Data-Driven and Minimal-Type Compartmental Insulin-Glucose Models: Theory and Applications

This chapter initially presents the results of a computational study that compares simulated compartmental and Volterra models of the dynamic effects of insulin on blood glucose concentration in humans. In this context, we employ the general class of Volterra-type models that are estimated from input-output data, and the widely used “minimal model” as well as an augmented form of it, which incorporates the effect of insulin secretion by the pancreas. We demonstrate both the equivalence between the two approaches analytically and the feasibility of obtaining accurate Volterra models from insulin-glucose data generated from the compartmental models. We also present results from applying the proposed approach to quantifying the dynamic interactions between spontaneous insulin and glucose fluctuations in a fasting dog. The results corroborate the proposition that it may be feasible to obtain data-driven models in a more general and realistic operating context, without resorting to the restrictive prior assumptions and simplifications regarding model structure and/or experimental protocols (e.g. glucose tolerance tests) that are necessary for the compartmental models proposed previously. These prior assumptions may lead to results that are improperly constrained or biased by preconceived (and possibly erroneous) notions—a risk that is avoided when we let the data guide the inductive selection of the appropriate model.