Glucose-insulin System Research Articles

Closed-loop control scheme for the Euglycemic Hyperinsulinemic Clamp: validation on virtual patients

A closed-loop control scheme is here investigated, for the Euglycemic Hyperinsulinemic Clamp (EHC), the gold standard experiment to estimate the individual insulin sensitivity. During the EHC large amounts of insulin are administered intra-venously to the subject, and plasma glycemia is maintained at a normal, baseline level by means of an exogenous glucose infusion, according to established protocols. Based on a Delay Differential Equation (DDE) model of the glucose-insulin system, a closed-loop control has been recently proposed by the same authors showing that, in way of principle, it is possible to design an observer-based control law for the exogenous glucose profile, by solely exploiting real-time plasma glucose measurements. This note further investigates the closed-loop control scheme in order to validate it in spite of the many sources of uncertainties and malfunctioning that inevitably arise. The main feature is to close the feedback onto a different, large-scale multi-compartmental model (standing for a Virtual Patient, VP), instead of the small-scale, DDE model adopted to design the control law. The chosen large-scale model for the VP has been recently accepted by the Food and Drug Administration as a substitute to animal trials for the preclinical testing of control strategies in artificial pancreas. A benchmark based on a population of heterogeneous virtual patients has been implemented and the very good results show the robustness of the proposed methodology.

Physical Activity Measured by Physical Activity Monitoring System Correlates with Glucose Trends Reconstructed from Continuous Glucose Monitoring

In type 1 diabetes mellitus (T1DM), physical activity (PA) lowers the risk of cardiovascular complications but hinders the achievement of optimal glycemic control, transiently boosting insulin action and increasing hypoglycemia risk. Quantitative investigation of relationships between PA-related signals and glucose dynamics, tracked using, for example, continuous glucose monitoring (CGM) sensors, have been barely explored. In the clinic, 20 control and 19 T1DM subjects were studied for 4 consecutive days. They underwent low-intensity PA sessions daily. PA was tracked by the PA monitoring system (PAMS), a system comprising accelerometers and inclinometers. Variations on glucose dynamics were tracked estimating first- and second-order time derivatives of glucose concentration from CGM via Bayesian smoothing. Short-time effects of PA on glucose dynamics were quantified through the partial correlation function in the interval (0, 60 min) after starting PA. Correlation of PA with glucose time derivatives is evident. In T1DM, the negative correlation with the first-order glucose time derivative is maximal (absolute value) after 15 min of PA, whereas the positive correlation is maximal after 40-45 min. The negative correlation between the second-order time derivative and PA is maximal after 5 min, whereas the positive correlation is maximal after 35-40 min. Control subjects provided similar results but with positive and negative correlation peaks anticipated of 5 min. Quantitative information on correlation between mild PA and short-term glucose dynamics was obtained. This represents a preliminary important step toward incorporation of PA information in more realistic physiological models of the glucose-insulin system usable in T1DM simulators, in development of closed-loop artificial pancreas control algorithms, and in CGM-based prediction algorithms for generation of hypoglycemic alerts.

Impact of sensor and measurement timing errors on model-based insulin sensitivity

A model-based insulin sensitivity parameter (SI) is often used in glucose–insulin system models to define the glycaemic response to insulin. As a parameter identified from clinical data, insulin sensitivity can be affected by blood glucose (BG) sensor error and measurement timing error, which can subsequently impact analyses or glycaemic variability during control. This study assessed the impact of both measurement timing and BG sensor errors on identified values of SI and its hour-to-hour variability within a common type of glucose–insulin system model.Retrospective clinical data were used from 270 patients admitted to the Christchurch Hospital ICU between 2005 and 2007 to identify insulin sensitivity profiles. We developed error models for the Abbott Optium Xceed glucometer and measurement timing from clinical data. The effect of these errors on the re-identified insulin sensitivity was investigated by Monte–Carlo analysis.The results of the study show that timing errors in isolation have little clinically significant impact on identified SI level or variability. The clinical impact of changes to SI level induced by combined sensor and timing errors is likely to be significant during glycaemic control. Identified values of SI were mostly (90th percentile) within 29% of the true value when influenced by both sources of error. However, these effects may be overshadowed by physiological factors arising from the critical condition of the patients or other under-modelled or un-modelled dynamics. Thus, glycaemic control protocols that are designed to work with data from glucometers need to be robust to these errors and not be too aggressive in dosing insulin.

Glucose–insulin regulation model with subcutaneous insulin injection and evaluation using diabetic inpatients data

Closed-loop insulin delivery systems often implement glucose measurement and insulin administration in the subcutis. However some existing models for glucose–insulin system ignored the dynamics of subcutaneous glucose and subcutaneously-injected insulin. This paper reports a two-compartment model that includes glucose and insulin dynamics in subcutis, and its evaluation using patient data. Clinical information such as glucose level, insulin dosage, insulin injection time and meals of anonymous diabetes inpatients was collected. Measured glucose level of the diabetic inpatients agrees with that of computer simulation. Due to the lack of glucose–insulin model with subcutaneously-injected insulin for type 2 diabetic patients, our model was compared with existing model for type 1 subjects. The new glucose–insulin model can mimic dynamics of glucose and insulin under the disturbance of insulin injections and meals. Model parameters were estimated using nonlinear least square method and their effect on pathology and physiology of diabetes were analyzed.

Physical exercise ameliorates the toxic effect of fluoride on the insulin–glucose system

Daily intake of water with fluoride concentrations >1.5 mg/l produces insulin resistance (IR). On the other hand, physical activity increases insulin sensitivity in the muscle. Therefore, the aim of this study was to evaluate the effect of physical activity on IR in rats treated with sodium fluoride (NaF) in drinking water. Sprague-Dawley rats were divided into three groups (n=10/group): Control (drinking water without NaF), NaF (drinking water with NaF 15 mg/l for 30 days), and Exercise (daily running on a treadmill for 60 min at 2.25 m/min and drinking water with NaF 15 mg/l for 30 days). IR was evaluated with the homeostasis model assessment-IR (HOMA-IR) index using fasting plasma levels of glucose and insulin. IR increased in rats treated with 15 mg/l NaF in drinking water. A decrease in IR was observed in rats that performed physical activity and drank water with 15 mg/l NaF; the Exercise group also showed an increase in the amounts of bone fluoride. The variation in the HOMA-IR values could be the consequence of variation in the sensitivity of tissues to insulin or decrease in plasma fluoride levels due to bone fluoride intake. These findings indicate that the performance of daily physical activity could reduce the negative effects of the chronic ingestion of NaF on glucose homeostasis.

A Closed-Loop Artificial Pancreas Using a Proportional Integral Derivative with Double Phase Lead Controller Based on a New Nonlinear Model of Glucose Metabolism

Most closed-loop insulin delivery systems rely on model-based controllers to control the blood glucose (BG) level. Simple models of glucose metabolism, which allow easy design of the control law, are limited in their parametric identification from raw data. New control models and controllers issued from them are needed. A proportional integral derivative with double phase lead controller was proposed. Its design was based on a linearization of a new nonlinear control model of the glucose-insulin system in type 1 diabetes mellitus (T1DM) patients validated with the University of Virginia/Padova T1DM metabolic simulator. A 36 h scenario, including six unannounced meals, was tested in nine virtual adults. A previous trial database has been used to compare the performance of our controller with their previous results. The scenario was repeated 25 times for each adult in order to take continuous glucose monitoring noise into account. The primary outcome was the time BG levels were in target (70-180 mg/dl). Blood glucose values were in the target range for 77% of the time and below 50 mg/dl and above 250 mg/dl for 0.8% and 0.3% of the time, respectively. The low blood glucose index and high blood glucose index were 1.65 and 3.33, respectively. The linear controller presented, based on the linearization of a new easily identifiable nonlinear model, achieves good glucose control with low exposure to hypoglycemia and hyperglycemia.

H∞ Static Output Feedback Control for a Fractional-Order Glucose-Insulin System

This paper presents the H∞ static output feedback control of nonlinear fractional-order glucose-insulin systems. In this paper, it is an attempt to incorporate fractional-order into the mathematical minimal model of glucose-insulin system dynamics and it is still an interesting challenge to show, how the order of a fractional differential system affects the dynamics of system in the presence of meal disturbance. A static output feedback control is considered for the problem. Sufficient conditions are derived in terms of linear matrix inequalities (LMIs) formulation by using the fractional Lyapunov direct method where the fractional-order a belongs to 0 < α < 1. Finally, numerical simulations are carried out to illustrate our proposed results and show that the nonlinear fractional-order glucose-insulin systems are as stable as their integer order counterpart in the presence of exogenous glucose infusion or meal disturbance.

Fuzzy-Logic-Based Supervisor of Insulin Bolus Delivery for Patients with Type 1 Diabetes Mellitus

In this article, a fuzzy-logic-based supervisor of insulin bolus delivery for type 1 diabetes mellitus (T1DM) is proposed. The proposed supervisor incorporates expert knowledge into three phases, including recall, inference, and learning phases. A recently developed and well-acknowledged meal simulation model of the glucose–insulin system for T1DM was employed to create virtual subjects for testing. Data from virtual subjects were used to identify an intermediate physiological model, and then our proposed supervisor was synthesized based on this intermediate model. The key features of this fuzzy-logic-based supervisor are that the implementation does not need an online model and it can gradually be updated meal-by-meal. In addition, only two blood glucose measurements between each meal are needed for updating the insulin bolus delivery. The simulation results show that effective and robust glycemic control performance can be achieved. This methodology can be widely applied to patients with continuous subcutaneous insulin infusion (CSII) or multiple daily injections (MDI).

Regulation of the Human Plasma Glycemia by Means of Glucose Measurements and Subcutaneous Insulin Administration

A glucose control problem is considered, with the aim to regulate a basal hyperglycemic state down to a safe euglycemic level. A discrete Delay Differential Equation (DDE) model of the glucose-insulin system is considered, that properly takes into account also the pancreatic insulin release, not negligible in Type 2 diabetic patients. Insulin is supposed to be administered subcutaneously. A geometric approach is considered, according to which the feedback linearization with delay cancelation theory is applied. In order to use only glucose measurements to synthesize the control law an observer for nonlinear delay systems is exploited, and the local convergence of the tracking error to zero is theoretically proven. Simulations are performed in a virtual environment, that properly takes into account input saturation: numerical results show the effectiveness of the proposed approach as well as that of the observer.

Design and Analysis of a Sliding Table Controller for Diabetes

A discrete insulin infusion based on long-time interval measurement is the classic technique for diabetes treatment. Nevertheless, in this research, a closed-loop control system was proposed for continuous drug infusion to overcome the drawbacks of these typical discrete methods and develop more practical diabetes therapy systems. A blood glucose-insulin system was implemented relying on continuous insulin injection model. Based on this model, two controllers were designed to deal with the control dilemma of the resulting highly nonlinear plant. The controllers designed in this paper are: proportional integral derivative (PID), and sliding table controllers. Simulation results have shown that the sliding table controller can outperform the PID controller even with severe circumstances of disturbance in glucose, such as exercise, delay or noise in glucose sensor and nutrition mixed meal absorption at meal times.

Metabolic and hormonal responses to a single session of kumite (free non-contact fight) and kata (highly ritualized fight) in karate athletes

BackgroundSeveral studies report martial arts as a good model for investigating neuroendocrine responses to competitive fighting. However, little is known on the metabolic responses elicited by elite athletes during fighting. In particular, the metabolic picture in elite athletes of martial arts is little known.AimIn the present study, our aim was to investigate the acute effects of a session of karate practice on the glucose-insulin system.Subjects and methodsTen healthy individuals (6M/4F; BMI: 22.1 ± 0.7 kg/m2; 21.9 ± 1.1 years, mean ± SE) who practice karate in national or international competitions were enrolled. All participants completed two experimental trials in a randomised-crossover fashion. A basal blood sample was collected from each athlete to assess plasma glucose, insulin, cortisol, testosterone and catecholamines, before karate training session. In two separate days, another blood sample was collected from each participants after 3 min of real fighting (kumite) and 3 min of ritualized simulation of combat (kata).ResultsIn both trials, plasma glucose resulted to be higher at the end the of performance compared to the basal (p < 0.001 after kumite and p < 0.02 after kata). In contrast, insulin was similar in the basal and after physical activity in the two trials. Catecholamines were higher after kata and kumite sessions with respect to the basal values (p < 0.04) and, in particular, epinephrine post-kumite values were much greater than those measured after kata.ConclusionsOur results indicate that unlike performances of karate (kumite and kata) elicit different plasma glucose increases. In particular, we found that glucose and epinephrine concentrations increased more after kumite than after kata.

An Online Failure Detection Method of the Glucose Sensor-Insulin Pump System: Improved Overnight Safety of Type-1 Diabetic Subjects

Sensors for real-time continuous glucose monitoring (CGM) and pumps for continuous subcutaneous insulin infusion (CSII) have opened new scenarios for Type-1 diabetes treatment. However, occasional failures of either CGM or CSII may expose diabetic patients to possibly severe risks, especially overnight (e.g., inappropriate insulin administration). In this contribution, we present a method to detect in real time such failures by simultaneously using CGM and CSII data streams and a black-box model of the glucose-insulin system. First, an individualized state-space model of the glucose-insulin system is identified offline from CGM and CSII data collected during a previous monitoring. Then, this model, CGM and CSII real-time data streams are used online to obtain predictions of future glucose concentrations together with their confidence intervals by exploiting a Kalman filtering approach. If glucose values measured by the CGM sensor are not consistent with the predictions, a failure alert is generated in order to mitigate the risks for patient safety. The method is tested on 100 virtual patients created by using the UVA/Padova Type-1 diabetic simulator. Three different types of failures have been simulated: spike in the CGM profile, loss of sensitivity of glucose sensor, and failure in the pump delivery of insulin. Results show that, in all cases, the method is able to correctly generate alerts, with a very limited number of false negatives and a number of false positives, on average, lower than 10%. The use of the method in three subjects supports the simulation results, demonstrating that the accuracy of the method in generating alerts in presence of failures of the CGM sensor-CSII pump system can significantly improve safety of Type-1 diabetic patients overnight.

A Hybrid Neural Network Model Predictive Control with Zone Penalty Weights for Type 1 Diabetes Mellitus

In this paper, a hybrid neural network model is developed to predict and control the blood glucose (BG) of the patient who has type 1 diabetes mellitus (T1DM). The proposed model consists of two parts: a linear finite impulse response (FIR) model and a nonlinear autoregressive exogenous input (NARX) network. A recently developed and well-acknowledged meal simulation model of the glucose-insulin system for T1DM is employed to create virtual subjects. Data from virtual subjects are used to identify an intermediate physiological model, and then our proposed hybrid model is trained and validated based on this intermediate model. The key features of the resulting hybrid model are that it reveals satisfactory accuracy of long-term prediction and does not require an immeasurable state for model initialization. The developed hybrid model is then embedded in a nonlinear model predictive control (MPC) controller with zone penalty weights, and this closed-loop controller is implemented on these virtual subjects for simulation-based preclinical testing. The results show that promising glycemic control performance can be achieved. Moreover, this overall BG control methodology is easily portable and has the ability to arbitrarily start the therapeutic control at any initial point.

Modeling Disease Progression and Rosiglitazone Intervention in Type 2 Diabetic Goto-Kakizaki Rats

The pharmacokinetics (PK) and pharmacodynamics (PD) of rosiglitazone were studied in type 2 diabetic (T2D) Goto-Kakizaki (GK) rats that received daily doses of 0, 5, or 10 mg/kg for 23 days followed by 60 days of washout. Blood glucose, plasma insulin, and hemoglobin A1c were determined over time. Oral glucose tolerance tests were performed before and at the end of treatment and after 20 days of washout to determine insulin sensitivity and β-cell function. Rosiglitazone effectively lowered glucose by inhibiting hepatic glucose production and enhancing insulin sensitivity. The glucose-insulin inter-regulation was characterized by a feedback model: glucose and insulin have their own production (k(in)) and elimination (k(out)) rate constants, whereas glucose stimulates insulin production (k(inI)) and insulin, in turn, promotes glucose utilization (k(outG)). Animal handling and placebo treatment affected glucose turnover with k(pl) = 0.388 kg/mg/day. The PK of rosiglitazone was fitted with a one-compartment model with first-order absorption. The effect of rosiglitazone was described as inhibition of k(inG) with I(max) = 0.296 and IC(50) = 1.97 μg/ml. Rosiglitazone also stimulated glucose utilization by improving insulin sensitivity with a linear factor S(R) = 0.0796 kg/mg. In GK rats, 23 days of treatment increased body weight but did not cause hemodilution. Weight gain was characterized with body weight input (k(s)(w)) and output (k(d)(w)), and rosiglitazone inhibited k(d)(w) with ID(50) = 96.8 mg/kg. The mechanistic PK/PD model quantitatively described the glucose-insulin system and body weights under chronic rosiglitazone treatment in T2D rats.

Target-Mediated Pharmacokinetic and Pharmacodynamic Model of Exendin-4 in Rats, Monkeys, and Humans

A mechanism-based pharmacokinetic-pharmacodynamic (PK/PD) model was developed for exendin-4 to account for receptor-mediated endocytosis via glucagon-like peptide 1 receptor (GLP-1R) as the primary mechanism for its nonlinear disposition. Time profiles of exendin-4 concentrations after intravenous, subcutaneous, and continuous intravenous infusion doses in rats, intravenous and subcutaneous doses in monkeys, and intravenous infusion and subcutaneous doses in humans were examined. Mean data for glucose and insulin after glucose challenges during exendin-4 treatment in healthy rats were analyzed. The PK model components included receptor binding, subsequent internalization and degradation, nonspecific tissue distribution, and linear first-order elimination from plasma. The absorption rate constant (k(a)) decreased with increasing doses in all three species. The clearance from the central compartment (CL(c)) (rats, 3.62 ml/min; monkeys, 2.39 ml · min(-1) · kg(-1); humans, 1.48 ml · min(-1) · kg(-1)) was similar to reported renal clearances. Selected PK parameters (CL(c), V(c), and k(off)) correlated allometrically with body weight. The equilibrium dissociation constant (K(D)) was within the reported range in rats (0.74 nM), whereas the value in monkeys (0.12 pM) was much lower than that in humans (1.38 nM). The effects of exendin-4 on the glucose-insulin system were described by a feedback model with a biphasic effect equation driven by free exendin-4 concentrations. Our generalized nonlinear PK/PD model for exendin-4 taking into account of drug binding to GLP-1R well described PK profiles after various routes of administration over a large range of doses in three species along with PD responses in healthy rats. The present model closely reflects underlying mechanisms of disposition and dynamics of exendin-4.

Endogenous insulin secretion in critically ill patients

Glucose-insulin system models can be used for improved glycemic control of critically ill patients. A key component of glucose-insulin models is pancreatic insulin secretion. There are limited data in the literature quantifying insulin secretion in critically ill patients at physiologic levels. This study presents a model of pancreatic insulin secretion in critically ill patients based on data from a critically ill population.

Discussion on: “Time-Delay Model-Based Control of the Glucose–Insulin System, by Means of a State Observer”

Time-delay systems are ubiquitous in nature and engineering. Delays account for transmission, diffusion and migration phenomena as well as maturation and aging in physical, biological, ecological, epidemiological and population systems. Lotka-Volterra models describing prey-predator models or Pearl-Verhulst equations for population dynamics are instances of deterministic models aiming to describe population evolution. These models do not account for aging/maturation of the population and this is the reason why refinement of the models have been proposed.

Time-Delay Model-Based Control of the Glucose–Insulin System, by Means of a State Observer

The problem of tracking a desired plasma glucose evolution is considered, for cases of basal hyperglycemia. A time-delay model is used to describe the glucose–insulin regulatory system, aiming to detail the endogenous pancreatic insulin release, which is not negligible in Type 2 diabetic patients. Insulin is assumed to be administered by means of intra-venous infusions. Only measurements of glycemia are considered: to this aim a nonlinear observer for time-delay systems is used to estimate the plasma insulin concentration. In the spirit of the separation theorem, a nonlinear control law is proposed, based on the exact input/output feedback linearization, which makes use of the observer estimates instead of the full state measurements. The local convergence of the tracking error to zero is theoretically proved. Simulations are performed in a virtual environment, taking into account the standard technology concerning blood glucose sensors and insulin delivery devices. Numerical results show the robustness of the proposed approach with respect to the uncertainties of the model parameters, as well as to the glucose measurement errors and insulin pump malfunctioning.

Impact of sensor and measurement timing errors on model-based insulin sensitivity

A model-based insulin sensitivity parameter ( SI ) is often used in glucose-insulin system models to define the glycaemic response to insulin. As a parameter identified from clinical data, insulin sensitivity can be affected by blood glucose (BG) sensor error and measurement timing error, which can subsequently impact analyses or glycaemic variability during control. This study assesses the impact of both measurement timing and BG sensor errors on identified values of SI and its hour-to-hour variability within the ICING-type glucose-insulin system models. Retrospective clinical data was used from 270 patients of the Christchurch Hospital intensive care unit (ICU). An error model was created for the Arkray Super-Glucocard II glucometer used in Christchurch from manufacturer supplied data. Timing error was estimated from recent, computerised clinical data. Monte Carlo analysis was used to quantify the impact of these random errors by identifying SI profiles from data incorporating errors and comparing them to the ‘true’ SI profile (without additional errors) at each patient hour. To consolidate comparisons over the n = 100 Monte Carlo simulations, the width of the interquartile range (IQR) was used for percentage difference from the true SI level and for percentage hour-to-hour variability. The results of the study show that timing errors in isolation have little clinically significant impact on identified SI level or variability. The clinical impact of changes to SI level induced by combined sensor and timing errors is likely to be limited during glycaemic control. Identified values of SI were typically within 12% of the true value when influenced by both sources of error. In contrast, for variability, 95% of patient hours had an IQR of 34.9%, indicating that for half the simulations the hour-to-hour variability of SI was within ±17.5%. The results of this study indicate that the impact of sensor or timing errors on SI level is unlikely to be clinically significant. The effects are probably overshadowed by physiological factors arising from the critical condition of the patients or other under-modelled or un-modelled dynamics. In contrast, the impact of errors on hour-to-hour SI variability is more pronounced and may impact the way the SI parameter is utilised for control and analysis

Interstitial insulin kinetic parameters for a 2-compartment insulin model with saturable clearance

Abstract 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.