Evaluation of model complexity in model predictive control within an exercise-enabled artificial pancreas

Model predictive control (MPC) algorithms have been used often within artificial pancreas control systems both in-silico and in clinical studies. Increasingly complex models in the controller can more accurately predict the glycemic response, but they introduce increased computational complexity which can be challenging to implement especially within an embedded environment where computational resources are limited. Less complex models are also preferable in that they can be evaluated in silico against more complex plant models. There has not yet been an evaluation of how the complexity of models used within an MPC impacts performance within an artificial pancreas. A model within an artificial pancreas MPC algorithm should be as complex as necessary to accurately predict a glycemic response to meals, exercise, stress, and other disturbances, but not overly complex. In this paper, we evaluate four glucoregulatory models used within an MPC, starting with a 4-state model and increasing in complexity up to six states. We evaluate the complexity using an in-silico population derived from a more complex glucoregulatory model (9 state variables). We assess how complexity of the model impacts performance both in terms of standard control metrics such as settling time and overshoot as well as clinically relevant metrics such as percent time in euglycemia (glucose between 70 and 180 mg/dl), percent time in hypoglycemia (70 mg/dl) and percent time in hyperglycemia (>180 mg/dl). We find that model complexity matters far less than how well the model parameters match the individual subjects. When the simplest model is used, but fit to an individual subject's data, it performed comparably with more complex models. We selected a middle-complexity model and integrated it into our previously published exercise-enabled MPC model and evaluated it in a virtual patient population both with and without the exercise model present. We found that increasing complexity by modeling exercise is critical to help enable early insulin shut-off by the controller to avoid hypoglycemia.