and insulin features, that are included in Hovorka's Model. This is a nonlinear model with relative degree five. It includes most of physiological parameters of glucose system and insulin action. It has two glucose and insulin compartments. It describes in details the insulin action and the rate of appearance of subcutaneously injected insulin. An intestinal glucose absorption function is proposed to describe better the process of glucose production from ingested food. A renal excretion function is proposed in order to model kidneys filtration excretion. Hovorka's non-insulin-dependent function has been smoothed to avoid discontinuities in the system. For both models Homogeneous Quasi-Continuous Controllers of order three and five are used giving a good performance from a medical point of view.

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