An integrated glucose-insulin model to describe oral glucose tolerance test data in type 2 diabetics

Differential expression of coagulation pathway-related proteins in diabetic urine exosomes

BACKGROUND

Coagulation function monitoring is important for the occurrence and development of diabetes. A total of 16 related proteins are involved in coagulation, but how these proteins change in diabetic urine exosomes is unclear. To explore the expression changes of coagulation-related proteins in urine exosomes and their possible roles in the pathogenesis of diabetes, we performed proteomic analysis and finally applied them to the noninvasive monitoring of diabetes.

METHODS

Subject urine samples were collected. LC-MS/MS was used to collect the information on coagulation-related proteins in urine exosomes. ELISA, mass spectrometry and western blotting were used to further verify the differential protein expression in urine exosomes. Correlations with clinical indicators were explored, and receiver operating characteristic (ROC) curves were drawn to evaluate the value of differential proteins in diabetes monitoring.

RESULTS

Analyzing urine exosome proteomics data, eight coagulation-related proteins were found in this study. Among them, F2 was elevated in urine exosomes of diabetic patients compared with healthy controls. The results of ELISA, mass spectrometry and western blotting further verified the changes in F2. Correlation analysis showed that the expression of urine exosome F2 was correlated with clinical lipid metabolism indexes, and the concentration of F2 was strongly positively correlated with blood TG levels (P < 0.05). ROC curve analysis showed that F2 protein in urine exosomes had a good monitoring value for diabetes.

CONCLUSION

Coagulation-related proteins were expressed in urine exosomes. Among them, F2 was increased in diabetic urine exosomes and may be a potential biomarker for monitoring diabetic changes.

A mechanistic modeling platform of SGLT2 inhibition: Implications for type 1 diabetes

Type 1 diabetes mellitus (T1DM) is an autoimmune disease characterized by abnormally high blood glucose concentrations due to dysfunction of the insulin-producing beta-cells in the pancreas. Dapagliflozin, an inhibitor of renal glucose reabsorption, has the potential to improve often suboptimal glycemic control in patients with T1DM through insulin-independent mechanisms and to partially mitigate the adverse effects associated with long-term insulin administration. In this work, we have adapted a systems pharmacology model of type 2 diabetes mellitus to describe the T1DM condition and characterize the effect of dapagliflozin on short- and long-term glycemic markers under various treatment scenarios. The developed platform serves as a quantitative tool for the in silico evaluation of the insulin-glucose-dapagliflozin crosstalk, optimization of the treatment regimens, and it can be further expanded to include additional therapies or other aspects of the disease.

Impact of Obesity on Postprandial Triglyceride Contribution to Glucose Homeostasis, Assessed with a Semimechanistic Model

The integrated glucose-insulin model is a semimechanistic model describing glucose and insulin after a glucose challenge. Similarly, a semiphysiologic model of the postprandial triglyceride (TG) response in chylomicrons and VLDL-V6 was recently published. We have developed the triglyceride-insulin-glucose-GLP-1 (TIGG) model by integrating these models and active GLP-1. The aim was to characterize, using the TIGG model, the postprandial response over 13 hours following a high-fat meal in 3 study populations based on body mass index categories: lean, obese, and very obese. Differential glucose and lipid regulation were observed between the lean population and obese or very obese populations. A population comparison revealed further that fasting glucose and insulin were elevated in obese and very obese when compared with lean; and euglycemia was achieved at different times postmeal between the obese and very obese populations. Postprandial insulin was incrementally elevated in the obese and very obese populations compared with lean. Postprandial chylomicrons TGs were similar across populations, whereas the postprandial TGs in VLDL-V6 were increased in the obese and very obese populations compared with lean. Postprandial active GLP-1 was diminished in the very obese population compared with lean or obese. The TIGG model described the response following a high-fat meal in individuals who are lean, obese, and very obese and provided insight into the possible regulation of glucose homeostasis in the extended period after the meal by utilizing lipids. The TIGG-model is the first model to integrate glucose and insulin regulation, incretin effect, and postprandial TGs response in chylomicrons and VLDL-V6.

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.

Pharmacometrics Approaches and its Applications in Diabetes: An Overview

Type 2 diabetes mellitus is the most prevalent and progressive in nature. As the time progress, the multifaceted complications and comorbidities associated to diabetes worsen in the form of macrovascular or microvascular or both. Pharmacometrics modeling is a step forward in minimizing the risk or at least understanding the factors associated to its progression with the passage of time. These models investigate diabetes treatments effects and the progression factors with different viewpoints incorporating insulin-glucose dynamics, dose-response and pharmacokinetics, and pharmacodynamics relationships. Pharmacometrics modeling is an innovative approach in a sense that it is taking us away from the conventional analysis by providing all the opportunities in improving the decision-making in health sector. It has been suggested that we can achieve greater statistical power for determining drug effects through model-based evaluation than through traditional evaluations. The main aim of this review was to evaluate pharmacometrics approaches used in modeling diabetes progression through time and also the integrated models describing glucose-insulin dynamics.

An Updated Organ-Based Multi-Level Model for Glucose Homeostasis: Organ Distributions, Timing, and Impact of Blood Flow

Glucose homeostasis is the tight control of glucose in the blood. This complex control is important, due to its malfunction in serious diseases like diabetes, and not yet sufficiently understood. Due to the involvement of numerous organs and sub-systems, each with their own intra-cellular control, we have developed a multi-level mathematical model, for glucose homeostasis, which integrates a variety of data. Over the last 10 years, this model has been used to insert new insights from the intra-cellular level into the larger whole-body perspective. However, the original cell-organ-body translation has during these years never been updated, despite several critical shortcomings, which also have not been resolved by other modeling efforts. For this reason, we here present an updated multi-level model. This model provides a more accurate sub-division of how much glucose is being taken up by the different organs. Unlike the original model, we now also account for the different dynamics seen in the different organs. The new model also incorporates the central impact of blood flow on insulin-stimulated glucose uptake. Each new improvement is clear upon visual inspection, and they are also supported by statistical tests. The final multi-level model describes >300 data points in >40 time-series and dose-response curves, resulting from a large variety of perturbations, describing both intra-cellular processes, organ fluxes, and whole-body meal responses. We hope that this model will serve as an improved basis for future data integration, useful for research and drug developments within diabetes.

The tryptic peptides of hemoglobin for diagnosis of type 2 diabetes mellitus using label-free and standard-free LC-ESI-DMRM

N-1-(deoxyfructosyl) valine of β-hemoglobin, commonly referred to as HbA1c, is the “gold standard” for clinical detection of diabetes. Instead of quantifying the full-length HbA1c glycated protein, in the present study, we proposed the peptide-based strategy to quantify the depletion of the tryptic peptides of hemoglobin for the diagnosis of type 2 diabetes mellitus (T2DM). The peptides were discovered and validated as T2DM biomarkers by label-free LC-ESI-DMRM method without reference material. The glucose could react with hemoglobin's free amino group of N-terminus and ϵ-amino group of lysine residues and leave the modification on the hemoglobin tryptic peptides. Thus, there are two types of peptides in the hemoglobin: sensitive peptides and insensitive peptides to glucose due to the differential sensitivity of lysine residues to glycation. To discover two types of peptides of hemoglobin, we first developed the assay of liquid chromatography-electrospray ionization mass spectrometry coupled with dynamic multiple reaction monitoring. The protein coverage reaches 94.2%. Moreover, the hemoglobin was incubated with the 500 mmol/L glucose for 20 days, 40 days and 60 days in vitro to screen the sensitive peptides and insensitive peptides to glucose. A total of 14 sensitive peptides and 4 insensitive peptides were discovered. Furthermore, the LC-ESI-DMRM method was also utilized to validated the glucose-sensitive peptides by 40 clinical samples with healthy control individuals (n = 20) and type 2 diabetes mellitus patients (n = 20). Three putative sensitive peptides (LLGNVLVCVLAHHFGK, VVAGVANALAHKYH, LRVDPVNFK) from the hemoglobin showed excellent sensitivity and specificity based on receiver operating characteristic analysis and were verified as the promising biomarkers for the diagnosis of diabetes mellitus. And one peptide (LLVVYPWTQR) was found as glucose-insensitive peptide. Taken together, the findings of this study suggest that quantification of hemoglobin tryptic peptides using label-free and standard-free LC-ESI-DMRM is an alternative method for the diagnosis of T2DM, which could be combined with other MS-based blood biomarkers for diagnosis of multiple diseases in MS single shot.

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The peptide-based strategy is proposed to quantify the depletion of peptides of hemoglobin for the diagnosis of T2DM.

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Three glucose-sensitive peptides of hemoglobin are expected to become the putative biomarkers for T2DM.

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The peptide VVAGVANALAHKYH shows excellent sensitivity and specificity to classify between healthy group and T2DM group.

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The label-free and standard-free assay is very simple and suitable for clinical diagnosis of T2DM.

A model-based approach to investigating the relationship between glucose-insulin dynamics and dapagliflozin treatment effect in patients with type 2 diabetes

AIMS

To develop a quantitative systems pharmacology model to describe the effect of dapagliflozin (a sodium-glucose co-transporter-2 [SGLT2] inhibitor) on glucose-insulin dynamics in type 2 diabetes mellitus (T2DM) patients, and to identify key determinants of treatment-mediated glycated haemoglobin (HbA1c) reduction.

MATERIALS AND METHODS

Glycaemic control during dapagliflozin treatment was mechanistically characterized by integrating components representing dapagliflozin pharmacokinetics (PK), glucose-insulin homeostasis, renal glucose reabsorption, and HbA1c formation. The model was developed using PK variables, glucose, plasma insulin, and urinary glucose excretion (UGE) from a phase IIa dapagliflozin trial in patients with T2DM (NCT00162305). The model was used to predict dapagliflozin-induced HbA1c reduction; model predictions were compared to actual data from phase III trials (NCT00528879, NCT00683878, NCT00680745 and NCT00673231).

RESULTS

The integrated glucose-insulin-dapagliflozin model successfully described plasma glucose and insulin levels, as well as UGE in response to oral glucose tolerance tests and meal intake. HbA1c reduction was also well predicted. The results show that dapagliflozin-mediated glycaemic control is anticorrelated to steady-state insulin concentration and insulin sensitivity.

CONCLUSIONS

The developed model framework is the first to integrate SGLT2 inhibitor mechanism of action with both short-term glucose-insulin dynamics and long-term glucose control (HbA1c). The results suggest that dapagliflozin treatment is beneficial in patients with inadequate glycaemic control from insulin alone and this benefit increases as insulin control diminishes.

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.

Evolving data analysis of an Oral Lipid Tolerance Test toward the standard for the Oral Glucose Tolerance Test: Cross species modeling effects of AZD7687 on plasma triacylglycerol

We have developed a novel mechanistic pharmacokinetic-pharmacodynamic (PK/PD) model to describe the time course of plasma triglyceride (TAG) after Oral Lipid Tolerance Test (OLTT) and the effects of AZD7687, an inhibitor of diacylglycerol acyltransferase 1 (DGAT1), in humans, rats, and mice. Pharmacokinetic and plasma TAG data were obtained both in animals and in two phase I OLTT studies. In the PK/PD model, the introduction of exogenous TAG is represented by a first order process. The endogenous production and removal of TAG from plasma are described with a turnover model. AZD7687 inhibits the contribution of exogenous TAG into circulation. One or two compartment models with first order absorption was used to describe the PK of AZD7687 for the different species. Nonlinear mixed effect modeling was used to fit the model to the data. The effects of AZD7687 on the plasma TAG time course during an OLTT as well as interindividual variability were well described by the model in all three species. Meal fat content or data from single vs repeated dosing did not affect model parameter estimates. Body mass index was found to be a significant covariate on the plasma TAG baseline. The system parameters of the model will facilitate analysis for other compounds and provide tools to bring the standard of OLTT data analysis closer to the analyses of Oral Glucose Tolerance Test data maximizing knowledge gain.

Toward Better Understanding of Insulin Therapy by Translation of a PK-PD Model to Visualize Insulin and Glucose Action Profiles

Insulin replacement therapy is a fundamental treatment for glycemic control for managing diabetes. The engineering of insulin analogues has focused on providing formulations with action profiles that mimic as closely as possible the pattern of physiological insulin secretion that normally occurs in healthy individuals without diabetes. Hence, it may be helpful to practitioners to visualize insulin concentration profiles and associated glucose action profiles. Expanding on a previous analysis that established a pharmacokinetic (PK) model to describe typical profiles of insulin concentration over time following subcutaneous administration of various insulin formulations, the goal of the current analysis was to link the PK model to an integrated glucose‐insulin (IGI) systems pharmacology model. After the pharmacokinetic‐pharmacodynamic (PK‐PD) model was qualified by comparing model predictions with clinical observations, it was used to project insulin (PK) and glucose (PD) profiles of common insulin regimens and dosing scenarios. The application of the PK‐PD model to clinical scenarios was further explored by incorporating the impact of several hypothetical factors together, such as changing the timing or frequency of administration in a multiple‐dosing regimen over the course of a day, administration of more than 1 insulin formulation, or insulin dosing adjusted for carbohydrates in meals. Visualizations of insulin and glucose profiles for commonly prescribed regimens could be rapidly generated by implementing the linked subcutaneous insulin PK‐IGI model using the R statistical program (version 3.4.4) and a contemporary web‐based interface, which could enhance clinical education on glycemic control with insulin therapy.

Study Design Selection in Early Clinical Anti-Hyperglycemic Drug Development: A Simulation Study of Glucose Tolerance Tests

In antidiabetic drug development, phase I studies usually involve short‐term glucose provocations. Multiple designs are available for these provocations (e.g., meal tolerance tests (MTTs) and graded glucose infusions (GGIs)). With a highly nonlinear, complex system as the glucose homeostasis, the various provocations will contribute with different information offering a rich choice. Here, we investigate the most appropriate study design in phase I for several hypothetical mechanisms of action of a study drug. Five drug effects in diabetes therapeutic areas were investigated using six study designs. Power to detect drug effect was assessed using the likelihood ratio test, whereas precision and accuracy of the quantification of drug effect was assessed using stochastic simulation and estimations. An overall summary was developed to aid designing the studies of antihyperglycemic drug development using model‐based analysis. This guidance is to be used when the integrated glucose insulin model is used, involving the investigated drug mechanisms of action.

Comparison of Power, Prognosis, and Extrapolation Properties of Four Population Pharmacodynamic Models of HbA1c for Type 2 Diabetes

Reusing published models saves time; time to be used for informing decisions in drug development. In antihyperglycemic drug development, several published HbA1c models are available but selecting the appropriate model for a particular purpose is challenging. This study aims at helping selection by investigating four HbA1c models, specifically the ability to identify drug effects (shape, site of action, and power) and simulation properties. All models could identify glucose effect nonlinearities, although for detecting the site of action, a mechanistic glucose model was needed. Power was highest for models using mean plasma glucose to drive HbA1c formation. Insulin contribution to power varied greatly depending on the drug target; it was beneficial only if the drug target was insulin secretion. All investigated models showed good simulation properties. However, extrapolation with the mechanistic model beyond 12 weeks resulted in drug effect overprediction. This investigation aids drug development in decisions regarding model choice if reusing published HbA1c models.

Integrated model of insulin and glucose kinetics describing both hepatic glucose and pancreatic insulin regulation

BACKGROUND AND OBJECTIVES

Modeling of glucose kinetics has to a large extent been based on models with plasma insulin as a known forcing function. Furthermore, population-based statistical methods for parameter estimation in these models have mainly addressed random inter-individual variations and not intra-individual variations in the parameters. Here we present an integrated whole-body model of glucose and insulin kinetics which extends the well-known two-compartment glucose minimal model. The population-based estimation technique allow for quantification of both random inter- and intra-individual variation in selected parameters using simultaneous data series on glucose and insulin.

METHODS

We extend the two-compartment glucose model into a whole-body model for both glucose and insulin using a simple model for the pancreas compartment which includes feedback of glucose on both insulin secretion and formation of insulin in pancreas. The model has 15 unknown parameters of which 8 have been selected for both intra- and inter-individual variations. The statistical technique for parameter estimation is based on first order conditional estimation.

RESULTS

The model has been evaluated on two datasets: Study group 1 includes 13 healthy subjects with 3-5 repeated IVGTT series of simultaneous plasma glucose and insulin measurements and Study group 2 includes 26 obese patients (3 subgroups: 10 type 2 diabetes (T2D), 7 impaired glucose tolerance (IGT) and 9 normal glucose tolerance (NGT)) with a single IVGTT series. In general the estimated population parameters compares well with reported values in similar studies. Overall the model fits the data series well and the random variation in the 8 selected parameters can account for both intra- and inter-individual variations in the data series. Simulation studies perform reasonable in response to either a slow glucose infusion or a staircase experiment with increasing glucose infusion. Furthermore, the parameters related to the pancreas compartment add useful interpretations in relation to discrimination between populations with varying degree of glucose intolerance.

CONCLUSIONS

We report a new and improved whole-body model of glucose and insulin kinetics which performs robustly under differing conditions and adds useful interpretations in relation to glucose intolerance.

An automated sampling importance resampling procedure for estimating parameter uncertainty

Quantifying the uncertainty around endpoints used for decision-making in drug development is essential. In nonlinear mixed-effects models (NLMEM) analysis, this uncertainty is derived from the uncertainty around model parameters. Different methods to assess parameter uncertainty exist, but scrutiny towards their adequacy is low. In a previous publication, sampling importance resampling (SIR) was proposed as a fast and assumption-light method for the estimation of parameter uncertainty. A non-iterative implementation of SIR proved adequate for a set of simple NLMEM, but the choice of SIR settings remained an issue. This issue was alleviated in the present work through the development of an automated, iterative SIR procedure. The new procedure was tested on 25 real data examples covering a wide range of pharmacokinetic and pharmacodynamic NLMEM featuring continuous and categorical endpoints, with up to 39 estimated parameters and varying data richness. SIR led to appropriate results after 3 iterations on average. SIR was also compared with the covariance matrix, bootstrap and stochastic simulations and estimations (SSE). SIR was about 10 times faster than the bootstrap. SIR led to relative standard errors similar to the covariance matrix and SSE. SIR parameter 95% confidence intervals also displayed similar asymmetry to SSE. In conclusion, the automated SIR procedure was successfully applied over a large variety of cases, and its user-friendly implementation in the PsN program enables an efficient estimation of parameter uncertainty in NLMEM.

Model-Based Evaluation of Proximal Sodium Reabsorption Through SGLT2 in Health and Diabetes and the Effect of Inhibition With Canagliflozin

Sodium-glucose cotransporter 2 inhibitors (SGLT2i) reduce glucose levels in diabetes by inhibiting renal glucose reabsorption in the proximal tubule (PT), resulting in urinary glucose excretion. A recent large cardiovascular outcomes trial suggested that the SGLT2i empagliflozin may also decrease risk of renal dysfunction. Because sodium (Na) and glucose reabsorption are coupled through SGLT2, it is hypothesized that the renal benefits may be derived from lowering Na reabsorption in the PT, which would lead to favorable renal hemodynamic changes. However, the quantitative contribution of SGLT2 to PT Na reabsorption, as well as the differences between healthy and diabetic subjects, and the impact of SGLT2i on PT Na reabsorption are unknown. In this study we extended an existing mathematical model of glucose dynamics to account for renal glucose filtration and excretion. We utilized this model to quantify glucose and Na reabsorption through SGLT2 in healthy, controlled, and uncontrolled diabetes and following treatment with canagliflozin. In healthy, controlled diabetic, and uncontrolled diabetic states, Na reabsorption through SGLT2 was found to be 5.7%, 11.5%, and 13.7% of total renal Na reabsorption, and 7.1% to 9.5%, 14.4% to 19.2%, and 17.1% to 22.8% of sodium reabsorption in the PT alone. The model predicted that treatment of controlled diabetes with canagliflozin returns PT Na reabsorption through SGLT2 to normal levels. The degree of increased PT Na reabsorption due to SGLT2 is likely sufficient to drive pathologic changes in renal hemodynamics, and restoration of normal Na reabsorption through SGLT2 may contribute to beneficial renal effects of SGLT2 inhibition.

Simulation-Based Evaluation of Dose-Titration Algorithms for Rapid-Acting Insulin in Subjects with Type 2 Diabetes Mellitus Inadequately Controlled on Basal Insulin and Oral Antihyperglycemic Medications

BACKGROUND

The purpose of this prospective, model-based simulation approach was to evaluate the impact of various rapid-acting mealtime insulin dose-titration algorithms on glycemic control (hemoglobin A1c [HbA1c]).

METHODS

Seven stepwise, glucose-driven insulin dose-titration algorithms were evaluated with a model-based simulation approach by using insulin lispro. Pre-meal blood glucose readings were used to adjust insulin lispro doses. Two control dosing algorithms were included for comparison: no insulin lispro (basal insulin+metformin only) or insulin lispro with fixed doses without titration.

RESULTS

Of the seven dosing algorithms assessed, daily adjustment of insulin lispro dose, when glucose targets were met at pre-breakfast, pre-lunch, and pre-dinner, sequentially, demonstrated greater HbA1c reduction at 24 weeks, compared with the other dosing algorithms. Hypoglycemic rates were comparable among the dosing algorithms except for higher rates with the insulin lispro fixed-dose scenario (no titration), as expected. The inferior HbA1c response for the "basal plus metformin only" arm supports the additional glycemic benefit with prandial insulin lispro.

CONCLUSIONS

Our model-based simulations support a simplified dosing algorithm that does not include carbohydrate counting, but that includes glucose targets for daily dose adjustment to maintain glycemic control with a low risk of hypoglycemia.

Influence of Meals and Glycemic Changes on QT Interval Dynamics

Thorough QT/QTc studies have become an integral part of early drug development programs, with major clinical and regulatory implications. This analysis expands on existing pharmacodynamic models of QT interval analysis by incorporating the influence of glycemic changes on the QT interval in a semimechanistic manner. A total of 21 healthy subjects enrolled in an open-label phase 1 pilot study and provided continuous electrocardiogram monitoring and plasma glucose and insulin concentrations associated with a 24-hour baseline assessment. The data revealed a transient decrease in QTc, with peak suppression occurring approximately 3 hours after the meal. A semimechanistic modeling approach was applied to evaluate temporal delays between meals and subsequent changes that might influence QT measurements. The food effect was incorporated into a model of heart rate dynamics, and additional delayed effects of the meal on QT were incorporated using a glucose-dependent hypothetical transit compartment. The final model helps to provide a foundation for the future design and analysis of QT studies that may be confounded by meals. This study has significant implications for QT study assessment following a meal or when a cohort is receiving a medication that influences postprandial glucose concentrations.

Leveraging a Clinical Phase Ib Proof-of-Concept Study for the GPR40 Agonist MK-8666 in Patients With Type 2 Diabetes for Model-Informed Phase II Dose Selection

GPR40 mediates free fatty acid–induced insulin secretion in beta cells. We investigated the safety, pharmacokinetics, and glucose response of MK‐8666, a partial GPR40 agonist, after once‐daily multiple dosing in type 2 diabetes patients. This double‐blind, multisite, parallel‐group study randomized 63 patients (placebo, n = 18; 50 mg, n = 9; 150 mg, n = 18; 500 mg, n = 18) for 14‐day treatment. The results showed no serious adverse effects or treatment‐related hypoglycemia. One patient (150‐mg group) showed mild‐to‐moderate transaminitis at the end of dosing. Median MK‐8666 T_max was 2.0–2.5 h and mean apparent terminal half‐life was 22–32 h. On Day 15, MK‐8666 reduced fasting plasma glucose by 54.1 mg/dL (500 mg), 36.0 mg/dL (150 mg), and 30.8 mg/dL (50 mg) more than placebo, consistent with translational pharmacokinetic/pharmacodynamic model predictions. Maximal efficacy for longer‐term assessment is projected at 500 mg based on exposure–response analysis. In conclusion, MK‐8666 was generally well tolerated with robust glucose‐lowering efficacy.

Implications for Drug Characterization in Glucose Tolerance Tests Without Insulin: Simulation Study of Power and Predictions Using Model-Based Analysis

In antihyperglycemic drug development, drug effects are usually characterized using glucose provocations. Analyzing provocation data using pharmacometrics has shown powerful, enabling small studies. In preclinical drug development, high power is attractive due to the experiment sizes; however, insulin is not always available, which potentially impacts power and predictive performance. This simulation study was performed to investigate the implications of performing model-based drug characterization without insulin. The integrated glucose-insulin model was used to simulate and re-estimated oral glucose tolerance tests using a crossover design of placebo and study compound. Drug effects were implemented on seven different mechanisms of action (MOA); one by one or in two-drug combinations. This study showed that exclusion of insulin may severely reduce the power to distinguish the correct from competing drug effect, and to detect a primary or secondary drug effect, however, it did not affect the predictive performance of the model.

Drug-disease modeling in the pharmaceutical industry - where mechanistic systems pharmacology and statistical pharmacometrics meet

Modeling & simulation (M&S) methodologies are established quantitative tools, which have proven to be useful in supporting the research, development (R&D), regulatory approval, and marketing of novel therapeutics. Applications of M&S help design efficient studies and interpret their results in context of all available data and knowledge to enable effective decision-making during the R&D process. In this mini-review, we focus on two sets of modeling approaches: population-based models, which are well-established within the pharmaceutical industry today, and fall under the discipline of clinical pharmacometrics (PMX); and systems dynamics models, which encompass a range of models of (patho-)physiology amenable to pharmacological intervention, of signaling pathways in biology, and of substance distribution in the body (today known as physiologically-based pharmacokinetic models) - which today may be collectively referred to as quantitative systems pharmacology models (QSP). We next describe the convergence - or rather selected integration - of PMX and QSP approaches into 'middle-out' drug-disease models, which retain selected mechanistic aspects, while remaining parsimonious, fit-for-purpose, and able to address variability and the testing of covariates. We further propose development opportunities for drug-disease systems models, to increase their utility and applicability throughout the preclinical and clinical spectrum of pharmaceutical R&D.

Characterizing the dynamic interaction among gastric emptying, glucose absorption, and glycemic control in nondiabetic obese adults

The effects of altered gastric emptying on glucose absorption and kinetics are not well understood in nondiabetic obese adults. The aim of this work was to develop a physiology-based model that can characterize and compare interactions among gastric emptying, glucose absorption, and glycemic control in nondiabetic obese and lean healthy adults. Dynamic glucose, insulin, and gastric emptying (measured with breath test) data from 12 nondiabetic obese and 12 lean healthy adults were available until 180 min after an oral glucose tolerance test (OGTT) with 10, 25, and 75 g of glucose. A physiology-based model was developed to characterize glucose kinetics applying nonlinear mixed-effects modeling with NONMEM7.3. Glucose kinetics after OGTT was described by a one-compartment model with an effect compartment to describe delayed insulin effects on glucose clearance. After the interactions between individual gastric emptying and glucose absorption profiles were accounted for, the glucose absorption rate was found to be similar in nondiabetic obese and lean controls. Baseline glucose concentration was estimated to be only marginally higher in nondiabetic obese subjects (4.9 vs. 5.2 mmol/l), whereas insulin-dependent glucose clearance in nondiabetic obese subjects was found to be cut in half compared with lean controls (0.052 vs. 0.029 l/min) and the insulin concentration associated with 50% of insulin-dependent glucose elimination rate was approximately twofold higher in nondiabetic obese subjects compared with lean controls (7.1 vs. 15.3 μU/ml). Physiology-based models can characterize and compare the dynamic interaction among gastric emptying, glucose absorption and glycemic control in populations of interest such as lean healthy and nondiabetic obese adults.

Application of the integrated glucose-insulin model for cross-study characterization of T2DM patients on metformin background treatment

AIM

The integrated glucose-insulin (IGI) model is a semi-mechanistic physiological model which can describe the glucose-insulin homeostasis system following various glucose challenge settings. The aim of the present work was to apply the model to a large and diverse population of metformin-only-treated type 2 diabetes mellitus (T2DM) patients and identify patient-specific covariates.

METHODS

Data from four clinical studies were pooled, including glucose and insulin concentration-time profiles from T2DM patients on stable treatment with metformin alone following mixed-meal tolerance tests. The data were collected from a wide range of patients with respect to the duration of diabetes and level of glycaemic control.

RESULTS

The IGI model was expanded by four patient-specific covariates. The level of glycaemic control, represented by baseline glycosylated haemoglobin was identified as a significant covariate for steady-state glucose, insulin-dependent glucose clearance and the magnitude of the incretin effect, while baseline body mass index was a significant covariate for steady-state insulin levels. In addition, glucose dose was found to have an impact on glucose absorption rate. The developed model was used to simulate glucose and insulin profiles in different groups of T2DM patients, across a range of glycaemic control, and it was found accurately to characterize their response to the standard oral glucose challenge.

CONCLUSIONS

The IGI model was successfully applied to characterize differences between T2DM patients across a wide range of glycaemic control. The addition of patient-specific covariates in the IGI model might be valuable for the future development of antidiabetic treatment and for the design and simulation of clinical studies.

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.

Glucose Homeostatic Law: Insulin Clearance Predicts the Progression of Glucose Intolerance in Humans

Homeostatic control of blood glucose is regulated by a complex feedback loop between glucose and insulin, of which failure leads to diabetes mellitus. However, physiological and pathological nature of the feedback loop is not fully understood. We made a mathematical model of the feedback loop between glucose and insulin using time course of blood glucose and insulin during consecutive hyperglycemic and hyperinsulinemic-euglycemic clamps in 113 subjects with variety of glucose tolerance including normal glucose tolerance (NGT), impaired glucose tolerance (IGT) and type 2 diabetes mellitus (T2DM). We analyzed the correlation of the parameters in the model with the progression of glucose intolerance and the conserved relationship between parameters. The model parameters of insulin sensitivity and insulin secretion significantly declined from NGT to IGT, and from IGT to T2DM, respectively, consistent with previous clinical observations. Importantly, insulin clearance, an insulin degradation rate, significantly declined from NGT, IGT to T2DM along the progression of glucose intolerance in the mathematical model. Insulin clearance was positively correlated with a product of insulin sensitivity and secretion assessed by the clamp analysis or determined with the mathematical model. Insulin clearance was correlated negatively with postprandial glucose at 2h after oral glucose tolerance test. We also inferred a square-law between the rate constant of insulin clearance and a product of rate constants of insulin sensitivity and secretion in the model, which is also conserved among NGT, IGT and T2DM subjects. Insulin clearance shows a conserved relationship with the capacity of glucose disposal among the NGT, IGT and T2DM subjects. The decrease of insulin clearance predicts the progression of glucose intolerance.

Semimechanistic model describing gastric emptying and glucose absorption in healthy subjects and patients with type 2 diabetes

The integrated glucose-insulin (IGI) model is a previously published semimechanistic model that describes plasma glucose and insulin concentrations after glucose challenges. The aim of this work was to use knowledge of physiology to improve the IGI model's description of glucose absorption and gastric emptying after tests with varying glucose doses. The developed model's performance was compared to empirical models. To develop our model, data from oral and intravenous glucose challenges in patients with type 2 diabetes and healthy control subjects were used together with present knowledge of small intestinal transit time, glucose inhibition of gastric emptying, and saturable absorption of glucose over the epithelium to improve the description of gastric emptying and glucose absorption in the IGI model. Duodenal glucose was found to inhibit gastric emptying. The performance of the saturable glucose absorption was superior to linear absorption regardless of the gastric emptying model applied. The semiphysiological model developed performed better than previously published empirical models and allows better understanding of the mechanisms underlying glucose absorption. In conclusion, our new model provides a better description and improves the understanding of dynamic glucose tests involving oral glucose.

The Effects of a GLP-1 Analog on Glucose Homeostasis in Type 2 Diabetes Mellitus Quantified by an Integrated Glucose Insulin Model

In recent years, several glucagon-like peptide-1 (GLP-1)-based therapies for the treatment of type 2 diabetes mellitus (T2DM) have been developed. The aim of this work was to extend the semimechanistic integrated glucose-insulin model to include the effects of a GLP-1 analog on glucose homeostasis in T2DM patients. Data from two trials comparing the effect of steady-state liraglutide vs. placebo on the responses of postprandial glucose and insulin in T2DM patients were used for model development. The effect of liraglutide was incorporated in the model by including a stimulatory effect on insulin secretion. Furthermore, for one of the trials an inhibitory effect on glucose absorption was included to account for a delay in gastric emptying. As other GLP-1 receptor agonists have similar modes of action, it is believed that the model can also be used to describe the effect of other receptor agonists on glucose homeostasis.

Modeling and design of challenge tests: Inflammatory and metabolic biomarker study examples

Given the complexity of pharmacological challenge experiments, it is perhaps not surprising that design and analysis, and in turn interpretation and communication of results from a quantitative point of view, is often suboptimal. Here we report an inventory of common designs sampled from anti-inflammatory, respiratory and metabolic disease drug discovery studies, all of which are based on animal models of disease involving pharmacological and/or patho/physiological interaction challenges. The corresponding data are modeled and analyzed quantitatively, the merits of the respective approach discussed and inferences made with respect to future design improvements. Although our analysis is limited to these disease model examples, the challenge approach is generally applicable to the vast majority of pharmacological intervention studies. In the present five Case Studies results from pharmacodynamic effect models from different therapeutic areas were explored and analyzed according to five typical designs. Plasma exposures of test compounds were assayed by either liquid chromatography/mass spectrometry or ligand binding assays. To describe how drug intervention can regulate diverse processes, turnover models of test compound-challenger interaction, transduction processes, and biophase time courses were applied for biomarker response in eosinophil count, IL6 response, paw-swelling, TNFα response and glucose turnover in vivo. Case Study 1 shows results from intratracheal administration of Sephadex, which is a glucocorticoid-sensitive model of airway inflammation in rats. Eosinophils in bronchoalveolar fluid were obtained at different time points via destructive sampling and then regressed by the mixed-effects modeling. A biophase function of the Sephadex time course was inferred from the modeled eosinophil time courses. In Case Study 2, a mouse model showed that the time course of cytokine-induced IL1β challenge was altered with or without drug intervention. Anakinra reversed the IL1β induced cytokine IL6 response in a dose-dependent manner. This Case Study contained time courses of test compound (drug), challenger (IL1β) and cytokine response (IL6), which resulted in high parameter precision. Case Study 3 illustrates collagen-induced arthritis progression in the rat. Swelling scores (based on severity of hind paw swelling) were used to describe arthritis progression after the challenge and the inhibitory effect of two doses of an orally administered test compound. In Case Study 4, a cynomolgus monkey model for lipopolysaccharide LPS-induced TNFα synthesis and/or release was investigated. This model provides integrated information on pharmacokinetics and in vivo potency of the test compounds. Case Study 5 contains data from an oral glucose tolerance test in rats, where the challenger is the same as the pharmacodynamic response biomarker (glucose). It is therefore convenient to model the extra input of glucose simultaneously with baseline data and during intervention of a glucose-lowering compound at different dose levels. Typically time-series analyses of challenger- and biomarker-time data are necessary if an accurate and precise estimate of the pharmacodynamic properties of a test compound is sought. Erosion of data, resulting in the single-point assessment of drug action after a challenge test, should generally be avoided. This is particularly relevant for situations where one expects time-curve shifts, tolerance/rebound, impact of disease, or hormetic concentration-response relationships to occur.

A semi-mechanistic model for the effects of a novel glucagon receptor antagonist on glucagon and the interaction between glucose, glucagon, and insulin applied to adaptive phase II design

A potent novel compound (MK-3577) was developed for the treatment of type 2 diabetes mellitus (T2DM) through blocking the glucagon receptor. A semi-mechanistic model was developed to describe the drug effect on glucagon and the interaction between glucagon, insulin, and glucose in healthy subjects (N = 36) during a glucagon challenge study in which glucagon, octreotide (Sandostatin), and basal insulin were infused for 2 h starting from 3, 12, or 24 h postdose of a single 0-900 mg MK-3577 administration. The drug effect was modeled by using an inhibitory E max model (I max = 0.96 and IC50 = 13.9 nM) to reduce the ability of glucagon to increase the glucose production rate (GPROD). In addition, an E max model (E max = 0.79 and EC50 = 575 nM) to increase glucagon secretion by the drug was used to account for the increased glucagon concentrations prechallenge (via compensatory feedback). The model adequately captured the observed profiles of glucagon, glucose, and insulin pre- and postchallenge. The model was then adapted for the T2DM patient population. A linear model to correlate fasting plasma glucose (FPG) to weighted mean glucose (WMG) was developed and provided robust predictions to assist with the dose adjustment for the interim analysis of a phase IIa study.

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.

Population pharmacodynamic modeling of hyperglycemic clamp and meal tolerance tests in patients with type 2 diabetes mellitus

In this study, glucose and insulin concentration-time profiles in subjects with type 2 diabetes mellitus (T2DM) under meal tolerance test (MTT) and hyperglycemic clamp (HGC) conditions were co-modeled simultaneously. Blood glucose and insulin concentrations were obtained from 20 subjects enrolled in a double-blind, placebo-controlled, randomized, two-way crossover study. Patients were treated with palosuran or placebo twice daily for 4 weeks and then switched to the alternative treatment after a 4-week washout period. The MTT and HGC tests were performed 1 h after drug administration on days 28 and 29 of each treatment period. Population data analysis was performed using NONMEM. The HGC model incorporates insulin-dependent glucose clearance and glucose-induced insulin secretion. This model was extended for the MTT, in which glucose absorption was described using a transit compartment with a mean transit time of 62.5 min. The incretin effect (insulin secretion triggered by oral glucose intake) was also included, but palosuran did not influence insulin secretion or sensitivity. Glucose clearance was 0.164 L/min with intersubject and interoccasion variability of 9.57% and 31.8%. Insulin-dependent glucose clearance for the HGC was about 3-fold greater than for the MTT (0.0111 vs. 0.00425 L/min/[mU/L]). The maximal incretin effect was estimated to enhance insulin secretion 2-fold. The lack of palosuran effect coupled with a population-based analysis provided quantitative insights into the variability of glucose and insulin regulation in patients with T2DM following multiple glucose tolerance tests. Application of these models may also prove useful in antihyperglycemic drug development and assessing glucose-insulin homeostasis.

Dose selection using a semi-mechanistic integrated glucose-insulin-glucagon model: designing phase 2 trials for a novel oral glucokinase activator

Selecting dosing regimens for phase 2 studies for a novel glucokinase activator LY2599506 is challenging due to the difficulty in modeling and assessing hypoglycemia risk. A semi-mechanistic integrated glucose-insulin-glucagon (GIG) model was developed in NONMEM based on pharmacokinetic, glucose, insulin, glucagon, and meal data obtained from a multiple ascending dose study in patients with Type 2 diabetes mellitus treated with LY2599506 for up to 26 days. The series of differential equations from the NONMEM model was translated into an R script to prospectively predict 24-h glucose profiles following LY2599506 treatment for 3 months for a variety of doses and dosing regimens. The reduction in hemoglobin A1c (HbA1c) at the end of the 3-month treatment was estimated using a transit compartment model based on the simulated fasting glucose values. Two randomized phase 2 studies, one with fixed dosing and the other employing conditional dose titration were conducted. The simulation suggested that (1) Comparable HbA1c lowering with lower hypoglycemia risk occurs with titration compared to fixed-dosing; and (2) A dose range of 50-400 mg BID provides either greater efficacy or lower hypoglycemia incidence or both than glyburide. The predictions were in reasonable agreement with the observed clinical data. The model predicted HbA1c reduction and hypoglycemia risk provided the basis for the decision to focus on the dose-titration trial and for the selection of doses for the demonstration of superiority of LY2599506 to glyburide. The integrated GIG model represented a valuable tool for the evaluation of hypoglycemia incidence.

Assessment of glycemic response to an oral glucokinase activator in a proof of concept study: application of a semi-mechanistic, integrated glucose-insulin-glucagon model

A proof of concept study was conducted to investigate the safety and tolerability of a novel oral glucokinase activator, LY2599506, during multiple dose administration to healthy volunteers and subjects with Type 2 diabetes mellitus (T2DM). To analyze the study data, a previously established semi-mechanistic integrated glucose-insulin model was extended to include characterization of glucagon dynamics. The model captured endogenous glucose and insulin dynamics, including the amplifying effects of glucose on insulin production and of insulin on glucose elimination, as well as the inhibitory influence of glucose and insulin on hepatic glucose production. The hepatic glucose production in the model was increased by glucagon and glucagon production was inhibited by elevated glucose concentrations. The contribution of exogenous factors to glycemic response, such as ingestion of carbohydrates in meals, was also included in the model. The effect of LY2599506 on glucose homeostasis in subjects with T2DM was investigated by linking a one-compartment, pharmacokinetic model to the semi-mechanistic, integrated glucose-insulin-glucagon system. Drug effects were included on pancreatic insulin secretion and hepatic glucose production. The relationships between LY2599506, glucose, insulin, and glucagon concentrations were described quantitatively and consequently, the improved understanding of the drug-response system could be used to support further clinical study planning during drug development, such as dose selection.

Study reanalysis using a mechanism-based pharmacokinetic/pharmacodynamic model of pramlintide in subjects with type 1 diabetes

This report describes a pharmacokinetic/pharmacodynamic model for pramlintide, an amylinomimetic, in type 1 diabetes mellitus (T1DM). Plasma glucose and drug concentrations were obtained following bolus and 2-h intravenous infusions of pramlintide at three dose levels or placebo in 25 T1DM subjects during the postprandial period in a crossover study. The original clinical data were reanalyzed by mechanism-based population modeling. Pramlintide pharmacokinetics followed a two-compartment model with zero-order infusion and first-order elimination. Pramlintide lowered overall postprandial plasma glucose AUC (AUC(net)) and delayed the time to peak plasma glucose after a meal (T (max)). The delay in glucose T (max) and reduction of AUC(net) indicate that overall plasma glucose concentrations might be affected by differing mechanisms of action of pramlintide. The observed increase in glucose T (max) following pramlintide treatment was independent of dose within the studied dose range and was adequately described by a dose-independent, maximum pramlintide effect on gastric emptying of glucose in the model. The inhibition of endogenous glucose production by pramlintide was described using a sigmoidal function with capacity and sensitivity parameter estimates of 0.995 for I (max) and 23.8 pmol/L for IC(50). The parameter estimates are in good agreement with literature values and the IC(50) is well within the range of postprandial plasma amylin concentrations in healthy humans, indicating physiological relevance of the pramlintide effect on glucagon secretion in the postprandial state. This model may prove to be useful in future clinical studies of other amylinomimetics or antidiabetic drugs with similar mechanisms of action.

Mechanism-based population modelling of the effects of vildagliptin on GLP-1, glucose and insulin in patients with type 2 diabetes

AIM

To build a mechanism-based population pharmacodynamic model to describe and predict the time course of active GLP-1, glucose and insulin in type 2 diabetic patients after treatment with various doses of vildagliptin.

METHODS

Vildagliptin concentrations, DPP-4 activity, active GLP-1, glucose and insulin concentrations from 13 type 2 diabetic patients after oral vildagliptin doses of 10, 25 or 100 mg and placebo twice daily for 28 days were co-modelled. The population PK/PD model was developed utilizing the MC-PEM algorithm in parallelized S-ADAPT version 1.56.

RESULTS

In the PD model, active GLP-1 production was stimulated by gastrointestinal intake of nutrients. Active GLP-1 was primarily metabolized by DPP-4 and an additional non-saturable pathway. Increased plasma glucose stimulated secretion of insulin which stimulated utilization of glucose. Active GLP-1 stimulated both glucose-dependent insulin secretion and insulin-dependent glucose utilization. Complete inhibition of DPP-4 resulted in an approximately 2.5-fold increase of active GLP-1 half-life.

CONCLUSIONS

The effects of vildagliptin in patients with type 2 diabetes on several PD endpoints were successfully described by the proposed model. The mechanisms of vildagliptin on glycaemic control could be evaluated from a variety of aspects such as effects of DPP-4 on GLP-1, effects of GLP-1 on insulin secretion and effects on hepatic and peripheral insulin sensitivity. The present model can be used to predict the effects of other dosage regimens of vildagliptin on DPP-4 inhibition, active GLP-1, glucose and insulin concentrations, or can be modified and applied to other incretin-related anti-diabetes therapies.

Mechanism-based disease progression modeling of type 2 diabetes in Goto-Kakizaki rats

The dynamics of aging and type 2 diabetes (T2D) disease progression were investigated in normal [Wistar-Kyoto (WKY)] and diabetic [Goto-Kakizaki (GK)] rats and a mechanistic disease progression model was developed for glucose, insulin, and glycosylated hemoglobin (HbA1c) changes over time. The study included 30 WKY and 30 GK rats. Plasma glucose and insulin, blood glucose and HbA1c concentrations and hematological measurements were taken at ages 4, 8, 12, 16 and 20 weeks. A mathematical model described the development of insulin resistance (IR) and β-cell function with age/growth and diabetes progression. The model utilized transit compartments and an indirect response model to quantitate biomarker changes over time. Glucose, insulin and HbA1c concentrations in WKY rats increased to a steady-state at 8 weeks due to developmental changes. Glucose concentrations at 4 weeks in GK rats were almost twice those of controls, and increased to a steady-state after 8 weeks. Insulin concentrations at 4 weeks in GK rats were similar to controls, and then hyperinsulinemia occurred until 12-16 weeks of age indicating IR. Subsequently, insulin concentrations in GK rats declined to slightly below WKY controls due to β-cell failure. HbA1c showed a delayed increase relative to glucose. Modeling of HbA1c was complicated by age-related changes in hematology in rats. The diabetes model quantitatively described the glucose/insulin inter-regulation and HbA1c production and reflected the underlying pathogenic factors of T2D--IR and β-cell dysfunction. The model could be extended to incorporate other biomarkers and effects of various anti-diabetic drugs.

The Unscented Kalman Filter estimates the plasma insulin from glucose measurement

Understanding the simultaneous interaction within the glucose and insulin homeostasis in real-time is very important for clinical treatment as well as for research issues. Until now only plasma glucose concentrations can be measured in real-time. To support a secure, effective and rapid treatment e.g. of diabetes a real-time estimation of plasma insulin would be of great value. A novel approach using an Unscented Kalman Filter that provides an estimate of the current plasma insulin concentration is presented, which operates on the measurement of the plasma glucose and Bergman's Minimal Model of the glucose insulin homeostasis. We can prove that process observability is obtained in this case. Hence, a successful estimator design is possible. Since the process is nonlinear we have to consider estimates that are not normally distributed. The symmetric Unscented Kalman Filter (UKF) will perform best compared to other estimator approaches as the Extended Kalman Filter (EKF), the simplex Unscented Kalman Filter (UKF), and the Particle Filter (PF). The symmetric UKF algorithm is applied to the plasma insulin estimation. It shows better results compared to the direct (open loop) estimation that uses a model of the insulin subsystem.

An integrated model for the glucose-insulin system

The integrated glucose-insulin model was originally developed on a variety of intravenous glucose provocation experiments in healthy volunteers and type 2 diabetic patients. The model, which simultaneously describes time-courses of glucose and insulin based on mechanism-based components for production, elimination and homeostatic feedback, has been further extended to oral glucose provocations, meal tests and insulin administration. The model has been used to describe experiments ranging from 4 to 24 hr. Applications of the integrated glucose-insulin model include the clinical assessment of the mechanism of action of anti-diabetic drugs and the magnitude of their effects. Finally, the model was used for optimizing the design of provocation experiments.

An integrated glucose-insulin model to describe oral glucose tolerance test data in healthy volunteers

The extension of the previously developed integrated models for glucose and insulin (IGI) to include the oral glucose tolerance test (OGTT) in healthy volunteers could be valuable to better understand the differences between healthy individuals and those with type 2 diabetes mellitus (T2DM). Data from an OGTT in 23 healthy volunteers were used. Analysis was based on the previously developed intravenous model with extensions for glucose absorption and incretin effect on insulin secretion. The need for additional structural components was evaluated. The model was evaluated by simulation and a bootstrap. Multiple glucose and insulin concentration peaks were observed in most individuals as well as hypoglycemic episodes in the second half of the experiment. The OGTT data were successfully described by the extended basic model. An additional control mechanism of insulin on glucose production improved the description of the data. The model showed good predictive properties, and parameters were estimated with good precision. In conclusion, a previously presented integrated model has been extended to describe glucose and insulin concentrations in healthy volunteers following an OGTT. The characterization of the differences between the healthy and diabetic stages in the IGI model could potentially be used to extrapolate drug effect from healthy volunteers to T2DM.

Incorporating physiological and biochemical mechanisms into pharmacokinetic-pharmacodynamic models: a conceptual framework

The aim of this conceptual framework paper is to contribute to the further development of the modelling of effects of drugs or toxic agents by an approach which is based on the underlying physiology and pathology of the biological processes. In general, modelling of data has the purpose (1) to describe experimental data, (2a) to reduce the amount of data resulting from an experiment, e.g. a clinical trial and (2b) to obtain the most relevant parameters, (3) to test hypotheses and (4) to make predictions within the boundaries of experimental conditions, e.g. range of doses tested (interpolation) and out of the boundaries of the experimental conditions, e.g. to extrapolate from animal data to the situation in man. Describing the drug/xenobiotic-target interaction and the chain of biological events following the interaction is the first step to build a biologically based model. This is an approach to represent the underlying biological mechanisms in qualitative and also quantitative terms, thus being inherently connected in many aspects to systems biology. As the systems biology models may contain variables in the order of hundreds connected with differential equations, it is obvious that it is in most cases not possible to assign values to the variables resulting from experimental data. Reduction techniques may be used to create a manageable model which, however, captures the biologically meaningful events in qualitative and quantitative terms. Until now, some success has been obtained by applying empirical pharmacokinetic/pharmacodynamic models which describe direct and indirect relationships between the xenobiotic molecule and the effect, including tolerance. Some of the models may have physiological components built in the structure of the model and use parameter estimates from published data. In recent years, some progress toward semi-mechanistic models has been made, examples being chemotherapy-induced myelosuppression and glucose-endogenous insulin-antidiabetic drug interactions. We see a way forward by employing approaches to bridge the gap between systems biology and physiologically based kinetic and dynamic models. To be useful for decision making, the 'bridging' model should have a well founded mechanistic basis, but being reduced to the extent that its parameters can be deduced from experimental data, however capturing the biological/clinical essential details so that meaningful predictions and extrapolations can be made.