Modeling glucose and free fatty acid kinetics during insulin-modified intravenous glucose tolerance test in healthy humans: role of counterregulatory response

Mathematical modeling reveals differential dynamics of insulin action models on glycerol and glucose in adolescent girls with obesity

Under healthy conditions, the pancreas responds to a glucose challenge by releasing insulin. Insulin suppresses lipolysis in adipose tissue, thereby decreasing plasma glycerol concentration, and it regulates plasma glucose concentration through action in muscle and liver. Insulin resistance (IR) occurs when more insulin is required to achieve the same effects, and IR may be tissue-specific. IR emerges during puberty as a result of high concentrations of growth hormone and is worsened by youth-onset obesity. Adipose, liver, and muscle tissue exhibit distinct dose-dependent responses to insulin in multi-phase hyperinsulinemic-euglycemic (HE) clamps, but the HE clamp protocol does not address potential differences in the dynamics of tissue-specific insulin responses. Changes to the dynamics of insulin responses would alter glycemic control in response to a glucose challenge. To investigate the dynamics of insulin acting on adipose tissue, we developed a novel differential-equations based model that describes the coupled dynamics of glycerol concentrations and insulin action during an oral glucose tolerance test in female adolescents with obesity and IR. We compared these dynamics to the dynamics of insulin acting on muscle and liver as assessed with the oral minimal model applied to glucose and insulin data collected under the same protocol. We found that the action of insulin on glycerol peaks approximately 67 min earlier (p < 0.001) and follows the dynamics of plasma insulin more closely compared to insulin action on glucose as assessed by the parameters representing the time constants for insulin action on glucose and glycerol (p < 0.001). These findings suggest that the dynamics of insulin action show tissue-specific differences in our IR adolescent population, with adipose tissue responding to insulin more quickly compared to muscle and liver. Improved understanding of the tissue-specific dynamics of insulin action may provide novel insights into the progression of metabolic disease in patient populations with diverse metabolic phenotypes.

Glucose Effectiveness from Short Insulin-Modified IVGTT and Its Application to the Study of Women with Previous Gestational Diabetes Mellitus

BACKGROUND

This study aimed to design a simple surrogate marker (i.e., predictor) of the minimal model glucose effectiveness (S_G), namely calculated S_G (CS_G), from a short insulin-modified intravenous glucose tolerance test (IM-IVGTT), and then to apply it to study women with previous gestational diabetes mellitus (pGDM).

METHODS

CS_G was designed using the stepwise model selection approach on a population of subjects (n=181) ranging from normal tolerance to type 2 diabetes mellitus (T2DM). CS_G was then tested on a population of women with pGDM (n=57). Each subject underwent a 3-hour IM-IVGTT; women with pGDM were observed early postpartum and after a follow-up period of up to 7 years and classified as progressors (PROG) or non-progressors (NONPROG) to T2DM. The minimal model analysis provided a reference S_G.

RESULTS

CS_G was described as CS_G=1.06×10⁻²+5.71×10⁻²×K_G/G_peak, K_G being the mean slope (absolute value) of loge glucose in 10-25- and 25-50-minute intervals, and G_peak being the maximum of the glucose curve. Good agreement between CS_G and S_G in the general population and in the pGDM group, both at baseline and follow-up (even in PROG and NONPROG subgroups), was shown by the Bland-Altman plots (<5% observations outside limits of agreement), and by the test for equivalence (equivalence margin not higher than one standard deviation). At baseline, the PROG subgroup showed significantly lower S_G and CS_G values compared to the NONPROG subgroup (P<0.03).

CONCLUSION

CS_G is a valid S_G predictor. In the pGDM group, glucose effectiveness appeared to be impaired in women progressing to T2DM.

Modelling the effects of glucagon during glucose tolerance testing

Background

Glucose tolerance testing is a tool used to estimate glucose effectiveness and insulin sensitivity in diabetic patients. The importance of such tests has prompted the development and utilisation of mathematical models that describe glucose kinetics as a function of insulin activity. The hormone glucagon, also plays a fundamental role in systemic plasma glucose regulation and is secreted reciprocally to insulin, stimulating catabolic glucose utilisation. However, regulation of glucagon secretion by α-cells is impaired in type-1 and type-2 diabetes through pancreatic islet dysfunction. Despite this, inclusion of glucagon activity when modelling the glucose kinetics during glucose tolerance testing is often overlooked. This study presents two mathematical models of a glucose tolerance test that incorporate glucose-insulin-glucagon dynamics. The first model describes a non-linear relationship between glucagon and glucose, whereas the second model assumes a linear relationship.

Results

Both models are validated against insulin-modified and glucose infusion intravenous glucose tolerance test (IVGTT) data, as well as insulin infusion data, and are capable of estimating patient glucose effectiveness (s_G) and insulin sensitivity (s_I). Inclusion of glucagon dynamics proves to provide a more detailed representation of the metabolic portrait, enabling estimation of two new diagnostic parameters: glucagon effectiveness (s_E) and glucagon sensitivity (δ).

Conclusions

The models are used to investigate how different degrees of pax‘tient glucagon sensitivity and effectiveness affect the concentration of blood glucose and plasma glucagon during IVGTT and insulin infusion tests, providing a platform from which the role of glucagon dynamics during a glucose tolerance test may be investigated and predicted.

Integrated model of insulin and glucose kinetics describing both hepatic glucose and pancreatic insulin regulation

BACKGROUND AND OBJECTIVES

Modeling of glucose kinetics has to a large extent been based on models with plasma insulin as a known forcing function. Furthermore, population-based statistical methods for parameter estimation in these models have mainly addressed random inter-individual variations and not intra-individual variations in the parameters. Here we present an integrated whole-body model of glucose and insulin kinetics which extends the well-known two-compartment glucose minimal model. The population-based estimation technique allow for quantification of both random inter- and intra-individual variation in selected parameters using simultaneous data series on glucose and insulin.

METHODS

We extend the two-compartment glucose model into a whole-body model for both glucose and insulin using a simple model for the pancreas compartment which includes feedback of glucose on both insulin secretion and formation of insulin in pancreas. The model has 15 unknown parameters of which 8 have been selected for both intra- and inter-individual variations. The statistical technique for parameter estimation is based on first order conditional estimation.

RESULTS

The model has been evaluated on two datasets: Study group 1 includes 13 healthy subjects with 3-5 repeated IVGTT series of simultaneous plasma glucose and insulin measurements and Study group 2 includes 26 obese patients (3 subgroups: 10 type 2 diabetes (T2D), 7 impaired glucose tolerance (IGT) and 9 normal glucose tolerance (NGT)) with a single IVGTT series. In general the estimated population parameters compares well with reported values in similar studies. Overall the model fits the data series well and the random variation in the 8 selected parameters can account for both intra- and inter-individual variations in the data series. Simulation studies perform reasonable in response to either a slow glucose infusion or a staircase experiment with increasing glucose infusion. Furthermore, the parameters related to the pancreas compartment add useful interpretations in relation to discrimination between populations with varying degree of glucose intolerance.

CONCLUSIONS

We report a new and improved whole-body model of glucose and insulin kinetics which performs robustly under differing conditions and adds useful interpretations in relation to glucose intolerance.

Quantification of adipose tissue insulin sensitivity

In metabolically healthy humans, adipose tissue is exquisitely sensitive to insulin. Similar to muscle and liver, adipose tissue lipolysis is insulin resistant in adults with central obesity and type 2 diabetes. Perhaps uniquely, however, insulin resistance in adipose tissue may directly contribute to development of insulin resistance in muscle and liver because of the increased delivery of free fatty acids to those tissues. It has been hypothesized that insulin adipose tissue resistance may precede other metabolic defects in obesity and type 2 diabetes. Therefore, precise and reproducible quantification of adipose tissue insulin sensitivity, in vivo, in humans, is an important measure. Unfortunately, no consensus exists on how to determine adipose tissue insulin sensitivity. We review the methods available to quantitate adipose tissue insulin sensitivity and will discuss their strengths and weaknesses.