Modeling the glucose–insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays

In the glucose–insulin regulatory system, ultradian insulin secretory oscillations are observed to have a period of 50–150 min. After pioneering work traced back to the 1960s, several mathematical models have been proposed during the last decade to model these ultradian oscillations as well as the metabolic system producing them. These currently existing models still lack some of the key physiological aspects of the glucose–insulin system. Applying the mass conservation law, we introduce two explicit time delays and propose a more robust alternative model for better understanding the glucose–insulin endocrine metabolic regulatory system and the ultradian insulin secretory oscillations for the cases of continuous enteral nutrition and constant glucose infusion. We compare the simulation profiles obtained from this two time delay model with those from the other existing models. As a result, we notice many unique features of this two delay model. Based on our intensive simulations, we suspect that one of the possibly many causes of ultradian insulin secretion oscillations is the time delay of the insulin secretion stimulated by the elevated glucose concentration.