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     

Modeling the glucose-insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays

In the glucose-insulin regulatory system, ultradian insulin secretory oscillations are observed to have a period of 50-150 min. After pioneering work traced back to the 1960s, several mathematical models have been proposed during the last decade to model these ultradian oscillations as well as the metabolic system producing them. These currently existing models still lack some of the key physiological aspects of the glucose-insulin system. Applying the mass conservation law, we introduce two explicit time delays and propose a more robust alternative model for better understanding the glucose-insulin endocrine metabolic regulatory system and the ultradian insulin secretory oscillations for the cases of continuous enteral nutrition and constant glucose infusion. We compare the simulation profiles obtained from this two time delay model with those from the other existing models. As a result, we notice many unique features of this two delay model. Based on our intensive simulations, we suspect that one of the possibly many causes of ultradian insulin secretion oscillations is the time delay of the insulin secretion stimulated by the elevated glucose concentration.     

Modeling the physiological glucose-insulin dynamic system on diabetics

A novel mathematical model is presented to describe the dynamic behavior of plasma glucose and insulin on diabetic subjects. Though various models have been proposed to simulate the short-term (a variety of intravenous glucose or insulin injection) glucose-insulin dynamics, it is intended to construct a modified delay differential equations (DDEs) model based on the human glucose-insulin metabolic system. Five specific adjustable parameters inside the model are defined as the factors of the major physiological functions. Then several clinical data sets (56 subjects) which includes the information of food ingestion and exogenous insulin injection are verified and the model could practically reflect the dynamics and oscillation behavior on diabetic subjects by varying the adjustable parameters. Moreover, the corresponding parameters are fairly helpful to identify the patient's conditions of major physiological functions. This generic glucose-insulin dynamic model can be expected to develop such advanced therapy strategies for diabetics in the future.     

Metabolic factors affecting the reproductive axis in male sheep

Changes in food intake affect the reproductive axis in both sexes, and the nutritional signals involved and the sites that receive those signals are now beginning to be unravelled. Our studies have focussed on the mature male sheep, a model in which high food intake stimulates GnRH-LH pulse frequency for only 10-20 days but continues to promote testicular growth over several months. Different signals and different target organs seem to be responsible for these short- and long-term responses. Short-term dietary treatments lead to changes in blood concentrations of glucose, fatty acids, insulin and leptin, and concentrations of glucose, insulin, leptin and some amino acids in cerebrospinal fluid. It seems unlikely that amino acids affect GnRH-LH secretion directly in sheep. Intracerebroventricular infusions of insulin specifically increase LH pulse frequency, but intravenous, intra-abomasal or intracerebroventricular infusions of glucose have no effect, despite their effects on cerebrospinal fluid insulin concentrations. The addition of fatty acids to the diet also increases LH pulse frequency, but does not affect the concentrations of insulin or leptin in the cerebrospinal fluid. It appears that acute responses to changes in nutrition involve a range of alternative pathways, possibly including interactions among insulin, leptin and energy substrates. Effects of long-term dietary treatments on testicular size are only partly dependent on the GnRH-LH system (that is, on brain control) and so must also depend on other, as yet unknown, pathways. Concepts of 'metabolic sensing and integration' are being developed from the basis of existing knowledge of the central control of appetite and reproduction.     

Dual effect of insulin on in vitro leptin secretion by adipose tissue

Although it is widely accepted that insulin stimulates leptin secretion, a dual action was observed using a validated in vitro system, i.e., an early (less than 48 h) inhibitory action, followed later (48-96 h) by a clear-cut stimulation. While the inhibitory phase was observed at every glucose concentration tested (from 1 to 25 mM), the stimulatory phase required the presence of physiological or supraphysiological glucose concentrations. In fact, leptin secretion was virtually eliminated in the presence of glucose uptake inhibitors. This dual effect of insulin was not due to modifications of the ob mRNA levels, suggesting that it depends entirely on posttranslational mechanisms. In conclusion, insulin appears to induce an early inhibition of leptin secretion by the adipose cell, followed later by a stimulatory effect secondary to the metabolic changes triggered by the insulin-induced increase in glucose uptake.     

A model of beta-cell mass, insulin, and glucose kinetics: pathways to diabetes

Diabetes is a disease of the glucose regulatory system that is associated with increased morbidity and early mortality. The primary variables of this system are beta-cell mass, plasma insulin concentrations, and plasma glucose concentrations. Existing mathematical models of glucose regulation incorporate only glucose and/or insulin dynamics. Here we develop a novel model of beta -cell mass, insulin, and glucose dynamics, which consists of a system of three nonlinear ordinary differential equations, where glucose and insulin dynamics are fast relative to beta-cell mass dynamics. For normal parameter values, the model has two stable fixed points (representing physiological and pathological steady states), separated on a slow manifold by a saddle point. Mild hyperglycemia leads to the growth of the beta -cell mass (negative feedback) while extreme hyperglycemia leads to the reduction of the beta-cell mass (positive feedback). The model predicts that there are three pathways in prolonged hyperglycemia: (1) the physiological fixed point can be shifted to a hyperglycemic level (regulated hyperglycemia), (2) the physiological and saddle points can be eliminated (bifurcation), and (3) progressive defects in glucose and/or insulin dynamics can drive glucose levels up at a rate faster than the adaptation of the beta -cell mass which can drive glucose levels down (dynamical hyperglycemia).     

Adipocyte-selective reduction of the leptin receptors induced by antisense RNA leads to increased adiposity,dyslipidemia, and insulin resistance

Although recent evidence suggests that leptin can directly regulate a wide spectrum of peripheral functions, including fat metabolism, genetic examples are still needed to illustrate the physiological significance of direct actions of leptin in a given peripheral tissue. To this end, we used a technical knock-out approach to reduce the expression of leptin receptors specifically in white adipose tissue. The evaluation of leptin receptor reduction in adipocytes was based on real time PCR analysis of the mRNA levels, Western blot analysis of the proteins, and biochemical analysis of leptin signaling capability. Despite a normal level of leptin receptors in the hypothalamus and normal food intake, mutant mice developed increased adiposity, decreased body temperature, hyperinsulinemia, hypertriglyceridemia, impaired glucose tolerance and insulin sensitivity, as well as elevated hepatic and skeletal muscle triglyceride levels. In addition, a variety of genes involved in regulating fat and glucose metabolism were dysregulated in white adipose tissue. These include tumor necrosis factor-alpha, adiponectin, leptin, fatty acid synthase, sterol regulatory element-binding protein 1, glycerol kinase, and beta3-adrenergic receptor. Furthermore, the mutant mice are significantly more sensitive to high fat feeding with regard to developing obesity and severe insulin resistance. Thus, we provide a genetic model demonstrating the physiological importance of a peripheral effect of leptin in vivo. Importantly, this suggests the possibility that leptin resistance at the adipocyte level might be a molecular link between obesity and type 2 diabetes.     

Comparative acute effects of leptin and insulin on gluconeogenesis and ketogenesis in perfused rat liver

The acute effects of physiological levels of leptin (10 ng ml(-1)) and insulin (20 microU ml(-1)) on hepatic gluconeogenesis and ketogenesis were compared. Leptin or insulin alone decreased (p<0.05) the activation of hepatic glucose, L-lactate and urea production from L-alanine. However, the hepatic glucose production was not modified if leptin was combined with insulin. These results indicated that both, i.e. leptin and insulin, could promote a non-additive reduction in the rate of catabolism of L-alanine. However, in contrast with insulin (p<0.05), leptin did not inhibit the activation of hepatic glucose production from pyruvate or glycerol. On the other hand, activation of hepatic production of acetoacetate and beta-hydroxybutyrate from octanoate was not affected by leptin or insulin. Thus, our data demonstrate that the acute effect of leptin on hepatic metabolism was partially similar to insulin (activation of glucose production from L-alanine and activation of acetoacetate or beta-hydroxybutyrate production from octanoate) and partially different from insulin (activation of glucose production from pyruvate or glycerol).     

Influence of thyroid dysfunction on serum concentrations of adipocytokines

Thyroid hormones act on several aspects of metabolic and energy homeostasis influencing body weight, thermogenesis, and lipolysis in adipose tissue. Adipocytokines are biologically active substances produced by adipocyte with different physiological functions. These substances have multiple effects on several tissues acting on the intermediate and energy metabolism. For these reasons, attention has recently been focused on the possible relationship between adipocytokines, thyroid status, and thyroid dysfunction. Leptin, a signal of satiety to the brain and regulator of insulin and glucose metabolism, reflects the amount of fat storage and is considered as a pro-inflammatory adipocytokine. Adiponectin is inversely related to the degree of adiposity, increases insulin sensitivity, and may have antiatherogenic and anti-inflammatory properties. Resistin impairs glucose homeostasis and insulin action in mice but not in humans. Resistin might be considered a pro-inflammatory adipocytokine and participate in obesity-associated inflammation. Several reports indicate that leptin regulates thyroid function at hypothalamic-hypophyseal level and, conversely, thyroid hormones might control leptin metabolism at least in some animals studies. Both adiponectin and thyroid hormones share some physiological actions as reduction of body fat by increasing thermogenesis and lipid oxidation. Resistin also seems to be regulated by thyroid hormones, at least in rats. Thyroid dysfunction does not significantly affect serum leptin concentrations. Serum levels of adiponectin are no influenced by thyroid hypofunction; however, hyperthyroidism is associated with normal or elevated adiponectin levels. Finally, discordant results in resistin levels in thyroid dysfunction have been reported in humans.     

Intracerebroventricular leptin infusion improves glucose homeostasis in lean type 2 diabetic MKR mice via hepatic vagal and non-vagal mechanisms

MKR mice, lacking insulin-like growth factor 1 receptor (IGF-1R) signaling in skeletal muscle, are lean yet hyperlipidemic, hyperinsulinemic, and hyperglycemic, with severe insulin resistance and elevated hepatic and skeletal muscle levels of triglycerides. We have previously shown that chronic peripheral administration of the adipokine leptin improves hepatic insulin sensitivity in these mice independently of its effects on food intake. As central leptin signaling has been implicated in the control of peripheral glucose homeostasis, here we examined the ability of central intracerebroventricular leptin administration to affect energy balance and peripheral glucose homeostasis in non-obese diabetic male MKR mice. Central leptin significantly reduced food intake, body weight gain and adiposity, as well as serum glucose, insulin, leptin, free fatty acid and triglyceride levels relative to ACSF treated controls. These reductions were accompanied by increased fat oxidation as measured by indirect calorimetry, as well as increased oxygen consumption. Central leptin also improved glucose tolerance and hepatic insulin sensitivity determined using the euglycemic-hyperinsulinemic clamps relative to pair fed vehicle treated controls, as well as increasing the rate of glucose disappearance. Hepatic vagotomy only partially reversed the ability of central leptin to improve glucose tolerance. These results demonstrate that central leptin dramatically improves insulin sensitivity independently of its effects on food intake, in a lean mouse model of type 2 diabetes. The findings also suggest that: 1) both hepatic vagal and non-vagal pathways contribute to this improvement, and 2) central leptin alters glucose disposal in skeletal muscle in this model.     

Effects of acute or prolonged exposure to human leptin on isolated human islet function

The adipocyte-derived hormone leptin has been reported to inhibit, have no effect, or potentiate insulin secretion in-vitro; these effects mainly depend on the species considered, the concentrations used, and the length of exposure. We investigated the direct effects of recombinant human leptin (HL) on human pancreatic beta cell function by studying insulin secretion (IS), hexokinase and glucokinase activity and Km, and potassium channel permeability in purified human islets (HI). In acute experiments, no effect of 1, 5, 20, or 50 ng/ml HL on glucose or arginine stimulated insulin release was found, whereas 500 ng/ml HL caused a significant decrease of glucose induced IS. After 24h pre-culture with either 20 or 500 ng/ml HL, a significant reduction of glucose (but not arginine) stimulated IS was observed. Exposure to leptin caused a significant increase of potassium channel permeability, whereas hexokinase and glucokinase activity and Km remained unchanged. These results suggest that physiological human leptin concentration is able to importantly affect glucose (but not arginine) stimulated insulin release from human islets only after prolonged exposure. This effect is probably mediated by changes of potassium channel permeability, and is not accompanied by modifications of glucose phosphorylating enzymes properties.     

Insulin regulates leptin secretion from 3T3-L1 adipocytes by a PI 3 kinase independent mechanism

To better define the molecular mechanisms underlying leptin release from adipocytes, we developed a novel protocol that maximizes leptin production from 3T3-L1 adipocytes. The addition of a PPARgamma agonist to the Isobutylmethylxanthine/Dexamethasone/Insulin differentiation cocktail increased leptin mRNA levels by 5-fold, maintained insulin sensitivity, and yielded mature phenotype in cultured adipocytes. Under these conditions, acute insulin stimulation for 2 h induced a two-fold increase in leptin secretion, which was independent of new protein synthesis, and was not due to alterations in glucose metabolism. Stimulation with insulin for 15 min induced the same level of leptin release and was blocked by Brefeldin A. Inhibiting PI 3-kinase with wortmannin had no effect on insulin stimulation of leptin secretion. These studies show that insulin can stimulate leptin release via a PI3K independent mechanism and provide a cellular system for studying the effect of insulin and potentially other mediators on leptin secretion.     

Reversal of the sex difference in plasma leptin levels in obese children with impaired glucose tolerance

INTRODUCTION: Basal leptin level has been demonstrated to correlate positively with many indices of obesity, as well as insulin resistance. However, to date, little is known about regulation of leptin in obese children with incipient glucose metabolic disorders. OBJECTIVE: The aim of this study was to define the precise influence of the glucose tolerance status on plasma leptin in obese boys and girls separately. MATERIAL AND METHODS: 70 obese children with impaired glucose tolerance (IGT) and well-matched 70 normal glucose-tolerant (NGT) subjects were examined. Fasting and 2-h post glucose load plasma glucose and insulin levels as well as fasting leptin levels were determined, apart from anthropometric measurements. RESULTS: Leptin levels were significantly lower in girls with IGT compared to NGT girl (17.7+/-6.5 microg/L vs. 23.1+/-7.7 microg/L; p<.001). No such difference was observed in boys. In a multiple regression analysis adjusting for age and adiposity, in the female group plasma glucose and insulin levels 2-h after glucose load were the best predictors of fasting plasma leptin (r=-0.49, p<.005 and r=0.34, p<.05; respectively). In boys, plasma insulin level 2-h after glucose load was the independent determinant of leptin (r=0.36, p<.05). CONCLUSION: The differences between regulation of leptin synthesis in girls and boys with simple obesity were found. The stimulatory effect of insulin on leptin synthesis was greater in girls with normoglycemia than in girls with impaired glucose tolerance.     

Reversal of the sex difference in plasma leptin levels in obese children with impaired glucose tolerance

INTRODUCTION: Basal leptin level has been demonstrated to correlate positively with many indices of obesity, as well as insulin resistance. However, to date, little is known about regulation of leptin in obese children with incipient glucose metabolic disorders. OBJECTIVE: The aim of this study was to define the precise influence of the glucose tolerance status on plasma leptin in obese boys and girls separately. MATERIAL AND METHODS: 70 obese children with impaired glucose tolerance (IGT) and well-matched 70 normal glucose-tolerant (NGT) subjects were examined. Fasting and 2-h post glucose load plasma glucose and insulin levels as well as fasting leptin levels were determined, apart from anthropometric measurements. RESULTS: Leptin levels were significantly lower in girls with IGT compared to NGT girl (17.7+/-6.5 microg/L vs. 23.1+/-7.7 microg/L; p<.001). No such difference was observed in boys. In a multiple regression analysis adjusting for age and adiposity, in the female group plasma glucose and insulin levels 2-h after glucose load were the best predictors of fasting plasma leptin (r=-0.49, p<.005 and r=0.34, p<.05; respectively). In boys, plasma insulin level 2-h after glucose load was the independent determinant of leptin (r=0.36, p<.05). CONCLUSION: The differences between regulation of leptin synthesis in girls and boys with simple obesity were found. The stimulatory effect of insulin on leptin synthesis was greater in girls with normoglycemia than in girls with impaired glucose tolerance.     

A Study to Determine if Acute Maternal and Fetal Hyperglycemia/Insulinemia Induces Leptin Production during Pregnancy.

BACKGROUND: In pregnant primates, the effect of post-prandial hyperglycemic or insulinemic states on leptin production is not known. Our goal was to conduct a controlled study using an established pregnant baboon model ( PAPIO ANUBIS) to determine whether acute glucose changes would have an effect on maternal or fetal plasma leptin levels. METHODS: Two animals were operated on at 138 and 140 days of gestation (term approximately 184 days) by placing 4 cannulae in the maternal aorta, inferior vena cava, fetal carotid artery, and the amniotic cavity. At 145 and 150 days, glucose infusions were started via the maternal femoral vein. Animal 1 received 7.5 gm of glucose over a 2-hour period at 145th day. Animal 2 received 20 gm of glucose over a 1-hour period at 150th day. Both animals remained AD LIBITUM throughout the experiments. Maternal and fetal blood samples were obtained from the arterial lines before the glucose infusion and at half hour intervals to include 30 minutes post-infusion. RESULTS: Significant changes from baseline concentrations were observed for maternal and fetal glucose and insulin concentrations in response to both glucose challenges. Maternal and fetal plasma leptin concentrations did not correlate with glucose or insulin changes. CONCLUSION: This preliminary study demonstrated that in primates, acute changes in circulating maternal or fetal glucose or insulin concentration do not affect maternal or fetal plasma leptin concentrations. These results suggest that alterations in leptin secretion by the maternal-placental-fetal unit may only occur in pathological states.     

Effects of leptin administration on the endocrine pancreas and liver in the lizard Podarcis sicula

In this study, we investigated the presence of leptin receptor in pancreatic islets and the effect of exogenous leptin administration in Podarcis sicula on glucose metabolism. Our data show the presence of leptin receptor immunoreactivity in the endocrine pancreas suggesting that leptin may act at a peripheral level as previously postulated in mammals. The effects of short- and long-term and dose-response treatment with supraphysiological concentrations of leptin on circulating levels of insulin, glucagon and glucose in the blood have been evaluated. Taken together, our results indicate that leptin treatment was followed by an increase in insulin, glucagon and glucose in the blood, depending on the dose of leptin. Moreover, leptin treatment brought about a decrease of glycogen and the appearance of tyrosine-phosphorylated proteins in the liver. This study shows that in the lizard P. sicula leptin is involved in glucose metabolism.     

Leptin concentrations in plasma and follicular fluid from prepubertal gilts as influenced by fasting, refeeding and insulin.

This study's aim was to examine whether fasting and refeeding would influence leptin levels in both plasma and follicular fluid from prepubertal gilts, and whether insulin affects leptin levels in fasting gilts. In experiment 1, four gilts were fasted for 72 h and then refed. Blood samples were withdrawn during normoalimentation, at the end of fasting, and for 4 h after refeeding. All samples were assayed for leptin; alternate samples were assayed for insulin, glucose and non-esterified fatty acids (NEFA). Fasting caused a decrease in leptin, glucose and insulin levels in plasma, while NEFA concentrations increased. In experiment 2, four gilts were given insulin as a bolus (0.2 IU/kg body weight) after 68 h of fasting. Blood samples were collected every 15 min around insulin administration and were assayed for leptin, insulin and glucose. This experiment shows that insulin administration increases leptin levels during fasting. In experiment 3, gilts were ovariectomized during normal alimentation (n=4), after 48 h of fasting (n=4), and after 48 h of realimentation following 48 h of fasting (n=4). Leptin levels in both plasma and follicular fluid collected after 48 h of fasting were significantly lower than those observed during normoalimentation or refeeding. In conclusion, a transient increase in insulin during fasting is effective in restoring leptin concentrations; in addition, leptin levels in follicular fluid parallel those in plasma.     

Genistein restricts leptin secretion from rat adipocytes

The isoflavones--genistein and daidzein -- compounds found in high concentrations in soy play an important role in prevention of many diseases and affect some metabolic pathways. In the performed experiment it was demonstrated that genistein (5mg/kg b.w.) administered intragastrically for three days to male Wistar rats substantially diminished blood leptin level. Studies with isolated rat adipocytes revealed that this phytoestrogen strongly restricted leptin secretion from these cells. These effects were not accompanied by any changes in leptin gene expression in adipocytes. Daidzein-- an analogue of genistein -- used at similar concentrations did not affect blood leptin concentration, leptin secretion and expression of its gene. To determine the influence of genistein and daidzein on leptin release, adipocytes isolated from the epididymal fat tissue were incubated for 2h in Krebs--Ringer buffer. Leptin secretion stimulated by glucose with insulin was significantly diminished by genistein (0.25--1mM). This effect of genistein may arise from several aspects of its action in adipocytes documented in the literature such as the inhibition of glucose transport and metabolism, the attenuation of insulin signalling, the inhibition of cAMP phosphodiesterase and the stimulation of lipolysis. However, the bypassing of the restrictive action of genistein on glucose transport and glycolysis (by the use of alanine instead of glucose) and on insulin action (by the use of nicotinic acid) was not sufficient to restore leptin secretion from isolated adipocytes. It was also demonstrated that the restriction of the stimulatory influence of genistein on cAMP/protein kinase A (PKA) pathway (by the inhibition of PKA activity) did not improve leptin release. Results obtained in our experiments point at the restriction of glucose metabolism following formation of pyruvate as the pivotal reason of the inhibitory action of genistein on leptin release.     

Programming of intermediate metabolism in young lambs affected by late gestational maternal undernourishment

Effects of moderate maternal undernourishment during late gestation on the intermediary metabolism and maturational changes in young lambs were investigated. 20 twin-bearing sheep, bred to two different rams, were randomly allocated the last 6 wk of gestation to either a NORM diet [barley, protein supplement, and silage ad libitum approximately 15 MJ metabolizable energy (ME)/day] or a LOW diet (50% of ME intake in NORM, offered exclusively as silage approximately 7 MJ ME/day). Post partum, ewes were fed to requirement. After weaning, lambs were fed concentrate and hay ad libitum. At 10 and 19 wk of age, lambs were subjected to an intravenous glucose tolerance test (IGTT) followed by 24 h of fasting. Heat energy (HE) was determined in a respiration chamber at 9 or 20 wk of age. LOW lambs had a lower birth weight and continued to be lighter throughout the experiment. Glucose tolerance did not differ between groups. However, 19-wk-old LOW lambs secreted less insulin during IGTT, released more NEFA, and tended to have lower leptin during fasting than NORM. Surprisingly, several metabolite and hormone responses during IGTT and fasting were greatly influenced by the paternal heritage. In conclusion, when lambs entered adolescence (19 wk) programming effects of late prenatal malnutrition on the glucose-insulin homeostasis and metabolism were manifested: LOW lambs had less insulin-secretory capacity, but this was apparently compensated for by increased target tissue sensitivity for insulin, and adipose lipolytic capacity increased during fasting. Thereby, glucose may be spared through increased lipid oxidation, but overall energetic efficiency is apparently deteriorated rather than improved.