A mathematical model of the oral glucose tolerance test illustrating the effects of the incretins

Nonlinear modeling of oral glucose tolerance test response to evaluate associations with aging outcomes

As people age, their ability to maintain homeostasis in response to stressors diminishes. Physical frailty, a syndrome characterized by loss of resilience to stressors, is thought to emerge due to dysregulation of and breakdowns in communication among key physiological systems. Dynamical systems modeling of these physiological systems aims to model the underlying processes that govern response to stressors. We hypothesize that dynamical systems model summaries are predictive of age-related declines in health and function. In this study, we analyze data obtained during 75-gram oral-glucose tolerance tests (OGTT) on 1,120 adults older than 50 years of age from the Baltimore Longitudinal Study on Aging. We adopt a two-stage modeling approach. First, we fit OGTT curves with the Ackerman model-a nonlinear, parametric model of the glucose-insulin system-and with functional principal components analysis. We then fit linear and Cox proportional hazards models to evaluate whether usual gait speed and survival are associated with the stage-one model summaries. We also develop recommendations for identifying inadequately-fitting nonlinear model fits in a cohort setting with numerous heterogeneous response curves. These recommendations include: (1) defining a constrained parameter space that ensures biologically plausible model fits, (2) evaluating the relative discrepancy between predicted and observed responses of biological interest, and (3) identifying model fits that have notably poor model fit summary measures, such as [Formula: see text], relative to other fits in the cohort. The Ackerman model was unable to adequately fit 36% of the OGTT curves. The stage-two regression analyses found no associations between Ackerman model summaries and usual gait speed, nor with survival. The second functional principal component score was associated with faster gait speed (p<0.01) and improved survival (p<0.01).

Glucagon-like peptide-1 and interleukin-6 interaction in response to physical exercise: An in-silico model in the framework of immunometabolism

BACKGROUND AND OBJECTIVE

Glucagon-like peptide 1 (GLP-1) is classically identified as an incretin hormone, secreted in response to nutrient ingestion and able to enhance glucose-stimulated insulin secretion. However, other stimuli, such as physical exercise, may enhance GLP-1 plasma levels, and this exercise-induced GLP-1 secretion is mediated by interleukin-6 (IL-6), a cytokine secreted by contracting skeletal muscle. The aim of the study is to propose a mathematical model of IL-6-induced GLP-1 secretion and kinetics in response to physical exercise of moderate intensity.

METHODS

The model includes the GLP-1 subsystem (with two pools: gut and plasma) and the IL-6 subsystem (again with two pools: skeletal muscle and plasma); it provides a parameter of possible clinical relevance representing the sensitivity of GLP-1 to IL-6 (k0). The model was validated on mean IL-6 and GLP-1 data derived from the scientific literature and on a total of 100 virtual subjects.

RESULTS

Model validation provided mean residuals between 0.0051 and 0.5493 pg⋅mL-1 for IL-6 (in view of concentration values ranging from 0.8405 to 3.9718 pg⋅mL-1) and between 0.0133 and 4.1540 pmol⋅L-1 for GLP-1 (in view of concentration values ranging from 0.9387 to 17.9714 pmol⋅L-1); a positive significant linear correlation (r = 0.85, p<0.001) was found between k0 and the ratio between areas under GLP-1 and IL-6 curve, over the virtual subjects.

CONCLUSIONS

The model accurately captures IL-6-induced GLP-1 kinetics in response to physical exercise.

Effects of Carbohydrate and Fats in Turkish Patients with Type 2 Diabetes

Aim: This study aimed to assess the effects of different kinds of diet, which were similar in total energy density but different in carbohydrate and fats, on some blood parameters in type 2 diabetics. Materials and Methods: In this study, 33 type 2 diabetics, participants were offered two different kinds of lunches within 7 days intervals. Venous blood samples were collected from the participants half an hour before and after the consumption of these meals (0-180 minutes). Blood parameters such as glucose, insulin, low-density lipoprotein (LDL-C), high-density lipoprotein (HDL-C), and triglyceride were analyzed through blood samples. Results: There was no significance between the values of the change in blood glucose before and after their consumption of the standard meal and etli ekmek. After the consumption of the etli ekmek difference between the participants’ mean insulin level values at 60 and 90 minutes was lower than the standard meal. The values under the curve (AUC) were found to be significant (p

Mathematical model of insulin kinetics accounting for the amino acids effect during a mixed meal tolerance test

Amino acids (AAs) are well known to be involved in the regulation of glucose metabolism and, in particular, of insulin secretion. However, the effects of different AAs on insulin release and kinetics have not been completely elucidated. The aim of this study was to propose a mathematical model that includes the effect of AAs on insulin kinetics during a mixed meal tolerance test. To this aim, five different models were proposed and compared. Validation was performed using average data, derived from the scientific literature, regarding subjects with normal glucose tolerance (CNT) and with type 2 diabetes (T2D). From the average data of the CNT and T2D people, data for two virtual populations (100 for each group) were generated for further model validation. Among the five proposed models, a simple model including one first-order differential equation showed the best results in terms of model performance (best compromise between model structure parsimony, estimated parameters plausibility, and data fit accuracy). With regard to the contribution of AAs to insulin appearance/disappearance (kAA model parameter), model analysis of the average data from the literature yielded 0.0247 (confidence interval, CI: 0.0168 - 0.0325) and -0.0048 (CI: -0.0281 - 0.0185) μU·ml-1/(μmol·l-1·min), for CNT and T2D, respectively. This suggests a positive effect of AAs on insulin secretion in CNT, and negligible effect in T2D. In conclusion, a simple model, including single first-order differential equation, may help to describe the possible AAs effects on insulin kinetics during a physiological metabolic test, and provide parameters that can be assessed in the single individuals.

A Pilot Study to Assess Glucose, Insulin, and Incretin Responses Following Novel High Resistant Starch Rice Ingestion in Healthy Men

INTRODUCTION

A newly developed resistant starch (RS) rice line with double mutation of starch synthase IIIa and branching enzyme IIb (ss3a/be2b) exhibits a tenfold greater percentage RS value than the wild-type rice line. Currently, the effects of cooked rice with such high RS content on secretion and action of glucagon-like peptide-1 (GLP-1) and glucose-dependent insulinotropic polypeptide (GIP) are unclear. Therefore, we conducted a pilot study to assess postprandial responses of GLP-1 and GIP along with glucose and insulin and also gastric emptying after ingestion of the high-RS cooked rice with ss3a/be2b in healthy subjects.

METHODS

In a non-randomized crossover design, five healthy men ingested two test foods, control (low-RS) and high-RS cooked rice, with at least 1-week washout period between testing days. Plasma glucose, serum insulin, plasma total GLP-1, plasma total GIP, and also gastric emptying rate were measured after ingestion of each test food, and the incremental area under the curves (iAUC) was calculated for each biochemical parameter using the values from 0 to 180 min after ingestion.

RESULTS

The high-RS cooked rice ingestion tended to reduce iAUC-glucose (p = 0.06) and significantly reduced iAUC-insulin (p < 0.01) and iAUC-GLP-1 (p < 0.05) but not iAUC-GIP (p = 0.21) relative to control cooked rice ingestion. In addition, the high-RS cooked rice ingestion did not affect gastric emptying.

CONCLUSIONS

The present results indicate that the suppressive effects of the high-RS cooked rice ingestion on postprandial responses of glucose and insulin may be provided through attenuation in GLP-1 secretion along with its low digestibility into glucose. We suggest that the high-RS rice with ss3a/be2b may serve as a better carbohydrate source and also as a novel functional food for dietary interventions to improve postprandial hyperglycemia and hyperinsulinemia without both enhancing GLP-1 secretion and affecting gastric emptying in patients with diabetes.

Assessing the Effect of Incretin Hormones and Other Insulin Secretagogues on Pancreatic Beta-Cell Function: Review on Mathematical Modelling Approaches

Mathematical modelling in glucose metabolism has proven very useful for different reasons. Several models have allowed deeper understanding of the relevant physiological and pathophysiological aspects and promoted new experimental activity to reach increased knowledge of the biological and physiological systems of interest. Glucose metabolism modelling has also proven useful to identify the parameters with specific physiological meaning in single individuals, this being relevant for clinical applications in terms of precision diagnostics or therapy. Among those model-based physiological parameters, an important role resides in those for the assessment of different functional aspects of the pancreatic beta cell. This study focuses on the mathematical models of incretin hormones and other endogenous substances with known effects on insulin secretion and beta-cell function, mainly amino acids, non-esterified fatty acids, and glucagon. We found that there is a relatively large number of mathematical models for the effects on the beta cells of incretin hormones, both at the cellular/organ level or at the higher, whole-body level. In contrast, very few models were identified for the assessment of the effect of other insulin secretagogues. Given the opportunities offered by mathematical modelling, we believe that novel models in the investigated field are certainly advisable.

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 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.

Postprandial glucose-lowering effect of premeal consumption of protein-enriched, dietary fiber-fortified bar in individuals with type 2 diabetes mellitus or normal glucose tolerance

AIMS/INTRODUCTION

Protein preload improves postprandial glycemia by stimulating secretion of insulin and incretin hormones. However, it requires a large dose of protein to produce a significant effect. The present study was carried out to investigate the postprandial glucose-lowering effect of a premeal protein-enriched, dietary fiber-fortified bar (PFB), which contains moderate amounts of protein, in individuals with type 2 diabetes mellitus or normal glucose tolerance (NGT).

MATERIALS AND METHODS

The participants (15 type 2 diabetes mellitus and 15 NGT) were randomly assigned to either a premeal or postmeal PFB group and underwent two mixed meal tolerance tests, 1 week apart in reverse order. Plasma levels of glucose, insulin, glucagon-like peptide-1 and glucose-dependent insulinotropic polypeptide were measured.

RESULTS

During the mixed meal tolerance tests, the incremental area under the curve from 0 to 180 min of plasma glucose levels was lower with premeal PFB than with postmeal PFB in the type 2 diabetes mellitus (14,723 ± 1,310 mg min/dL vs 19,642 ± 1,367 mg min/dL; P = 0.0002) and NGT participants (3,943 ± 416 mg min/dL vs 4,827 ± 520 mg min/dL, P = 0.0296). In the type 2 diabetes mellitus participants, insulinogenic index and the incremental area under the curve from 0 to 180 min of plasma total glucagon-like peptide-1 levels were higher with premeal PFB than with postmeal PFB, but not in the NGT participants. There was no difference in postprandial glucose-dependent insulinotropic polypeptide levels between premeal and postmeal PFB in both groups.

CONCLUSIONS

Acute administration of premeal PFB decreased postprandial glucose excursion in both type 2 diabetes mellitus and NGT participants. In the type 2 diabetes mellitus participants, premeal PFB augmented the early-phase insulin secretion, possibly through enhancing glucagon-like peptide-1 secretion.

A closed-loop multi-level model of glucose homeostasis

BACKGROUND

The pathophysiologic processes underlying the regulation of glucose homeostasis are considerably complex at both cellular and systemic level. A comprehensive and structured specification for the several layers of abstraction of glucose metabolism is often elusive, an issue currently solvable with the hierarchical description provided by multi-level models. In this study we propose a multi-level closed-loop model of whole-body glucose homeostasis, coupled with the molecular specifications of the insulin signaling cascade in adipocytes, under the experimental conditions of normal glucose regulation and type 2 diabetes.

METHODOLOGY/PRINCIPAL FINDINGS

The ordinary differential equations of the model, describing the dynamics of glucose and key regulatory hormones and their reciprocal interactions among gut, liver, muscle and adipose tissue, were designed for being embedded in a modular, hierarchical structure. The closed-loop model structure allowed self-sustained simulations to represent an ideal in silico subject that adjusts its own metabolism to the fasting and feeding states, depending on the hormonal context and invariant to circadian fluctuations. The cellular level of the model provided a seamless dynamic description of the molecular mechanisms downstream the insulin receptor in the adipocytes by accounting for variations in the surrounding metabolic context.

CONCLUSIONS/SIGNIFICANCE

The combination of a multi-level and closed-loop modeling approach provided a fair dynamic description of the core determinants of glucose homeostasis at both cellular and systemic scales. This model architecture is intrinsically open to incorporate supplementary layers of specifications describing further individual components influencing glucose metabolism.

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.

Application of the Oral Minimal Model to Korean Subjects with Normal Glucose Tolerance and Type 2 Diabetes Mellitus

BACKGROUND

The oral minimal model is a simple, useful tool for the assessment of β-cell function and insulin sensitivity across the spectrum of glucose tolerance, including normal glucose tolerance (NGT), prediabetes, and type 2 diabetes mellitus (T2DM) in humans.

METHODS

Plasma glucose, insulin, and C-peptide levels were measured during a 180-minute, 75-g oral glucose tolerance test in 24 Korean subjects with NGT (n=10) and T2DM (n=14). The parameters in the computational model were estimated, and the indexes for insulin sensitivity and β-cell function were compared between the NGT and T2DM groups.

RESULTS

The insulin sensitivity index was lower in the T2DM group than the NGT group. The basal index of β-cell responsivity, basal hepatic insulin extraction ratio, and post-glucose challenge hepatic insulin extraction ratio were not different between the NGT and T2DM groups. The dynamic, static, and total β-cell responsivity indexes were significantly lower in the T2DM group than the NGT group. The dynamic, static, and total disposition indexes were also significantly lower in the T2DM group than the NGT group.

CONCLUSION

The oral minimal model can be reproducibly applied to evaluate β-cell function and insulin sensitivity in Koreans.

Prehepatic secretion and disposal of insulin in obese adolescents as estimated by three-hour, eight-sample oral glucose tolerance tests

The body compensates for early-stage insulin resistance by increasing insulin secretion. A reliable and easy-to-use mathematical assessment of insulin secretion and disposal could be a valuable tool for identifying patients at risk for the development of type 2 diabetes. Because the pathophysiology of insulin resistance is incompletely understood, assessing insulin metabolism with minimal assumptions regarding its metabolic regulation is a major challenge. To assess insulin secretion and indexes of insulin disposal, our marginalized and regularized absorption approach (MRA) was applied to a sparse sampling oral glucose tolerance test (OGTT) protocol measuring the insulin and C-peptide concentrations. Identifiability and potential bias of metabolic parameters were estimated from published data with dense sampling. The MRA was applied to OGTT data from 135 obese adolescents to demonstrate its clinical applicability. Individual prehepatic basal and dynamic insulin secretion and clearance levels were determined with a precision and accuracy greater than 10% of the nominal value. The intersubject variability in these parameters was approximately four times higher than the intrasubject variability, and there was a strong negative correlation between prehepatic secretion and plasma clearance of insulin. MRA-based analysis provides reliable estimates of insulin secretion and clearance, thereby enabling detailed glucose homeostasis characterization based on restricted datasets that are obtainable during routine patient care.

Requirements for multi-level systems pharmacology models to reach end-usage: the case of type 2 diabetes

We are currently in the middle of a major shift in biomedical research: unprecedented and rapidly growing amounts of data may be obtained today, from in vitro, in vivo and clinical studies, at molecular, physiological and clinical levels. To make use of these large-scale, multi-level datasets, corresponding multi-level mathematical models are needed, i.e. models that simultaneously capture multiple layers of the biological, physiological and disease-level organization (also referred to as quantitative systems pharmacology-QSP-models). However, today's multi-level models are not yet embedded in end-usage applications, neither in drug research and development nor in the clinic. Given the expectations and claims made historically, this seemingly slow adoption may seem surprising. Therefore, we herein consider a specific example-type 2 diabetes-and critically review the current status and identify key remaining steps for these models to become mainstream in the future. This overview reveals how, today, we may use models to ask scientific questions concerning, e.g., the cellular origin of insulin resistance, and how this translates to the whole-body level and short-term meal responses. However, before these multi-level models can become truly useful, they need to be linked with the capabilities of other important existing models, in order to make them 'personalized' (e.g. specific to certain patient phenotypes) and capable of describing long-term disease progression. To be useful in drug development, it is also critical that the developed models and their underlying data and assumptions are easily accessible. For clinical end-usage, in addition, model links to decision-support systems combined with the engagement of other disciplines are needed to create user-friendly and cost-efficient software packages.

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.

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.

Identification of an integrated mathematical model of standard oral glucose tolerance test for characterization of insulin potentiation in health

Two new formulations, respectively denominated INT_M1 and INT_M2, of an integrated mathematical model to describe the glycemic and insulinemic responses to a 75 g oral glucose tolerance test (OGTT) are proposed and compared. The INT_M1 assumes a single compartment for the intestine and the derivative of a power exponential function for the gastric emptying rate, while, in the INT_M2, a nonlinear three-compartment system model is adopted to produce a more realistic, multiphase gastric emptying rate. Both models were implemented in a Matlab-based, two-step procedure for estimation of seven adjustable coefficients characterizing the gastric emptying rate and the incretin, insulin and glucose kinetics. Model behaviour was tested vs. mean plasma glucagon-like peptide 1 (GLP-1), glucose-dependent insulinotropic polypeptide (GIP), glucose and insulin measurements from two different laboratories, where glycemic profiles observed during a 75 g OGTT were matched in healthy subjects (HC1- and HC2-group, respectively) by means of an isoglycemic intravenous glucose (I-IVG) infusion. Under the hypothesis of an additive effect of GLP-1 and GIP on insulin potentiation, our results demonstrated a substantial equivalence of the two models in matching the data. Model parameter estimates showed to be suitable markers of differences observed in the OGTT and matched I-IVG responses from the HC1-group compared to the HC2-group. Model implementation in our two-step parameter estimation procedure enhances the possibility of a prospective application for individualization of the incretin effect in a single subject, when his/her data are plugged in.

Bariatric surgery and T2DM improvement mechanisms: a mathematical model

Background

Consensus exists that several bariatric surgery procedures produce a rapid improvement of glucose homeostasis in obese diabetic patients, improvement apparently uncorrelated with the degree of eventual weight loss after surgery. Several hypotheses have been suggested to account for these results: among these, the anti-incretin, the ghrelin and the lower-intestinal dumping hypotheses have been discussed in the literature. Since no clear-cut experimental results are so far available to confirm or disprove any of these hypotheses, in the present work a mathematical model of the glucose-insulin-incretin system has been built, capable of expressing these three postulated mechanisms. The model has been populated with critically evaluated parameter values from the literature, and simulations under the three scenarios have been compared.

Results

The modeling results seem to indicate that the suppression of ghrelin release is unlikely to determine major changes in short-term glucose control. The possible existence of an anti-incretin hormone would be supported if an experimental increase of GIP concentrations were evident post-surgery. Given that, on the contrary, collected evidence suggests that GIP concentrations decrease post-surgery, the lower-intestinal dumping hypothesis would seem to describe the mechanism most likely to produce the observed normalization of Type 2 Diabetes Mellitus (T2DM) after bariatric surgery.

Conclusions

The proposed model can help discriminate among competing hypotheses in a context where definitive data are not available and mechanisms are still not clear.

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

The rate of appearance (R(a)) of exogenous glucose in plasma after glucose ingestion is presently measured by tracer techniques that cannot be used in standard clinical testing such as the oral glucose tolerance test (OGTT). We propose a mathematical model that represents in a simple way the gastric emptying, the transport of glucose along the intestinal tract, and its absorption from gut lumen into portal blood. The model gives the R(a) time course in terms of parameters with a physiological counterpart and provides an expression for the release of incretin hormones as related to glucose transit into gut lumen. Glucose absorption was represented by assuming two components related to a proximal and a distal transporter. Model performance was evaluated by numerical simulations. The model was then validated by fitting OGTT glucose and GLP-1 data in healthy controls and type 2 diabetic patients, and useful information was obtained for the rate of gastric emptying, the rate of glucose absorption, the R(a) profile, the insulin sensitivity, and the glucose effectiveness. Model-derived estimates of insulin sensitivity were well correlated (r = 0.929 in controls and 0.886 in diabetic patients) to data obtained from the euglycemic hyperinsulinemic clamp. Although the proposed OGTT analysis requires the measurement of an additional hormone concentration (GLP-1), it appears to be a reasonable choice since it avoids complex and expensive techniques, such as isotopes for glucose R(a) measurement and direct assessment of gastric emptying and intestinal transit, and gives additional correlated information, thus largely compensating for the extra expense.

Predictive performance for population models using stochastic differential equations applied on data from an oral glucose tolerance test

Several articles have investigated stochastic differential equations (SDEs) in PK/PD models, but few have quantitatively investigated the benefits to predictive performance of models based on real data. Estimation of first phase insulin secretion which reflects beta-cell function using models of the OGTT is a difficult problem in need of further investigation. The present work aimed at investigating the power of SDEs to predict the first phase insulin secretion (AIR (0-8)) in the IVGTT based on parameters obtained from the minimal model of the OGTT, published by Breda et al. (Diabetes 50(1):150-158, 2001). In total 174 subjects underwent both an OGTT and a tolbutamide modified IVGTT. Estimation of parameters in the oral minimal model (OMM) was performed using the FOCE-method in NONMEM VI on insulin and C-peptide measurements. The suggested SDE models were based on a continuous AR(1) process, i.e. the Ornstein-Uhlenbeck process, and the extended Kalman filter was implemented in order to estimate the parameters of the models. Inclusion of the Ornstein-Uhlenbeck (OU) process caused improved description of the variation in the data as measured by the autocorrelation function (ACF) of one-step prediction errors. A main result was that application of SDE models improved the correlation between the individual first phase indexes obtained from OGTT and AIR (0-8) (r = 0.36 to r = 0.49 and r = 0.32 to r = 0.47 with C-peptide and insulin measurements, respectively). In addition to the increased correlation also the properties of the indexes obtained using the SDE models more correctly assessed the properties of the first phase indexes obtained from the IVGTT. In general it is concluded that the presented SDE approach not only caused autocorrelation of errors to decrease but also improved estimation of clinical measures obtained from the glucose tolerance tests. Since, the estimation time of extended models was not heavily increased compared to basic models, the applied method is concluded to have high relevance not only in theory but also in practice.

A survey of bioengineering research in Canada-2007

Research activity in bioengineering at Canadian universities has been surveyed. Details were provided by chemical engineering departments in response to a common request for information on activities by individual researchers and for key publications. The information provided has been grouped by topics within the broad theme of "Bioengineering," and contributions from individual departments have been summarized within these topics. Although many aspects of bioengineering research are being pursued in Canada, it would appear as though environmental biotechnology, biomaterials, and tissue/cell culture are the most active areas under investigation.