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Glucose effectiveness, defined as the ability of glucose itself to increase glucose utilization and inhibit hepatic glucose production, is an important mechanism maintaining normoglycemia. We conducted a minimal modeling analysis of glucose effectiveness at zero insulin (GEZI) using intravenous glucose tolerance test data from subjects with type 2 diabetes (T2D, n=154) and non-diabetic (ND) subjects (n=343). A hierarchical statistical analysis was performed, which provided a formal mechanism for pooling the data from all study subjects, to yield a single composite population model that quantifies the role of subject specific characteristics such as weight, height, age, sex, and glucose tolerance. Based on the resulting composite population model, GEZI was reduced from 0.021 min–1 (standard error – 0.00078 min–1) in the ND population to 0.011 min–1 (standard error – 0.00045 min–1) in T2D. The resulting model was also employed to calculate the proportion of the non–insulin-dependent net glucose uptake in each subject receiving an intravenous glucose load. Based on individual parameter estimates, the fraction of total glucose disposal independent of insulin was 72.8% ± 12.0% in the 238 ND subjects over the course of the experiment, indicating the major contribution to the whole-body glucose clearance under non-diabetic conditions. This fraction was significantly reduced to 48.8% ± 16.9% in the 30 T2D subjects, although still accounting for approximately half of the total in the T2D population based on our modeling analysis. Given the potential application of glucose effectiveness as a predictor of glucose intolerance and as a potential therapeutic target for treating diabetes, more investigations of glucose effectiveness in other disease conditions can be conducted using the hierarchical modeling framework reported herein.

In 1978, Thomas J. Sorensen defended a thesis in chemical engineering at the University of California, Berkeley, where he proposed an extensive model of glucose-insulin control, model which was thereafter widely employed for virtual patient simulation. The original model, and even more so its subsequent implementations by other Authors, presented however a few imprecisions in reporting the correct model equations and parameter values. The goal of the present work is to revise the original Sorensen's model, to clearly summarize its defining equations, to supplement it with a missing gastrio-intestinal glucose absorption and to make an implementation of the revised model available on-line to the scientific community.

Several models for the long-term development of T2DM already exist, focusing on the dynamics of the interaction between glycemia, insulinemia and β-cell mass. Current models consider representative (fasting or daily average) glycemia and insulinemia as characterizing the compensation state of the subject at some instant in slow time. This implies that only these representative levels can be followed through time and that the role of fast glycemic oscillations is neglected. An improved model (DPM15) for the long-term progression of T2DM is proposed, introducing separate peripheral and hepatic (liver and kidney) insulin actions. The DPM15 model no longer uses near-equilibrium approximation to separate fast and slow time scales, but rather describes, at each step in slow time, a complete day in the life of the virtual subject in fast time. The model can thus represent both fasting and postprandial glycemic levels and describe the effect of interventions acting on insulin-enhanced tissue glucose disposal or on insulin-inhibited hepatic glucose output, as well as on insulin secretion and β-cell replicating ability. The model can simulate long-term variations of commonly used clinical indices (HOMA-B, HOMA-IR, insulinogenic index) as well as of Oral Glucose Tolerance or Euglycemic Hyperinsulinemic Clamp test results. The model has been calibrated against observational data from the Diabetes Prevention Program study: it shows good adaptation to observations as a function of very plausible values of the parameters describing the effect of such interventions as Placebo, Intensive LifeStyle and Metformin administration.

The most well-known and widely used mathematical representations of the physiology of a diabetic individual are the Sorensen and Hovorka models as well as the UVAPadova Simulator. While the Hovorka model and the UVAPadova Simulator only describe the glucose metabolism of a subject with type 1 diabetes, the Sorensen model was formulated to simulate the behaviour of both normal and diabetic individuals. The UVAPadova model is the most known model, accepted by the FDA, with a high level of complexity. The Hovorka model is the simplest of the three models, well documented and used primarily for the development of control algorithms. The Sorensen model is the most complete, even though some modifications were required both to the model equations (adding useful compartments for modelling subcutaneous insulin delivery) and to the parameter values. In the present work several simulated experiments, such as IVGTTs and OGTTs, were used as tools to compare the three formulations in order to establish to what extent increasing complexity translates into richer and more correct physiological behaviour. All the equations and parameters used for carrying out the simulations are provided.

Published compact and extended models of the glucose-insulin physiologic control system are compared, in order to understand why a specific functional form of the compact model proved to be necessary for a satisfactory representation of acute perturbation experiments such as the Intra Venous Glucose Tolerance Test (IVGTT). A spectrum of IVGTT's of virtual subjects ranging from normal to IFG to IGT to frank T2DM were simulated using an extended model incorporating the population-of-controllers paradigm originally hypothesized by Grodsky, and proven to be able to capture a wide array of experimental results from heterogeneous perturbation procedures. The simulated IVGTT's were then fitted with the Single-Delay Model (SDM), a compact model with only six free parameters, previously shown to be very effective in delivering precise estimates of insulin sensitivity and secretion during an IVGTT. Comparison of the generating, extended-model parameter values with the obtained compact model estimates shows that the functional form of the nonlinear insulin-secretion term, empirically found to be necessary for the compact model to satisfactorily fit clinical observations, captures the pancreatic reserve level of the simulated virtual patients. This result supports the validity of the compact model as a meaningful analysis tool for the clinical assessment of insulin sensitivity.