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. SI was compared with measures of body adiposity and β-cell function. Although lean individuals showed a wide range of SI, body mass index and SI 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 SI and the β-cell measures was more clearly curvilinear and reciprocal for fasting insulin (P < 0.0001), first-phase insulin response (AIRglucose; P < 0.0001), glucose potentiation slope (n = 56; P < 0.005), and β-cell secretory capacity (AIRmax; n = 43; P < 0.0001). The curvilinear relationship between SI and the β-cell measures could not be distinguished from a hyperbola, i.e., SI × 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 SI, 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.
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Original Articles|
November 01 1993
Quantification of the Relationship Between Insulin Sensitivity and β-Cell Function in Human Subjects: Evidence for a Hyperbolic Function
Steven E Kahn;
Steven E Kahn
Divisions of Metabolism, Endocrinology, and Nutrition and General Internal Medicine, Department of Medicine, and Department of Epidemiology, University of Washington and Veterans Affairs Medical Center
Seattle, Washington
Department of Physiology and Biophysics, University of Southern California
Los Angeles, California
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Ronald L Prigeon;
Ronald L Prigeon
Divisions of Metabolism, Endocrinology, and Nutrition and General Internal Medicine, Department of Medicine, and Department of Epidemiology, University of Washington and Veterans Affairs Medical Center
Seattle, Washington
Department of Physiology and Biophysics, University of Southern California
Los Angeles, California
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David K McCulloch;
David K McCulloch
Divisions of Metabolism, Endocrinology, and Nutrition and General Internal Medicine, Department of Medicine, and Department of Epidemiology, University of Washington and Veterans Affairs Medical Center
Seattle, Washington
Department of Physiology and Biophysics, University of Southern California
Los Angeles, California
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Edward J Boyko;
Edward J Boyko
Divisions of Metabolism, Endocrinology, and Nutrition and General Internal Medicine, Department of Medicine, and Department of Epidemiology, University of Washington and Veterans Affairs Medical Center
Seattle, Washington
Department of Physiology and Biophysics, University of Southern California
Los Angeles, California
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Richard N Bergman;
Richard N Bergman
Divisions of Metabolism, Endocrinology, and Nutrition and General Internal Medicine, Department of Medicine, and Department of Epidemiology, University of Washington and Veterans Affairs Medical Center
Seattle, Washington
Department of Physiology and Biophysics, University of Southern California
Los Angeles, California
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Micheal W Schwartz;
Micheal W Schwartz
Divisions of Metabolism, Endocrinology, and Nutrition and General Internal Medicine, Department of Medicine, and Department of Epidemiology, University of Washington and Veterans Affairs Medical Center
Seattle, Washington
Department of Physiology and Biophysics, University of Southern California
Los Angeles, California
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James L Neifing;
James L Neifing
Divisions of Metabolism, Endocrinology, and Nutrition and General Internal Medicine, Department of Medicine, and Department of Epidemiology, University of Washington and Veterans Affairs Medical Center
Seattle, Washington
Department of Physiology and Biophysics, University of Southern California
Los Angeles, California
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W Kenneth Ward;
W Kenneth Ward
Divisions of Metabolism, Endocrinology, and Nutrition and General Internal Medicine, Department of Medicine, and Department of Epidemiology, University of Washington and Veterans Affairs Medical Center
Seattle, Washington
Department of Physiology and Biophysics, University of Southern California
Los Angeles, California
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James C Beard;
James C Beard
Divisions of Metabolism, Endocrinology, and Nutrition and General Internal Medicine, Department of Medicine, and Department of Epidemiology, University of Washington and Veterans Affairs Medical Center
Seattle, Washington
Department of Physiology and Biophysics, University of Southern California
Los Angeles, California
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Jerry P Palmer
Jerry P Palmer
Divisions of Metabolism, Endocrinology, and Nutrition and General Internal Medicine, Department of Medicine, and Department of Epidemiology, University of Washington and Veterans Affairs Medical Center
Seattle, Washington
Department of Physiology and Biophysics, University of Southern California
Los Angeles, California
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Address correspondence and reprint requests to Dr. Steven E. Kahn, VA Medical Center (151L), 1660 South Columbian Way, Seattle, WA 98108
Diabetes 1993;42(11):1663–1672
Article history
Received:
October 26 1992
Revision Received:
June 17 1993
Accepted:
June 17 1993
PubMed:
8405710
Citation
Steven E Kahn, Ronald L Prigeon, David K McCulloch, Edward J Boyko, Richard N Bergman, Micheal W Schwartz, James L Neifing, W Kenneth Ward, James C Beard, Jerry P Palmer; Quantification of the Relationship Between Insulin Sensitivity and β-Cell Function in Human Subjects: Evidence for a Hyperbolic Function. Diabetes 1 November 1993; 42 (11): 1663–1672. https://doi.org/10.2337/diab.42.11.1663
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