Control-oriented modeling of glucose insulin dynamics with dynamic insulin sensitivity

This work proposes a physiologically interpretable, control-oriented model of glucose–insulin dynamics that explicitly accounts for time-varying insulin sensitivity. The proposed model combines a single-compartment glucose subsystem, two-compartment insulin pharmacokinetics, two-compartment meal absorption, and a dynamic state for insulin sensitivity driven by circadian modulation. Under basal, fasting conditions, the model predicts two basal operating regimes: (i) one in which a constant basal insulin infusion leads to a periodic glucose trajectory, and (ii) one in which a periodic basal insulin infusion is used to maintain a constant basal glucose level. Structural identifiability and sensitivity analyses are used to define a practically estimable parameter subset for personalization. The model is validated both in silico on the commercial UVA/Padova adult cohort and on free-living data from thirteen subjects of the TAILOR/3 study. Compared with a previous control-oriented linear formulation, the proposed model provides improved prediction accuracy, with higher goodness of fit and lower root mean squared error. On clinical data, the improvement holds for every subject over the identification period, while over a two-day open-loop validation horizon the proposed model yields a positive fit on eleven subjects out of thirteen, against nine for the linear benchmark and without ever failing on a subject on which the benchmark remains usable, with performance markedly lower than in silico, as expected given real-life uncertainties. These results indicate that explicitly modeling dynamic insulin sensitivity can improve physiological fidelity and prediction performance, supporting the development of more personalized model-based strategies for automated insulin delivery.