A minimal model of insulin secretion and kinetics to assess hepatic insulin extraction

Tailoring the Padova Type 2 Diabetes Simulator for Treatment Guidance in Target Populations

OBJECTIVE

The Padova type 2 diabetes (T2D) simulator (T2DS) has been recently proposed to optimize T2D treatments including novel long-acting insulins. It consists of a physiological model and an in silico population describing glucose dynamics, derived from early-stage T2D subjects studied with sophisticated tracer-based experimental techniques. This limits T2DS domain of validity to this specific sub-population. Conversely, running simulations in insulin-naïve or advanced T2D subjects, would be more valuable. However, it is rarely possible or cost-effective to run complex experiments in such populations. Therefore, we propose a method for tuning the T2DS to any desired T2D sub-population using published clinical data. As case study, we extended the T2DS to insulin-naïve T2D subjects, who need to start insulin therapy to compensate the reduced insulin function.

METHODS

T2DS model was identified based on literature data of the target population. The estimated parameters were used to generate a virtual cohort of insulin-naïve T2D subjects (inC1). A model of basal insulin degludec (IDeg) was also incorporated into the T2DS to enable basal insulin therapy. The resulting tailored T2DS was assessed by simulating IDeg therapy initiation and comparing simulated vs. clinical trial outcomes. For further validation, this procedure was reiterated to generate a new cohort of insulin-naïve T2D (inC2) assuming inC1 as target population.

RESULTS

No statistically significant differences were found when comparing fasting plasma glucose and IDeg dose, neither in clinical data vs. inC1, nor inC1 vs. inC2.

CONCLUSIONS

The tuned T2DS allowed reproducing the main findings of clinical studies in insulin-naïve T2D subjects.

SIGNIFICANCE

The proposed methodology makes the Padova T2DS usable for supporting treatment guidance in target T2D populations.

Increased Insulin Secretion and Glucose Effectiveness in Obese Patients with Type 2 Diabetes following Bariatric Surgery

Background

β-cell dysfunction and insulin resistance are the main mechanisms causing glucose intolerance in type 2 diabetes (T2D). Bariatric surgeries, i.e., sleeve gastrectomy (SG) and Roux-en-Y gastric bypass (RYGB), are procedures both known to induce weight loss, increase insulin action, and enhance β-cell function, but hepatic insulin extraction and glucose effectiveness may also play a role.

Methods

To determine the contribution of these regulators on glucose tolerance after bariatric surgery, an oral glucose tolerance test (OGTT) was performed before and 2 months after surgery in 9 RYGB and 7 SG subjects. Eight healthy subjects served as metabolic controls. Plasma glucose, insulin, C-peptide, GLP-1, and GIP were measured during each OGTT. Insulin sensitivity and secretion, glucose effectiveness, and glucose rate of appearance were determined via oral minimal models.

Results

RYGB and SG resulted in similar weight reductions (13%, RYGB (p < 0.01); 14%, SG (p < 0.05)). Two months after surgery, insulin secretion (p < 0.05) and glucose effectiveness both improved equally in the two groups (11%, RYGB (p < 0.01); 8%, SG (p > 0.05)), whereas insulin sensitivity remained virtually unaltered. Bariatric surgery resulted in a comparable increase in the GLP-1 response during the OGTT, whereas GIP concentrations remained unaltered. Following surgery, oral glucose intake resulted in a comparable increase in hepatic insulin extraction, the response in both RYGB and SG patients significantly exceeding the response observed in the control subjects.

Conclusions

These results demonstrate that the early improvement in glucose tolerance in obese T2D after RYGB and SG surgeries is attributable mainly to increased insulin secretion and glucose effectiveness, while insulin sensitivity seems to play only a minor role. This trial is registered with NCT02713555.

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.

A New Index of Insulin Sensitivity from Glucose Sensor and Insulin Pump Data: In Silico and In Vivo Validation in Youths with Type 1 Diabetes

Background: Estimation of insulin sensitivity (SI) and its daily variation are key for optimizing insulin therapy in patients with type 1 diabetes (T1D). We recently developed a method for SI estimation from continuous glucose monitoring (CGM) and continuous subcutaneous insulin infusion (CSII) data in adults with T1D (SISP) and validated it under restrained experimental conditions. Herein, we validate in vivo a new version of SISP performing well in daily life unrestrained conditions. Methods: The new SISP was tested in both simulated and real data. The simulated dataset consists of 100 virtual adults of the UVa/Padova T1D Simulator monitored during an open-loop experiment, whereas the real dataset consists of 10 youths with T1D monitored during a hybrid closed-loop meal study. In both datasets, participants underwent two consecutive meals (breakfast and lunch, at 7 and 11 am) with the same carbohydrate content (70 g). Plasma glucose and insulin were measured during each meal to estimate the oral glucose minimal model SI (SIMM). CGM and CSII data were used for SISP calculation, which was then validated against the gold standard SIMM. Results: SISP was estimated with good precision (median coefficient of variation <20%) in 100% of the real and 91% of the simulated meals. SISP and SIMM were highly correlated, both in the simulated and real datasets (R = 0.82 and R = 0.83, P < 0.001), and exhibited a similar intraday pattern. Conclusions: SISP is suitable for estimating SI in both closed- and open-loop settings, provided that the subject wears a CGM sensor and a subcutaneous insulin pump.

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.

A software interface for in silico testing of type 2 diabetes treatments

BACKGROUND AND OBJECTIVE

The increasing incidence of diabetes continuously stimulates the research on new antidiabetic drugs. Computer simulation can save time and costs, alleviating the need of animal trials and providing useful information for optimal experiment design and drug dosing. We recently presented a type 2 diabetes (T2D) simulator as tool for in silico testing of new molecules and guiding treatment optimization. Here we present a user-friendly interface aimed to increase the usability of the simulator.

METHOD

The simulator, based on a large-scale glucose, insulin, and C-peptide model and equipped with 100 virtual subjects well describing system dynamics in a real T2D population, is extended to incorporate pharmacokinetics/pharmacodynamics (PK/PD) of a drug of interest. A graphical interface is developed on top of the simulator, allowing an easy design of in silico experiments: specifically, it is possible to select the population size to test, design the experiment (crossover or parallel), its duration and the sampling grid, choose glucose and insulin doses, and define treatment PK/PD and dose administered. The simulator also provides the outcome metrics requested by the user, and performs statistical comparisons among treatments and/or placebo.

RESULTS

To illustrate the potential of the simulator, we provided a case study using metformin and liraglutide. Literature-based PK/PD models of metformin and liraglutide have been incorporated in the simulator, by modulating key drug-sensitive model parameters. An in silico placebo-controlled trial has been done by simulating a three-arm meal tolerance test with subjects receiving placebo, metformin 850 mg, liraglutide 1.80 mg, respectively. The obtained results are in agreement with the clinical evidences, in terms of main glucose, insulin, and C-peptide outcome metrics.

CONCLUSIONS

We developed a user-friendly software interface for the T2D simulator to support the design and test of new antidiabetic drugs and treatments. This increases the simulator usability, making it suitable also for users who have low experience with computer programming.

The Impact of Exogenous Insulin Input on Calculating Hepatic Clearance Parameters

OBJECTIVE

Model-based metabolic tests require accurate identification of subject-specific parameters from measured assays. Insulin assays are used to identify insulin kinetics parameters, such as general and first-pass hepatic clearances. This study assesses the impact of intravenous insulin boluses on parameter identification precision.

METHOD

Insulin and C-peptide data from two intravenous glucose tolerance test (IVGTT) trials of healthy adults (N = 10 × 2; denoted A and B), with (A) and without (B) insulin modification, were used to identify insulin kinetics parameters using a grid search. Monte Carlo analysis (N = 1000) quantifies variation in simulation error for insulin assay errors of 5%. A region of parameter values around the optimum was identified whose errors are within variation due to assay error. A smaller optimal region indicates more precise practical identifiability. Trial results were compared to assess identifiability and precision.

RESULTS

Trial B, without insulin modification, has optimal parameter regions 4.7 times larger on average than Trial A, with 1-U insulin bolus modification. Ranges of optimal parameter values between trials A and B increase from 0.04 to 0.12 min^-1 for hepatic clearance and from 0.07 to 0.14 for first-pass clearance on average. Trial B's optimal values frequently lie outside physiological ranges, further indicating lack of distinct identifiability.

CONCLUSIONS

A small 1-U insulin bolus improves identification of hepatic clearance parameters by providing a smaller region of optimal parameter values. Adding an insulin bolus in metabolic tests can significantly improve identifiability and outcome test precision. Assay errors necessitate insulin modification in clinical tests to ensure identifiability and precision.

Modeling Between-Subject Variability in Subcutaneous Absorption of a Long-Acting Insulin Glargine 100 U/mL by a Nonlinear Mixed Effects Approach

Subcutaneous insulin absorption is well-known to vary significantly both between and within subjects (BSV and WSV, respectively). This variability considerably obstacles the establishing of a reproducible and effective insulin therapy. Some models exist to describe the subcutaneous kinetics of both fast and long-acting insulin analogues; however, none of them account for the BSV. The aim of this study is to develop a nonlinear mixed effects model able to describe the BSV observed in the subcutaneous absorption of a long-acting insulin glargine 100 U/mL. Four stochastic models of the BSV were added to a previously validated model of subcutaneous absorption of insulin glargine 100 U/mL. These were assessed on a database of 47 subjects with type 1 diabetes. The best model was selected based on residual analysis, precision of the estimates and parsimony criteria. The selected model provided good fit of individual data, precise population parameter estimates and allowed quantifying the BSV of the insulin glargine 100 U/mL pharmacokinetics. Future model development will include the description of the WSV of long- acting insulin absorption.

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.

β-cell function in black South African women: exploratory associations with insulin clearance, visceral and ectopic fat

The role of ectopic fat, insulin secretion and clearance in the preservation ofβ-cell function in black African women with obesity who typically present with hyperinsulinaemia is not clear. We aim to examine the associations between disposition index (DI, an estimate of β-cell function), insulin secretion and clearance and ectopic fat deposition. This is a cross-sectional study of 43 black South African women (age 20-35 years) with obesity (BMI 30-40 kg/m2) and without type 2 diabetes that measured the following: DI, insulin sensitivity (SI), acute insulin response (AIRg), insulin secretion rate (ISR), hepatic insulin extraction and peripheral insulin clearance (frequently sampled i.v. glucose tolerance test); pancreatic and hepatic fat, visceral adipose tissue (VAT) and abdominal s.c. adipose tissue (aSAT) volume (MRI), intra-myocellular (IMCL) and extra-myocellular fat content (EMCL) (magnetic resonance spectroscopy). DI correlated positively with peripheral insulin clearance (β 55.80, P = 0.002). Higher DI was associated with lower VAT, pancreatic fat and soleus fat, but VAT explained most of the variance in DI (32%). Additionally, higher first phase ISR (P = 0.033) and lower hepatic insulin extraction (P = 0.022) were associated with lower VAT, independent from SI, rather than with ectopic fat. In conclusion, peripheral insulin clearance emerged as an important correlate of DI. However, VAT was the main determinant of a lower DI above ectopic fat depots. Importantly, VAT, but not ectopic fat, is associated with both lower insulin secretion and higher hepatic insulin extraction. Prevention of VAT accumulation in young black African women should, therefore, be an important target for beta cell preservation.

Modeling Between-Subject Variability in Subcutaneous Absorption of a Fast-Acting Insulin Analogue by a Nonlinear Mixed Effects Approach

Despite the great progress made in insulin preparation and titration, many patients with diabetes are still experiencing dangerous fluctuations in their blood glucose levels. This is mainly due to the large between- and within-subject variability, which considerably hampers insulin therapy, leading to defective dosing and timing of the administration process. In this work, we present a nonlinear mixed effects model describing the between-subject variability observed in the subcutaneous absorption of fast-acting insulin. A set of 14 different models was identified on a large and frequently-sampled database of lispro pharmacokinetic data, collected from 116 subjects with type 1 diabetes. The tested models were compared, and the best one was selected on the basis of the ability to fit the data, the precision of the estimated parameters, and parsimony criteria. The selected model was able to accurately describe the typical trend of plasma insulin kinetics, as well as the between-subject variability present in the absorption process, which was found to be related to the subject’s body mass index. The model provided a deeper understanding of the insulin absorption process and can be incorporated into simulation platforms to test and develop new open- and closed-loop treatment strategies, allowing a step forward toward personalized insulin therapy.

Model-Based Assessment of C-Peptide Secretion and Kinetics in Post Gastric Bypass Individuals Experiencing Postprandial Hyperinsulinemic Hypoglycemia

Assessment of insulin secretion is key to diagnose postprandial hyperinsulinemic hypoglycemia (PHH), an increasingly recognized complication following bariatric surgery. To this end, the Oral C-peptide Minimal Model (OCMM) can be used. This usually requires fixing C-peptide (CP) kinetics to the ones derived from the Van Cauter population model (VCPM), which has never been validated in PHH individuals. The objective of this work was to test the validity of the OCMM coupled with the VCPM in PHH subjects and propose a method to overcome the observed limitations. Two cohorts of adults with PHH after gastric bypass (GB) underwent either a 75 g oral glucose (9F/3M; age=42±9 y; BMI=28.3±6.9 kg/m²) or a 60 g mixed-meal (7F/3M; age = 43 ± 11 y; BMI=27.5±4.2 kg/m²) tolerance test. The OCMM was identified on CP concentration data with CP kinetics fixed to VCPM (VC approach). In both groups, the VC approach underestimated CP-peak and overestimated CP-tail suggesting CP kinetics predicted by VCPM to be inaccurate in this population. Thus, the OCMM was identified using CP kinetics estimated from the data (DB approach) using a Bayesian Maximum a Posteriori estimator. CP data were well predicted in all the subjects using the DB approach, highlighting a significantly faster CP kinetics in patients with PHH compared to the one predicted by VCPM. Finally, a simulation study was used to validate the proposed approach. The present findings question the applicability of the VCPM in patients with PHH after GB and call for CP bolus experiments to develop a reliable CP kinetic model in this population.

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.

Mechanistic evaluation of the effect of sodium-dependent glucose transporter 2 inhibitors on delayed glucose absorption in patients with type 2 diabetes mellitus using a quantitative systems pharmacology model of human systemic glucose dynamics

Sodium-dependent glucose transporter (SGLT) 2 is specifically expressed in the kidney, while SGLT1 is present in the kidneys and small intestine. SGLT2 inhibitors are a class of oral antidiabetic drugs that lower elevated plasma glucose levels by promoting the urinary excretion of excess glucose through the inhibition of renal glucose reuptake. The inhibition selectivity for SGLT2 over SGLT1 (SGLT2/1 selectivity) of marketed SGLT2 inhibitors is diverse, while SGLT2/1 selectivity of canagliflozin is relatively low. Although canagliflozin suppresses postprandial glucose levels, the degree of contribution for SGLT1 inhibition to this effect remains unproven. To analyze the effect of SGLT2 inhibitors on postprandial glucose level, we constructed a novel quantitative systems pharmacology (QSP) model, called human systemic glucose dynamics (HSGD) model, integrating intestinal absorption, metabolism, and renal reabsorption of glucose. This HSGD model reproduced the postprandial plasma glucose concentration-time profiles during a meal tolerance test under different clinical trial conditions. Simulations after canagliflozin administration showed a dose-dependent delay of time (T_max,glc ) to reach maximum concentration of glucose (C_max,glc ), and the delay of T_max,glc disappeared when inhibition of SGLT1 was negated. In addition, contribution ratio of intestinal SGLT1 inhibition to the decrease in C_max,glc was estimated to be 23%-28%, when 100 and 300 mg of canagliflozin are administered. This HSGD model enabled us to provide the partial contribution of intestinal SGLT1 inhibition to the improvement of postprandial hyperglycemia as well as to quantitatively describe the plasma glucose dynamics following SGLT2 inhibitors.

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.

In Silico Head-to-Head Comparison of Insulin Glargine 300 U/mL and Insulin Degludec 100 U/mL in Type 1 Diabetes

Background: Second-generation long-acting insulin glargine 300 U/mL (Gla-300) and degludec 100 U/mL (Deg-100) provide novel basal insulin therapies for the treatment of type 1 diabetes (T1D). Both offer a flatter pharmacokinetic (PK) profile than the previous generation of long-acting insulins, thus improving glycemic control while reducing hypoglycemic events. This work describes an in silico head-to-head comparison of the two basal insulins on 24-h glucose profiles and was used to guide the design of a clinical trial. Materials and Methods: The Universities of Virginia (UVA)/Padova T1D simulator describes the intra-/interday variability of glucose-insulin dynamics and thus provides a robust bench-test for assessing glucose control for basal insulin therapies. A PK model describing subcutaneous absorption of Deg-100, in addition to the one already available for Gla-300, has been developed based on T1D clinical data and incorporated into the simulator. One hundred in silico T1D subjects received a basal insulin dose (Gla-300 or Deg-100) for 12 weeks (8 weeks uptitration, 4 weeks stable dosing) by morning or evening administration in a basal/bolus regimen. The virtual patients were uptitrated to their individual doses with two different titration rules. Results: The last 2-week simulated continuous glucose monitoring data were used to calculate various outcome metrics for both basal insulin treatments, with primary outcome being the percent time in glucose target (70-140 mg/dL). The simulations show no statistically significant difference for Gla-300 versus Deg-100 in the main endpoints. Conclusions: This work suggests comparable glucose control using either Gla-300 or Deg-100 and was used to guide the design of a clinical trial intended to compare second-generation long-acting insulin analogues.

Optimal Designs for Model-Based Assessment of Insulin Sensitivity and Glucose Effectiveness

The integrated minimal model allows assessment of clinical diagnosis indices, for example, insulin sensitivity (S_I ) and glucose effectiveness (S_G ), from data of the insulin-modified intravenous glucose tolerance test (IVGTT), which is laborious with an intense sampling schedule, up to 32 samples. The aim of this study was to propose a more informative, although less laborious, IVGTT design to be used for model-based assessment of S_I and S_G . The IVGTT design was optimized simultaneously for all design variables: glucose and insulin infusion doses, time of glucose dose and start of insulin infusion, insulin infusion duration, sampling times, and number of samples. Design efficiency was used to compare among different designs. The simultaneously optimized designs showed a profound higher efficiency than both standard rich (32 samples) and sparse (10 samples) designs. The optimized designs, after removing replicate sample times, were 1.9 and 7.1 times more efficient than the standard rich and sparse designs, respectively. After including practical aspects of the designs, for example, sufficient duration between samples and avoidance of prolonged hypoglycemia, we propose 2 practical designs with fewer sampling times and lower input of glucose and insulin than standard designs, constrained to prevent hypoglycemia. The optimized practical rich design is equally efficient in assessing S_I and S_G as the rich standard design, but with half the number of the samples, while the optimized practical sparse design has 1 less sample and requires 4.6 times fewer individuals for equal certainty when assessing S_I and S_G than the sparse standard design.

In Silico Cloning of Target Type 2 Diabetes Population for Treatments Development and Decision Support. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2020;2020:5111-5114. [PMID: 33019136 DOI: 10.1109/embc44109.2020.9175271]

Therapies for treatment of type 2 diabetes (T2D) involve a variety of medications, depending on the stage of T2D progression. It is now an accepted knowledge that in silico trials can help to accelerate drug development and support treatment optimization. A T2D simulator (T2DS), consisting of a model of the glucose-insulin system and an in silico population describing glucose-insulin dynamics in T2D subjects, has been recently developed based on early-stage T2D data, studied with sophisticated experimental techniques. This limits the domain of validity of the simulator to this specific sub-population of T2D. Here we proposed a method for tuning the T2DS to any desired T2D target population, e.g. insulin-naïve (i.e., not experienced with insulin) patients, without the need to resort to complex and expensive clinical studies. This will allow to use the T2DS for testing treatments in the target population. To illustrate the methodology, we used a case study: extending the T2DS to reproduce the behavior of insulin-naïve T2D subjects. The methodology described here can be extended to other stages of T2D, allowing an extensive in silico testing phase of different treatments before human trials.

Dual glucagon-like peptide-1 receptor/glucagon receptor agonist SAR425899 improves beta-cell function in type 2 diabetes

AIM

To evaluate the change in insulin sensitivity, β-cell function and glucose absorption after 28 days of treatment with high and low doses of SAR425899, a novel dual glucagon-like peptide-1 receptor/glucagon receptor agonist, versus placebo.

MATERIALS AND METHODS

Thirty-six overweight to obese subjects with type 2 diabetes were randomized to receive daily subcutaneous administrations of low-dose SAR425899 (0.03, 0.06 and 0.09 mg) and high-dose SAR425899 (0.06, 0.12 and 0.18 mg) or placebo for 28 days; dose escalation occurred after days 7 and 14. Mixed meal tolerance tests were conducted before treatment (day -1) and on days 1 and 28. Oral glucose and C-peptide minimal models were used to quantify metabolic indices of insulin sensitivity, β-cell responsiveness and glucose absorption.

RESULTS

With low-dose SAR425899, high-dose SAR425899 and placebo, β-cell function from day -1 to day 28 increased by 163%, 95% and 23%, respectively. The change in area under the curve for the rate of meal glucose appearance between 0 and 120 minutes was -32%, -20% and 8%, respectively.

CONCLUSIONS

After 28 days of treatment, SAR425899 improved postprandial glucose control by significantly enhancing β-cell function and slowing glucose absorption rate.

Modeling Subcutaneous Absorption of Long-Acting Insulin Glargine in Type 1 Diabetes

OBJECTIVE

Subcutaneous (sc) administration of long-acting insulin analogs is often employed in multiple daily injection (MDI) therapy of type 1 diabetes (T1D) to cover patient's basal insulin needs. Among these, insulin glargine 100 U/mL (Gla-100) and 300 U/mL (Gla-300) are formulations indicated for once daily sc administration in MDI therapy of T1D. A few semi-mechanistic models of sc absorption of insulin glargine have been proposed in the literature, but were not quantitatively assessed on a large dataset. The aim of this paper is to propose a model of sc absorption of insulin glargine able to describe the data and provide precise model parameters estimates with a clear physiological interpretation.

METHODS

Three candidate models were identified on a total of 47 and 77 insulin profiles of T1D subjects receiving a single or repeated sc administration of Gla-100 or Gla-300, respectively. Model comparison and selection were performed on the basis of their ability to describe the data and numerical identifiability.

RESULTS

The most parsimonious model is linear two-compartment and accounts for the insulin distribution between the two compartments after sc administration through parameter k. Between the two formulations, we report a lower fraction of insulin in the first versus second compartment (k = 86% versus 94% in Gla-100 versus Gla-300, p < 0.05), a lower dissolution rate from the first to the second compartment ([Formula: see text] versus 0.0008 min^-1 in Gla-100 versus Gla-300, p << 0.001), and a similar rate of insulin absorption from the second compartment to plasma ([Formula: see text] versus 0.0016 min^-1 in Gla-100 versus Gla-300, p = NS), in accordance with the mechanisms of insulin glargine protraction.

CONCLUSIONS

The proposed model is able to both accurately describe plasma insulin data after sc administration and precisely estimate physiologically plausible parameters.

SIGNIFICANCE

The model can be incorporated in simulation platforms potentially usable for optimizing basal insulin treatment strategies.

Translation Between Two Models; Application with Integrated Glucose Homeostasis Models

PURPOSE

For some biological systems, there exist several models with somewhat different features and perspectives. We propose an evaluation method for NLME models by analyzing real and simulated data from the model of main interest using a structurally different, but similar, NLME model. We showcase this method using the Integrated Glucose Insulin (IGI) model and the Integrated Minimal Model (IMM). Additionally, we try to map parameters carrying similar information between the two models.

METHODS

A bootstrap of real data and simulated datasets from both the IMM and IGI models were analyzed with the two models. Important parameters of the IMM were mapped to IGI parameters using a large IMM simulated dataset analyzed under the IGI model.

RESULTS

Comparison of the parameters estimated from real data and data simulated with the IMM and analyzed with the IGI model demonstrated differences between real and IMM-simulated data. Comparison of the parameters estimated from real data and data simulated with the IGI model and analyzed with the IMM also demonstrated differences but to a lower extent. The strongest parameter correlations were found for: insulin-dependent glucose clearance (IGI) ~ insulin sensitivity (IMM); insulin-independent glucose clearance (IGI) ~ glucose effectiveness (IMM); and insulin effect parameter (IGI) ~ insulin action (IMM).

CONCLUSIONS

We demonstrated a new approach to investigate models' ability to simulate real-life-like data, and the information captured in each model in comparison to real data, and the IMM clinically used parameters were successfully mapped to their corresponding IGI parameters.

Elevated insulin levels following 7 days of increased sedentary time are due to lower hepatic extraction and not higher insulin secretion

Higher insulin following sedentary behavior may be due to increased insulin secretion (IS), decreased hepatic insulin extraction (HIE), or a combination of both. Ten healthy adults completed glucose tolerance tests following 7 days of normal activity and 7 days of increased sitting. There were no differences in IS; however, HIE at 120 min after ingestion (85.4% ± 7.2% vs. 74.6% ± 6.6%, p < 0.05) and the area under the curve (73.6% ± 9.4% vs. 67.5% ± 11.3%, p < 0.05) were reduced following 7 days of increased sedentary time.

Model-Based Conditional Weighted Residuals Analysis for Structural Model Assessment

Nonlinear mixed effects models are widely used to describe longitudinal data to improve the efficiency of drug development process or increase the understanding of the studied disease. In such settings, the appropriateness of the modeling assumptions is critical in order to draw correct conclusions and must be carefully assessed for any substantial violations. Here, we propose a new method for structure model assessment, based on assessment of bias in conditional weighted residuals (CWRES). We illustrate this method by assessing prediction bias in two integrated models for glucose homeostasis, the integrated glucose-insulin (IGI) model, and the integrated minimal model (IMM). One dataset was simulated from each model then analyzed with the two models. CWRES outputted from each model fitting were modeled to capture systematic trends in CWRES as well as the magnitude of structural model misspecifications in terms of difference in objective function values (ΔOFV_Bias). The estimates of CWRES bias were used to calculate the corresponding bias in conditional predictions by the inversion of first-order conditional estimation method’s covariance equation. Time, glucose, and insulin concentration predictions were the investigated independent variables. The new method identified correctly the bias in glucose sub-model of the integrated minimal model (IMM), when this bias occurred, and calculated the absolute and proportional magnitude of the resulting bias. CWRES bias versus the independent variables agreed well with the true trends of misspecification. This method is fast easily automated diagnostic tool for model development/evaluation process, and it is already implemented as part of the Perl-speaks-NONMEM software.

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

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

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.

Long-acting Insulin in Diabetes Therapy: In Silico Clinical Trials with the UVA/Padova Type 1 Diabetes Simulator

The University of Virginia /Padova Type 1 Diabetes (TID) simulator has been widely used for testing artificial pancreas controllers, and, recently, novel insulin formulations and glucose sensors. However, a module describing the pharmacokinetics of the new long-acting insulin analogues is not available. The aim of this contribution is to reproduce multiple daily insulin injection (MDI) therapy, with insulin glargine 100 U/mL (Gla-100) as basal insulin, using the TID simulator. This was achieved by developing a model of Gla-100 and by incorporating it into the simulator. The methodology described here can be extended to other insulins, allowing an extensive in silico testing of different long-acting insulin analogues under various settings before starting human trials.

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.

Increase in hepatic and decrease in peripheral insulin clearance characterize abnormal temporal patterns of serum insulin in diabetic subjects

Insulin plays a central role in glucose homeostasis, and impairment of insulin action causes glucose intolerance and leads to type 2 diabetes mellitus (T2DM). A decrease in the transient peak and sustained increase of circulating insulin following an infusion of glucose accompany T2DM pathogenesis. However, the mechanism underlying this abnormal temporal pattern of circulating insulin concentration remains unknown. Here we show that changes in opposite direction of hepatic and peripheral insulin clearance characterize this abnormal temporal pattern of circulating insulin concentration observed in T2DM. We developed a mathematical model using a hyperglycemic and hyperinsulinemic-euglycemic clamp in 111 subjects, including healthy normoglycemic and diabetic subjects. The hepatic and peripheral insulin clearance significantly increase and decrease, respectively, from healthy to borderline type and T2DM. The increased hepatic insulin clearance reduces the amplitude of circulating insulin concentration, whereas the decreased peripheral insulin clearance changes the temporal patterns of circulating insulin concentration from transient to sustained. These results provide further insight into the pathogenesis of T2DM, and thus may contribute to develop better treatment of this condition.

Type 2 diabetes mellitus (T2DM) is one of the fastest growing public health problems, characterized by chronic hyperglycemia with the failure of glucose homeostasis. Evaluating alteration in biological functions regulating circulating glucose concentration is complicated due to the mutual relation between circulating glucose and insulin. A team led by Wataru Ogawa at Kobe University designed clinical experiments for breaking such feedback relations, and a team led by Shinya Kuroda at University of Tokyo developed mathematical models for specifically quantifying the functions from the clinical data. The estimated model parameters revealed the significant increase in hepatic and decrease in peripheral insulin clearance, which occur before and after insulin delivery into systemic circulation, respectively, from healthy to T2DM subjects. Model analysis suggested these insulin clearances centrally regulate the dynamics of circulating insulin concentration in the glucose-insulin regulatory system.

Performance of individually measured vs population-based C-peptide kinetics to assess β-cell function in the presence and absence of acute insulin resistance

AIMS

To compare the performance of population-based kinetics with that of directly measured C-peptide kinetics when used to calculate β-cell responsivity indices, and to study people with and without acute insulin resistance to ensure that population-based kinetics apply to all conditions where β-cell function is measured.

METHODS

Somatostatin was used to inhibit endogenous insulin secretion in 56 people without diabetes. Subsequently, a C-peptide bolus was administered and the changing concentrations were used to calculate individual kinetic measures of C-peptide clearance. In addition, the participants were studied on 2 occasions in random order using an oral glucose tolerance test (OGTT). On one occasion, free fatty acid elevation, to cause insulin resistance, was achieved by infusion of Intralipid + heparin. The Disposition Index (DI) was then estimated by the oral minimal model using either population-based or individual C-peptide kinetics.

RESULTS

There were marked differences in the exchange variables (k ₁₂ and k ₂₁ ) of the model describing C-peptide kinetics, but smaller differences in the fractional clearance; that is, the irreversible loss from the accessible compartment (k ₀₁ ), obtained from population-based estimates compared with experimental measurement. Because it is predominantly influenced by k ₀₁ , DI estimated using individual kinetics correlated well with DI estimated using population-based kinetics.

CONCLUSIONS

These data support the use of population-based measures of C-peptide kinetics to estimate β-cell function during an OGTT.

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.

Modeling Subcutaneous Absorption of Fast-Acting Insulin in Type 1 Diabetes

OBJECTIVE

Subcutaneous (sc) administration of fast-acting insulin analogues is the key in conventional therapy of type 1 diabetes (T1D). A model of sc insulin absorption would be helpful for optimizing insulin therapy and test new open- and closed-loop treatment strategies in in silico platforms. Some models have been published in the literature, but none was assessed on a frequently-sampled large dataset of T1D subjects. The aim here is to propose a model of sc absorption of fast-acting insulin, which is able to describe the data and precisely estimate model parameters with a clear physiological interpretation.

METHODS

Three candidate models were identified on 116 T1D subjects, who underwent a single sc injection of fast-acting insulin and were compared on the basis of their ability to describe the data and their numerical identifiability.

RESULTS

A linear two-compartment model including a subject-specific delay in sc insulin absorption is proposed. On average, a delay of 7.6 min in insulin appearance in the first compartment is detected, then the insulin is slowly absorbed into plasma (in 23% of the subjects) with a rate of 0.0034 min-1, while the remaining diffuses into the second compartment, with a rate constant of 0.028 min-1, and then finally absorbed into plasma with a rate constant of 0.014 min-1.

CONCLUSION

Among the three tested models, the one proposed here is the only one able to both accurately describe plasma insulin data after a single sc injection and precisely estimate physiologically plausible parameters. The model needs to be further tested in case of variable sc insulin delivery and/or multiple insulin doses.

SIGNIFICANCE

Results are expected to help the development of new open- and closed-loop insulin treatment strategies.

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.

Computer Simulation Model to Train Medical Personnel on Glucose Clamp Procedures

OBJECTIVE

A glucose clamp procedure is the most reliable way to quantify insulin pharmacokinetics and pharmacodynamics, but skilled and trained research personnel are required to frequently adjust the glucose infusion rate. A computer environment that simulates glucose clamp experiments can be used for efficient personnel training and development and testing of algorithms for automated glucose clamps.

METHODS

We built 17 virtual healthy subjects (mean age, 25±6 years; mean body mass index, 22.2±3 kg/m²), each comprising a mathematical model of glucose regulation and a unique set of parameters. Each virtual subject simulates plasma glucose and insulin concentrations in response to intravenous insulin and glucose infusions. Each virtual subject provides a unique response, and its parameters were estimated from combined intravenous glucose tolerance test-hyperinsulinemic-euglycemic clamp data using the Bayesian approach. The virtual subjects were validated by comparing their simulated predictions against data from 12 healthy individuals who underwent a hyperglycemic glucose clamp procedure.

RESULTS

Plasma glucose and insulin concentrations were predicted by the virtual subjects in response to glucose infusions determined by a trained research staff performing a simulated hyperglycemic clamp experiment. The total amount of glucose infusion was indifferent between the simulated and the real subjects (85±18 g vs. 83±23 g; p=NS) as well as plasma insulin levels (63±20 mU/L vs. 58±16 mU/L; p=NS).

CONCLUSIONS

The virtual subjects can reliably predict glucose needs and plasma insulin profiles during hyperglycemic glucose clamp conditions. These virtual subjects can be used to train personnel to make glucose infusion adjustments during clamp experiments.

Asymptotic tracking and disturbance rejection of the blood glucose regulation system

Type 1 diabetes patients need external insulin to maintain blood glucose within a narrow range from 65 to 108 mg/dl (3.6 to 6.0 mmol/l). A mathematical model for the blood glucose regulation is required for integrating a glucose monitoring system into insulin pump technology to form a closed-loop insulin delivery system on the feedback of the blood glucose, the so-called "artificial pancreas". The objective of this paper is to treat the exogenous glucose from food as a glucose disturbance and then develop a closed-loop feedback and feedforward control system for the blood glucose regulation system subject to the exogenous glucose disturbance. For this, a mathematical model for the glucose disturbance is proposed on the basis of experimental data, and then incorporated into an existing blood glucose regulation model. Because all the eigenvalues of the disturbance model have zero real parts, the center manifold theory is used to establish blood glucose regulator equations. We then use their solutions to synthesize a required feedback and feedforward controller to reject the disturbance and asymptotically track a constant glucose reference of 90  mg/dl. Since the regulator equations are nonlinear partial differential equations and usually impossible to solve analytically, a linear approximation solution is obtained. Our numerical simulations show that, under the linear approximate feedback and feedforward controller, the blood glucose asymptotically tracks its desired level of 90 mg/dl approximately.

Exercise training and metformin, but not exercise training alone, decreases insulin production and increases insulin clearance in adults with prediabetes

Adding metformin to exercise does not augment the effect of training alone to boost whole body insulin sensitivity and lower circulating insulin concentrations. Although lower insulin concentrations (lower supply) following lifestyle and/or pharmacological interventions are primarily attributed to reductions in insulin secretion that match increases in peripheral insulin sensitivity (lower demand), it is unclear whether exercise and/or metformin exert direct effects on insulin production, extraction, or clearance. Thirty-six middle-aged, obese, sedentary adults with prediabetes were randomized to placebo (P), metformin (M), exercise and placebo (E+P), or exercise and metformin (E+M) for 12 wk. Fasting plasma proinsulin (an indicator of insulin production), C-peptide, insulin, and glucose were collected before and after the intervention. Peripheral insulin sensitivity (euglycemic clamp), hepatic insulin extraction, insulin clearance, body weight, and cardiorespiratory fitness were also measured. Fasting proinsulin was unchanged following P (19.4 ± 10.1 vs. 22.6 ± 15.0 pmol/l), E+P (15.1 ± 7.4 vs. 15.5 ± 7.4 pmol/l), or M (24.8 ± 18.9 vs. 16.7 ± 20.3 pmol/l) but was significantly reduced after E+M (18.6 ± 11.9 vs. 13.9 ± 6.7 pmol/l; P = 0.04). Insulin clearance was significantly greater following M (384.6 ± 19.4 vs. 477.4 ± 49.9; P = 0.03) and E+M (400.1 ± 32.0 vs. 482.9 ± 33.9; P = 0.02) but was unchanged in P or E+P. In this study, metformin combined with exercise training reduced circulating proinsulin, and both groups taking metformin increased insulin clearance. This suggests that adding metformin to exercise may augment or attenuate training effects depending on the outcome or organ system being assessed.NEW & NOTEWORTHY Exercise is increasingly viewed as medication, creating a need to understand its interactions with other common medications. Research suggests metformin, a widely prescribed diabetes medication, may diminish the benefits of exercise when used in combination. In this study, however, metformin combined with exercise training, but not exercise alone, lowered proinsulin concentrations and increased insulin clearance in adults with prediabetes. This may directly influence personalized prescriptions of lifestyle and/or pharmacology to reduce diabetes risk.

Men Are from Mars, Women Are from Venus: Sex Differences in Insulin Action and Secretion

Sex difference plays a substantial role in the regulation of glucose metabolism in healthy glucose-tolerant humans. The factors which may contribute to the sex-related differences in glucose metabolism include differences in lifestyle (diet and exercise), sex hormones, and body composition. Several epidemiological and observational studies have noted that impaired glucose tolerance is more common in women than men. Some of these studies have attributed this to differences in body composition, while others have attributed impaired insulin sensitivity as a cause of impaired glucose tolerance in women. We studied postprandial glucose metabolism in 120 men and 90 women after ingestion of a mixed meal. Rates of meal glucose appearance, endogenous glucose production, and glucose disappearance were calculated using a novel triple-tracer isotope dilution method. Insulin action and secretion were calculated using validated physiological models. While rate of meal glucose appearance was higher in women than men, rates of glucose disappearance were higher in elderly women than elderly men while young women had lower rates of glucose disappearance than young men. Hence, sex has an impact on postprandial glucose metabolism, and sex differences in carbohydrate metabolism may have important implications for approaches to prevent and manage diabetes in an individual.

Incorporation of inhaled insulin into the FDA accepted University of Virginia/Padova Type 1 Diabetes Simulator

The University of Virginia/Padova Type 1 Diabetes (T1DM) Simulator has been extensively used in artificial pancreas research mostly for testing and design of control algorithms. However, it also offers the possibility of testing new insulin analogs and alternative routes of delivery given that subcutaneous insulin administration present significant delays & variability. Inhaled insulin appears an important candidate to improve post-prandial glucose control given its rapid appearance in plasma. In this contribution, we present the results of incorporating a pharmacokinetic model of inhaled Technosphere(®) Insulin (TI) into the T1DM simulator. In particular, we successfully reproduced in silico the post-prandial glucose control observed in T1DM subjects treated with TI given at meal time, and the post-prandial glucose dynamics in response to different timing of TI dose.

Improving Efficacy of Inhaled Technosphere Insulin (Afrezza) by Postmeal Dosing: In-silico Clinical Trial with the University of Virginia/Padova Type 1 Diabetes Simulator

BACKGROUND

Technosphere(®) insulin (TI), an inhaled human insulin with a fast onset of action, provides a novel option for the control of prandial glucose. We used the University of Virginia (UVA)/Padova simulator to explore in-silico the potential benefit of different dosing regimens on postprandial glucose (PPG) control to support the design of further clinical trials. Tested dosing regimens included at-meal or postmeal dosing, or dosing before and after a meal (split dosing).

METHODS

Various dosing regimens of TI were compared among one another and to insulin lispro in 100 virtual type-1 patients. Individual doses were identified for each regimen following different titration rules. The resulting postprandial glucose profiles were analyzed to quantify efficacy and the risk for hypoglycemic events.

RESULTS

This approach allowed us to assess the benefit/risk for each TI dosing regimen and to compare results with simulations of insulin lispro. We identified a new titration rule for TI that could significantly improve the efficacy of treatment with TI.

CONCLUSION

In-silico clinical trials comparing the treatment effect of different dosing regimens with TI and of insulin lispro suggest that postmeal dosing or split dosing of TI, in combination with an appropriate titration rule, can achieve a superior postprandial glucose control while providing a lower risk for hypoglycemic events than conventional treatment with subcutaneously administered rapid-acting insulin products.

Hepatic and Extrahepatic Insulin Clearance Are Differentially Regulated: Results From a Novel Model-Based Analysis of Intravenous Glucose Tolerance Data

Insulin clearance is a highly variable and important factor that affects circulating insulin concentrations. We developed a novel model-based method to estimate both hepatic and extrahepatic insulin clearance using plasma insulin and C-peptide profiles obtained from the insulin-modified frequently sampled intravenous glucose tolerance test. Data from 100 African immigrants without diabetes (mean age 38 years, body weight 81.7 kg, fasting plasma glucose concentration 83 mg/dL, and fasting insulin concentration 37 pmol/L) were used. Endogenous insulin secretion (calculated by C-peptide deconvolution) and insulin infusion rates were used as inputs to a new two-compartment model of insulin kinetics and hepatic and extrahepatic clearance parameters were estimated. Good agreement between modeled and measured plasma insulin profiles was observed (mean normalized root mean square error 6.8%), and considerable intersubject variability in parameters of insulin clearance among individuals was identified (the mean [interquartile range] for hepatic extraction was 25.8% [32.7%], and for extrahepatic insulin clearance was 20.7 mL/kg/min [11.7 mL/kg/min]). Parameters of insulin clearance were correlated with measures of insulin sensitivity and acute insulin response to glucose. The method described appears promising for future research aimed at characterizing variability in insulin clearance and the mechanisms involved in the regulation of insulin clearance.

Model-Based Quantification of Glucagon-Like Peptide-1-Induced Potentiation of Insulin Secretion in Response to a Mixed Meal Challenge

BACKGROUND

Glucagon-like peptide-1 (GLP-1) is a powerful insulin secretagogue that is secreted in response to meal ingestion. The ability to quantify the effect of GLP-1 on insulin secretion could provide insights into the pathogenesis and treatment of diabetes. We used a modification of a model of GLP-1 action on insulin secretion using data from a hyperglycemic clamp with concomitant GLP-1 infusion. We tested this model using data from a mixed meal test (MMT), thereby measuring GLP-1-induced potentiation of insulin secretion in response to a meal.

MATERIALS AND METHODS

The GLP-1 model is based on the oral C-peptide minimal model and assumes that over-basal insulin secretion depends linearly on GLP-1 concentration through the parameter Π, representing the β-cell sensitivity to GLP-1. The model was tested on 62 subjects across the spectrum of glucose tolerance (age, 53 ± 1 years; body mass index, 29.7 ± 0.6 kg/m(2)) studied with an MMT and provided a precise estimate of both β-cell responsivity and Π indices. By combining Π with a measure of L-cell responsivity to glucose, one obtains a potentiation index (PI) (i.e., a measure of the L-cell's function in relation to prevailing β-cell sensitivity to GLP-1).

RESULTS

Model-based measurement of GLP-1-induced insulin secretion demonstrates that the PI is significantly reduced in people with impaired glucose tolerance, compared with those with normal glucose tolerance.

CONCLUSIONS

We describe a model that can quantitate the GLP-1-based contribution to insulin secretion in response to meal ingestion. This methodology will allow a better understanding of β-cell function at various stages of glucose tolerance.

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

GOAL

Quantitative assessment of hepatic insulin extraction (HE) after an oral glucose challenge, e.g., a meal, is important to understand the regulation of carbohydrate metabolism. The aim of the current study is to develop a model of system for estimating HE.

METHODS

Nine different models, of increasing complexity, were tested on data of 204 normal subjects, who underwent a mixed meal tolerance test, with frequent measurement of plasma glucose, insulin, and C-peptide concentrations. All these models included a two-compartment model of C-peptide kinetics, an insulin secretion model, a compartmental model of insulin kinetics (with number of compartments ranging from one to three), and different HE descriptions, depending on plasma glucose and insulin. Model performances were compared on the basis of data fit, precision of parameter estimates, and parsimony criteria.

RESULTS

The three-compartment model of insulin kinetics, coupled with HE depending on glucose concentration, showed the best fit and a good ability to precisely estimate the parameters. In addition, the model calculates basal and total indices of HE ( HE_b and HE_tot, respectively), and provides an index of HE sensitivity to glucose ( S_G^HE ).

CONCLUSION

A new physiologically based HE model has been developed, which allows an improved quantitative description of glucose regulation.

SIGNIFICANCE

The use of the new model provides an in-depth description of insulin kinetics, thus enabling a better understanding of a given subject's metabolic state.

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.

Human insulin dynamics in women: a physiologically based model

Currently available models of insulin dynamics are mostly based on the classical compartmental structure and, thus, their physiological utility is limited. In this work, we describe the development of a physiologically based model and its application to data from 154 patients who underwent an insulin-modified intravenous glucose tolerance test (IM-IVGTT). To determine the time profile of endogenous insulin delivery without using C-peptide data and to evaluate the transcapillary transport of insulin, the hepatosplanchnic, renal, and peripheral beds were incorporated into the circulatory model as separate subsystems. Physiologically reasonable population mean estimates were obtained for all estimated model parameters, including plasma volume, interstitial volume of the peripheral circulation (mainly skeletal muscle), uptake clearance into the interstitial space, hepatic and renal clearance, as well as total insulin delivery into plasma. The results indicate that, at a population level, the proposed physiologically based model provides a useful description of insulin disposition, which allows for the assessment of muscle insulin uptake.

C-Peptide-based assessment of insulin secretion in the Zucker Fatty rat: a modelistic study

A C-peptide-based assessment of β-cell function was performed here in the Zucker fatty rat, a suitable animal model of human metabolic syndrome. To this aim, a 90-min intravenous glucose tolerance test (IVGTT) was performed in seven Zucker fatty rats (ZFR), 7-to-9week-old, and seven age-matched Zucker lean rats (ZLR). The minimal model of C-peptide (CPMM), originally introduced for humans, was adapted to Zucker rats and then applied to interpret IVGTT data. For a comprehensive evaluation of glucose tolerance in ZFR, CPMM was applied in combination with the minimal model of glucose kinetics (GKMM). Our results showed that the present CPMM-based interpretation of data is able to: 1) provide a suitable fit of C-Peptide data; 2) achieve a satisfactory estimation of parameters of interest 3) quantify both insulin secretion by estimating the time course of pre-hepatic secretion rate, SR(t), and total insulin secretion, TIS, and pancreatic sensitivity by means of three specific indexes of β-cell responsiveness to glucose stimulus (first-phase, Ф₁, second-phase, Ф₂, and steady-state, Ф_ss, never assessed in Zucker rats before; 4) detect the significant enhancement of insulin secretion in the ZFR, in face of a severe insulin-resistant state, previously observed only using a purely experimental approach. Thus, the methodology presented here represents a reliable tool to assess β-cell function in the Zucker rat, and opens new possibilities for the quantification of further processes involved in glucose homeostasis such as the hepatic insulin degradation.

Adding liraglutide to the backbone therapy of biguanide in patients with coronary artery disease and newly diagnosed type-2 diabetes (the AddHope2 study): a randomised controlled study protocol

INTRODUCTION

Newly diagnosed type 2 diabetes mellitus (T2DM) in patients with coronary artery disease (CAD) more than doubles the risk of death compared with otherwise matched glucose tolerant patients. The biguanide metformin is the drug of choice in treatment of T2DM and has shown to ameliorate cardiovascular morbidity in patients with T2DM and myocardial infarction (MI). The incretin hormone, glucagon-like peptide-1 (GLP-1) improves β-cell function, insulin sensitivity and causes weight loss and has been suggested to have beneficial effects on cardiac function. The GLP-1 receptor agonist (GLP-1RA), liraglutide, is currently used for treatment of T2DM but its potential effect on cardiac function has not been investigated in detail. We hypothesised that liraglutide added to metformin backbone therapy in patients with CAD and newly diagnosed T2DM will improve β-cell function and left ventricular systolic function during dobutamine stress.

METHODS AND ANALYSES

40 patients with CAD and newly diagnosed T2DM will receive the intervention liraglutide+metformin and placebo+metformin in this investigator-initiated, double blind, randomised, placebo-controlled, cross-over 12 plus 12 weeks intervention study with a 2-week washout period. The primary cardiovascular end point is changes in left ventricular ejection fraction during stress echocardiography. The primary endocrine end point is β-cell function evaluated during a frequently sampled intravenous glucose tolerance test. Secondary end points include heart rate variability, diurnal blood pressure, glucagon suppression and inflammatory response (urine, blood and adipose tissue).

ETHICS AND DISSEMINATION

This study is approved by the Danish Medicines Agency, the Danish Dataprotection Agency and the Regional Committee on Biomedical Research Ethics of the Capital Region of Denmark. The trial will be carried out under the guidance from the GCP unit at Copenhagen University Hospital of Bispebjerg and in accordance with the ICH-GCP guidelines and the Helsinki Declaration.

TRIAL REGISTRATIONS NUMBER

Clinicaltrials.gov ID: NCT01595789, EudraCT: 2011-005405-78.

A novel hierarchal-based approach to measure insulin sensitivity and secretion in at-risk populations

The pathogenesis of type 2 diabetes is characterized by insulin resistance and insulin secretory dysfunction. Few existing metabolic tests measure both characteristics, and no such tests are inexpensive enough to enable widespread use. A hierarchical approach uses 2 down-sampled tests in the dynamic insulin sensitivity and secretion test (DISST) family to first determine insulin sensitivity (SI) using 4 glucose measurements. Second the insulin secretion is determined for only participants with reduced SI using 3 C-peptide measurements from the original test. The hierarchical approach is assessed via its ability to classify 214 individual test responses of 71 females with an elevated risk of type 2 diabetes into 5 bins with equivalence to the fully sampled DISST. Using an arbitrary SI cut-off, 102 test responses were reassayed for C-peptide and unique insulin secretion characteristics estimated. The hierarchical approach correctly classified 84.5% of the test responses and 94.4% of the responses of individuals with increased fasting glucose. The hierarchical approach is a low-cost methodology for measuring key characteristics of type 2 diabetes. Thus the approach could provide an economical approach to studying the pathogenesis of type 2 diabetes, or in early risk screening. As the higher cost test uses the same clinical protocol as the low-cost test, the cost of the additional information is limited to the assay cost of C-peptide, and no additional procedures or callbacks are required.

Use of a simple liquid meal test to evaluate insulin sensitivity and beta-cell function in children

Insulin sensitivity and β-cell function are useful indices of metabolic disease risk but are difficult to assess in young children because of the invasive nature of commonly used methodology. A meal-based method for assessing insulin sensitivity and β-cell function may at least partially alleviate concerns. The objectives of this study were to: (i) determine the association of insulin sensitivity assessed by liquid meal test with that determined by an insulin-modified frequently sampled intravenous glucose tolerance test (FSIGT); (ii) examine the association of insulin sensitivity derived from each test with measures of body composition, fat distribution and metabolic health (lipids, fasting insulin and glucose, and surrogate indices of insulin sensitivity); and (iii) examine the associations of indices of β-cell function derived from each test with total and regional adiposity. Forty-seven children (7-12 years) underwent both a liquid meal test and an FSIGT. The insulin sensitivity index derived from the meal test (SI-meal) was positively associated with that from the FSIGT (SI-FSIGT; r = 0.63; P < 0.001), and inversely with all measures of insulin secretion derived from the meal test. Both SI-meal and SI-FSIGT were associated with measures of total and regional adiposity. SI-meal, but not SI-FSIGT, was associated with triglycerides and fasting insulin, after adjusting for ethnicity, gender, pubertal stage and fat mass. Basal insulin secretion measured during the meal test was positively associated with all measures of adiposity, independent of insulin sensitivity. In conclusion, a liquid meal offers a valid and sensitive means of assessing insulin sensitivity and β-cell responsivity in young children.