Quantification of the Relationship Between Insulin Sensitivity and β-Cell Function in Human Subjects: Evidence for a Hyperbolic Function

Abstract

To determine the relationship between insulin sensitivity and β-cell function, we quantified the insulin sensitivity index using the minimal 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 β-cell function. Although lean individuals showed a wide range of S_I, body mass index and S_I were related in a curvilinear manner (P < 0.0001) so that on average, an increase in body mass index was associated generally with a lower value for SI. The relationship between the S_I and the β-cell measures was more clearly curvilinear and reciprocal for fasting insulin (P < 0.0001), first-phase insulin response (AIR_glucose; P < 0.0001), glucose potentiation slope (n = 56; P < 0.005), and β-cell secretory capacity (AIR_max; n = 43; P < 0.0001). The curvilinear relationship between S_I and the β-cell measures could not be distinguished from a hyperbola, i.e., S_I × β-cell function = constant. This hyperbolic relationship described the data significantly better than a linear function (P < 0.05). The nature of this relationship is consistent with a regulated feedback loop control system such that for any difference in S_I, a proportionate reciprocal difference occurs in insulin levels and responses in subjects with similar carbohydrate tolerance. We conclude that in human subjects with normal glucose tolerance and varying degrees of obesity, β-cell function varies quantitatively with differences in insulin sensitivity. Because the function governing this relationship is a hyperbola, when insulin sensitivity is high, large changes in insulin sensitivity produce relatively small changes in insulin levels and responses, whereas when insulin sensitivity is low, small changes in insulin sensitivity produce relatively large changes in insulin levels and responses. Percentile plots based on knowledge of this interaction are presented for evaluating β-cell function in populations and over time.