An islet population model of the endocrine pancreas.

An islet population model is proposed for pancreatic insulin secretion. Without detailing the chain of biochemical events giving rise to the delivery of insulin packets, the effect of the islets' bursting response to varying glucose concentration is described by a simple second order nonlinear model, of the same functional form for all islets, but with a random distribution of parameter values over the one million islets considered. The islet equations are coupled to a traditional model of the glucose/insulin dynamics to complete a description of the feed-back control of the glucose/insulin system. The model is thus based upon the completely random cooperation of a large number of independent controllers, all reacting to the same prevailing plasma glucose concentrations, but with distributed reaction characteristics. It is shown that the proposed model is able to replicate in silico different observed phenomena such as low frequency glycemia-insulinemia oscillations (ultradian oscillations, with a period between 50 and 150 min, amplified by constant glucose administration and entrained by an oscillating exogenous glucose infusion), as well as concordant induction of high-frequency insulin oscillations by a rapid periodic pulsatile glucose infusion. In order to reproduce by simulation all of the above observed phenomena, a single set of (hyper-)parameters has been used throughout, showing that it is indeed possible that a single model may explain the results of several published experimental protocols.