Origins and History of the Minimal Model of Glucose Regulation

Abstract

It has long been hoped that our understanding of the pathogenesis of diabetes would be helped by the use of mathematical modeling. In 1979 Richard Bergman and Claudio Cobelli worked together to find a "minimal model" based upon experimental data from Bergman's laboratory. Model was chosen as the simplest representation based upon physiology known at the time. The model itself is two quasi-linear differential equations; one representing insulin kinetics in plasma, and a second representing the effects of insulin and glucose itself on restoration of the glucose after perturbation by intravenous injection. Model would only be sufficient if it included a delay in insulin action; that is, insulin had to enter a remote compartment, which was interstitial fluid (ISF). Insulin suppressed endogenous glucose output (by liver) slowly. Delay proved to be due to initial suppression of lipolysis; resultant lowering of free fatty acids reduced liver glucose output. Modeling also demanded that normalization of glucose after injection included an effect of glucose itself on glucose disposal and endogenous glucose production - these effects were termed "glucose effectiveness." Insulin sensitivity was calculated from fitting the model to intravenous glucose tolerance test data; the resulting insulin sensitivity index, SI, was validated with the glucose clamp method in human subjects. Model allowed us to examine the relationship between insulin sensitivity and insulin secretion. Relationship was described by a rectangular hyperbola, such that Insulin Secretion x Insulin Sensitivity = Disposition Index (DI). Latter term represents ability of the pancreatic beta-cells to compensate for insulin resistance due to factors such as obesity, pregnancy, or puberty. DI has a genetic basis, and predicts the onset of Type 2 diabetes. An additional factor was clearance of insulin by the liver. Clearance varies significantly among animal or human populations; using the model, clearance was shown to be lower in African Americans than Whites (adults and children), and may be a factor accounting for greater diabetes prevalence in African Americans. The research outlined in the manuscript emphasizes the powerful approach by which hypothesis testing, experimental studies, and mathematical modeling can work together to explain the pathogenesis of metabolic disease.

Keywords: diabetes; disposition index; glucose effectiveness; insulin clearance; mathematical model; metabolism.

Figure 1

Guyton model of the cardiovascular system.

Figure 2

Biphasic insulin release from perfused pancreas.

Figure 3

Bergman model of insulin secretion.

Figure 4

Early IVGTTs with frequent blood sampling.

Figure 5

IVGTT phases.

Figure 6

Closed loop system of glucose regulation.

Figure 7

Models tested to determine “optimal” degree of complexity. Model 6 was chosen and was designated the “minimal model.”

Figure 8

Equations of the minimal model and their “translation.”

Figure 9

Schematic of insulin transport from blood to interstitial fluid.

Figure 10

IVGTT protocol and minimal model output. Insulin data are”input” to the minimal model, which determines the best fit of the glucose dynamics and model parameters for that IVGTT.

Figure 11

S_I equivalence between minimal model and clamp.

Figure 12

Disposition index (DI).

Figure 13

Cited publications pertaining to the DI.

Figure 14

Predictive impact of DI on diabetes risk.

Figure 15

Factors contributing to glucose tolerance.

Figure 16

Model of insulin clearance.

Figure 17

Hypothesis of the pathogenesis of Type 2 diabetes. It is suggested that increased plasma free fatty acids cause a reduction in hepatic insulin clearance, possibly by downregulation of IDE. A large proportion of insulin secreted by the β-cells therefore bypasses first-pass degradation, resulting in peripheral hyperinsulinemia. Higher plasma insulin downregulates skeletal muscle insulin sensitivity, stressing β-cells, and resulting in diabetes.

Figure 18

Simple model of glucose/lactate kinetics. Glucose enters hepatocytes, independent of insulin, and follows the glycolytic pathway via glucokinase. Lactate exits the liver and is a surrogate for glucokinase activation and “glucose effectiveness”.

Figure 19

Importance of modeling in the scientific method.