A Model for the Estimation of Hepatic Insulin Extraction After a Meal

Modeling Glucose, Insulin, C-Peptide, and Lactate Interplay in Adolescents During an Oral Glucose Tolerance Test

BACKGROUND

Lactate is not considered just a "waste product" of anaerobic glycolysis anymore. It has been proved to play a key role in several metabolic diseases, such as in the metabolic dysfunction-associated steatotic liver disease, obesity, and diabetes. The capability of simulating glucose-insulin-lactate interaction would be useful to design and test drugs targeting lactate metabolism in such pathological conditions. Minimal models are available, which describe and quantify glucose-lactate interaction but models to simulate postprandial glucose-insulin-C-peptide-lactate time courses are missing. The aim of this study is to fill this gap.

METHODS

Starting from the Padova Type 2 Diabetes Simulator (T2DS), we first added a description of glucose-lactate kinetics and then created a population of 100 in silico subjects to match glucose-insulin-C-peptide-lactate data of 44 adolescents with/without obesity who underwent a standard oral glucose tolerance test (OGTT) of 75 g.

RESULTS

The developed model accurately predicts all molecules time courses, guaranteeing precise model parameter estimates (percent coefficient of variation [CV%] median [25th-75th percentile] = 19 [9-29]%). The generated in silico population shows good agreement with the clinical data in terms of area under the curve (AUC) (P = .6, .6, .9, .6 for glucose, insulin, C-peptide, and lactate, respectively) and parameter distributions (P > .1).

CONCLUSIONS

We have developed a simulator to describe glucose, insulin, C-peptide, and lactate kinetics during an OGTT, which captures the behavior of a real population of adolescents with/without obesity both in terms of average and intersubject variability. Such simulator can be used to investigate the pharmacodynamics of drugs targeting lactate metabolic pathway in various pathological conditions.

A pathway model of glucose-stimulated insulin secretion in the pancreatic β-cell

The pancreas plays a critical role in maintaining glucose homeostasis through the secretion of hormones from the islets of Langerhans. Glucose-stimulated insulin secretion (GSIS) by the pancreatic β-cell is the main mechanism for reducing elevated plasma glucose. Here we present a systematic modeling workflow for the development of kinetic pathway models using the Systems Biology Markup Language (SBML). Steps include retrieval of information from databases, curation of experimental and clinical data for model calibration and validation, integration of heterogeneous data including absolute and relative measurements, unit normalization, data normalization, and model annotation. An important factor was the reproducibility and exchangeability of the model, which allowed the use of various existing tools. The workflow was applied to construct a novel data-driven kinetic model of GSIS in the pancreatic β-cell based on experimental and clinical data from 39 studies spanning 50 years of pancreatic, islet, and β-cell research in humans, rats, mice, and cell lines. The model consists of detailed glycolysis and phenomenological equations for insulin secretion coupled to cellular energy state, ATP dynamics and (ATP/ADP ratio). Key findings of our work are that in GSIS there is a glucose-dependent increase in almost all intermediates of glycolysis. This increase in glycolytic metabolites is accompanied by an increase in energy metabolites, especially ATP and NADH. One of the few decreasing metabolites is ADP, which, in combination with the increase in ATP, results in a large increase in ATP/ADP ratios in the β-cell with increasing glucose. Insulin secretion is dependent on ATP/ADP, resulting in glucose-stimulated insulin secretion. The observed glucose-dependent increase in glycolytic intermediates and the resulting change in ATP/ADP ratios and insulin secretion is a robust phenomenon observed across data sets, experimental systems and species. Model predictions of the glucose-dependent response of glycolytic intermediates and biphasic insulin secretion are in good agreement with experimental measurements. Our model predicts that factors affecting ATP consumption, ATP formation, hexokinase, phosphofructokinase, and ATP/ADP-dependent insulin secretion have a major effect on GSIS. In conclusion, we have developed and applied a systematic modeling workflow for pathway models that allowed us to gain insight into key mechanisms in GSIS in the pancreatic β-cell.

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.

Modeling Intraperitoneal Insulin Absorption in Patients with Type 1 Diabetes

Standard insulin therapy to treat type 1 diabetes (T1D) consists of exogenous insulin administration through the subcutaneous (SC) tissue. Despite recent advances in insulin formulations, the SC route still suffers from delays and large inter/intra-subject variability that limiting optimal glucose control. Intraperitoneal (IP) insulin administration, despite its higher invasiveness, was shown to represent a valid alternative to the SC one. To date, no mathematical model describing the absorption and distribution of insulin after IP administration is available. Here, we aim to fill this gap by using data from eight patients with T1D, treated by implanted IP pump, studied in a hospitalized setting, with frequent measurements of plasma insulin and glucose concentration. A battery of models describing insulin kinetics after IP administration were tested. Model comparison and selection were performed based on model ability to predict the data, precision of parameters and parsimony criteria. The selected model assumed that the insulin absorption from the IP space was described by a linear, two-compartment model, coupled with a two-compartment model of whole-body insulin kinetics with hepatic insulin extraction controlled by hepatic insulin. Future developments include model incorporation into the UVa/Padova T1D Simulator for testing open- and closed-loop therapies with IP insulin administration.

Limitations of the fasting proinsulin to insulin ratio as a measure of β-cell health in people with and without impaired glucose tolerance

BACKGROUND

The fasting proinsulin to insulin ratio is elevated in people with type 2 diabetes and has been suggested as a marker of β-cell health. However, its utility in discriminating between individuals with varying degrees of β-cell dysfunction is unclear. Proinsulin has a very different half-life to insulin and unlike insulin does not undergo hepatic extraction prior to reaching the systemic circulation. Given these limitations, we sought to examine the relationship between fasting and postprandial concentrations of β-cell polypeptides (proinsulin, insulin and C-peptide) in people with normal and impaired glucose tolerance in differing metabolic environments.

DESIGN

Subjects were studied on two occasions in random order while undergoing an oral challenge. During one study day, free fatty acids were elevated (to induce insulin resistance) by infusion of Intralipid with heparin. Proinsulin to insulin and proinsulin to C-peptide ratios were calculated for the 0-, 30-, 60- and 240-minute time points. Insulin action (Si) and β-cell responsivity (Φ) indices were calculated using the oral minimal model.

RESULTS

The fasting proinsulin to c-peptide or fasting proinsulin to insulin ratios did not differ between groups and did not predict subsequent β-cell responsivity to glucose during the glycerol or Intralipid study days in either group.

CONCLUSIONS

Among nondiabetic individuals, the fasting proinsulin to insulin ratio is not a useful marker of β-cell function.

The Padova Type 2 Diabetes Simulator from Triple-Tracer Single-Meal Studies: In Silico Trials Also Possible in Rare but Not-So-Rare Individuals

Background:In silico trials in type 2 diabetes (T2D) would be useful for testing diabetes treatments and accelerating the development of new antidiabetic drugs. In this study, we present a T2D simulator able to reproduce the variability observed in a T2D population. The simulator also allows to safely experiment on virtual subjects with severe (and possibly rare) pathological conditions. Methods: A meal simulation model of glucose, insulin, and C-peptide systems, made of 15 differential equations and 39 parameters, has been identified using a system decomposition and forcing function Bayesian strategy on data of 51 T2D subjects undergoing a single triple-tracer mixed meal. One hundred T2D in silico subjects have been generated from the joint distribution of estimated model parameters. A case study is presented to illustrate the simulator use for testing a virtual drug (improving insulin action and secretion) in a subpopulation of rare, extremely impaired, T2D subjects. Results: The model well fitted T2D data and parameters were estimated with precision. Simulated plasma glucose, insulin, and C-peptide well matched the data (e.g., median [25^th-75^th percentile] glucose area under the curves of 6.9 [6.1-8.5] 10⁴ mg/dL·min in silico vs. 7.0 [5.6-8.2] 10⁴ mg/dL·min in vivo). The potential use of the simulator was shown in a case study, in which the (virtual) antidiabetic drug dose was optimized for very insulin-resistant T2D subjects. Conclusions: We have developed a T2D simulator that captures the behavior of T2D population during a meal, both in terms of average and intersubject variability. The simulator represents a cost-effective way to test new antidiabetic drugs, before moving to human trials.

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.

The Measurement of Insulin Clearance

Insulin clearance has recently been highlighted as a fundamental aspect of glucose metabolism, as it has been hypothesized that its impairment could be related to an increased risk of developing type 2 diabetes. This review focuses on methods used to calculate insulin clearance: from the early surrogate indices employing C-peptide:insulin molar ratio, to direct measurement methods used in animal models, to modeling-based techniques to estimate the components of insulin clearance (hepatic versus extrahepatic). The methods are explored and interpreted by critically highlighting advantages and limitations.

Type 2 diabetes: one disease, many pathways

Diabetes is a chronic, progressive disease that calls for longitudinal data and analysis. We introduce a longitudinal mathematical model that is capable of representing the metabolic state of an individual at any point in time during their progression from normal glucose tolerance to type 2 diabetes (T2D) over a period of years. As an application of the model, we account for the diversity of pathways typically followed, focusing on two extreme alternatives, one that goes through impaired fasting glucose (IFG) first and one that goes through impaired glucose tolerance (IGT) first. These two pathways are widely recognized to stem from distinct metabolic abnormalities in hepatic glucose production and peripheral glucose uptake, respectively. We confirm this but go beyond to show that IFG and IGT lie on a continuum ranging from high hepatic insulin resistance and low peripheral insulin resistance to low hepatic resistance and high peripheral resistance. We show that IFG generally incurs IGT and IGT generally incurs IFG on the way to T2D, highlighting the difference between innate and acquired defects and the need to assess patients early to determine their underlying primary impairment and appropriately target therapy. We also consider other mechanisms, showing that IFG can result from impaired insulin secretion, that non-insulin-dependent glucose uptake can also mediate or interact with these pathways, and that impaired incretin signaling can accelerate T2D progression. We consider whether hyperinsulinemia can cause insulin resistance in addition to being a response to it and suggest that this is a minor effect.

Chatteringfree hybrid adaptive neuro-fuzzy inference system-particle swarm optimisation data fusion-based BG-level control

In this study, a closed-loop control scheme is proposed for the glucose-insulin regulatory system in type-1 diabetic mellitus (T1DM) patients. Some innovative hybrid glucose-insulin regulators have combined artificial intelligence such as fuzzy logic and genetic algorithm with well known Palumbo model to regulate the blood glucose (BG) level in T1DM patients. However, most of these approaches have focused on the glucose reference tracking, and the qualitative of this tracking such as chattering reduction of insulin injection has not been well-studied. Higher-order sliding mode (HoSM) controllers have been employed to attenuate the effect of chattering. Owing to the delayed nature and non-linear property of glucose-insulin mechanism as well as various unmeasurable disturbances, even the HoSM methods are partly successful. In this study, data fusion of adaptive neuro-fuzzy inference systems optimised by particle swarm optimisation has been presented. The excellent performance of the proposed hybrid controller, i.e. desired BG-level tracking and chattering reduction in the presence of daily glucose-level disturbances is verified.

Online Glucose Prediction Using Computationally Efficient Sparse Kernel Filtering Algorithms in Type-1 Diabetes

Streaming data from continuous glucose monitoring (CGM) systems enable the recursive identification of models to improve estimation accuracy for effective predictive glycemic control in patients with type-1 diabetes. A drawback of conventional recursive identification techniques is the increase in computational requirements, which is a concern for online and real-time applications such as the artificial pancreas systems implemented on handheld devices and smartphones where computational resources and memory are limited. To improve predictions in such computationally constrained hardware settings, efficient adaptive kernel filtering algorithms are developed in this paper to characterize the nonlinear glycemic variability by employing a sparsification criterion based on the information theory to reduce the computation time and complexity of the kernel filters without adversely deteriorating the predictive performance. Furthermore, the adaptive kernel filtering algorithms are designed to be insensitive to abnormal CGM measurements, thus compensating for measurement noise and disturbances. As such, the sparsification-based real-time model update framework can adapt the prediction models to accurately characterize the time-varying and nonlinear dynamics of glycemic measurements. The proposed recursive kernel filtering algorithms leveraging sparsity for improved computational efficiency are applied to both in-silico and clinical subjects, and the results demonstrate the effectiveness of the proposed methods.

MALDI-TOF mass spectrometry-based quantification of C-peptide in diabetes patients

BACKGROUND

Serum C-peptide concentrations reflect insulin secretion and beta cell function and can be used to diagnose and distinguish type-1 and type-2 diabetes. C-peptide is a more accurate indicator of insulin status than direct insulin measurement for monitoring patients with diabetes. However, the current methods available for C-peptide quantification exhibit poor reproducibility, are costly, and require highly trained laboratory personnel. Here, we have developed and evaluated a matrix-assisted laser desorption ionization time-of-flight mass spectrometry (MALDI-TOF MS)-based assay to standardize C-peptide measurements, providing highly accurate and comparable results across testing systems and laboratories.

METHODS

C-peptide from human serum was enriched using antibody-conjugated magnetic beads. The eluted isolates were further modified with 6-aminoquinolyl-N-hydroxysuccinimidyl carbamate (AQC) to enhance the ionization of naturally acidic C-peptide. After desalting with ZipTips, the samples were subjected to MALDI-TOF MS analysis. Recombinant human C-peptide was used to develop the assay, and a heavy isotope labeled human C-peptide was used as an internal standard for quantification.

RESULTS

The MALDI-TOF MS method was validated in accordance with the restrictions of the device, with a limit of quantitation of 25 pmol/L. A correlation between the MAL-DI-TOF MS assay and a reference method was conducted using patient samples. The resulting regression revealed good agreement.

CONCLUSIONS

A simple, high-throughput, cost effective and quantitative MALDI-TOF MS C-peptide assay has been successfully developed and validated in clinical serum samples.

Postprandial Insulin Response and Clearance Among Black and White Women: The Federal Women's Study

CONTEXT

Postprandial hyperinsulinemia might be an important cardiometabolic risk determinant in black compared with white women. However, the contributions of insulin clearance and β-cell function to racial differences in postprandial insulin response are unknown.

OBJECTIVE

To compare, by race and menopause, early insulin response to oral and intravenous glucose and to measure postprandial intact glucagon-like peptide 1 (GLP-1) concentrations, insulin clearance, and β-cell function.

DESIGN AND PARTICIPANTS

119 federally employed women without diabetes [87 premenopausal (52 black, 35 white) and 32 postmenopausal (19 black, 13 white)] underwent an oral glucose tolerance test, insulin-modified frequently sampled intravenous glucose test (IM-FSIGT), and mixed meal tolerance test (MMTT).

OUTCOME MEASURES

Early insulin response was measured as follows: (i) insulinogenic index (oral glucose tolerance test); (ii) acute insulin response to glucose (IM-FSIGT); and (iii) ratio of incremental insulin/glucose area under the curve in the first 30 minutes of the MMTT. Insulin clearance was assessed during the IM-FSIGT and MMTT. During the MMTT, intact GLP-1 was measured and β-cell function assessed using the insulin secretion rate and β-cell responsivity indexes.

RESULTS

Black pre-menopausal and postmenopausal women had a greater insulin response and lower insulin clearance and greater dynamic β-cell responsivity (P ≤ 0.05 for all). No differences were found in the total insulin secretion rates or intact GLP-1 concentrations.

CONCLUSIONS

Greater postprandial hyperinsulinemia in black pre-menopausal and postmenopausal women was associated with lower hepatic insulin clearance and heightened β-cell capacity to rapid changes in glucose, but not to higher insulin secretion. The relationship of increased β-cell secretory capacity, reduced insulin clearance, and ambient hyperinsulinemia to the development of cardiometabolic disease requires further investigation.

Dissection of hepatic versus extra-hepatic insulin clearance: Ethnic differences in childhood

AIMS

Adult African American (AA) women have one third of the hepatic insulin clearance of European American (EA) women. This lower hepatic (but not extra-hepatic) insulin clearance in AA individuals is associated with higher plasma insulin concentrations. This study aims to understand whether impairment of hepatic insulin clearance is seen in AA individuals since childhood, possibly suggesting that genetic/epigenetic factors, rather than lifestyle only, contribute to this.

MATERIALS AND METHODS

A total of 203 children (105 male and 98 female (55 AA, 88 EA and 60 Hispanic American [HA]; ages, 7-13 years; mean BMI, 19 kg/m² )) underwent the frequently applied intravenous glucose tolerance test (FSIGT) at the University of Alabama at Birmingham, General Clinical Research Center and Department of Nutrition Sciences. Glucose, insulin and C-peptide levels were measured and hepatic and extra-hepatic insulin clearances were calculated using mathematical modelling.

RESULTS

Fractional hepatic insulin extraction (FE_L ) was lower in AA than in EA children (mean (SD), 19% (20%) vs 33% (20%); P = 0.0007). Adjusting for age, Tanner stage and body fat, FE_L was lower in AA than in EA children (P = 0.0012), and there was a slight sex-related difference (FE_L, 24% (10%) vs 29% (10%) in boys vs girls; P = 0.04). Extra-hepatic insulin clearance did not differ with ethnicity (27 (12), 21 (12) and 24 (28) mL/kg/min for AA, HA and EA children, respectively; P > 0.05).

CONCLUSIONS

At a young age, FE_L is lower in AAs than in EAs, which does not rule out genetic/epigenetic factors. These differences are related to hyperinsulinaemia and, over time, could possibly contribute to metabolic disorders in AA individuals.

Quantitative path to deep phenotyping: Possible importance of reduced hepatic insulin degradation to type 2 diabetes mellitus pathogenesis

Diabetes is often thought of as one of two diseases: Type 1 diabetes (T1D), which is caused by immunological destruction of the beta-cells, and Type 2 diabetes (T2D), which is due to a combination of insulin resistance and relative failure of the beta-cells to compensate for the resistance. It is becoming clear, however, that even within these two definitions there may be considerable heterogeneity (1). There are several approaches to examine heterogeneity of T2D. Among these approaches are the use of biomarkers to categorize the disease, or the examination of variants in the genome. A third approach – the one we have been using in our laboratory – is to identify specific phenotypes which may contribute to failure to regulate the glucose level. We have identified a small group of such phenotypes which can be distinguished and measured using clinical protocols and/or mathematical modeling.

Model-Fusion-Based Online Glucose Concentration Predictions in People with Type 1 Diabetes

Accurate predictions of glucose concentrations are necessary to develop an artificial pancreas (AP) system for people with type 1 diabetes (T1D). In this work, a novel glucose forecasting paradigm based on a model fusion strategy is developed to accurately characterize the variability and transient dynamics of glycemic measurements. To this end, four different adaptive filters and a fusion mechanism are proposed for use in the online prediction of future glucose trajectories. The filter fusion mechanism is developed based on various prediction performance indexes to guide the overall output of the forecasting paradigm. The efficiency of the proposed model fusion based forecasting method is evaluated using simulated and clinical datasets, and the results demonstrate the capability and prediction accuracy of the data-based fusion filters, especially in the case of limited data availability. The model fusion framework may be used in the development of an AP system for glucose regulation in patients with T1D.

Hepatic but Not Extrahepatic Insulin Clearance Is Lower in African American Than in European American Women

African Americans (AAs) tend to have higher plasma insulin concentrations than European Americans (EAs); the increased insulin concentrations have been attributed to increased secretion and/or decreased insulin clearance by liver or other tissues. This work characterizes the contributions of hepatic versus extrahepatic insulin degradation related to ethnic differences between AAs and EAs. By using a recently developed mathematical model that uses insulin and C-peptide measurements from the insulin-modified, frequently sampled intravenous glucose tolerance test (FSIGT), we estimated hepatic versus extrahepatic insulin clearance in 29 EA and 18 AA healthy women. During the first 20 min of the FSIGT, plasma insulin was approximately twice as high in AAs as in EAs. In contrast, insulin was similar in AAs and EAs after the 20-25 min intravenous insulin infusion. Hepatic insulin first-pass extraction was two-thirds lower in AAs versus EAs in the overnight-fasted state. In contrast, extrahepatic insulin clearance was not lower in AAs than in EAs. The difference in insulin degradation between AAs and EAs can be attributed totally to liver clearance. The mechanism underlying reduced insulin degradation in AAs remains to be clarified, as does the relative importance of reduced liver clearance to increased risk for type 2 diabetes.