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

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 fast-slow model of diabetes progression: Insights into mechanisms of response to the interventions in the Diabetes Prevention Program

Several models for the long-term development of T2DM already exist, focusing on the dynamics of the interaction between glycemia, insulinemia and β-cell mass. Current models consider representative (fasting or daily average) glycemia and insulinemia as characterizing the compensation state of the subject at some instant in slow time. This implies that only these representative levels can be followed through time and that the role of fast glycemic oscillations is neglected. An improved model (DPM15) for the long-term progression of T2DM is proposed, introducing separate peripheral and hepatic (liver and kidney) insulin actions. The DPM15 model no longer uses near-equilibrium approximation to separate fast and slow time scales, but rather describes, at each step in slow time, a complete day in the life of the virtual subject in fast time. The model can thus represent both fasting and postprandial glycemic levels and describe the effect of interventions acting on insulin-enhanced tissue glucose disposal or on insulin-inhibited hepatic glucose output, as well as on insulin secretion and β-cell replicating ability. The model can simulate long-term variations of commonly used clinical indices (HOMA-B, HOMA-IR, insulinogenic index) as well as of Oral Glucose Tolerance or Euglycemic Hyperinsulinemic Clamp test results. The model has been calibrated against observational data from the Diabetes Prevention Program study: it shows good adaptation to observations as a function of very plausible values of the parameters describing the effect of such interventions as Placebo, Intensive LifeStyle and Metformin administration.

Bifurcation analysis in a delay model of IVGTT glucose-insulin interaction

In this paper, a delayed differential model based on the intravenous glucose tolerance test is considered. The conditions to determine stability or instability of the model's steady state are obtained. We obtain the necessary conditions for the appearance of a bifurcation, and we investigate the direction and stability of the local bifurcation. For this purpose, the normal form theory is used. In addition, the numerical diagrams in the direction of theoretical results are drawn.

Consistency of compact and extended models of glucose-insulin homeostasis: The role of variable pancreatic reserve

Published compact and extended models of the glucose-insulin physiologic control system are compared, in order to understand why a specific functional form of the compact model proved to be necessary for a satisfactory representation of acute perturbation experiments such as the Intra Venous Glucose Tolerance Test (IVGTT). A spectrum of IVGTT’s of virtual subjects ranging from normal to IFG to IGT to frank T2DM were simulated using an extended model incorporating the population-of-controllers paradigm originally hypothesized by Grodsky, and proven to be able to capture a wide array of experimental results from heterogeneous perturbation procedures. The simulated IVGTT’s were then fitted with the Single-Delay Model (SDM), a compact model with only six free parameters, previously shown to be very effective in delivering precise estimates of insulin sensitivity and secretion during an IVGTT. Comparison of the generating, extended-model parameter values with the obtained compact model estimates shows that the functional form of the nonlinear insulin-secretion term, empirically found to be necessary for the compact model to satisfactorily fit clinical observations, captures the pancreatic reserve level of the simulated virtual patients. This result supports the validity of the compact model as a meaningful analysis tool for the clinical assessment of insulin sensitivity.

Blood Glucose Level Prediction for Diabetics Based on Nutrition and Insulin Administration Logs Using Personalized Mathematical Models

According to recent surveys, the current ways of diabetics trying to estimate their insulin need based on experience and conjecture are sometimes inefficient in practice. This paper proposes a prediction algorithm and presents the validation of the model in outpatient care. The algorithm consists of two state-of-the-art models that calculate nutrition absorption and glycaemia including insulin evolution. The combined model is extended with personalized parameter training including genetic algorithm and Nelder-Mead method, and a more realistic, diurnal parameter profile as a representation of the natural biorhythm. This method implemented in a user-friendly application can help diabetics calculate their insulin need. The tests were performed on a data set including a clinical trial involving more than 20 diabetic patients. We experienced 55% improvement in the results due to model training compared to the tests based on literature parameters. In the best case, 92.5% of the predicted blood glucose level values were in the range of clinically acceptable errors, which means around 2.8 mmol/l root mean square error. The results of the validation based on outpatient data are promising compared to others found in the literature. Handling other important factors such as physical activity and stress remains a challenge for future research.

Oscillatory dynamics of an intravenous glucose tolerance test model with delay interval

Type 2 diabetes mellitus (T2DM) has become prevalent pandemic disease in view of the modern life style. Both diabetic population and health expenses grow rapidly according to American Diabetes Association. Detecting the potential onset of T2DM is an essential focal point in the research of diabetes mellitus. The intravenous glucose tolerance test (IVGTT) is an effective protocol to determine the insulin sensitivity, glucose effectiveness, and pancreatic β-cell functionality, through the analysis and parameter estimation of a proper differential equation model. Delay differential equations have been used to study the complex physiological phenomena including the glucose and insulin regulations. In this paper, we propose a novel approach to model the time delay in IVGTT modeling. This novel approach uses two parameters to simulate not only both discrete time delay and distributed time delay in the past interval, but also the time delay distributed in a past sub-interval. Normally, larger time delay, either a discrete or a distributed delay, will destabilize the system. However, we find that time delay over a sub-interval might not. We present analytically some basic model properties, which are desirable biologically and mathematically. We show that this relatively simple model provides good fit to fluctuating patient data sets and reveals some intriguing dynamics. Moreover, our numerical simulation results indicate that our model may remove the defect in well known Minimal Model, which often overestimates the glucose effectiveness index.

Incorporating bolus and infusion pharmacokinetics into the ICING insulin model

The ICING model has been successfully used to guide clinical decisions on insulin administration in critical illness. However, insulin pharmacokinetics in the ICING model can be improved to better describe both intravenous (IV) bolus and infusion insulin administration. Patient data from 217 Dynamic Insulin Sensitivity and Secretion Tests (DISST) and 36 Intravenous Glucose Tolerance Tests (IVGTT) from independent dietary intervention studies was used to fit model parameters to a model structure that conforms to known behaviour. The DISST tests measured both endogenous and exogenous IV insulin bolus responses, while the IVGTT measured exogenous IV insulin infusion dynamics. Unidentifiable parameters were given physiologically justified values, with knowledge on relative insulin clearance rates used to constrain parameter values. The resulting whole-cohort description was able to simultaneously describe both IV bolus and infusion dynamics, and improves ICING model descriptive capability. Improved infusion dynamics will allow better description of subcutaneous insulin, the insulin administration route favoured in outpatient care of diabetes.

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.

Plasma volume expansion from the intravenous glucose tolerance test before and after hip replacement surgery

BACKGROUND

Hyperosmotic glucose is injected intravenously when an intravenous glucose tolerance test (IVGTT) is initiated. The extent and time period of plasma volume expansion that occurs in response to the glucose load has not been studied in the perioperative setting.

METHODS

Twenty-two non-diabetic patients aged between 57 and 76 years (mean 68) underwent an IVGTT, during which 0.3 g/kg of glucose 30% (1 ml/kg) was injected as a bolus over one minute, one day before and two days after hip replacement surgery. Twelve blood samples were collected over 75 minutes from each patient. The turnover of both the exogenous glucose and the injected fluid volume was calculated by means of mass balance and volume kinetic analysis.

RESULTS

The IVGTT raised plasma glucose by 9 mmol/L and the plasma volume by 8%. The extracellular fluid volume increased by 320 (SD 60) ml of which 2/3 could be accounted for in the plasma. The half-life of the exogenous glucose averaged 30 minutes before surgery and 36 minutes postoperatively (P < 0.02). The glucose elimination governed 86% of the decay of the plasma volume expansion, which occurred with a half-life of 12 minutes before to 21 minutes after the surgery (median, P < 0.001).

CONCLUSION

Hyperosmotic glucose translocated intracellular water to the plasma volume rather than to the entire extracellular fluid volume. The preferential re-distribution acts to dilute the plasma concentrations used to quantify insulin sensitivity and ß-cell function from an IVGTT. The greater-than-expected plasma dilution lasted longer after than before surgery.

Evaluation of a mathematical model of diabetes progression against observations in the Diabetes Prevention Program

The seminal publication of the Diabetes Prevention Program (DPP) results in 2002 has provided insight into the impact of major therapies on the development of diabetes over a time span of a few years. In the present work, the publicly available DPP data set is used to calibrate and evaluate a recently developed mechanistic mathematical model for the long-term development of diabetes to assess the model's ability to predict the natural history of disease progression and the effectiveness of preventive interventions. A general population is generated from which virtual subject samples corresponding to the DPP enrollment criteria are selected. The model is able to reproduce with good fidelity the observed time courses of both diabetes incidence and average glycemia, under realistic hypotheses on evolution of disease and efficacy of the studied therapies, for all treatment arms. Model-based simulations of the long-term evolution of the disease are consistent with the transient benefits observed with conventional therapies and with promising effects of radical improvement of insulin sensitivity (as by metabolic surgery) or of β-cell protection. The mechanistic diabetes progression model provides a credible tool by which long-term implications of antidiabetic interventions can be evaluated.

The range of time delay and the global stability of the equilibrium for an IVGTT model

Diabetes mellitus has become a prevalent disease in the world. Diagnostic protocol for the onset of diabetes mellitus is the initial step in the treatments. The intravenous glucose tolerance test (IVGTT) has been considered as the most accurate method to determine the insulin sensitivity and glucose effectiveness. It is well known that there exists a time delay in insulin secretion stimulated by the elevated glucose concentration level. However, the range of the length of the delay in the existing IVGTT models are not fully discussed and thus in many cases the time delay may be assigned to a value out of its reasonable range. In addition, several attempts had been made to determine when the unique equilibrium point is globally asymptotically stable. However, all these conditions are delay-independent. In this paper, we discuss the range of the time delay and provide easy-to-check delay-dependent conditions for the global asymptotic stability of the equilibrium point for a recent IVGTT model through Liapunov function approach. Estimates of the upper bound of the delay for global stability are given in corollaries. In addition, the numerical simulation in this paper is fully incorporated with functional initial conditions, which is natural and more appropriate in delay differential equation systems.

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.