Intestinal transit of a glucose bolus and incretin kinetics: a mathematical model with application to the oral glucose tolerance test

An extended minimal model of OGTT: estimation of α- and β-cell dysfunction, insulin resistance, and the incretin effect

Loss of insulin sensitivity, α- and β-cell dysfunction, and impairment in incretin effect have all been implicated in the pathophysiology of type 2 diabetes (T2D). Parsimonious mathematical models are useful in quantifying parameters related to the pathophysiology of T2D. Here, we extend the minimum model developed to describe the glucose-insulin-glucagon dynamics in the isoglycemic intravenous glucose infusion (IIGI) experiment to the oral glucose tolerance test (OGTT). The extended model describes glucose and hormone dynamics in OGTT including the contribution of the incretin hormones, glucose-dependent insulinotropic polypeptide (GIP), and glucagon-like peptide-1 (GLP-1), to insulin secretion. A new function describing glucose arrival from the gut is introduced. The model is fitted to OGTT data from eight individuals with T2D and eight weight-matched controls (CS) without diabetes to obtain parameters related to insulin sensitivity, β- and α-cell function. The parameters, i.e., measures of insulin sensitivity, a1, suppression of glucagon secretion, k1, magnitude of glucagon secretion, γ2, and incretin-dependent insulin secretion, γ3, were found to be different between CS and T2D with P values < 0.002, <0.017, <0.009, <0.004, respectively. A new rubric for estimating the incretin effect directly from modeling the OGTT is presented. The average incretin effect correlated well with the experimentally determined incretin effect with a Spearman rank test correlation coefficient of 0.67 (P < 0.012). The average incretin effect was found to be different between CS and T2D (P < 0.032). The developed model is shown to be effective in quantifying the factors relevant to T2D pathophysiology.NEW & NOTEWORTHY A new extended model of oral glucose tolerance test (OGTT) has been developed that includes glucagon dynamics and incretin contribution to insulin secretion. The model allows the estimation of parameters related to α- and β-cell dysfunction, insulin sensitivity, and incretin action. A new function describing the influx of glucose from the gut has been introduced. A new rubric for estimating the incretin effect directly from the OGTT experiment has been developed. The effect of glucose dose was also investigated.

The ameliorating effects of mesenchymal stem cells compared to α-tocopherol on apoptosis and autophagy in streptozotocin-induced diabetic rats: Implication of PI3K/Akt signaling pathway and entero-insular axis

Bone marrow-derived mesenchymal stem cells (BM-MSCs) are considered a novel regenerative therapy that holds much potential. This study aimed to examine and compare the ameliorative effects of BM-MSCs compared to α-tocopherol (α-Toc) on apoptosis, autophagy, and β-cell function in a rat model of streptozotocin (STZ)-induced diabetes and further analyzed the implications and interrelations of the entero-insular axis, and type I phosphoinositide 3-kinase (PI3K)/Akt signaling. Forty adult male albino rats were categorized into four groups (n = 10, in each): control group, STZ-induced diabetic group (single i.p. injection of STZ 45 mg/kg), diabetic and treated with BM-MSCs injection, diabetic and treatment with α-Toc p.o. The serum glucose, insulin, nitric oxide (NO), and catalase (CAT) were measured. Histopathological examination of the pancreas, the expression levels of insulin, CD44, caspase-3, autophagy markers, P13K/Akt, and pancreas/duodenum homeobox protein 1, in pancreatic tissue, and glucose-dependent insulinotropic polypeptide (GIP) in the duodenum were detected by hematoxylin and eosin staining, immunofluorescence labeling, and by quantitative real-time polymerase chain reaction. The diabetic rats showed reduced insulin, hyperglycemia, nitrosative stress (NO, CAT), augmented apoptosis (caspase 3), impaired autophagy (p62/SQSTM1, LC3), downregulated PI3K/Akt pathway and increased GIP expression, and degeneration of pancreatic islets. Treatment with either BM-MSCs or α-Toc suppressed the nitrosative stress, reduced apoptosis, recovered autophagy, upregulated PI3K/Akt pathway, and subsequently increased insulin levels, decreased blood glucose, and downregulated GIP expression with partial restoration of pancreatic islets. Based on our findings, the cytoprotective effects of BM-MSCs and α-Toc in type 1-induced diabetes appeared to be related to repaired autophagy and recovered PI3K/Akt signaling. Moreover, we reported their novel effects on reversing intestinal GIP expression level. The effect of BM-MSCs was notably superior to that of α-Toc.

Bayesian analysis of Glucose dynamics during the Oral Glucose Tolerance Test (OGTT)

This paper proposes a model that considers the action and timing of insulin and glucagon in glucose homeostasis after an oral stimulus. We use the Bayesian paradigm to infer kinetic rates, namely insulin and glucagon secretion, gastrointestinal emptying, and basal glucose concentration in blood. We identify two insulin scores related to glucose concentration in both blood and the gastrointestinal tract. The scores allow us to suggest a classification for individuals with impaired insulin sensitivity.

A mathematical model of food intake

The metabolic, hormonal and psychological determinants of the feeding behavior in humans are numerous and complex. A plausible model of the initiation, continuation and cessation of meals taking into account the most relevant such determinants would be very useful in simulating food intake over hours to days, thus providing input into existing models of nutrient absorption and metabolism. In the present work, a meal model is proposed, incorporating stomach distension, glycemic variations, ghrelin dynamics, cultural habits and influences on the initiation and continuation of meals, reflecting a combination of hedonic and appetite components. Given a set of parameter values (portraying a single subject), the timing and size of meals are stochastic. The model parameters are calibrated so as to reflect established medical knowledge on data of food intake from the National Health and Nutrition Examination Survey (NHANES) database during years 2015 and 2016.

Dipeptidyl-Peptidase-IV Inhibitors, Imigliptin and Alogliptin, Improve Beta-Cell Function in Type 2 Diabetes

OBJECTS

Imigliptin is a novel dipeptidyl peptidase-4 inhibitor. In the present study, we aimed to evaluate the effects of imigliptin and alogliptin on insulin resistance and beta-cell function in Chinese patients with type-2 diabetes mellitus (T2DM).

METHODS

A total of 37 Chinese T2DM patients were randomized to receive 25 mg imigliptin, 50 mg imigliptin, placebo, and 25 mg alogliptin (positive drug) for 13 days. Oral glucose tolerance tests were conducted at baseline and on day 13, followed by the oral minimal model (OMM).

RESULTS

Imigliptin or alogliptin treatment, compared with their baseline or placebo, was associated with higher beta-cell function parameters (φ_s and φ_tot) and lower glucose area under the curve (AUC) and postprandial glucose levels. The changes in the AUC for the glucose appearance rate between 0 and 120 min also showed a decrease in imigliptin or alogliptin groups. However, the insulin resistance parameter, fasting glucose, was not changed. For the homeostatic model assessment (HOMA-β and HOMA-IR) parameters or secretory units of islets in transplantation index (SUIT), no statistically significant changes were found both within treatments and between treatments.

CONCLUSIONS

After 13 days of treatment, imigliptin and alogliptin could decrease glycemic levels by improving beta-cell function. By comparing OMM with HOMA or SUIT results, glucose stimulation might be more sensitive for detecting changes in beta-cell function.

Mathematical Modeling for the Physiological and Clinical Investigation of Glucose Homeostasis and Diabetes

Mathematical modeling in the field of glucose metabolism has a longstanding tradition. The use of models is motivated by several reasons. Models have been used for calculating parameters of physiological interest from experimental data indirectly, to provide an unambiguous quantitative representation of pathophysiological mechanisms, to determine indices of clinical usefulness from simple experimental tests. With the growing societal impact of type 2 diabetes, which involves the disturbance of the glucose homeostasis system, development and use of models in this area have increased. Following the approaches of physiological and clinical investigation, the focus of the models has spanned from representations of whole body processes to those of cells, i.e., from in vivo to in vitro research. Model-based approaches for linking in vivo to in vitro research have been proposed, as well as multiscale models merging the two areas. The success and impact of models has been variable. Two kinds of models have received remarkable interest: those widely used in clinical applications, e.g., for the assessment of insulin sensitivity and β-cell function and some models representing specific aspects of the glucose homeostasis system, which have become iconic for their efficacy in describing clearly and compactly key physiological processes, such as insulin secretion from the pancreatic β cells. Models are inevitably simplified and approximate representations of a physiological system. Key to their success is an appropriate balance between adherence to reality, comprehensibility, interpretative value and practical usefulness. This has been achieved with a variety of approaches. Although many models concerning the glucose homeostasis system have been proposed, research in this area still needs to address numerous issues and tackle new opportunities. The mathematical representation of the glucose homeostasis processes is only partial, also because some mechanisms are still only partially understood. For in vitro research, mathematical models still need to develop their potential. This review illustrates the problems, approaches and contribution of mathematical modeling to the physiological and clinical investigation of glucose homeostasis and diabetes, focusing on the most relevant and stimulating models.

A revised Sorensen model: Simulating glycemic and insulinemic response to oral and intra-venous glucose load

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.

A Novel Synthetic Model of the Glucose-Insulin System for Patient-Wise Inference of Physiological Parameters From Small-Size OGTT Data

Existing mathematical models for the glucose-insulin (G-I) dynamics often involve variables that are not susceptible to direct measurement. Standard clinical tests for measuring G-I levels for diagnosing potential diseases are simple and relatively cheap, but seldom give enough information to allow the identification of model parameters within the range in which they have a biological meaning, thus generating a gap between mathematical modeling and any possible physiological explanation or clinical interpretation. In the present work, we present a synthetic mathematical model to represent the G-I dynamics in an Oral Glucose Tolerance Test (OGTT), which involves for the first time for OGTT-related models, Delay Differential Equations. Our model can represent the radically different behaviors observed in a studied cohort of 407 normoglycemic patients (the largest analyzed so far in parameter fitting experiments), all masked under the current threshold-based normality criteria. We also propose a novel approach to solve the parameter fitting inverse problem, involving the clustering of different G-I profiles, a simulation-based exploration of the feasible set, and the construction of an information function which reshapes it, based on the clinical records, experimental uncertainties, and physiological criteria. This method allowed an individual-wise recognition of the parameters of our model using small size OGTT data (5 measurements) directly, without modifying the routine procedures or requiring particular clinical setups. Therefore, our methodology can be easily applied to gain parametric insights to complement the existing tools for the diagnosis of G-I dysregulations. We tested the parameter stability and sensitivity for individual subjects, and an empirical relationship between such indexes and curve shapes was spotted. Since different G-I profiles, under the light of our model, are related to different physiological mechanisms, the present method offers a tool for personally-oriented diagnosis and treatment and to better define new health criteria.

Logical design of oral glucose ingestion pattern minimizing blood glucose in humans

Excessive increase in blood glucose level after eating increases the risk of macroangiopathy, and a method for not increasing the postprandial blood glucose level is desired. However, a logical design method of the dietary ingestion pattern controlling the postprandial blood glucose level has not yet been established. We constructed a mathematical model of blood glucose control by oral glucose ingestion in three healthy human subjects, and predicted that intermittent ingestion 30 min apart was the optimal glucose ingestion patterns that minimized the peak value of blood glucose level. We confirmed with subjects that this intermittent pattern consistently decreased the peak value of blood glucose level. We also predicted insulin minimization pattern, and found that the intermittent ingestion 30 min apart was optimal, which is similar to that of glucose minimization pattern. Taken together, these results suggest that the glucose minimization is achieved by suppressing the peak value of insulin concentration, rather than by enhancing insulin concentration. This approach could be applied to design optimal dietary ingestion patterns.

A system model of the effects of exercise on plasma Interleukin-6 dynamics in healthy individuals: Role of skeletal muscle and adipose tissue

Interleukin-6 (IL-6) has been recently shown to play a central role in glucose homeostasis, since it stimulates the production and secretion of Glucagon-like Peptide-1 (GLP-1) from intestinal L-cells and pancreas, leading to an enhanced insulin response. In resting conditions, IL-6 is mainly produced by the adipose tissue whereas, during exercise, skeletal muscle contractions stimulate a marked IL-6 secretion as well. Available mathematical models describing the effects of exercise on glucose homeostasis, however, do not account for this IL-6 contribution. This study aimed at developing and validating a system model of exercise’s effects on plasma IL-6 dynamics in healthy humans, combining the contributions of both adipose tissue and skeletal muscle. A two-compartment description was adopted to model plasma IL-6 changes in response to oxygen uptake’s variation during an exercise bout. The free parameters of the model were estimated by means of a cross-validation procedure performed on four different datasets. A low coefficient of variation (<10%) was found for each parameter and the physiologically meaningful parameters were all consistent with literature data. Moreover, plasma IL-6 dynamics during exercise and post-exercise were consistent with literature data from exercise protocols differing in intensity, duration and modality. The model successfully emulated the physiological effects of exercise on plasma IL-6 levels and provided a reliable description of the role of skeletal muscle and adipose tissue on the dynamics of plasma IL-6. The system model here proposed is suitable to simulate IL-6 response to different exercise modalities. Its future integration with existing models of GLP-1-induced insulin secretion might provide a more reliable description of exercise’s effects on glucose homeostasis and hence support the definition of more tailored interventions for the treatment of type 2 diabetes.

A Novel Insulin/Glucose Model after a Mixed-Meal Test in Patients with Type 1 Diabetes on Insulin Pump Therapy

Current closed-loop insulin delivery methods stem from sophisticated models of the glucose-insulin (G/I) system, mostly based on complex studies employing glucose tracer technology. We tested the performance of a new minimal model (GLUKINSLOOP 2.0) of the G/I system to characterize the glucose and insulin dynamics during multiple mixed meal tests (MMT) of different sizes in patients with type 1 diabetes (T1D) on insulin pump therapy (continuous subcutaneous insulin infusion, CSII). The GLUKINSLOOP 2.0 identified the G/I system, provided a close fit of the G/I time-courses and showed acceptable reproducibility of the G/I system parameters in repeated studies of identical and double-sized MMTs. This model can provide a fairly good and reproducible description of the G/I system in T1D patients on CSII, and it may be applied to create a bank of “virtual” patients. Our results might be relevant at improving the architecture of upcoming closed-loop CSII systems.

A Simple, Realistic Stochastic Model of Gastric Emptying

Several models of Gastric Emptying (GE) have been employed in the past to represent the rate of delivery of stomach contents to the duodenum and jejunum. These models have all used a deterministic form (algebraic equations or ordinary differential equations), considering GE as a continuous, smooth process in time. However, GE is known to occur as a sequence of spurts, irregular both in size and in timing. Hence, we formulate a simple stochastic process model, able to represent the irregular decrements of gastric contents after a meal. The model is calibrated on existing literature data and provides consistent predictions of the observed variability in the emptying trajectories. This approach may be useful in metabolic modeling, since it describes well and explains the apparently heterogeneous GE experimental results in situations where common gastric mechanics across subjects would be expected.

A Computational Method to Determine Glucose Infusion Rates for Isoglycemic Intravenous Glucose Infusion Study

The results of the isoglycemic intravenous glucose infusion (IIGI) study need to mimic the dynamic glucose profiles during the oral glucose tolerance test (OGTT) to accurately calculate the incretin effect. The glucose infusion rates during IIGI studies have historically been determined by experienced research personnel using the manual ad-hoc method. In this study, a computational method was developed to automatically determine the infusion rates for IIGI study based on a glucose-dynamics model. To evaluate the computational method, 18 subjects with normal glucose tolerance underwent a 75 g OGTT. One-week later, Group 1 (n = 9) and Group 2 (n = 9) underwent IIGI studies using the ad-hoc method and the computational method, respectively. Both methods were evaluated using correlation coefficient, mean absolute relative difference (MARD), and root mean square error (RMSE) between the glucose profiles from the OGTT and the IIGI study. The computational method exhibited significantly higher correlation (0.95 ± 0.03 versus 0.86 ± 0.10, P = 0.019), lower MARD (8.72 ± 1.83% versus 13.11 ± 3.66%, P = 0.002), and lower RMSE (10.33 ± 1.99 mg/dL versus 16.84 ± 4.43 mg/dL, P = 0.002) than the ad-hoc method. The computational method can facilitate IIGI study, and enhance its accuracy and stability. Using this computational method, a high-quality IIGI study can be accomplished without the need for experienced personnel.

Glucose homeostasis during short-term and prolonged exposure to high altitudes

Most of the literature related to high altitude medicine is devoted to the short-term effects of high-altitude exposure on human physiology. However, long-term effects of living at high altitudes may be more important in relation to human disease because more than 400 million people worldwide reside above 1500 m. Interestingly, individuals living at higher altitudes have a lower fasting glycemia and better glucose tolerance compared with those who live near sea level. There is also emerging evidence of the lower prevalence of both obesity and diabetes at higher altitudes. The mechanisms underlying improved glucose control at higher altitudes remain unclear. In this review, we present the most current evidence about glucose homeostasis in residents living above 1500 m and discuss possible mechanisms that could explain the lower fasting glycemia and lower prevalence of obesity and diabetes in this population. Understanding the mechanisms that regulate and maintain the lower fasting glycemia in individuals who live at higher altitudes could lead to new therapeutics for impaired glucose homeostasis.

Altered pattern of the incretin effect as assessed by modelling in individuals with glucose tolerance ranging from normal to diabetic

AIMS/HYPOTHESIS

Oral glucose elicits a higher insulin secretory response than intravenous glucose at matched glucose concentrations. This potentiation, known as the incretin effect, is typically expressed as the difference between the total insulin response to oral vs intravenous glucose. This approach does not describe the dynamics of insulin secretion potentiation. We developed a model for the simultaneous analysis of oral and isoglycaemic intravenous glucose responses to dissect the impact of hyperglycaemia and incretin effect on insulin secretion and beta cell function.

METHODS

Fifty individuals (23 with normal glucose tolerance [NGT], 17 with impaired glucose tolerance [IGT] and ten with type 2 diabetes) received an OGTT and an isoglycaemic test with measurement of plasma glucose, insulin, C-peptide, glucagon-like peptide-1 (GLP-1) and glucose-dependent insulinotropic polypeptide (GIP). Our model featured an incretin potentiation factor (PINCR) for the dose–response function relating insulin secretion to glucose concentration, and an effect on early secretion (rate sensitivity).

RESULTS

In NGT, PINCR rapidly increased and remained sustained during the whole OGTT (mean PINCR>1, p<0.009). The increase was transient in IGT and virtually absent in diabetes. Mean PINCR was significantly but loosely correlated with GLP-1 AUC (r=0.49, p<0.006), while the relationship was not significant for GIP. An incretin effect on rate sensitivity was present in all groups (p<0.002).

CONCLUSIONS/INTERPRETATION

The onset of the incretin effect is rapid and sustained in NGT, transient in IGT and virtually absent in diabetes. The profiles of the incretin effect are poorly related to those of the incretin hormones.

Simulation of oral glucose tolerance tests and the corresponding isoglycemic intravenous glucose infusion studies for calculation of the incretin effect

The incretin effect, which is a unique stimulus of insulin secretion in response to oral ingestion of nutrients, is calculated by the difference in insulin secretory responses from an oral glucose tolerance test (OGTT) and a corresponding isoglycemic intravenous glucose infusion (IIGI) study. The OGTT model of this study, which is individualized by fitting the glucose profiles during an OGTT, was developed to predict the glucose profile during an IIGI study in the same subject. Also, the model predicts the insulin and incretin profiles during both studies. The incretin effect, estimated by simulation, was compared with that measured by physiologic studies from eight human subjects with normal glucose tolerance, and the result exhibited a good correlation (r > 0.8); the incretin effect from the simulation was 56.5% ± 10.6% while the one from the measured data was 52.5% ± 19.6%. In conclusion, the parameters of the OGTT model have been successfully estimated to predict the profiles of both OGTTs and IIGI studies. Therefore, with glucose data from the OGTT alone, this model could control and predict the physiologic responses, including insulin secretion during OGTTs and IIGI studies, which could eventually eliminate the need for complex and cumbersome IIGI studies in incretin research.

Routine OGTT: a robust model including incretin effect for precise identification of insulin sensitivity and secretion in a single individual

In order to provide a method for precise identification of insulin sensitivity from clinical Oral Glucose Tolerance Test (OGTT) observations, a relatively simple mathematical model (Simple Interdependent glucose/insulin MOdel SIMO) for the OGTT, which coherently incorporates commonly accepted physiological assumptions (incretin effect and saturating glucose-driven insulin secretion) has been developed. OGTT data from 78 patients in five different glucose tolerance groups were analyzed: normal glucose tolerance (NGT), impaired glucose tolerance (IGT), impaired fasting glucose (IFG), IFG+IGT, and Type 2 Diabetes Mellitus (T2DM). A comparison with the 2011 Salinari (COntinuos GI tract MOdel, COMO) and the 2002 Dalla Man (Dalla Man MOdel, DMMO) models was made with particular attention to insulin sensitivity indices IS_COMO, IS_DMMO and k_xgi (the insulin sensitivity index for SIMO). ANOVA on k_xgi values across groups resulted significant overall (P<0.001), and post-hoc comparisons highlighted the presence of three different groups: NGT (8.62×10⁻⁵±9.36×10⁻⁵ min⁻¹pM⁻¹), IFG (5.30×10⁻⁵±5.18×10⁻⁵) and combined IGT, IFG+IGT and T2DM (2.09×10⁻⁵±1.95×10⁻⁵, 2.38×10⁻⁵±2.28×10⁻⁵ and 2.38×10⁻⁵±2.09×10⁻⁵ respectively). No significance was obtained when comparing IS_COMO or IS_DMMO across groups. Moreover, k_xgi presented the lowest sample average coefficient of variation over the five groups (25.43%), with average CVs for IS_COMO and IS_DMMO of 70.32% and 57.75% respectively; k_xgi also presented the strongest correlations with all considered empirical measures of insulin sensitivity. While COMO and DMMO appear over-parameterized for fitting single-subject clinical OGTT data, SIMO provides a robust, precise, physiologically plausible estimate of insulin sensitivity, with which habitual empirical insulin sensitivity indices correlate well. The k_xgi index, reflecting insulin secretion dependency on glycemia, also significantly differentiates clinically diverse subject groups. The SIMO model may therefore be of value for the quantification of glucose homeostasis from clinical OGTT data.

Nutrient infusion bypassing duodenum-jejunum improves insulin sensitivity in glucose-tolerant and diabetic obese subjects

The mechanisms of type 2 diabetes remission after bariatric surgery is still not fully elucidated. In the present study, we tried to simulate the Roux-en-Y gastric bypass with a canonical or longer biliary limb by infusing a liquid formula diet into different intestinal sections. Nutrients (Nutrison Energy) were infused into mid- or proximal jejunum and duodenum during three successive days in 10 diabetic and 10 normal glucose-tolerant subjects. Plasma glucose, insulin, C-peptide, glucagon, incretins, and nonesterified fatty acids (NEFA) were measured before and up to 360 min following. Glucose rate of appearance (Ra) and insulin sensitivity (SI), secretion rate (ISR), and clearance were assessed by mathematical models. SI increased when nutrients were delivered in mid-jejunum vs. duodenum (SI × 10⁴ min⁻¹·pM⁻¹: 1.11 ± 0.44 vs. 0.62 ± 0.22, P < 0.015, in controls and 0.79 ± 0.34 vs. 0.40 ± 0.20, P < 0.05, in diabetic subjects), whereas glucose Ra was not affected. In controls, Sensitivity of NEFA production was doubled in mid-jejunum vs. duodenum (2.80 ± 1.36 vs. 1.13 ± 0.78 × 10⁶, P < 0.005) and insulin clearance increased in mid-jejunum vs. duodenum (2.05 ± 1.05 vs. 1.09 ± 0.38 l/min, P < 0.03). Bypass of duodenum and proximal jejunum by nutrients enhances insulin sensitivity, inhibits lipolysis, and increases insulin clearance. These results may further our knowledge of the effects of bariatric surgery on both insulin resistance and diabetes.