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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.

Insulin has been utilized in the treatment of type 1 diabetes (T1D) for 100 years. While there is still no cure for T1D, insulin administration has undergone a remarkable evolution which has contributed to improvements in quality of life and life expectancy in individuals with T1D. The advent of faster-acting and longer-acting insulins allowed for the implementation of insulin regimens more closely resembling normal insulin physiology. These improvements afforded better glycemic control, which is crucial for limiting microvascular complications and improving T1D outcomes. Suspension of insulin delivery in response to actual and forecasted hypoglycemia has improved quality of life and mitigated hypoglycemia without compromising glycemic control. Advances in continuous glucose monitoring (CGM) and insulin pumps, efforts to model glucose and insulin kinetics, and the application of control theory to T1D have made the automation of insulin delivery a reality. This review will summarize the past, present, and future of insulin administration in T1D.

Background Intraperitoneal insulin delivery has proven to safely overcome a major limit of subcutaneous delivery—meal announcement—and has been able to optimize glycemic control in adults under controlled experimental conditions. In addition, intraperitoneal delivery avoids peripheral hyperinsulinemia resulting from the subcutaneous route and restores a physiological liver gradient. Methods Relying on a unique data set of intraperitoneal closed-loop insulin delivery obtained with a Model Predictive Controller (MPC), we develop a compartmental model of intraperitoneal insulin kinetics, which, once included in the UVa/Padova T1D simulator, will facilitate the investigation of various control strategies, for example, the simpler Proportional Integral Derivative controller versus MPC. Results Intraperitoneal insulin kinetics can be described with a 2-compartment model including liver and plasma. Conclusion Intraperitoneal insulin transit is fast enough to render irrelevant the addition of a peritoneal compartment, proving the peritoneum being a virtual—not actual—transit space for insulin delivery.

IntroductionPostbariatric hypoglycaemia (PBH) is an increasingly recognized late metabolic complication of Roux-en-Y gastric bypass (GB) surgery. PBH typically manifests with a fact occurring post-meal hyperglycaemic peak, followed by a disproportionately exaggerated insulin response leading to low glucose levels. On this basis, we evaluated the effect of a single dose of empagliflozin 10mg vs. placebo on parameters of insulin kinetics.Materials and methodsInsulin secretion, hepatic insulin extraction and total insulin clearance were evaluated after a single of empagliflozin 10mg vs. placebo followed by a standardized liquid mixed meal were evaluated in 11 subjects with confirmed PBH after GB over 3h. Parameters of interest were calculated using established mathematical models. Indices were compared between the groups using the Wilcoxon signed-rank test.ResultsTotal beta-cell responsiveness tends to be lower with empagliflozin vs. placebo (24.83±11.00 vs. 27.15±9.68 [10−9 min-1], p=0.150). Total first-pass hepatic insulin extraction increased after empagliflozin compared to placebo (49.6±14.2 vs. 39.7±12.1 %, p=0.006), while no significant effect of empaglizflozin on basal first-pass hepatic insulin extraction was observed (79.7±7.1 vs. 81.1±6.6 %, p=0.521). Total insulin clearance resulted to be significantly lower after empagliflozin compared to placebo (3.91±1.58 vs. 3.00±1.27 l/min, p=0.002).ConclusionThe present analysis suggests that the hypoglycaemia-attenuating effect of SGLT2-inhibition in patients with PBH is mainly mediated by an increment in insulin clearance, with also a tendency to a reduction in insulin secretion.

We read, with interest, the recent publication by Tricò et al. [...]

Graphical abstract, Highlights • Insulin resistance (IR) is key to the development of numerous metabolic diseases. • HMB is a nutraceutical with contentious effects on IR in animal models. • The effect of HMB during a glucose challenge on insulin resistance is unknown. • HMB improved insulin sensitivity to a glucose challenge in young, but not older men. • Clinical trials are needed to establish the chronic effect of HMB on glycaemic control., Insulin resistance (IR) is a key feature in the development of numerous metabolic diseases. The cornerstone for treatment for IR remains diet and exercise, however these have poor rates of adherence. Beta-hydroxy-beta-methylbutyrate (HMB) is a nutraceutical with contentious effects on IR in animal models. The aim of this study was to evaluate the impact of acute HMB on IR in humans during an oral glucose tolerance test (OGTT). Young and older male volunteers underwent two 75 g OGTT with or without 3 g HMB. In young men, HMB significantly reduced the insulin area-under-the-curve (AUC), with no difference in glucose AUC, resulting in a numerical increase in the Cederholm index of insulin sensitivity. In older men, HMB had no effect on insulin or glucose responses. In conclusion, acute HMB may improve IR following a glucose load in young men; however, this does not appear to be sustained into older age.

Variations in feeding behaviour between animals result from individual variations in their metabolism as affected by diet composition. The study aimed to link the within-day dynamics of voluntary feed intake and those of blood metabolites and insulin in growing pigs havingad libitumaccess to feed and receiving diets differing in dietary fibre levels and aleurone supplementation. A total of forty pigs (body weight: 35 kg) had access to diets providedad libitum, which differed by fibre content (13 or 18 % neutral-detergent fibre) and aleurone supplementation (0, 2 or 4 g/kg). Feeding behaviour was individually recorded for 1 week. The kinetic of plasma metabolites and insulin was followed for 1 h after a voluntary test meal. Dietary fibre level did not affect the daily feed intake but increased meal size and meal duration. Aleurone supplementation (4 g/kg) decreased the daily feed intake and number of meals. Dietary fibre level only decreased insulin concentration measured 15 min after meal beginning. Aleurone supplementation (4 g/kg) decreased glycaemia in the first hour after the meal and insulinaemia 15 min after the meal. Free access to feed led to high variability in pre-prandial metabolites and insulin concentrations, resulting in different test meal size irrespective of diet composition. Animals were then spread over different profiles combining feeding behaviour and fasted status to explain different profiles of regulation of feed intake. Plasma metabolites and insulin kinetics were affected by diet composition but also by animal characteristics. Individual variability should be considered when diet composition is used to modulate feeding behaviour.

Optimizing feeding regimens in early life to maximize lifelong growth and production are essential in the dairy industry. This study investigated the effects of milk replacer (MR) feeding frequency and calf age on behavior, and glucose and insulin kinetics of pre- and post-weaned calves fed an elevated plane of MR. Ten male Holstein calves (42.2±1.8 kg BW) were blocked by BW and randomly assigned to two treatments offering 8 l MR/day (150 g/l) in two (2×; meal size 4 l) or four (4×; meal size 2 l) feedings via an automated calf feeder. Milk replacer was gradually stepped down by 1 l/day during week 8, with calves being weaned by week 9. Water and pelleted calf starter were offered ad libitum. Individual intake of MR and starter were recorded daily, and BW was recorded weekly. The number of visits to the MR feeder (rewarded and unrewarded), and behaviors such as lying, cross-sucking, non-nutritive sucking and occupancy time in the feeder were recorded for individual calves from weeks 4 to 10. Jugular catheters were placed on weeks 4, 7 and 10 to facilitate postprandial blood sampling and glucose tolerance tests. Statistical analysis was conducted using the PROC GLIMMIX procedure (SAS) for behavioral observations, and the MIXED procedure (SAS) with repeated measures for BW, intake, plasma glucose and plasma insulin data. Final BW, starter and MR intake did not differ between treatments. There were no differences in observed calf behaviors; with the exception that 2× calves visited the MR feeder more often (Plt;0.01; total: unrewarded and rewarded). Baseline concentrations (mmol/l) and the maximum change in glucose (delta, mmol/l) were greater and lower (P=0.02) in 4×compared to 2×calves, respectively. Postprandial insulin AUC240 tended (P=0.09) to be greater in 2×calves, compared to 4×calves at week 7. Similarly, T max (min), AUC240 and delta values (µU/ml) were greater (P⩽0.05) in 2×calves, compared to 4×calves. No treatment ×age interactions were observed for glucose or insulin during the glucose tolerance tests. Therefore, we conclude that feeding an elevated plane of MR (8 l/day) at a lower frequency (2× v. 4×) increased feeder visits, but not other hunger-related behaviors, and while postprandial glucose and insulin parameters varied, insulin sensitivity remained stable in Holstein dairy calves up to 10 weeks of age in calves consuming similar levels of calf starter.

We thank Dr. Landry and colleagues [...]

Background Models of human glucose–insulin physiology have been developed for a range of uses, with similarly different levels of complexity and accuracy. STAR (Stochastic Targeted) is a model-based approach to glycaemic control. Elevated blood glucose concentrations (hyperglycaemia) are a common complication of stress and prematurity in very premature infants, and have been associated with worsened outcomes and higher mortality. This research identifies and validates the model parameters for model-based glycaemic control in neonatal intensive care. Methods C-peptide, plasma insulin, and BG from a cohort of 41 extremely pre-term (median age 27.2 [26.2–28.7] weeks) and very low birth weight infants (median birth weight 839 [735–1000] g) are used alongside C-peptide kinetic models to identify model parameters associated with insulin kinetics in the NICING (Neonatal Intensive Care Insulin–Nutrition–Glucose) model. A literature analysis is used to determine models of kidney clearance and body fluid compartment volumes. The full, final NICING model is validated by fitting the model to a cohort of 160 glucose, insulin, and nutrition data records from extremely premature infants from two different NICUs (neonatal intensive care units). Results Six model parameters related to insulin kinetics were identified. The resulting NICING model is more physiologically descriptive than prior model iterations, including clearance pathways of insulin via the liver and kidney, rather than a lumped parameter. In addition, insulin diffusion between plasma and interstitial spaces is evaluated, with differences in distribution volume taken into consideration for each of these spaces. The NICING model was shown to fit clinical data well, with a low model fit error similar to that of previous model iterations. Conclusions Insulin kinetic parameters have been identified, and the NICING model is presented for glycaemic control neonatal intensive care. The resulting NICING model is more complex and physiologically relevant, with no loss in bedside-identifiability or ability to capture and predict metabolic dynamics.

Parametric sensitivities of nonsmooth glucose-insulin kinetics models are investigated in this article. In particular, we study several variations on a model of the so-called Intravenous Glucose Tolerance Test (IVGTT), which measures a subject’s insulin response to glucose over time and yields data useful for characterizing and diagnosing diabetes. Nonsmoothness refers here to continuous behavior that is punctuated by “switches” (physiological events) arising due to biochemical and control thresholds being crossed. Insulin secretion from a typical pancreatic response and insulin infusion from an external device (for diabetic patients) are both considered here. The presence of nonsmoothness means that classical sensitivity theory and associated numerical methods are ill-equipped to handle these models. Motivated by this, lexicographic directional differentiation and lexicographic “sensitivity functions” are used, which are recently developed tools in nonsmooth analysis. Using this new approach, we derive nonsmooth sensitivity systems associated with the considered glucose kinetics models, whose unique solutions provide local sensitivity information analogous to classical forward parametric sensitivity functions. Moreover, the theory is practically implementable and the resulting sensitivity functions are computationally relevant, as they can be supplied to dedicated nonsmooth numerical methods (e.g., optimization). The nonsmooth sensitivity systems are solved numerically, giving new insights into the model, and thus into the dynamics of glucose kinetics under the simulated conditions. It is hoped that the results here may be used to improve the design of assessments for diabetes (e.g., the IVGTT) and its treatment.

The plasma concentration of insulin is determined by pancreatic beta cell secretion and the metabolic clearance of the hormone. It has been suggested that the concentration of insulin determines its metabolic clearance rate. Also, some reports suggest that clearance is saturable and insulin kinetics are non-linear even within physiologic ranges. We assessed the metabolic clearance rate of insulin at different physiologic concentrations to access if clearance changes with concentration. Using the dog model (n=12), insulin was infused peripherally at 3 incremental rates (dose-response) during the euglycemic clamp. Each infusion rate spanned 90mins, and the last 30mins was considered the steady state. The metabolic clearance rate of insulin was calculated as the ratio of the infusion rate to the steady state plasma concentration. The 3 infusion rates, 1.5, 3.0 and 4.5pmol/kg/min yielded steady state plasma insulin concentrations of 92 ± 8, 165 ± 12 and 256 ± 18pM respectively. The metabolic clearance rate of insulin was consistent and independent of dose (17.8 ±1.7, 19.1 ±1.2 and 18.6 ±1.4 ml/kg/min; p = ns) across the different plasma insulin infusion rates. Also, we found a strong linear correlation (r = 0.99) between the infusion rates and steady state insulin concentrations. Insulin kinetics are linear and the metabolic clearance of insulin is not saturable within physiologic ranges in the conscious dog. Though it’s possible that the site of degradation (i.e., liver vs. periphery) may change with dose.These data demonstrate that changing concentrations of plasma insulin within physiologic concentrations does not change the rate of insulin removal from the plasma. Disclosure I. Asare Bediako: None. R.L. Paszkiewicz: None. O.O. Woolcott: None. R.N. Bergman: Advisory Panel; Self; Ingredion, Inc.. Research Support; Self; AstraZeneca. Consultant; Self; GI Dynamics Inc.. Research Support; Self; National Institute of Diabetes and Digestive and Kidney Diseases. Consultant; Self; Novo Nordisk A/S.

The development and clinical testing of closed-loop systems (the artificial pancreas) is underpinned by advances in continuous glucose monitoring and benefits from concerted academic and industry collaborative efforts. This review describes the progress of the Artificial Pancreas Project at the University of Cambridge from 2006 to 2014. Initial studies under controlled laboratory conditions, designed to collect representative safety and performance data, were followed by short to medium free-living unsupervised outpatient studies demonstrating the safety and efficacy of closed-loop insulin delivery using a model predictive control algorithm. Accompanying investigations included assessment of the psychosocial impact and key factors affecting glucose control such as insulin kinetics and glucose absorption. Translation to other disease conditions such as critical illness and Type 2 diabetes took place. It is concluded that innovation of iteratively enhanced closed-loop systems will provide tangible means to improve outcomes and quality of life in people with Type 1 diabetes and their families in the next decade.

Inability to maintain blood glucose concentrations (BG) to a normal range is a common complication of prematurity and stress in neonatal intensive care units (NICUs). STAR (Stochastic TARgeted) glycaemic control uses physiological models to capture and predict patient glycaemic behaviour, and thus dose insulin safely and effectively for tight glycaemic control. STAR in the NICU has in past been based on a simple NICU model. In this study, clinical data is used to identify and validate insulin kinetic parameters of the more physiologically descriptive NICING (Neonatal Intensive Care Insulin-Nutrition-Glucose) model. C-peptide, plasma insulin and BG from a cohort of 41 extremely pre-term (median age 27.2 [26.2 - 28.7] weeks) and very low birth-weight infants (median birth weight 839 [735 - 1000] g) was used alongside C-peptide kinetic models to identify model parameters associated with insulin kinetics in the NICING model. These kinetic parameters in the NICING model were validated by fitting the model to a cohort of 160 glucose, insulin, and nutrition data records from extremely premature infants from two different NICUs. The model fits data and predicts changes in BG in a manner similar to the previous NICU model, indicating that it will perform safely and effectively in the clinical setting. However, the NICING model is more physiologically descriptive, capturing more insulin kinetics and allowing consistency with existing adult ICU glycaemic control protocols and other diabetes models.

Insulin is an anabolic hormone that plays a central role in glucose homeostasis. Synthesis, secretion and appearance of insulin in portal and peripheral circulation are complex and tightly regulated. As many of the tissues involved are not directly accessible, mathematical models have been developed to describe insulin kinetics. This paper presents a mathematical synthesis of models for the study of insulin kinetics and is meant as a supplemental to our recent review of glucose kinetics models, some of which encompass insulin sub-models. Models are described in steady and non-steady state and are grouped into compartmental and non-compartmental schemes.

The distribution and elimination of a bolus of glucose injected during hemodialysis (HD) was examined using a distributed double-pool regional blood flow model. Intracorporeal glucose disposal was assumed as insulin-independent (λ) in the central high-flow compartment comprising blood, brain, and internal organs, including pancreatic insulin secretion (a, C1) and hepatic insulin clearance (α). Insulin-dependent (γ) glucose utilization was allocated to the low-flow system comprising muscle, skin, and bone. This model was compared with a compact single-pool model using the same model parameters except for the distribution volume (V). Six parameters (C1, a, α, λ, γ, and V) were identified from data obtained in seven nondiabetic patients (59-115 kg). The fraction Fd of glucose removed by HD significantly (p < 0.05) correlated with baseline glucose concentration Cg,0 (5.561 ± 0.646 mmol/L; r = 0.535), extracorporeal clearance Kg (0.137 ± 0.024 L/min; r = 0.537), a (0.278 ± 0.095 L/mmol, r = -0.586), and λ (0.099 ± 0.078 L/min, r = -0.587). V was much larger in the double-compartment (17.8 ± 5.1 L) than in the single-compartment model (10.0 ± 3.0 L). The modeled glucose compartment volumes could be of interest for fluid management in HD patients. The use of extracorporeal glucose disposal to detect impaired glucose utilization (a, λ) remains to be validated in diabetic HD patients.

Glucose-insulin system models are commonly used for identifying insulin sensitivity, either for glycaemic control or diagnostic purposes. With physiological, 2-compartment insulin kinetics models, accurate kinetic parameter values are necessary to obtain reliable estimates of insulin sensitivity. This study combined data from 6 separate, published microdialysis studies to determine the best parameter values for the transcapillary diffusion rate ( n I ) and cellular insulin clearance rate ( n C ). The 6 studies (12 data sets) used microdialysis techniques to assay interstitial insulin concentrations simultaneously with plasma insulin concentration samples. The reported plasma insulin concentrations were used as input and interstitial insulin concentrations were simulated with the interstitial insulin kinetics sub-model. These simulated results were then compared to the reported interstitial measurements and an error value calculated as the mean absolute difference across the original measurement time points, normalised by the mean interstitial insulin concentration. The most appropriate set of parameter values was determined across the 12 data sets by combining the results. The results of this investigation suggest that the most appropriate values for the interstitial insulin kinetic parameters are n I = n C = 0.0060 min -1 . These parameter values are associated with an effective, interstitial insulin half-life t 1/2 = 58 mins, within the range of 25-130 mins reported by others.

This article is the conclusion of a two-part series on managing the difficult diabetic patient. In this section, problems with insulin kinetics are reviewed, including issues with absorption, duration of effect and anti-insulin antibodies. Guidelines about selecting an appropriate insulin type are provided for both dogs and cats, along with background information about the expected behaviour of the common types used in these species. A detailed approach to the insulin-resistant patient is described, along with specific suggestions for the evaluation of apparent insulin resistance. Unrelated hypoglycaemic disorders are also discussed.

Objective To review issues surrounding manage- ment of diabetes mellitus during times of extreme high temperatures. Methods Materials used for this article were identi- fied through a search of MEDLINE publications from 1966 to 2009. We chose English-language articles by using terms that cross-referenced diabetes mellitus, hot tempera- ture, heat, desert, and insulin. Results Persons with diabetes may have greater sus- ceptibility to adverse effects from heat (ie, increased num- ber of emergency department visits and hospitalizations, increased occurrence of dehydration and electrolyte abnor- malities, and higher death rate) than persons without dia- betes. Alterations in glucose homeostasis may occur, and changes in insulin kinetics and stability are possible. The impact of heat exposure on equipment performance (eg, glucometers) must be considered. Conclusions Having diabetes places a person at risk for heat-related health problems. Physicians must be aware of possible complications that diabetic patients may encounter in summer heat to prevent problems. Patient educational materials should be developed relating to self- management skills in the heat, and the topic should be in- cluded in standard diabetes education programs when ap- plicable. (Endocr Pract. 2010;16:506-511)

This study was designed to investigate the pharmacokinetics/pharmacodynamics (PK/PD) risk factors preceding the onset of type 2 diabetes using a population-based Bayesian nonlinear hierarchical model to describe the glucose-insulin kinetics. One hundred fifty-two healthy subjects with a family history of type 2 diabetes were recruited. Each subject received an intravenous glucose tolerance test (IVGTT) and the data of glucose and insulin was collected when entering the study. After the test, subjects were followed up to 25 years and further divided into the diabetic outcome group and non-diabetic outcome group according to the follow-up results. A glucose-insulin kinetic model was developed to account for the physiology and molecular biology of the insulin biphasic secretion and glucose-insulin interactions with a minimal structure. The population PK/PD parameters of the two groups were estimated from the proposed glucose-insulin kinetic model. The relationships between the population PK/PD parameters and the diabetic follow-up results were evaluated. A high insulin baseline concentration, a lower maximum insulin-dependent glucose removal and a lower insulin removal rate constant were found associated with the development of type 2 diabetes in the high risk population. The study shows that the very early pre-diabetic pharmacokinetic differences exist and can be helpful for prediction of development of type 2 diabetes.

The pharmacokinetics and pharmacodynamics of a Bentley Pharmaceuticals proprietary intranasal (IN) insulin formulation (Nasulin) were studied in healthy volunteers.Thirteen fasting healthy male volunteers received five doses of medication (one dose of 4 international units [IU] subcutaneous (SC) regular insulin and four doses of 25 IU IN insulin) at least 48 h apart. Serum insulin, serum C-peptide, and plasma glucose were measured in the 4 h after dosing. Profiles were compared for IN insulin spray following administration into the dominant nostril (more open at time of dosing) and into the nondominant nostril (less open at time of dosing).The formulation was generally well tolerated. A rise in serum insulin levels accompanied by a decrease in plasma glucose was seen following all doses. For IN doses, peak insulin levels were generally attained in 10-20 min and remained elevated for approximately 40-50 min; the resultant effect on glucose peaked at 40 min and waned approximately 2 h postdosing. As reported in other studies, the interindividual response to insulin was variable. The comparative absorption of IN insulin relative to SC insulin was 12.0% (dominant nostril) or 15.4% (nondominant nostril) over 2 h. This increased somewhat if sneezers and volunteers with moderately blocked nostrils were removed from the analysis.This IN formulation was generally well tolerated and relatively well absorbed. While both insulin data (maximal plasma concentration and area under the plasma concentration time curve) and glucose data (% fall) support a trend toward better absorption from the nondominant nostril, this did not reach statistical significance. Nasulin can be administered without reference to the nasal cycle.

Focused research is underway to improve the delivery of tight glycaemic control at the intensive care unit. A major component is the development of safe, efficacious and effective insulin titration algorithms, which are normally evaluated in time-consuming resource-demanding clinical studies. Simulation studies with virtual critically ill patients can substantially accelerate the development process. For this purpose, we created a model of glucoregulation in the critically ill. The model includes five submodels: a submodel of endogenous insulin secretion, a submodel of insulin kinetics, a submodel of enteral glucose absorption, a submodel of insulin action and a submodel of glucose kinetics. Model parameters are estimated utilizing prior knowledge and data collected routinely at the intensive care unit to represent the high intersubject and temporal variation in insulin needs in the critically ill. Bayesian estimation combined with the regularization method is used to estimate (i) time-invariant model parameters and (ii) a time-varying parameter, the basal insulin concentration, which represents the temporal variation in insulin sensitivity. We propose a validation process to validate virtual patients developed for the purpose of testing glucose controllers. The parameter estimation and the validation are exemplified using data collected in six critically ill patients treated at a medical intensive care unit. In conclusion, a novel glucoregulatory model has been developed to create a virtual population of critically ill facilitating in silico testing of glucose controllers at the intensive care unit.

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 ( ${\rm HE_{b}}$ and ${\rm HE_{tot}}$ , respectively), and provides an index of HE sensitivity to glucose ( ${\rm S}_G^{\rm HE}$ ). 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.

Modelling can enhance the diagnosis and control of metabolic disorders. Clinical effectiveness demands physiological accuracy, patient specificity and identification with limited data. A two-compartment insulin kinetics model and associated insulin-glucose pharmacodynamics are presented. Similarities with C-peptide kinetics are used to simplify parameter identification. Critical patient specific parameters are identified using a novel convex, integral-based method. The model and methods are validated within physiological ranges using euglycaemic clamp (N=146) and IVGTT data. The mean absolute errors in the resulting glucose and insulin profiles are eG = 5.9% ± 6.6% SD and eI = 6.2% ± 6.4% SD for the clamps and area under glucose and insulin profiles deviated and during IVGTT.

Hyperglycaemia in critically ill patients increases the risk of further complications and mortality. This paper introduces a model capable of capturing the essential glucose and insulin kinetics in patients from retrospective data gathered in an intensive care unit (ICU). The model uses two time-varying patient specific parameters for glucose effectiveness and insulin sensitivity. The model is mathematically reformulated in terms of integrals to enable a novel method for identification of patient specific parameters. The method was tested on long-term blood glucose recordings from 17 ICU patients, producing 4% average error, which is within the sensor error. One-hour forward predictions of blood glucose data proved acceptable with an error of 2-11%. All identified parameter values were within reported physiological ranges. The parameter identification method is more accurate and significantly faster computationally than commonly used non-linear, non-convex methods. These results verify the model's ability to capture long-term observed glucose-insulin dynamics in hyperglycemic ICU patients, as well as the fitting method developed. Applications of the model and parameter identification method for automated control of blood glucose and medical decision support are discussed.

We investigated insulin lispro kinetics with bolus and continuous subcutaneous insulin infusion (CSII) modes of insulin delivery. Seven subjects with type-1 diabetes treated by CSII with insulin lispro have been studied during prandial and postprandial conditions over 12 hours. Eleven alternative models of insulin kinetics have been proposed implementing a number of putative characteristics. We assessed 1) the effect of insulin delivery mode, i.e., bolus or basal, on the insulin absorption rate, the effects of 2) insulin association state and 3) insulin dose on the rate of insulin absorption, 4) the remote insulin effect on its volume of distribution, 5) the effect of insulin dose on insulin disappearance, 6) the presence of insulin degradation at the injection site, and finally 7) the existence of two pathways, fast and slow, of insulin absorption. An iterative two-stage parameter estimation technique was used. Models were validated through assessing physiological feasibility of parameter estimates, posterior identifiability, and distribution of residuals. Based on the principle of parsimony, best model to fit our data combined the slow and fast absorption channels and included local insulin degradation. The model estimated that 67(53-82)% [mean (interquartile range)] of delivered insulin passed through the slow absorption channel [absorption rate 0.011(0.004-0.029) min/sup -1/] with the remaining 33% passed through the fast channel [absorption rate 0.021(0.011-0.040) min/sup -1/]. Local degradation rate was described as a saturable process with Michaelis-Menten characteristics [V/sub MAX/=1.93(0.62-6.03) mU min/sup -1/, K/sub M/=62.6(62.6-62.6) mU]. Models representing the dependence of insulin absorption rate on insulin disappearance and the remote insulin effect on its volume of distribution could not be validated suggesting that these effects are not present or cannot be detected during physiological conditions.

The regulation of glucose metabolism, in healthy subjects, is based on a complex control system which aims to maintain plasma glucose concentrations within a narrow range (70÷180 mg/dl). Insulin, a hormone secreted by pancreatic beta-cells, is fundamental in maintaining glucose homeostasis, by reducing liver glucose production, while promoting its utilization by the insulin-dependent organs. The inability of beta-cells to adequately secrete insulin creates metabolic disorders which can result in glucose intolerance and even diabetes mellitus. There are two different kinds of diabetes: type 1 diabetes (T1DM), characterized by a total inability of pancreatic beta-cells to secrete insulin, and type 2 diabetes (T2DM), in which, because of insulin resistance, tissues are unable to appropriately utilize glucose, and insulin secretion is unable to compensate for this defect. Given the increasing prevalence of diabetes, a complete understanding of all the mechanisms involved in the glucose regulation system is essential. The liver is a fundamental organ in glucose regulation, since it is also responsible for circulating insulin levels by extracting about 50% of insulin appearing in the portal circulation, with every passage through it. A quantitative estimation of hepatic insulin extraction (HE), both in basal and dynamic physiological conditions (such as after an oral glucose load) is therefore a key aspect for a systematic description of glucose metabolism. Since a direct measurement of HE is very invasive, requiring the insertion of catheters into the portal and hepatic veins, indirect methods employing mathematical models are used. Such models require measurement of plasma concentrations and knowledge of the kinetics of C-peptide, and insulin secretion and clearance. This is facilitated by the fact that insulin and C-peptide are secreted in a 1:1 ratio by the beta-cells, and that the liver extracts insulin, but not C-peptide. The first model available in the literature for assessing HE was developed by Toffolo et al. and describes HE during an insulin modified intravenous glucose tolerance test (IM-IVGTT); this model estimates the insulin secretion rate (ISR) and the insulin delivery rate (IDR) from C-peptide and insulin concentrations, respectively. HE is subsequently derived from these two fluxes. More recently, Campioni et al. proposed a model to estimate HE after meal ingestion. In this case HE is described as a piecewise linear function, with a fixed number of breakpoints, which are the model parameters to be estimated. The main limitation of this approach is that, although allowing a reconstruction of the HE profile, it does not provide a mechanistic relationship between the involved variables, and thus the resulting model parameters do not have an easy physiological interpretation. Moreover, model structure makes the parameter identification vulnerable to noise, since the HE profile may vary rapidly to fit fluctuations in peripheral insulin concentrations. The aim of this work is to overcome the disadvantages of the available HE description by proposing a new physiological model of insulin kinetics and extraction. The best model is selected from seven, including an increasing number of compartments and different mechanistic descriptions of HE, each taking into account the influence of one or more modifiers, such as plasma glucose and insulin concentrations. In fact, during an oral test, one observes that, while glucose and insulin concentrations rise, the HE time course decreases in the meantime. These models are tested against data of a frequently sampled mixed meal (21 plasma samples) measured in 204 healthy subjects. The best model was selected according to standard criteria (ability to describe the data, precision of parameter estimates, model parsimony). Such a model describes insulin kinetics with three compartments, and HE as a function of plasma glucose concentration. One of the peculiarities of this model is to provide an index of HE sensitivity to glucose (SGHE), besides total (HEtot) and basal (HEb) HE indexes, already adopted in the literature. Moreover, the new model performs well even in data sets with less frequent sampling (11 samples). The new model was then applied to three further databases, involving subjects with different degrees of glucose tolerance, studied with a standard mixed meal or the oral glucose tolerance test (OGTT). The first data set is composed of 62 prediabetic subjects (including healthy, glucose intolerant subjects, and subjects with impaired fasting glucose), who underwent a triple tracer mixed meal and an OGTT. The model was able to describe data during both the tests, and HE indexes are shown to correlate with the degree of dysfunction in glucose metabolism. The second data set consists of 11 healthy and 14 T2DM subjects, matched for age, weight and body mass index (BMI), who underwent a mixed meal test with the triple tracer technique. Also in this case, the new model predicts the data, and the estimated HE indexes (HEb, HEtot, SGHE) differ significantly between the two groups. The last database is composed of 14 subjects with T2DM who were treated with vildagliptin or placebo before the meal; moreover, at t = 300 min, 0.02 unit/kg insulin was administered intravenously (over a 5-min period), thus allowing a better estimation of insulin kinetics. In this case the model was used in two different ways: at first, analyzing all the available plasma samples, then, neglecting the insulin infusion and just considering the former part of the test. Interestingly, the model provided a good correlation among the HE parameters in these two different occasions. In summary, we have developed a model of insulin kinetics which contains a new physiological description of HE. This model allows a good prediction of the available data during meals and OGTT in all the spectrum of glucose tolerance (healthy, intolerant and T2DM), also providing a powerful new index of HE sensitivity to glucose.

Two plasma insulin estimators are derived and evaluated in this paper. The estimators use continuously monitored plasma glucose, and they are based on a simple mathematical model of glucose-insulin metabolism. The first estimator (Estimator 1) was obtained from the glucose subsystem of the simplified model, which includes plasma glucose and interstitial insulin compartments. The second estimator (Estimator 2) was developed from the insulin kinetics subsystem of the simplified model. The performances of the estimators were compared using computer simulations and data from clinical intravenous glucose tolerance test procedures and from animal experiments.

This article reviews the concept of using the proper methods for the proper task, in this case measuring dose-to-dose accuracy of continuous subcutaneous insulin infusion pumps.

The interaction of insulin with metformin on muscle glucose metabolism was examined in the perfused rat hindquarter. Glucose, lactate, and insulin were measured at the inflow to and outflow from the hindquarter, which was perfused with human erythrocytes suspended in a Kreb's-Ringer albumin buffer for 120 min. Perfusions were performed with no additions (I) and with insulin infusions targeted to concentrations of 175 (II) and 350 pmol/l (III) as well as infusions targeted to levels of 0 (IV), 70 (V), and 175 pmol/l (VI) but in the presence of metformin (90 μg/ml). In the presence of metformin, identical infusion rates of insulin yielded higher insulin concentrations, namely 283 ± 19 vs. 202 ± 31 pmol/l for VI and II, respectively ( P < 0.05). Glucose uptake (GU) increased correspondingly to 79.8 ± 0.8 in VI from 60.8 ± 2.1 for IV and 50.1 ± 1.3 for II and 46.1 ± 2.7 mg/120 min for I ( P < 0.05). This enhanced GU was matched by increasing insulin levels using only a higher rate of its infusion (III): GU of 70.2 ± 2.4 mg/120 min with insulin of 334 ± 26 pmol/l ( P > 0.05). The simple concurrent presence of metformin and insulin [matching insulin concentrations in II rather than infusion rates (IV)] demonstrated no additonal effect on GU above that of metformin. The synergistic effects of metformin and insulin could thus be explained by a metformin-mediated decrease in the extraction of insulin by the hindquarter (4.8 ± 0.4% vs. 8.6 ± 0.9%, P< 0.05). This increases interstitial insulin (and, in a closed system, perfusate insulin), which acts on cell surface receptors to increase glucose uptake. The results demonstrate that the extracellular insulin concentration, rather than insulin internalization and degradation, is the primary determinant of insulin action on GU in muscle and that changes in tissue insulin extraction may alter local concentrations and, therefore, systemic insulin sensitivity. This provides both a physiological mechanism and a possible therapeutic target for improving insulin sensitivity.

The present paper aims at the design, the development and the evaluation of a personalized glucose-insulin metabolism model for patients with Type 1 Diabetes Mellitus (T1DM). The personalized model is based on the combined use of Compartmental Models (CMs) and a Self Organizing Map (SOM). The model receives information related to previous glucose levels, subcutaneous insulin infusion rates and the time and amount of carbohydrates ingested. Previous glucose measurements along with the outputs of the CMs which simulate the sc insulin kinetics and the glucose absorption from the gut into the blood, respectively, are fed into the SOM which simulates glucose kinetics in order for the latter to provide with future glucose profile. The personalized model is evaluated using data from the medical records of 12 patients with T1DM for the time being on insulin pumps and CGMS. The obtained results demonstrate the ability of the proposed model to capture the metabolic behavior of a patient with T1DM and to handle intra- and inter-patient variability.