Stability of the insulin–glucose feedback loop in Glucosafe: A comparison of pancreas models

Glucosafe is a medical decision support system developed for glycaemic control in critically ill patients. The system recommends nutrition and insulin doses based on a physiological insulin–glucose model. This model assumes constant endogenous insulin release, in contrast to experimental data from healthy humans where a dual-phase insulin release (i.e. a phase-1 and phase-2 response) has been found along with evidence of a 2-pool insulin system. We included two different pancreas models in Glucosafe, one with a phase-2 response (Phase 2 model) and one with a phase-1 and phase-2 response (Phase 1 + 2 model) and studied the stability of Glucosafe with each applied model.The pancreas models were fitted to plasma glucose and insulin data from 14 healthy subjects receiving meals, and compared by calculating the respective loop gains (LG) for each model. The models were also compared by short perturbations of the simulated blood glucose with 1 mmol/l increases over 10 min and measuring the predicted subsequent oscillations of blood glucose and endogenous insulin production. In this second comparison, the time constant (τ) for the decay of the oscillations was used as stability marker of the models.When fitting the models to the pooled data, a better fit (p < 10−7) was achieved with the Phase 1 + 2 model with an RMS error of 3.7 mU/l compared to the Phase 2 model with an RMS error of 5.2 mU/l. Blood glucose perturbations resulted in damped oscillations in both models. The Phase 1 + 2 model proved more stable (τ = 40 min) than the Phase 2 model (τ = 92 min) despite a slightly larger LG (6.6) compared to the Phase 2 model (6.1). The greater stability of the Phase 1 + 2 model is most likely due to the phase-lead nature of the phase-1 response, which in a linear system can improve stability.In conclusion, a pancreas model with both a phase-1 and phase-2 insulin response results in a Glucosafe model which is more stable than Glucosafe with a Phase 2 pancreas model. What remains to be investigated is to which extent the damped oscillations simulated by Glucosafe match the physiological response to a BG perturbation in normal subjects and in patients, and to investigate if a Phase-1 + 2 model improves accuracy of Glucosafe's BG predictions.