Mathematical model of blood glucose dynamics by emulating the pathophysiology of glucose metabolism in type 2 diabetes mellitus

Mathematical modelling has established itself as a theoretical tool to understand fundamental aspects of a variety of medical-biological phenomena. The predictive power of mathematical models on some chronic conditions has been helpful in its proper prevention, diagnosis, and treatment. Such is the case of the modelling of glycaemic dynamics in type 2 diabetes mellitus (T2DM), whose physiology-based mathematical models have captured the metabolic abnormalities of this disease. Through a physiology-based pharmacokinetic-pharmacodynamic approach, this work addresses a mathematical model whose structure starts from a model of blood glucose dynamics in healthy humans. This proposal is capable of emulating the pathophysiology of T2DM metabolism, including the effect of gastric emptying and insulin enhancing effect due to incretin hormones. The incorporation of these effects lies in the implemented methodology since the mathematical functions that represent metabolic rates, with a relevant contribution to hyperglycaemia, are adjusting individually to the clinical data of patients with T2DM. Numerically, the resulting model successfully simulates a scheduled graded intravenous glucose test and oral glucose tolerance tests at different doses. The comparison between simulations and clinical data shows an acceptable description of the blood glucose dynamics in T2DM. It opens the possibility of using this model to develop model-based controllers for the regulation of blood glucose in T2DM.