Stability analysis of insulin-glucose feedback in the Glucosafe pancreas model of endogenous insulin production

Abstract

Hyperglycemia is common in patients hospitalized for critical illness, trauma or after surgery, and is associated with increased morbidity and mortality. The Glucosafe system was developed to provide decision support for control of stress hyperglycemia in the intensive care unit. Glucosafe uses an insulin-glucose model to predict blood glucose (BG) concentrations, based on the patients previous and current insulin infusion, nutrition, and BG measurements. As endogenous insulin production is dependent on BG in a negative feedback loop, a pancreas model of endogenous insulin production was incorporated into the Glucosafe system. We investigated the stability of the feedback loop by calculating the loop gain of the model at different steady-state BG concentrations and insulin sensitivities. We also examining the models BG oscillations, after an initial perturbation, at different insulin sensitivities. Results show that both steady-state BG and insulin sensitivity influences the size of the loop gain. The largest loop gain (6.9) occurs at an insulin sensitivity of 1.2 and a BG of 5.5 mmol/l, where the BG perturbation resulted is damped oscillations of BG and endogenous insulin production. The BG dependent endogenous insulin production did not result in an unstable Glucosafe insulin-glucose model, although it did introduce damped oscillations in BG and insulin production during rapid increases in BG. It may be prudent to investigate if these oscillations can be decreased, possibly via the construction of a pancreas model which includes both a phase-1 and phase-2 response.