Practical issues in the identification of empirical models from simulated type 1 diabetes data

A model-based controller for an artificial beta-cell automatically regulates blood glucose levels based on available glucose measurements, insulin infusion and meal information, and model predictions of future glucose trends. Thus, the identification of simple, accurate models plays an important role in the development of an artificial beta-cell.

Glucose data simulated from a nonlinear physiological model of type 1 diabetes are used to identify linear dynamic models of two types: autoregressive exogenous input (ARX) and output-error (OE) models. The model inputs are meal carbohydrates and exogenous insulin, which in practice are often administered simultaneously and in the same ratio, i.e., the insulin-to-carbohydrate ratio. The effect of modeling these inputs as impulses versus time-smoothed profiles ("transformed inputs") is explored in depth. The models are evaluated based on their ability to describe the data from which they were identified (i.e., calibration data) as well as independent data (i.e., validation data).

In general, the best models described their calibration data more accurately using transformed inputs (R(Cal) (2) = 71% for the ARX models and R (Cal) (2) = 78% for the OE models) than using impulse inputs (R (Cal) (2) = 14% for the ARX models and R (Cal) (2) = 70% for the OE models). The only model/input combination that resulted in consistently accurate validation fits was the ARX models using transformed inputs (39%

When identifying non-physiologically based models from diabetes data with simultaneous and proportional meals and insulin boluses, model accuracy is improved by modeling the inputs as time-smoothed profiles. Also, while OE models describe their calibration data very well, ARX models more accurately describe validation data. Their versatility makes ARX models a more attractive choice for implementation in a model-based controller of an artificial beta-cell.