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A Novel Mathematical Model Detecting Early Individual Changes of Insulin Resistance



Insulin resistance (IR) and hyperinsulinemia as well as obesity play a key role in the metabolic syndrome (MetS), type 2 diabetes (T2D), and associated cardiovascular disease. Unfortunately, IR and hyperinsulinemia are often diagnosed late (i.e., when the MetS is already clinically evident). An earlier diagnosis of IR would be desirable to reduce its clinical consequences, in particular in view of the increasing prevalence of obesity and diabetes conditions. For this purpose, we developed a mathematical model capable of detecting early onset of IR through small variations of insulin sensitivity, glucose effectiveness, and first- or second-phase responses.

Materials and methods

Murine models provide controlled conditions to study various stages of IR. Various degrees of hypercholesterolemia, obesity, IR, and atherosclerosis were induced in low-density lipoprotein receptor-deficient mice by feeding them cholesterol- or sucrose-rich diets. IR was assessed by oral glucose tolerance tests. Controls included animals fed exclusively, or switched back to, regular chow. A nonlinear mathematical model of the order of 5 was developed by refining Bergman's "Minimal Model" and then applied to experimental data.


Different metabolic constellations consistently corresponded to specific and close-meshed changes in model parameters. Reduced second-phase glucose sensitivity characterized an early impaired glucose tolerance. Later stages showed an increased first-phase glucose sensitivity compensating for decreased insulin sensitivity. Finally, T2D was associated with both first- and second-phase sensitivities close to zero.


The new mathematical model detected various insulin-sensitive or -resistant metabolic stages of IR. It can therefore be implemented for quantitative metabolic risk assessment and may be of therapeutic value by anticipating the start of therapeutic interventions.

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