Mathematical models of insulin secretion in physiological and clinical investigations

Abstract

The discovery of the radioimmunoassay for the measurement of insulin concentration stimulated several clever studies which showed, both in vitro and in vivo, the peculiar biphasic pattern of the β-cell response to glucose stimulation. Physiologists took the challenge to describe with mathematical models those data, introducing tools that provided medical and biological research scientists with further knowledge of the nature of the complex processes involved in insulin secretion. Simulation models were therefore developed to account for the dependence on each other of the different features of the system behaviour to better understand them and to formulate hypotheses for further investigations. The disadvantages of these models (rather complex mathematical structure, unidentifiability, etc.) limited their use to a few applications, mostly as teaching tools. The use of models in the clinical setting required the individualization of the parameter set for a single subject from an experimental test as simple as possible. This led to the development of the minimal model of insulin appearance and kinetics. This model, fully identifiable, thus enables the furnishing of a personalized picture of insulin behaviour, providing insights on hormone secretion during a (frequently sampled) intravenous glucose tolerance test. However, this model analyzed systemic insulin concentration data and gave information only on post-hepatic insulin delivery. Since the liver takes up more than 50% of the released hormone, a further step was necessary to evaluate insulin secretion, i.e. the analysis of the behaviour of C-peptide, which is released equimolarly with insulin, but is not extracted by the liver. The last generation models are in fact descriptors of the systemic C-peptide dynamics, and are used to reconstruct its secretion which is assumed to be molarly equal to that of insulin. Mainly three models of pre-hepatic insulin appearance, based on this principle, have been developed and used in clinical studies.