Mathematical modelling of the intravenous glucose tolerance test

 Several attempts at building a satisfactory model of the glucose-insulin system are recorded in the literature. The minimal model, which is the model currently mostly used in physiological research on the metabolism of glucose, was proposed in the early eighties for the interpretation of the glucose and insulin plasma concentrations following the intravenous glucose tolerance test. It is composed of two parts: the first consists of two differential equations and describes the glucose plasma concentration time-course treating insulin plasma concentration as a known forcing function; the second consists of a single equation and describes the time course of plasma insulin concentration treating glucose plasma concentration as a known forcing function. The two parts are to be separately estimated on the available data. In order to study glucose-insulin homeostasis as a single dynamical system, a unified model would be desirable. To this end, the simple coupling of the original two parts of the minimal model is not appropriate, since it can be shown that, for commonly observed combinations of parameter values, the coupled model would not admit an equilibrium and the concentration of active insulin in the “distant” compartment would be predicted to increase without bounds. For comparison, a simple delay-differential model is introduced, is demonstrated to be globally asymptotically stable around a unique equilibrium point corresponding to the pre-bolus conditions, and is shown to have positive and bounded solutions for all times. The results of fitting the delay-differential model to experimental data from ten healthy volunteers are also shown. It is concluded that a global unified model is both theoretically desirable and practically usable, and that any such model ought to undergo formal analysis to establish its appropriateness and to exclude conflicts with accepted physiological notions. Received: 22 June 1998 / Revised version: 24 February 1999     

Simplification of the intravenous glucose tolerance test (ivGTT) in rats

A simplified technique was established for the intravenous glucose tolerance test (ivGTT) in unanesthetized rats. In order to evaluate the relation between insulin secretion, glucose load and glucose disappearance rate, precatheterized rats were given glucose ranging in dose from 0.25 to 2.0 g/kg bw by intravenous injection. A highly linear correlation was observed in glucose disappearance rate during a period of 4-32 min. A glucose load greater than 0.5 g/kg ow induced a maximum response in insulin secretion. Small blood samples were collected using the orbital bleeding technique at 4, 16 and 28 minutes after a glucose load of 1.0 g/kg bw had been given and then T1/2, the time taken for the glucose level to fall by one half, was calculated. The mean T1/2 was significantly longer in alloxan- or cyproheptadin-diabetic rats than that in the intacts. These data indicate that a glucose load of 1.0 g/kg administered by intravenous injection with the T1/2 calculated between 4 and 32 minutes would provide an accurate means of assessing pancreatic endocrine function.     

Changes in the serum composition of free-fatty acids during an intravenous glucose tolerance test

Recent studies suggest that measuring the free-fatty acids (FFA) during an intravenous glucose tolerance test (IVGTT) may provide information about the metabolic associations between serum FFA and carbohydrate and insulin metabolism. We evaluated the FFA profile during an IVGTT and determined whether this test changes the composition and concentration of FFA. An IVGTT was given to 38 severely obese persons before and 7 months after undergoing bariatric surgery and also to 12 healthy, nonobese persons. The concentration and composition of the FFA were studied at different times during the test. The concentration of FFA fell significantly faster during the IVGTT in the controls and in the severely obese persons with normal-fasting glucose (NFG) than in the severely obese persons with impaired-fasting glucose (IFG) or type 2 diabetes mellitus (T2DM) (P < 0.05). Significant differences were found in the time to minimum serum concentrations of FFA (control = NFG < IFG < T2DM) (P < 0.001). These variables improved after bariatric surgery in the three groups. The percentage of monounsaturated and n-6 polyunsaturated FFA in the control subjects and in the obese persons, both before and after surgery, decreased significantly during the IVGTT. In conclusion, during an IVGTT, severely obese persons with IFG or T2DM experienced a lower fall in the FFA than the severely obese persons with NFG and the controls, becoming normal after bariatric surgery.     

Ablation of capsaicin-sensitive afferent nerves affects insulin response during an intravenous glucose tolerance test

We investigated the role of sensory nerves in glucose tolerance in conscious Wistar rats neonatally treated with neurotoxin capsaicin or vehicle. Intravenous glucose tolerance tests (IVGTT, 150, 300 and 450 mg in 30 min) were performed to measure glucose tolerance, and glucose, insulin and glucagon levels were measured. Higher glucose concentration resulted in a greater insulin response in both capsaicin- and vehicle-treated rats. However, glucose-stimulated insulin secretion was attenuated in capsaicin-treated animals, even though glucose levels did not differ. Glucagon levels did not differ between both groups. These results show that capsaicin-sensitive nerves are involved in glucose-stimulated insulin secretion, but are not directly involved in the regulation of blood glucose levels. Moreover, they suggest that capsaicin-sensitive nerves could be involved in the regulation of insulin sensitivity. We hypothesize that sensory afferents could play a role in the aetiology of pathologies where glucohomeostatic mechanisms are disturbed, as is in type 2 diabetes mellitus.     

The relation between free fatty acid levels and tolerance for glucose in a triple glucose tolerance test

The improved glucose tolerance observed in a multiple glucose tolerance test (Staub-Traugott effect) has been observed in dogs with concomitant measurement of immunoreactive insulin (IRI) and plasma free fatty acid (FFA). It was possible to reduce and in one experiment eliminate the improved glucose tolerance observed in the Staub-Traugott procedure. This was done in successive experiments in which the glucose challenge dose was 1 × BW^{0 period; 7} grams: (1) by injecting octanoate (0.1 mmoles/kg each hour) at the same time as the glucose; (2) by supplementing the injections with the infusion of octanoate (0.1 mmoles/kg/15 mins) during the second and third hours; (3) by repeating this last procedure after a seven day fast. Similar experiments were carried out with a larger glucose challenge dose (1 g/kg).Glucose tolerance appeared to depend as strongly on FFA levels as it did on IRI levels, and improvement in glucose tolerance occurred only when there was an associated reduction in FFA for a given glucose challenge. A measure of the Staub-Traugott effect was defined in terms of the different glucose utilizations during a multiple glucose tolerance test. An increase in the mean FFA levels achieved before or during a multiple glucose tolerance test lessened or eliminated the Staub-Traugott effect.     

Evaluating the glucose tolerance test in mice

The objective of this study was to determine the optimal conditions under which to assess glucose tolerance in chow- and high-fat-fed C57BL/6J mice. Mice were fed either chow or high-fat diet for 8 wk. Variables tested were fasting duration (0-, 3-, 6-, and 24-h and overnight fasting), route of administration (intraperitoneal vs. oral) load of glucose given (2, 1, or 0.5 g/kg and fixed 50-mg dose), and state of consciousness. Basal glucose concentrations were increased in high-fat- compared with chow-fed mice following 6 h of fasting (9.1 +/- 0.3 vs. 7.9 +/- 0.4 mmol/l P = 0.01). Glucose tolerance was most different and therefore significant (P = 0.001) in high-fat-fed mice after 6 h of fasting (1,973 +/- 96 vs. 1,248 +/- 83 mmol.l(-1).120 min(-1)). The difference in glucose tolerance was greater following an OGTT (142%), in contrast to an IPGTT, with a 127% difference between high fat and chow. We also found that administering 2 g/kg of glucose resulted in a greater level of significance (P = 0.0008) in glucose intolerance in high-fat- compared with chow-fed mice. A fixed dose of 50 mg glucose regardless of body weight was enough to show glucose intolerance in high-fat- vs. chow-fed mice. Finally, high-fat-fed mice showed glucose intolerance compared with their chow-fed counterparts whether they were tested under conscious or anesthetized conditions. We conclude that 2 g/kg glucose administered orally following 6 h of fasting is best to assess glucose tolerance in mice under these conditions.     

Oral glucose tolerance test in polycystic ovary syndrome

OGTT was used to clarify the problem of hyperinsulinism and insulin resistance previously investigated by us in PCOS, using the tolbutamide test. The results of this latter investigation were in agreement with the previous found by us and with the similar already reported by other Authors. 26 women (7 obese), aged 14-34 years, affected by PCOS, were studied. The diagnosis of PCOS was made using clinical, hormonal, radiologic and echographic criteria. 16 age matched healthy women were used as controls. Glucose and insulin curves, glucose (GA) and insulin (IA) response areas and IA/GA ratio (insulin resistance in dex-IRI-) were studied by OGTT. Blood insulin values of patients resulted significantly more elevated than that of controls at any point of the curve and more significantly elevated were decreasing values. Mean values of insulin peaks, of insulin areas and of IRI resulted more elevated than that of controls. The presence of both an hyperinsulinism and an insulin resistance in PCOS seems therefore evident. A correlation was found between IRI values and plasma testosterone levels in non obese patients with increased urinary 17-ketosteroid output. A relationship between hyperandrogenism on one hand and hyperinsulinism and insulin resistance on the other is suggested.     

Advantages of the single delay model for the assessment of insulin sensitivity from the intravenous glucose tolerance test

Background  

The Minimal Model, (MM), used to assess insulin sensitivity (IS) from Intra-Venous Glucose-Tolerance Test (IVGTT) data, suffers from frequent lack of identifiability (parameter estimates with Coefficients of Variation (CV) less than 52%). The recently proposed Single Delay Model (SDM) is evaluated as a practical alternative.     

NEFA minimal model parameters estimated from the oral glucose tolerance test and the meal tolerance test

The kinetics of nonesterified fatty acid (NEFA) metabolism in humans requires quantification to facilitate understanding of diseases like type 1 and 2 diabetes, metabolic syndrome, and obesity, and the mechanisms underpinning various interventions. Oral glucose tolerance tests (OGTT) and glucose meal tolerance tests (MTT) are potentially useful procedures for enabling quantification of NEFA kinetics because they both cause transitory, but substantial, declines and then rebounds in plasma NEFA concentrations in response to physiologically relevant increases in plasma glucose. The Boston MINIMAL model of NEFA kinetics was developed to analyze data from the intravenous glucose tolerance test (IVGTT), but in this work, we present for the first time its application to modeling NEFA data from both OGTT and MTT studies. This model enables estimation of SFFA (micromol.l(-1).min(-1)) (a parameter describing the maximum rate of lipolysis), and KFFA (%/min) (a parameter related to NEFA oxidation rate). The model could well describe the trajectories of NEFA concentrations following an OGTT (R2 in excess of 0.97) but was not as successful with the MTT (R2>0.65). Model parameters derived from analysis of OGTT and MTT data were well identified with coefficients of variation generally less than 15%. Type 2 diabetes, body mass index, and dietary treatment (high-fat vs. high-glycemic-index diets) were all shown to have significant effects on model parameters. Modeling plasma NEFA concentrations over 24 h has helped to identify and quantify the extent that periprandial NEFA peaks and nocturnal elevation in plasma NEFA can be accounted for by our model.