A Mathematical Model for the Glucose Induced Insulin Release in Man

Abstract. The dynamics of the insulin response to intravenously administered glucose were studied in man. It was shown that (a) insulin response to prolonged stimulation is biphasic; (b) if the glucose stimulus is repeated with short intervals, inhibition of the second response occurs; (c) if longer time‐intervals are used, enhancement of the response is noted at the second stimulation. These findings suggest that when the pancreatic islets are exposed to hyperglycaemia, three, kinetically distinct phenomena are initiated. Glucose induces almost instantaneous initiation of insulin release. Shortly thereafter, the pancreas enters a refractory phase. Thirdly, and at a later stage, a state of potentiation is built up in the islets. The effect of glucose on insulin synthesis is not considered here.–Against this background, and based on an earlier model, a mathematical model for the analysis of the glucose‐insulin interplay during glucose infusions was constructed. The model describes the eventual occurrence of glucosuria, changes in the concentration of glucose in its pool, and mimics the effects of regulatory hormones when hypoglycemia appears. Insulin secretion is assumed to be con trolled, in a multiplicative manner, by an immediate glucose function, a hypothetical potentiator that is slowly generated by glucose, and a negative factor with a shorter time‐course which corresponds to the refractory phase of the pancreas. A three compartment model is used in the simulation of the metabolism and distribution of insulin after its release. Finally, glucose utilization is described as a multiplicative function, related to the prevailing concentrations of glucose in blood and insulin in the extracellular space.–This model is able to simulate all the experimental situations described in this report, both in normal man and in the diabetic syndrome, in which insulin secretion shows varying degrees of impairment. The results of the simulation of individual experiments are given either as a set of theoretical parameter values, or described as the insulin response of the model to a standard, hypothetical glucose stimulus. The latter alternative is an attractive method for objectively evaluating the insulin response to a standard glucose load in clinical materials.