Mathematical modeling and simulations of the pathophysiology of Type-2 Diabetes Mellitus

Abstract

The pathophysiology of Type 2 Diabetes Mellitus (T2DM) is modelled using a coupled system of non-linear deterministic differential equations. An attempt is made to construct to a clinically plausible mathematical model that incorporates the homeostasis associated with endocrinological regulation of glucose and glycogen levels in the human body, by the hormones, insulin and glucagon. The model variables include the concentrations of glucose in the venous blood plasma, the concentration of glycogen in the liver/tissues, the concentration of the hormone glucagon, and the concentration of insulin in the venous blood plasma. The physiological interactions between the model parameters are depicted by clinically measurable rate constants and biophysically quantifiable stoichiometric coefficients. The processes of gluconeogenesis, glycogenolysis, and pulsatile insulin secretion during type 2 diabetes are modelled using plausible auxiliary functions. Investigative computer simulations are performed to elucidate various hypothetical scenarios of glycemia, patho-physiology of T2DM and insulinoma associated hypoglycemia which results from excessive insulin production probably due to a tumor. This study has demonstrated the necessity of simultaneous monitoring of plasma glucose, glucagon, insulin, and glycogen levels in the proper assessment of the pathophysiology of type 2 diabetes and during determination of the therapeutic efficacy of anti-diabetic drugs.