Glucose fluxes during OGTT in adolescents assessed by a stable isotope triple tracer method

Developing the UVA/Padova Type 1 Diabetes Simulator: Modeling, Validation, Refinements, and Utility

Arguably, diabetes mellitus is one of the best quantified human conditions. In the past 50 years, the metabolic monitoring technologies progressed from occasional assessment of average glycemia via HbA1c, through episodic blood glucose readings, to continuous glucose monitoring (CGM) producing data points every few minutes. The high-temporal resolution of CGM data enabled increasingly intensive treatments, from decision support assisting insulin injection or oral medication, to automated closed-loop control, known as the "artificial pancreas." Throughout this progress, mathematical models and computer simulation of the human metabolic system became indispensable for the technological progress of diabetes treatment, enabling every step, from assessment of insulin sensitivity via the now classic Minimal Model of Glucose Kinetics, to in silico trials replacing animal experiments, to automated insulin delivery algorithms. In this review, we follow these developments, beginning with the Minimal Model, which evolved through the years to become large and comprehensive and trigger a paradigm change in the design of diabetes optimization strategies: in 2007, we introduced a sophisticated model of glucose-insulin dynamics and a computer simulator equipped with a "population" of N = 300 in silico "subjects" with type 1 diabetes. In January 2008, in an unprecedented decision, the Food and Drug Administration (FDA) accepted this simulator as a substitute to animal trials for the pre-clinical testing of insulin treatment strategies. This opened the field for rapid and cost-effective development and pre-clinical testing of new treatment approaches, which continues today. Meanwhile, animal experiments for the purpose of designing new insulin treatment algorithms have been abandoned.

Minimal and Maximal Models to Quantitate Glucose Metabolism: Tools to Measure, to Simulate and to Run in Silico Clinical Trials

Several models have been proposed to describe the glucose system at whole-body, organ/tissue and cellular level, designed to measure non-accessible parameters (minimal models), to simulate system behavior and run in silico clinical trials (maximal models). Here, we will review the authors' work, by putting it into a concise historical background. We will discuss first the parametric portrait provided by the oral minimal models-building on the classical intravenous glucose tolerance test minimal models-to measure otherwise non-accessible key parameters like insulin sensitivity and beta-cell responsivity from a physiological oral test, the mixed meal or the oral glucose tolerance tests, and what can be gained by adding a tracer to the oral glucose dose. These models were used in various pathophysiological studies, which we will briefly review. A deeper understanding of insulin sensitivity can be gained by measuring insulin action in the skeletal muscle. This requires the use of isotopic tracers: both the classical multiple-tracer dilution and the positron emission tomography techniques are discussed, which quantitate the effect of insulin on the individual steps of glucose metabolism, that is, bidirectional transport plasma-interstitium, and phosphorylation. Finally, we will present a cellular model of insulin secretion that, using a multiscale modeling approach, highlights the relations between minimal model indices and subcellular secretory events. In terms of maximal models, we will move from a parametric to a flux portrait of the system by discussing the triple tracer meal protocol implemented with the tracer-to-tracee clamp technique. This allows to arrive at quasi-model independent measurement of glucose rate of appearance (Ra), endogenous glucose production (EGP), and glucose rate of disappearance (Rd). Both the fast absorbing simple carbs and the slow absorbing complex carbs are discussed. This rich data base has allowed us to build the UVA/Padova Type 1 diabetes and the Padova Type 2 diabetes large scale simulators. In particular, the UVA/Padova Type 1 simulator proved to be a very useful tool to safely and effectively test in silico closed-loop control algorithms for an artificial pancreas (AP). This was the first and unique simulator of the glucose system accepted by the U.S. Food and Drug Administration as a substitute to animal trials for in silico testing AP algorithms. Recent uses of the simulator have looked at glucose sensors for non-adjunctive use and new insulin molecules.

Oral minimal model-based estimates of insulin sensitivity in obese youth depend on oral glucose tolerance test protocol duration

Introduction

The Oral Minimal Model (OMM), a differential-equations based mathematical model of glucose-insulin dynamics, utilizes data from a frequently sampled oral glucose tolerance test (OGTT) to quantify insulin sensitivity ( S I ). OMM-based estimates of S I can detect differences in insulin resistance (IR) across population groups and quantify effects of clinical or behavioral interventions. These estimates of S I have been validated in healthy adults using data from OGTTs with durations from 2 to 7 h. However, data demonstrating how protocol duration affects S I estimates in highly IR populations such as adolescents with obesity are limited.

Methods

A 6-h frequently sampled OGTT was performed in adolescent females with obesity. Two, 3-, and 4- hour implementations of OMM assuming an exponentially-decaying rate of glucose appearance beyond measured glucose concentrations were compared to the 6-h implementation. A 4- hour OMM implementation with truncated data (4h Tr) was also considered.

Results

Data from 68 participants were included (age 15.8 ± 1.2 years, BMI 35.4 ± 5.6 kg/m²). Although S I values were highly correlated for all implementations, they varied with protocol duration (2h: 2.86 ± 3.31, 3h: 2.55 ± 2.62, 4h: 2.81 ± 2.59, 4h tr: 3.13 ± 3.14, 6h: 3.06 ± 2.85 x 10^-4 dl/kg/min per U/ml). S I estimates based on 2 or 3 h of data underestimated S I values, whereas 4-h S I estimates more closely approximated 6-h S I values.

Discussion

These results suggest that OGTT protocol duration should be considered when implementing OMM to estimate S I in adolescents with obesity and other IR populations.

A novel natural tracer method to measure complex carbohydrate metabolism

While the triple tracer isotope dilution method has enabled accurate estimation of carbohydrate turnover after a mixed meal, use of the simple carbohydrate glucose as the carbohydrate source limits its translational applicability to everyday meals that typically contain complex carbohydrates. Hence, utilizing the natural enrichment of [¹³C]polysaccharide in commercially available grains, we devised a novel tracer method to measure postprandial complex carbohydrate turnover and indices of insulin action and β-cell function and compared the parameters to those obtained after a simple carbohydrate containing mixed meal. We studied healthy volunteers after either rice (n = 8) or sorghum (n = 8) and glucose (n = 16) containing mixed meals and modified the triple tracer technique to calculate carbohydrate turnover. All meals were matched for calories and macronutrient composition. Rates of meal glucose appearance (2,658 ± 736 vs. 4,487 ± 909 μM·kg^-1·2 h^-1), endogenous glucose production (-835 ± 283 vs. -1,123 ± 323 μM·kg^-1·2 h^-1) and glucose disappearance (1,829 ± 807 vs. 3,606 ± 839 μM·kg^-1·2 h^-1) differed (P < 0.01) between complex and simple carbohydrate containing meals, respectively. Interestingly, there were significant increase in indices of insulin sensitivity (32.5 ± 3.5 vs. 25.6 ± 3.2 10^-5 (dl·kg^-1·min^-2)/pM, P = 0.006) and β-cell responsivity (disposition index: 1,817 ± 234 vs. 1,236 ± 159 10^-14 (dl·kg^-1·min^-2)/pM, P < 0.005) with complex than simple carbohydrate meals. We present a novel triple tracer approach to estimate postprandial turnover of complex carbohydrate containing mixed meals. We also report higher insulin sensitivity and β-cell responsivity with complex than with simple carbohydrates in mixed meals of identical calorie and macronutrient compositions in healthy adults.

Modest changes to glycemic regulation are sufficient to maintain glucose fluxes in healthy young men following overfeeding with a habitual macronutrient composition

Currently, it is unclear whether short-term overfeeding in healthy people significantly affects postprandial glucose regulation, as most human overfeeding studies have utilized induced experimental conditions such as the euglycemic-hyperinsulinemic clamp technique to assess glucoregulation. The aim of this study was to quantify glucose fluxes [rates of meal glucose appearance (R_a), disposal (R_d), and endogenous glucose production (EGP)] in response to 5 and 28 days of overfeeding (+45% energy) while maintaining habitual macronutrient composition (31.0 ± 1.9% fat, 48.6 ± 2.2% carbohydrate, 16.7 ± 1.4% protein) in healthy, lean young men. Meal tolerance testing was combined with the triple-stable isotope glucose tracer approach. Visceral adipose volume increased by ~15% with 5 days of overfeeding, while there was no further change at 28 days. In contrast, body mass (+1.6 kg) and fat mass (+1.3 kg) were significantly increased only after 28 days of overfeeding. Fasting EGP, R_d, and insulin were increased at 5 but unchanged after 28 days. Postprandial glucose and insulin responses were unaltered by 5 days of overfeeding but were modestly increased after 28 days (P < 0.05). However, meal R_a and glucose R_d were significantly increased after both 5 and 28 days of overfeeding (P < 0.05). Despite this, overfeeding did not lead to alterations to postprandial EGP suppression. Thus, in contrast to findings from euglycemic-hyperinsulinemic clamp studies, chronic overfeeding did not affect the ability to suppress EGP or stimulate R_d under postprandial conditions. Rather, glucose flux was appropriately maintained following 28 days of overfeeding through modest increases in postprandial glycemia and insulinemia.

Endogenous glucose production after sequential meals in humans: evidence for more prolonged suppression after ingestion of a second meal

Single-meal studies have shown that carbohydrate ingestion causes rapid and persistent suppression of endogenous glucose production (EGP). However, little is known about the regulation of EGP under real-life eating patterns in which multiple carbohydrate-containing meals are consumed throughout the day. Therefore, we aimed to characterize the regulation of EGP in response to sequential meals, specifically during the breakfast-lunch transition. Nine healthy individuals (5 men, 4 women; 32 ± 2 yr; 25.0 ± 1.4 kg/m²) ingested two identical mixed meals, each containing 25 g of glucose, separated by 4 h, and EGP was determined by the variable infusion tracer-clamp approach. EGP was rapidly suppressed after both meals, with the pattern and magnitude of suppression being similar over the initial 75-min postmeal period. However, EGP suppression was more transient after breakfast compared with lunch, with EGP returning to basal rates 3 h after breakfast. In contrast, EGP remained in a suppressed state for the entire 4-h postlunch period. This occurred despite each meal eliciting similar plasma glucose and insulin responses. However, there was greater suppression of plasma glucagon levels after lunch, likely contributing to this response. These findings highlight the potential for distinct regulation of EGP with each meal of the day and suggest that EGP may be in a suppressed state for much of the day, since EGP did not return to basal rates even after a lunch meal containing a modest amount of carbohydrate.

A novel triple-tracer approach to assess postprandial protein turnover

Insulin and nutrients have profound effects on proteome homeostasis. Currently no reliable methods are available to measure postprandial protein turnover. A triple-tracer method was developed using phenylalanine stable isotope tracers to estimate appearance rates of ingested (R_{a meal}) and endogenous phenylalanine and the rate of phenylalanine disposal (R_d). This was compared with the "traditional" dual-tracer method, using one (1-CM)- and two (2-CM)-compartment models. For both methods, [¹³C₆]phenylalanine was given orally, and [¹⁵N]phenylalanine was constantly infused; the triple-tracer method added [²H₅]phenylalanine, infused at rates to mimic meal [¹³C₆]phenylalanine appearance. Additionally, incorporation of meal-derived phenylalanine into specific proteins was measured after purification by two-dimensional electrophoresis. The triple-tracer approach reduced modeling errors, allowing improved reconstruction of R_{a meal} with a tracer-to-tracee ratio that was more constant and better estimated R_d. The 2-CM better described phenylalanine kinetics and R_d than 1-CM. Thus, the triple-tracer approach using 2-CM is superior for measuring non-steady-state postprandial protein turnover. This novel approach also allows measurement of postprandial synthesis rates of specific plasma proteins. We offer a valid non-steady-state model to measure postprandial protein turnover and synthesis of plasma proteins that can safely be applied in adults, children, and pregnant women.

Measurement of postprandial glucose fluxes in response to acute and chronic endurance exercise in healthy humans

The effect of endurance exercise on enhancing insulin sensitivity and glucose flux has been well established with techniques such as the hyperinsulinemic clamp. Although informative, such techniques do not emulate the physiological postprandial state, and it remains unclear how exercise improves postprandial glycaemia. Accordingly, combining mixed-meal tolerance testing and the triple-stable isotope glucose tracer approach, glucose fluxes [rates of meal glucose appearance (Ra), disposal (Rd), and endogenous glucose production (EGP)] were determined following acute endurance exercise (1 h cycling; ~70% V̇o_2max) and 4 wk of endurance training (cycling 5 days/wk). Training was associated with a modest increase in V̇o_2max (~7%, P < 0.001). Postprandial glucose and insulin responses were reduced to the same extent following acute and chronic training. Interestingly, this was not accompanied by changes to rates of meal Ra, Rd, or degree of EGP suppression. Glucose clearance (Rd relative to prevailing glucose) was, however, enhanced with acute and chronic exercise. Furthermore, the duration of EGP suppression was shorter with acute and chronic exercise, with EGP returning toward fasting levels more rapidly than pretraining conditions. These findings suggest that endurance exercise influences the efficiency of the glucoregulatory system, where pretraining rates of glucose disposal and production were achieved at lower glucose and insulin levels. Notably, there was no influence of chronic training over and above that of a single exercise bout, providing further evidence that glucoregulatory benefits of endurance exercise are largely attributed to the residual effects of the last exercise bout.

Modelling the effect of insulin on the disposal of meal-attributable glucose in type 1 diabetes

The management of postprandial glucose excursions in type 1 diabetes has a major impact on overall glycaemic control. In this work, we propose and evaluate various mechanistic models to characterize the disposal of meal-attributable glucose. Sixteen young volunteers with type 1 diabetes were subject to a variable-target clamp which replicated glucose profiles observed after a high-glycaemic-load ([Formula: see text]) or a low-glycaemic-load ([Formula: see text]) evening meal. [6,6-[Formula: see text]] and [U-[Formula: see text];1,2,3,4,5,6,6-[Formula: see text]] glucose tracers were infused to, respectively, mimic: (a) the expected post-meal suppression of endogenous glucose production and (b) the appearance of glucose due to a standard meal. Six compartmental models (all a priori identifiable) were proposed to investigate the remote effect of circulating plasma insulin on the disposal of those glucose tracers from the non-accessible compartments, representing e.g. interstitium. An iterative population-based parameter fitting was employed. Models were evaluated attending to physiological plausibility, posterior identifiability of their parameter estimates, accuracy-via weighted fitting residuals-and information criteria (i.e. parsimony). The most plausible model, best representing our experimental data, comprised: (1) a remote effect x of insulin active above a threshold [Formula: see text] = 1.74 (0.81-2.50) [Formula: see text] min[Formula: see text] [median (inter-quartile range)], with parameter [Formula: see text] having a satisfactory support: coefficient of variation CV = 42.33 (31.34-65.34) %, and (2) steady-state conditions at the onset of the experiment ([Formula: see text]) for the compartment representing the remote effect, but not for the masses of the tracer that mimicked endogenous glucose production. Consequently, our mechanistic model suggests non-homogeneous changes in the disposal rates for meal-attributable glucose in relation to plasma insulin. The model can be applied to the in silico simulation of meals for the optimization of postprandial insulin infusion regimes in type 1 diabetes.

Accurate Measurement of Postprandial Glucose Turnover: Why Is It Difficult and How Can It Be Done (Relatively) Simply?

Fasting hyperglycemia occurs when an excessive rate of endogenous glucose production (EGP) is not accompanied by an adequate compensatory increase in the rate of glucose disappearance (Rd). The situation following food ingestion is more complex as the amount of glucose that reaches the circulation for disposal is a function of the systemic rate of appearance of the ingested glucose (referred to as the rate of meal appearance [Rameal]), the pattern and degree of suppression of EGP, and the rapidity of stimulation of the Rd In an effort to measure these processes, Steele et al. proposed what has come to be referred to as the dual-tracer method in which the ingested glucose is labeled with one tracer while a second tracer is infused intravenously at a constant rate. Unfortunately, subsequent studies have shown that although this approach is technically simple, the marked changes in plasma specific activity or the tracer-to-tracee ratio, if stable tracers are used, introduce a substantial error in the calculation of Rameal, EGP, and Rd, thereby leading to incorrect and at times misleading results. This Perspective discusses the causes of these so-called "nonsteady-state" errors and how they can be avoided by the use of the triple-tracer approach.

Direct analysis of [6,6-(2)H2]glucose and [U-(13)C6]glucose dry blood spot enrichments by LC-MS/MS

A liquid chromatography tandem mass spectrometry (LC-MS/MS) using multiple reaction monitoring (MRM) in a triple-quadrupole scan mode was developed and comprehensively validated for the determination of [6,6-(2)H2]glucose and [U-(13)C6]glucose enrichments from dried blood spots (DBS) without prior derivatization. The method is demonstrated with dried blood spots obtained from rats administered with a primed-constant infusion of [U-(13)C6]glucose and an oral glucose load enriched with [6,6-(2)H2]glucose. The sensitivity is sufficient for analysis of the equivalent to <5μL of blood and the overall method was accurate and precise for the determination of DBS isotopic enrichments.

Advancing our understanding of the glucose system via modeling: a perspective

The glucose story begins with Claude Bernard's discovery of glycogen and milieu interieur, continued with Banting's and Best's discovery of insulin and with Rudolf Schoenheimer's paradigm of dynamic body constituents. Tracers and compartmental models allowed moving to the first quantitative pictures of the system and stimulated important developments in terms of modeling methodology. Three classes of multiscale models, models to measure, models to simulate, and models to control the glucose system, are reviewed in their historical development with an eye to the future.

Absorption patterns of meals containing complex carbohydrates in type 1 diabetes

AIMS/HYPOTHESIS

Successful postprandial glycaemia management requires understanding of absorption patterns after meals containing variable complex carbohydrates. We studied eight young participants with type 1 diabetes to investigate a large low-glycaemic-load (LG) meal and another eight participants to investigate a high-glycaemic-load (HG) meal matched for carbohydrates (121 g).

METHODS

On Visit 1, participants consumed an evening meal. On follow-up Visit 2, a variable-target glucose clamp was performed to reproduce glucose and insulin levels from Visit 1. Adopting stable-label tracer dilution methodology, we measured endogenous glucose production on Visit 2 and subtracted it from total glucose appearance measured on Visit 1 to obtain meal-attributable glucose appearance.

RESULTS

After the LG meal, 25%, 50% and 75% of cumulative glucose appearance was at 88 ± 21, 175 ± 39 and 270 ± 54 min (mean ± SD), whereas glucose from the HG meal appeared significantly faster at 56 ± 12, 100 ± 25 and 153 ± 39 min (p < 0.001 to 0.003), and resulted in a 50% higher peak appearance (p < 0.001). Higher apparent bioavailability by 15% (p = 0.037) was observed after the LG meal. We documented a 20 min deceleration of dietary mixed carbohydrates compared with dietary glucose for the HG meal and a twofold deceleration for the LG meal.

CONCLUSIONS/INTERPRETATION

Absorption patterns may be influenced by glycaemic load and/or meal composition, affecting optimum prandial insulin dosing in type 1 diabetes.

Combining basal-bolus insulin infusion for tight postprandial glucose control: an in silico evaluation in adults, children, and adolescents

BACKGROUND

Achieving good postprandial glycemic control, without triggering hypoglycemia events, is a challenge of treatment strategies for type 1 diabetes subjects. Continuous subcutaneous insulin infusion, the gold standard of therapy, is based on heuristic adjustments of both basal and prandial insulin. Some tools, such as bolus calculators, are available to aid patients in selecting a meal-related insulin dose. However, they are still based on empiric parameters such as the insulin-to-carbohydrate ratio and on the physicians' and patients' ability to fit bolus mode to meal composition.

METHODS

In this article, a nonheuristic method for assessment of prandial insulin administration is presented and evaluated. An algorithm based on set inversion via interval analysis is used to coordinate basal and bolus insulin infusions to deal with postprandial glucose excursions. The evaluation is carried out through an in silico study using the 30 virtual patients available in the educational version of the Food and Drug Administration-accepted University of Virginia simulator. Results obtained using the standard bolus strategy and different coordinated basal-bolus solutions provided by the algorithm are compared.

RESULTS

Coordinated basal-bolus solutions improve postprandial glucose performance in most cases, mainly in terms of reducing hypoglycemia risk, but also increasing the percentage of time in normoglycemia. Moreover, glycemic variability is reduced considerably by using these innovative solutions.

CONCLUSIONS

The algorithm presented here is a robust nonheuristic alternative to deal with postprandial glycemic control. It is shown as a powerful tool that could be integrated in future smart insulin pumps.

beta-Cell function and insulin sensitivity in adolescents from an OGTT

Given the increase in the incidence of insulin resistance, obesity, and type 2 diabetes in children and adolescents, it would be of paramount importance to assess quantitative indices of insulin secretion and action during a physiological perturbation, such as a meal or an oral glucose-tolerance test (OGTT). A minimal model method is proposed to measure quantitative indices of insulin secretion and action in adolescents from an oral test. A 7 h, 21-sample OGTT was performed in 11 adolescents. The C-peptide minimal model was identified on C-peptide and glucose data to quantify indices of beta-cell function: static phi(s) and dynamic phi(d) responsivity to glucose from which total responsivity phi was also measured. The glucose minimal model was identified on glucose and insulin data to estimate insulin sensitivity, S(I), which was compared to a reference measure, S(I)(ref), provided by a tracer method. Disposition indices, which adjust insulin secretion for insulin action, were then calculated. Indices of beta-cell function were phi(s) = 51.35 +/- 8.89 x 10(-9)min(-1), phi(d) = 1,392 +/- 258 x 10(-9), and phi = 82.09 +/- 17.70 x 10(-9)min(-1). Insulin sensitivity was S(I) = 14.19 +/- 2.73 x 10(-4), not significantly different from S(I)(ref) = 14.96 +/- 3.04 x 10(-4) dl/kg.min per microU/ml, and well correlated: r = 0.98, P < 0.0001, thus indicating that S(I) can be accurately measured from an oral test. Disposition indices were DI(s) = 1,040 +/- 201 x 10(-14) dl/kg/min(2) per pmol/l, DI(d) = 33,178 +/- 10,720 x 10(-14) dl/kg/min per pmol/l, DI = 1,844 +/- 522 x 10(-14) dl/kg/min(2) per pmol/l. Virtually the same minimal model assessment was obtained with a reduced 3 h, 9-sample protocol. OGTT interpreted with C-peptide and glucose minimal model has the potential to provide novel insight regarding the regulation of glucose metabolism in adolescents, and to evaluate the effect of obesity and interventions such as diet and exercise.

Diabetes: Models, Signals, and Control

The control of diabetes is an interdisciplinary endeavor, which includes a significant biomedical engineering component, with traditions of success beginning in the early 1960s. It began with modeling of the insulin-glucose system, and progressed to large-scale in silico experiments, and automated closed-loop control (artificial pancreas). Here, we follow these engineering efforts through the last, almost 50 years. We begin with the now classic minimal modeling approach and discuss a number of subsequent models, which have recently resulted in the first in silico simulation model accepted as substitute to animal trials in the quest for optimal diabetes control. We then review metabolic monitoring, with a particular emphasis on the new continuous glucose sensors, on the analyses of their time-series signals, and on the opportunities that they present for automation of diabetes control. Finally, we review control strategies that have been successfully employed in vivo or in silico, presenting a promise for the development of a future artificial pancreas and, in particular, discuss a modular architecture for building closed-loop control systems, including insulin delivery and patient safety supervision layers. We conclude with a brief discussion of the unique interactions between human physiology, behavioral events, engineering modeling and control relevant to diabetes.