An essential component of any artificial pancreas is on the prediction of blood glucose levels as a function of exogenous and endogenous perturbations such as insulin dose, meal intake, and physical activity and emotional tone under natural living conditions. In this article, we present a new data-driven state-space dynamic model with time-varying coefficients that are used to explicitly quantify the time-varying patient-specific effects of insulin dose and meal intake on blood glucose fluctuations. Using the 3-variate time series of glucose level, insulin dose, and meal intake of an individual type 1 diabetic subject, we apply an extended Kalman filter (EKF) to estimate time-varying coefficients of the patient-specific state-space model. We evaluate our empirical modeling using (1) the FDA-approved UVa/Padova simulator with 30 virtual patients and (2) clinical data of 5 type 1 diabetic patients under natural living conditions. Compared to a forgetting-factor-based recursive ARX model of the same order, the EKF model predictions have higher fit, and significantly better temporal gain and J index and thus are superior in early detection of upward and downward trends in glucose. The EKF based state-space model developed in this article is particularly suitable for model-based state-feedback control designs since the Kalman filter estimates the state variable of the glucose dynamics based on the measured glucose time series. In addition, since the model parameters are estimated in real time, this model is also suitable for adaptive control.

An essential component of insulin therapy for type 1 diabetes involves the prediction of blood glucose levels as function of exogenous perturbations such as insulin dose and meal intake. Fluctuations in blood glucose are generated by a complex biophysical system and have demonstrated substantial variation at different times of a day within a subject and between subjects. In this paper, we present a new data-driven dynamic model with time-varying coefficients that are used to explicitly quantify the time-varying patient-specific effects of insulin dose and meal intake on blood glucose fluctuations. Using the 3-variate time series of blood glucose level, insulin dose and meal intake of an individual type 1 diabetic subject, we apply an extended Kalman Filter technique to estimate timevarying coefficients of the patient-specific model. We evaluate our empirical model using a FDA-approved simulator with 30 patients. The model developed in this paper can be used in model-based control such as adaptive control and model predictive control of blood glucose by means of an artificial pancreas.

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