Minimal model of glucose metabolism: Modified equations and its application in the study of insulin sensitivity in obese subjects

Abstract

As implemented in their program MINMOD, some of the parameters and variables of the equations representing Bergman and coworkers' minimal model of glucose metabolism have no simple rational relationship with the kinetic constants and constants of proportionality of the minimal model as such. In this work we implemented the original version of the minimal model, which does not suffer from this problem, and used it to investigate the source of insulin resistance among obese but otherwise healthy subjects. A fasting sampled intravenous glucose tolerance (FSIGT) test was performed in 38 healthy subjects of varying degrees of obesity (standard FSIGT test in 21 and tolbutamide FSIGT test in 17 subjects) in order to compare MINMOD and `modified' equations (M1). Insulin sensitivity index ( S I) in obese subjects was significantly lower than in lean subjects (4.58±3.5 vs. 11.7±4.3·10 −5 min −1(pmol·l −1) −1, P<0.0001). The lower S I in obese subjects was a consequence of a lower p 3 parameter (0.178±0.08 vs. 0.440±0.26·10 −5 min −2(pmol·l −1) −1, P<0.01), being p 2 similar between obese and lean subjects (0.389±0.19 vs. 0.376±0.19·10 −1 min −1, NS). S I index correlated with p 3 ( r=0.73, P<0.0001), but not with p 2 ( r=0.01, NS). Using these results and assuming that interstitial insulin is higher in obese subjects than in lean subjects, we have demonstrated that the proportionality constants of the model ( k 4 and k 6) were lower in obese subjects than in lean subjects, but not the rate constant for insulin transfer across capillaries, k 2. Our results suggest that the modified equations are a better theoretical approach to the minimal model method; and that low insulin sensitivity in obese subjects is due to receptor and/or post-receptor events rather than to slow transfer of insulin across capillary endothelium into the interstitial space.