Undermodeling affects minimal model indexes: insights from a two-compartment model

The classic (hereafter cold) and the labeled (hereafter hot) minimal models are powerful tools to investigate glucose metabolism. The cold model provides, from intravenous glucose tolerance test (IVGTT) data, indexes of glucose effectiveness (S_G) and insulin sensitivity (S_I) that measure the effect of glucose and insulin, respectively, to enhance glucose disappearance and inhibit endogenous glucose production. The hot model provides, from hot IVGTT data, indexes of glucose effectiveness ($S{*}_G$ ) and insulin sensitivity ($S{*}_I$ ) that, respectively, measure the effects of glucose and insulin on glucose disappearance only. Recent reports call for a reexamination of some of the assumptions of the minimal models. We have previously pointed out the criticality of the single-compartment description of glucose kinetics on which both the minimal models are founded. In this paper we evaluate the impact of single-compartment undermodeling on S_G, S_I,$S{*}_G$ , and$S{*}_I$ by using a two-compartment model to describe the glucose system. The relationships of the minimal model indexes to the analogous indexes measured with the glucose clamp technique are also examined. Theoretical analysis and simulation studies indicate that cold indexes are more affected than hot indexes by undermodeling. In particular, care must be exercised in the physiological interpretation of S_G, because this index is a local descriptor of events taking place in the initial portion of the IVGTT. As a consequence, S_G not only reflects glucose effect on glucose uptake and production but also the rapid exchange of glucose between the accessible and nonaccessible glucose pools that occurs in the early part of the test.