Recent advances in mathematical models for the understanding and treatment of Type 1 Diabetes Mellitus

Type 1 Diabetes Mellitus (T1DM) is a chronic autoimmune disease affecting around 80 million people in the world. Its pathophysiology is based on the malfunction of the glucose homeostasis given the deficiency in the production of the insulin hormone from pancreas. Therefore, after an ingestion of a high-carbohydrate meal, the patient with this condition is not able to recover back the right plasma glucose concentration by itself. Nowadays, there exists an approach to treat this condition from control engineering and it is based on the development of an artificial pancreas able to provide the needed doses of insulin and glucagon at a given time. However, one of the main concerns in the development of such an artificial pancreas is to provide, to the automatic controller, a reliable mathematical model about the physiology of the treated patient in order to perform the right decision making. Although the literature about mathematical modeling of diabetes is quite vast, the purpose of this paper is to provide an update about the recent advances about the diabetes modeling, mainly what is related to the glucose homeostasis. The review is mainly focused on the developments from the last ten years.