QUANTIFICATION OF THE RELATIONSHIP BETWEEN INSULIN SENSITIVITY AND BETA-CELL FUNCTION IN HUMAN-SUBJECTS - EVIDENCE FOR A HYPERBOLIC FUNCTION

To determine the relationship between insulin sensitivity and beta-cel l function, we quantified the insulin sensitivity index using the mini mal model in 93 relatively young, apparently healthy human subjects of varying degrees of obesity (55 male, 38 female; 18-44 yr of age; body mass index 19.5-52.2 kg/m2) and with fasting glucose levels <6.4 mM. S(I) was compared with measures of body adiposity and beta-cell functi on. Although lean individuals showed a wide range of S(I), body mass i ndex and S(I) were related in a curvilinear manner (P < 0.0001) so tha t on average, an increase in body mass index was associated generally with a lower value for S(I). The relationship between the S(I) and the beta-cell measures was more clearly curvilinear and reciprocal for fa sting insulin (P < 0.0001), first-phase insulin response (AIR(glucose) ; P < 0.0001), glucose potentiation slope (n = 56; P < 0.005), and bet a-cell secretory capacity (AIR(max); n = 43; P < 0.0001). The curvilin ear relationship between S(I) and the beta-cell measures could not be distinguished from a hyperbola, i.e., S(I) x beta-cell function = cons tant. This hyperbolic relationship described the data significantly be tter than a linear function (P < 0.05). The nature of this relationshi p is consistent with a regulated feedback loop control system such tha t for any difference in S(I) a proportionate reciprocal difference occ urs in insulin levels and responses in subjects with similar carbohydr ate tolerance. We conclude that in human subjects with normal glucose tolerance and varying degrees of obesity, beta-cell function varies qu antitatively with differences in insulin sensitivity. Because the func tion governing this relationship is a hyperbola, when insulin sensitiv ity is high, large changes in insulin sensitivity produce relatively s mall changes in insulin levels and responses, whereas when insulin sen sitivity is low, small changes in insulin sensitivity produce relative ly large changes in insulin levels and responses. Percentile plots bas ed on knowledge of this interaction are presented for evaluating beta- cell function in populations and over time.