  Objective: The design of an Artificial Pancreas (AP) to regulate blood
glucose levels requires reliable control methods. Model Predictive Control has
emerged as a promising approach for glycemia control. However, model--based
control methods require computationally simple and identifiable mathematical
models that represent glucose dynamics accurately, which is challenging due to
the complexity of glucose homeostasis. Methods: In this work, a simple model is
deduced to estimate blood glucose concentration in subjects with Type 1
Diabetes Mellitus (T1DM). Novel features in the model are power--law kinetics
for intraperitoneal insulin absorption and a separate glucagon sensitivity
state. Profile likelihood and a method based on singular value decomposition of
the sensitivity matrix are carried out to assess parameter identifiability and
guide a model reduction for improving the identification of parameters.
Results: A reduced model with 10 parameters is obtained and calibrated, showing
good fit to experimental data from pigs where insulin and glucagon boluses were
delivered in the intraperitoneal cavity. Conclusion: A simple model with
power--law kinetics can accurately represent glucose dynamics submitted to
intraperitoneal insulin and glucagon injections. The reduced model was found to
exhibit local practical as well as structural identifiability. Importance: The
proposed model facilitates intraperitoneal bi-hormonal model-based closed-loop
control in animal trials.
