Diabetes: Models, Signals, and Control

Mechanisms Underlying the Pathogenesis of Isolated Impaired Glucose Tolerance in Humans

CONTEXT

Prediabetes is a heterogeneous disorder classified on the basis of fasting glucose concentrations and 2-hour glucose tolerance.

OBJECTIVE

We sought to determine the relative contributions of insulin secretion and action to the pathogenesis of isolated impaired glucose tolerance (IGT).

DESIGN

The study consisted of an oral glucose tolerance test and a euglycemic clamp performed in two cohorts matched for anthropometric characteristics and fasting glucose but discordant for glucose tolerance.

SETTING

An inpatient clinical research unit at an academic medical center.

PATIENTS OR OTHER PARTICIPANTS

Twenty-five subjects who had normal fasting glucose (NFG) and normal glucose tolerance (NGT) and 19 NFG/IGT subjects participated in this study.

INTERVENTION(S)

Subjects underwent a seven-sample oral glucose tolerance test and a 4-hour euglycemic, hyperinsulinemic clamp on separate occasions. Glucose turnover during the clamp was measured using tracers, and endogenous hormone secretion was inhibited by somatostatin.

MAIN OUTCOME MEASURES

We sought to determine whether hepatic glucose metabolism, specifically the contribution of gluconeogenesis to endogenous glucose production, differed between subjects with NFG/NGT and those with NFG/IGT.

RESULTS

Endogenous glucose production did not differ between groups before or during the clamp. Insulin-stimulated glucose disappearance was lower in NFG/IGT (24.6 ± 2.2 vs 35.0 ± 3.6 μmol/kg/min; P = .03). The disposition index was decreased in NFG/IGT (681 ± 102 vs 2231 ± 413 × 10^-14 dL/kg/min² per pmol/L; P < .001).

CONCLUSIONS

We conclude that innate defects in the regulation of glycogenolysis and gluconeogenesis do not contribute to NFG/IGT. However, insulin-stimulated glucose disposal is impaired, exacerbating defects in β-cell function.

Predicting Insulin Treatment Scenarios with the Net Effect Method: Domain of Validity

BACKGROUND

A simulation methodology based on the net effect, a signal estimated from continuous glucose monitoring (CGM) and insulin data accounting for sources of glucose variability, for example, meals and exercise, has been proposed. This method has been recently used to "replay" real-life treatment scenarios and determine the minimal level of CGM sensor accuracy required for nonadjunctive use. Given the potential of the net effect method, it is important to assess its domain of validity.

METHODS

The UVA/Padova type 1 diabetes simulator is used to generate glucose and insulin data. The net effect signal is estimated and used to predict the glucose profiles resulting from the following therapy modifications: (1) basal insulin increase/decrease, (2) bolus reduction to prevent hypoglycemia, (3) bolus addition after CGM hyperalarms, (4) hypotreatment addition after CGM hypoalarms. Results of the net effect method are compared with the reference provided by the UVA/Padova simulator.

RESULTS

The net effect method (1) well predicts the effect of small basal insulin adjustments (±10%), but overestimates time in hypo/hyperglycemia for larger adjustments (±50%); (2) underestimates the bolus reduction required to prevent hypoglycemia; (3) underestimates time in hyperglycemia when introducing correction boluses; and (4) overestimates time in hypoglycemia when introducing hypotreatments.

CONCLUSIONS

The net effect method is reliable for small adjustments of basal insulin, while outside this domain of validity it can provide inaccurate results.

Physiology-Invariant Meal Detection for Type 1 Diabetes

BACKGROUND

Fully automated artificial pancreas systems require meal detectors to supplement blood glucose level regulation, where false meal detections can cause unnecessary insulin delivery with potentially fatal consequences, and missed detections may cause the patient to experience extreme hyperglycemia. Most existing meal detectors monitor various measures of glucose rate-of-change to detect meals where varying physiology and meal content complicate balancing detector sensitivity versus specificity.

METHODS

We developed a novel meal detector based on a minimal glucose-insulin metabolism model and show that the detector is, by design, invariant to patient-specific physiological parameters in the minimal model. Our physiological parameter-invariant (PAIN) detector achieves a near-constant false alarm rate across all individuals and is evaluated against three other major existing meal detectors on a clinical type 1 diabetes data set.

RESULTS

In the clinical evaluation, the PAIN-based detector achieves an 86.9% sensitivity for an average false alarm rate of two alarms per day. In addition, for all false alarm rates, the PAIN-based detector performance is significantly better than three other existing meal detectors. In addition, the evaluation results show that the PAIN-based detector uniquely (as compared with the other meal detectors) has low variance in detection and false alarm rates across all patients, without patient-specific personalization.

CONCLUSIONS

The PAIN-based meal detector has demonstrated better detection performance than existing meal detectors, and it has the unique strength of achieving a consistent performance across a population with varying physiology without any individual-level parameter tuning or training.

Using meta-differential evolution to enhance a calculation of a continuous blood glucose level

We developed a new model of glucose dynamics. The model calculates blood glucose level as a function of transcapillary glucose transport. In previous studies, we validated the model with animal experiments. We used analytical method to determine model parameters. In this study, we validate the model with subjects with type 1 diabetes. In addition, we combine the analytic method with meta-differential evolution. To validate the model with human patients, we obtained a data set of type 1 diabetes study that was coordinated by Jaeb Center for Health Research. We calculated a continuous blood glucose level from continuously measured interstitial fluid glucose level. We used 6 different scenarios to ensure robust validation of the calculation. Over 96% of calculated blood glucose levels fit A+B zones of the Clarke Error Grid. No data set required any correction of model parameters during the time course of measuring. We successfully verified the possibility of calculating a continuous blood glucose level of subjects with type 1 diabetes. This study signals a successful transition of our research from an animal experiment to a human patient. Researchers can test our model with their data on-line at https://diabetes.zcu.cz.

Periodic zone-MPC with asymmetric costs for outpatient-ready safety of an artificial pancreas to treat type 1 diabetes. AUTOMATICA : THE JOURNAL OF IFAC, THE INTERNATIONAL FEDERATION OF AUTOMATIC CONTROL 2016;71:237-246. [PMID: 27695131 PMCID: PMC5040369 DOI: 10.1016/j.automatica.2016.04.015]

A novel Model Predictive Control (MPC) law for an Artificial Pancreas (AP) to automatically deliver insulin to people with type 1 diabetes is proposed. The MPC law is an enhancement of the authors' zone-MPC approach that has successfully been trialled in-clinic, and targets the safe outpatient deployment of an AP. The MPC law controls blood-glucose levels to a diurnally time-dependent zone, and enforces diurnal, hard input constraints. The main algorithmic novelty is the use of asymmetric input costs in the MPC problem's objective function. This improves safety by facilitating the independent design of the controller's responses to hyperglycemia and hypoglycemia. The proposed controller performs predictive pump-suspension in the face of impending hypoglycemia, and subsequent predictive pump-resumption, based only on clinical needs and feedback. The proposed MPC strategy's benefits are demonstrated by in-silico studies as well as highlights from a US Food and Drug Administration approved clinical trial in which 32 subjects each completed two 25 hour closed-loop sessions employing the proposed MPC law.

Reducing Glucose Variability Due to Meals and Postprandial Exercise in T1DM Using Switched LPV Control: In Silico Studies

BACKGROUND

Time-varying dynamics is one of the main issues for achieving safe blood glucose control in type 1 diabetes mellitus (T1DM) patients. In addition, the typical disturbances considered for controller design are meals, which increase the glucose level, and physical activity (PA), which increases the subject's sensitivity to insulin. In previous works the authors have applied a linear parameter-varying (LPV) control technique to manage unannounced meals.

METHODS

A switched LPV controller that switches between 3 LPV controllers, each with a different level of aggressiveness, is designed to further cope with both unannounced meals and postprandial PA. Thus, the proposed control strategy has a "standard" mode, an "aggressive" mode, and a "conservative" mode. The "standard" mode is designed to be applied most of the time, while the "aggressive" mode is designed to deal only with hyperglycemia situations. On the other hand, the "conservative" mode is focused on postprandial PA control.

RESULTS

An ad hoc simulator has been developed to test the proposed controller. This simulator is based on the distribution version of the UVA/Padova model and includes the effect of PA based on Schiavon.(1) The test results obtained when using this simulator indicate that the proposed control law substantially reduces the risk of hypoglycemia with the conservative strategy, while the risk of hyperglycemia is scarcely affected.

CONCLUSIONS

It is demonstrated that the announcement, or anticipation, of exercise is indispensable for letting a mono-hormonal artificial pancreas deal with the consequences of postprandial PA. In view of this the proposed controller allows switching into a conservative mode when notified of PA by the user.

Modeling glucose and free fatty acid kinetics in glucose and meal tolerance test

BACKGROUND

Quantitative evaluation of insulin regulation on plasma glucose and free fatty acid (FFA) in response to external glucose challenge is clinically important to assess the development of insulin resistance (World J Diabetes 1:36-47, 2010). Mathematical minimal models (MMs) based on insulin modified frequently-sampled intravenous glucose tolerance tests (IM-FSIGT) are widely applied to ascertain an insulin sensitivity index (IEEE Rev Biomed Eng 2:54-96, 2009). Furthermore, it is important to investigate insulin regulation on glucose and FFA in postprandial state as a normal physiological condition. A simple way to calculate the appearance rate (Ra) of glucose and FFA would be especially helpful to evaluate glucose and FFA kinetics for clinical applications.

METHODS

A new MM is developed to simulate the insulin modulation of plasma glucose and FFA, combining IM-FSIGT with a mixed meal tolerance test (MT). A novel simple functional form for the appearance rate (Ra) of glucose or FFA in the MT is developed. Model results are compared with two other models for data obtained from 28 non-diabetic women (13 African American, 15 white).

RESULTS

The new functional form for Ra of glucose is an acceptable empirical approximation to the experimental Ra for a subset of individuals. When both glucose and FFA are included in FSIGT and MT, the new model is preferred using the Bayes Information Criterion (BIC).

CONCLUSIONS

Model simulations show that the new MM allows consistent application to both IM-FSIGT and MT data, balancing model complexity and data fitting. While the appearance of glucose in the circulation has an important effect on FFA kinetics in MT, the rate of appearance of FFA can be neglected for the time-period modeled.

A data driven nonlinear stochastic model for blood glucose dynamics

The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles.

One-Day Bayesian Cloning of Type 1 Diabetes Subjects: Toward a Single-Day UVA/Padova Type 1 Diabetes Simulator

OBJECTIVE

The UVA/Padova Type 1 Diabetes (T1DM) Simulator has been shown to be representative of a T1DM population observed in a clinical trial, but has not yet been identified on T1DM data. Moreover, the current version of the simulator is "single meal" while making it "single-day centric," i.e., by describing intraday variability, would be a step forward to create more realistic in silico scenarios. Here, we propose a Bayesian method for the identification of the model from plasma glucose and insulin concentrations only, by exploiting the prior model parameter distribution.

METHODS

The database consists of 47 T1DM subjects, who received dinner, breakfast, and lunch (respectively, 80, 50, and 60 CHO grams) in three 23-h occasions (one open- and one closed-loop). The model is identified using the Bayesian Maximum a Posteriori technique, where the prior parameter distribution is that of the simulator. Diurnal variability of glucose absorption and insulin sensitivity is allowed.

RESULTS

The model well describes glucose traces (coefficient of determination R² = 0.962 ± 0.027 ) and the posterior parameter distribution is similar to that included in the simulator. Absorption parameters at breakfast are significantly different from those at lunch and dinner, reflecting more rapid dynamics of glucose absorption. Insulin sensitivity varies in each individual but without a specific pattern.

CONCLUSION

The incorporation of glucose absorption and insulin sensitivity diurnal variability into the simulator makes it more realistic.

SIGNIFICANCE

The proposed method, applied to the increasing number of long-term artificial pancreas studies, will allow to describe week/month variability, thus further refining the simulator.

TCF7L2 Genotype and α-Cell Function in Humans Without Diabetes

The diabetes-associated allele in TCF7L2 increases the rate of conversion to diabetes; however, the mechanism by which this occurs remains elusive. We hypothesized that the diabetes-associated allele in this locus (rs7903146) impairs insulin secretion and that this defect would be exacerbated by acute free fatty acid (FFA)-induced insulin resistance. We studied 120 individuals of whom one-half were homozygous for the diabetes-associated allele TT at rs7903146 and one-half were homozygous for the protective allele CC. After a screening examination during which glucose tolerance status was determined, subjects were studied on two occasions in random order while undergoing an oral challenge. During one study day, FFA was elevated by infusion of Intralipid plus heparin. On the other study day, subjects received the same amount of glycerol as present in the Intralipid infusion. β-Cell responsivity indices were estimated with the oral C-peptide minimal model. We report that β-cell responsivity was slightly impaired in the TT genotype group. Moreover, the hyperbolic relationship between insulin secretion and β-cell responsivity differed significantly between genotypes. Subjects also exhibited impaired suppression of glucagon after an oral challenge. These data imply that a genetic variant harbored within the TCF7L2 locus impairs glucose tolerance through effects on glucagon as well as on insulin secretion.

A Model Approach: Mathematical modeling provides an increasingly clear picture of glucose and neural systems

Mathematical modeling of physiological systems is a fundamental milestone of biomedical engineering. Models allow for the quantitative understanding of the intimate functions of a biological system, estimating parameters that are not accessible to direct measurement and performing in silico trials by simulating and tracking a physiological system in case its function has been deranged. Modeling has always been central in the Italian biomedical engineering community. Here, we review the progress in two areas: glucose and neurocomputational modeling with an emphasis on their clinical impact.

A simplification of Cobelli's glucose-insulin model for type 1 diabetes mellitus and its FPGA implementation

Cobelli's glucose-insulin model is the only computer simulator of glucose-insulin interactions accepted by Food Drug Administration as a substitute to animal trials. However, it consists of multiple differential equations that make it hard to be implemented on a hardware platform. In this investigation, the Cobelli's model is simplified by Padé approximant method and implemented on a field-programmable gate array-based platform as a hardware model for predicting glucose changes in subjects with type 1 diabetes mellitus. Compared with the original Cobelli's model, the implemented hardware model provides a nearly perfect approximation in predicting glucose changes with rather small root-mean-square errors and maximum errors. The RMSE results for 30 subjects show that the method for simplifying and implementing Cobelli's model has good robustness and applicability. The successful hardware implementation of Cobelli's model will promote a wider adoption of this model that can substitute animal trials, provide fast and reliable glucose and insulin estimation, and ultimately assist the further development of an artificial pancreas system.

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.

A Review of Emerging Technologies for the Management of Diabetes Mellitus

OBJECTIVE

High prevalence of diabetes mellitus (DM) along with the poor health outcomes and the escalated costs of treatment and care poses the need to focus on prevention, early detection and improved management of the disease. The aim of this paper is to present and discuss the latest accomplishments in sensors for glucose and lifestyle monitoring along with clinical decision support systems (CDSSs) facilitating self-disease management and supporting healthcare professionals in decision making.

METHODS

A critical literature review analysis is conducted focusing on advances in: 1) sensors for physiological and lifestyle monitoring, 2) models and molecular biomarkers for predicting the onset and assessing the progress of DM, and 3) modeling and control methods for regulating glucose levels.

RESULTS

Glucose and lifestyle sensing technologies are continuously evolving with current research focusing on the development of noninvasive sensors for accurate glucose monitoring. A wide range of modeling, classification, clustering, and control approaches have been deployed for the development of the CDSS for diabetes management. Sophisticated multiscale, multilevel modeling frameworks taking into account information from behavioral down to molecular level are necessary to reveal correlations and patterns indicating the onset and evolution of DM.

CONCLUSION

Integration of data originating from sensor-based systems and electronic health records combined with smart data analytics methods and powerful user centered approaches enable the shift toward preventive, predictive, personalized, and participatory diabetes care.

SIGNIFICANCE

The potential of sensing and predictive modeling approaches toward improving diabetes management is highlighted and related challenges are identified.

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.

Dissecting Long-Term Glucose Metabolism Identifies New Susceptibility Period for Metabolic Dysfunction in Aged Mice

Metabolic disorders, like diabetes and obesity, are pathogenic outcomes of imbalance in glucose metabolism. Nutrient excess and mitochondrial imbalance are implicated in dysfunctional glucose metabolism with age. We used conplastic mouse strains with defined mitochondrial DNA (mtDNA) mutations on a common nuclear genomic background, and administered a high-fat diet up to 18 months of age. The conplastic mouse strain B6-mt^FVB, with a mutation in the mt-Atp8 gene, conferred β-cell dysfunction and impaired glucose tolerance after high-fat diet. To our surprise, despite of this functional deficit, blood glucose levels adapted to perturbations with age. Blood glucose levels were particularly sensitive to perturbations at the early age of 3 to 6 months. Overall the dynamics consisted of a peak between 3–6 months followed by adaptation by 12 months of age. With the help of mathematical modeling we delineate how body weight, insulin and leptin regulate this non-linear blood glucose dynamics. The model predicted a second rise in glucose between 15 and 21 months, which could be experimentally confirmed as a secondary peak. We therefore hypothesize that these two peaks correspond to two sensitive periods of life, where perturbations to the basal metabolism can mark the system for vulnerability to pathologies at later age. Further mathematical modeling may perspectively allow the design of targeted periods for therapeutic interventions and could predict effects on weight loss and insulin levels under conditions of pre-diabetic obesity.

How well do glucose variability measures predict patient glycaemic outcomes during treatment intensification in type 2 diabetes?

AIM

Despite links to clinical outcomes in patients with type 2 diabetes mellitus (T2DM), the clinical utility of glycaemic variability (GV) measures is unknown. We evaluated the correlation between baseline GV, and glycated haemoglobin (HbA1c) attainment and hypoglycaemic events during treatment intensification in a large group of patients.

METHODS

Patient-level data from six 24-week clinical trials of T2DM patients undergoing treatment intensification with basal insulin or comparators (N = 1699) were pooled. Baseline GV measures included standard deviation (SD), mean amplitude of glycaemic excursions (MAGE), mean absolute glucose (MAG), coefficient of variation (CV), high blood glucose index (HBGI), and low blood glucose index (LBGI) and were correlated with HbA1c change and hypoglycaemic events.

RESULTS

All mean GV measures, excluding CV which worsened, improved significantly from baseline to Week 24, with the largest proportional reduction obtained for HBGI (-65.5%). When assessed as mean individual percentage changes, only HBGI improved significantly. Baseline GV correlated positively with Week 24 HbA1c for SD, MAGE, and HBGI. Baseline HBGI and CV correlated negatively and positively, respectively, with Week 24 HbA1c change. Correlations also existed between most baseline GV measures and age, body mass index, Week 24 fasting plasma glucose, Week 24 postprandial plasma glucose, and hypoglycaemic events; statistical significance depended on the specific measure.

CONCLUSIONS

Pre-treatment GV is associated with glycaemic outcomes in T2DM patients undergoing treatment intensification over 24 weeks. HBGI might be the most robust predictor, warranting validation in dedicated prospective studies or randomized trials to assess the predictive value of measuring GV.

Identification of Main Factors Explaining Glucose Dynamics During and Immediately After Moderate Exercise in Patients With Type 1 Diabetes

BACKGROUND

Physical activity is recommended for patients with type 1 diabetes (T1D). However, without proper management, it can lead to higher risk for hypoglycemia and impaired glycemic control. In this work, we identify the main factors explaining the blood glucose dynamics during exercise in T1D. We then propose a prediction model to quantify the glycemic drop induced by a mild to moderate physical activity.

METHODS

A meta-data analysis was conducted over 59 T1D patients from 4 different studies in the United States and France (37 men and 22 women; 47 adults; weight, 71.4 ± 10.6 kg; age, 42 ± 10 years; 12 adolescents: weight, 60.7 ± 12.5 kg; age, 14.0 ± 1.4 years). All participants had physical activity between 3 and 5 pm at a mild to moderate intensity for approximately 30 to 45 min. A multiple linear regression analysis was applied to the data to identify the main parameters explaining the glucose dynamics during such physical activity.

RESULTS

The blood glucose at the beginning of exercise ([Formula: see text]), the ratio of insulin on board over total daily insulin ([Formula: see text]) and the age as a categorical variable (1 for adult, 0 for adolescents) were significant factors involved in glucose evolution at exercise (all P < .05). The multiple linear regression model has an R-squared of .6.

CONCLUSIONS

The main factors explaining glucose dynamics in the presence of mild-to-moderate exercise in T1D have been identified. The clinical parameters are formally quantified using real data collected during clinical trials. The multiple linear regression model used to predict blood glucose during exercise can be applied in closed-loop control algorithms developed for artificial pancreas.

Switched LPV Glucose Control in Type 1 Diabetes

OBJECTIVE

The purpose of this paper is to regulate the blood glucose level in Type 1 Diabetes Mellitus patients with a practical and flexible procedure that can switch among a finite number of distinct controllers, depending on the user's choice.

METHODS

A switched linear parameter-varying controller with multiple switching regions, related to hypo-, hyper-, and euglycemia situations, is designed. The key feature is to arrange the controller into a framework that provides stability and performance guaranty.

RESULTS

The closed-loop performance is tested on the complete in silico adult cohort of the UVA/Padova metabolic simulator, which has been accepted by the U.S. Food and Drug Administration in lieu of animal trials. The outcome produces comparable or improved results with respect to previous works.

CONCLUSION

The strategy is practical because it is based on a model tuned only with a priori patient information in order to cover the interpatient uncertainty. Results confirm that this control structure yields tangible improvements in minimizing risks of hyper- and hypoglycemia in scenarios with unannounced meals.

SIGNIFICANCE

This flexible procedure opens the possibility of taking into account, at the design stage, unannounced meals and/or patients' physical exercise.

Visual Predictive Check in Models with Time-Varying Input Function

The nonlinear mixed effects models are commonly used modeling techniques in the pharmaceutical research as they enable the characterization of the individual profiles together with the population to which the individuals belong. To ensure a correct use of them is fundamental to provide powerful diagnostic tools that are able to evaluate the predictive performance of the models. The visual predictive check (VPC) is a commonly used tool that helps the user to check by visual inspection if the model is able to reproduce the variability and the main trend of the observed data. However, the simulation from the model is not always trivial, for example, when using models with time-varying input function (IF). In this class of models, there is a potential mismatch between each set of simulated parameters and the associated individual IF which can cause an incorrect profile simulation. We introduce a refinement of the VPC by taking in consideration a correlation term (the Mahalanobis or normalized Euclidean distance) that helps the association of the correct IF with the individual set of simulated parameters. We investigate and compare its performance with the standard VPC in models of the glucose and insulin system applied on real and simulated data and in a simulated pharmacokinetic/pharmacodynamic (PK/PD) example. The newly proposed VPC performance appears to be better with respect to the standard VPC especially for the models with big variability in the IF where the probability of simulating incorrect profiles is higher.

Pharmacokinetic Model of the Transport of Fast-Acting Insulin From the Subcutaneous and Intradermal Spaces to Blood

Pharmacokinetic (PK) models describing the transport of insulin from the injection site to blood assist clinical decision making and are part of in silico platforms for developing and testing of insulin delivery strategies for treatment of patients with diabetes. The ability of these models to accurately describe all facets of the in vivo insulin transport is therefore critical for their application. Here, we propose a new model of fast-acting insulin analogs transport from the subcutaneous and intradermal spaces to blood that can accommodate clinically observed biphasic appearance and delayed clearance of injected insulin, 2 phenomena that are not captured by existing PK models. To develop the model we compare 9 insulin transport PK models which describe hypothetical insulin delivery pathways potentially capable of approximating biphasic appearance of exogenous insulin. The models are tested with respect to their ability to describe clinical data from 10 healthy volunteers which received 1 subcutaneous and 2 intradermal insulin injections on 3 different occasions. The optimal model, selected based on information and posterior identifiability criteria, assumes that insulin is delivered at the administrative site and is then transported to the bloodstream via 2 independent routes (1) diffusion-like process to the blood and (2) combination of diffusion-like processes followed by an additional compartment before entering the blood. This optimal model accounts for biphasic appearance and delayed clearance of exogenous insulin. It agrees better with the clinical data as compared to commonly used models and is expected to improve the in silico development and testing of insulin treatment strategies, including artificial pancreas systems.

Optimization of insulin pump therapy based on high order run-to-run control scheme

BACKGROUND AND OBJECTIVES

Continuous subcutaneous insulin infusion (CSII) pump is widely considered a convenience and promising way for type 1 diabetes mellitus (T1DM) subjects, who need exogenous insulin infusion. In the standard insulin pump therapy, there are two modes for insulin infusion: basal and bolus insulin. The basal-bolus therapy should be individualized and optimized in order to keep one subject's blood glucose (BG) level within the normal range; however, the optimization procedure is troublesome and it perturb the patients a lot. Therefore, an automatic adjustment method is needed to reduce the burden of the patients, and run-to-run (R2R) control algorithm can be used to handle this significant task.

METHODS

In this study, two kinds of high order R2R control methods are presented to adjust the basal and bolus insulin simultaneously. For clarity, a second order R2R control algorithm is first derived and studied. Furthermore, considering the differences between weekdays and weekends, a seventh order R2R control algorithm is also proposed and tested.

RESULTS

In order to simulate real situation, the proposed method has been tested with uncertainties on measurement noise, drifts, meal size, meal time and snack. The proposed method can converge even when there are ±60 min random variations in meal timing or ±50% random variations in meal size.

CONCLUSIONS

According to the robustness analysis, one can see that the proposed high order R2R has excellent robustness and could be a promising candidate to optimize insulin pump therapy.

A novel online recalibration strategy for continuous glucose measurement sensors employing LMI techniques

This paper considers the problem of online calibration and recalibration of continuous glucose monitoring devices. A parametric relation between interstitial and blood glucose is investigated and a constructive algorithm to adaptively estimate the parameters within this relation is proposed. The algorithm explicitly considers measurement uncertainty of the device used to collect the calibration measurements and enables automatic detection of measurements which are not suitable to be used for calibration. The method was assessed on clinical data from 17 diabetic patients and the improvements with respect to the current state of the art is shown.

A new insulin-glucose metabolic model of type 1 diabetes mellitus: An in silico study

Diabetes mellitus is a serious metabolic disease that threatens people's health. The artificial pancreas system (APS) has been generally considered as the ultimate cure of type 1 diabetes mellitus (T1DM). The simulation model of insulin-glucose metabolism is an essential part of an APS as it processes the measured glucose level and generates control signal to the insulin infusion system. This paper presents a new insulin-glucose metabolic model using model reduction methods applied to the popular but complex Cobelli's model. The performances of three different model reduction methods, namely Padé approximation, Routh approximation and system identification, are compared. The results of in silico simulation based on 30 virtual patients of three groups for adults, adolescents, and children show that the approximation error between this new model and the original Cobelli's model is so small that can be neglected. It can be concluded that the proposed simplified model can describe the insulin-glucose metabolism process rather accurately as well as can be easily implemented and integrated into an APS to make the APS technology more mature and closer to clinical use. The FPGA implementation, testing and further simplification possibility will be explored in the next stage of research.

How well do glucose variability measures predict patient glycaemic outcomes during treatment intensification in type 2 diabetes?

AIM

Despite links to clinical outcomes in patients with type 2 diabetes mellitus (T2DM), the clinical utility of glycaemic variability (GV) measures is unknown. We evaluated the correlation between baseline GV, and glycated haemoglobin (HbA1c) attainment and hypoglycaemic events during treatment intensification in a large group of patients.

METHODS

Patient-level data from six 24-week clinical trials of T2DM patients undergoing treatment intensification with basal insulin or comparators (N=1699) were pooled. Baseline GV measures included standard deviation (SD), mean amplitude of glycaemic excursions (MAGE), mean absolute glucose (MAG), coefficient of variation (CV), high blood glucose index (HBGI), and low blood glucose index (LBGI) were correlated with HbA1c change and hypoglycaemic events.

RESULTS

All mean GV measures, excluding CV which worsened, improved significantly from baseline to Week 24, with the largest proportional reduction obtained for HBGI (-65.5%). When assessed as mean individual percentage changes only HBGI improved significantly. Baseline GV correlated positively with Week 24 HbA1c for SD, MAGE, and HBGI. Baseline HBGI and CV correlated negatively and positively, respectively, with Week 24 HbA1c change. Correlations also existed between most baseline GV measures and age, body mass index, Week 24 fasting plasma glucose, Week 24 postprandial plasma glucose, and hypoglycaemic events; statistical significance depended on the specific measure.

CONCLUSIONS

Pre-treatment GV is associated with glycaemic outcomes in T2DM patients undergoing treatment intensification over 24 weeks. HBGI might be the most robust predictor, warranting validation in dedicated prospective studies or randomized trials to assess the predictive value of measuring GV.

Assessing sensor accuracy for non-adjunct use of continuous glucose monitoring

BACKGROUND

The level of continuous glucose monitoring (CGM) accuracy needed for insulin dosing using sensor values (i.e., the level of accuracy permitting non-adjunct CGM use) is a topic of ongoing debate. Assessment of this level in clinical experiments is virtually impossible because the magnitude of CGM errors cannot be manipulated and related prospectively to clinical outcomes.

MATERIALS AND METHODS

A combination of archival data (parallel CGM, insulin pump, self-monitoring of blood glucose [SMBG] records, and meals for 56 pump users with type 1 diabetes) and in silico experiments was used to "replay" real-life treatment scenarios and relate sensor error to glycemic outcomes. Nominal blood glucose (BG) traces were extracted using a mathematical model, yielding 2,082 BG segments each initiated by insulin bolus and confirmed by SMBG. These segments were replayed at seven sensor accuracy levels (mean absolute relative differences [MARDs] of 3-22%) testing six scenarios: insulin dosing using sensor values, threshold, and predictive alarms, each without or with considering CGM trend arrows.

RESULTS

In all six scenarios, the occurrence of hypoglycemia (frequency of BG levels ≤50 mg/dL and BG levels ≤39 mg/dL) increased with sensor error, displaying an abrupt slope change at MARD =10%. Similarly, hyperglycemia (frequency of BG levels ≥250 mg/dL and BG levels ≥400 mg/dL) increased and displayed an abrupt slope change at MARD=10%. When added to insulin dosing decisions, information from CGM trend arrows, threshold, and predictive alarms resulted in improvement in average glycemia by 1.86, 8.17, and 8.88 mg/dL, respectively.

CONCLUSIONS

Using CGM for insulin dosing decisions is feasible below a certain level of sensor error, estimated in silico at MARD=10%. In our experiments, further accuracy improvement did not contribute substantively to better glycemic outcomes.

Moving-horizon-like state estimation via continuous glucose monitor feedback in MPC of an artificial pancreas for type 1 diabetes

An extension of a novel state estimation scheme is presented. The proposed method is developed for model predictive control (MPC) of an artificial pancreas for automatic insulin delivery to people with type 1 diabetes mellitus; specifically, glycemia control based on feedback by a continuous glucose monitor. The state estimation strategy is akin to moving-horizon estimation, but effectively exploits knowledge of sensor recalibrations, ameliorates the effects of delays between measurements and the controller call, and accommodates irregularly sampled output measurements. The method performs a function fit and a sampling action to synthesize a mock output trajectory for constructing the state. In this paper the structure of the fitted function prototype is divorced from the structure of the function that is sampled, facilitating the strategic elimination of prediction artifacts that are not observed in the actual plant. The proposed estimation strategy is demonstrated using clinical data collected by a Dexcom G4 Platinum continuous glucose monitor.

Advancing our understanding of the glucose system via modeling: a perspective

The glucose story begins with Claude Bernard's discovery of glycogen and milieu interieur, continued with Banting's and Best's discovery of insulin and with Rudolf Schoenheimer's paradigm of dynamic body constituents. Tracers and compartmental models allowed moving to the first quantitative pictures of the system and stimulated important developments in terms of modeling methodology. Three classes of multiscale models, models to measure, models to simulate, and models to control the glucose system, are reviewed in their historical development with an eye to the future.

A Long-Term Model of the Glucose-Insulin Dynamics of Type 1 Diabetes

A new glucose-insulin model is introduced which fits with the clinical data from in- and outpatients for two days. Its stability property is consistent with the glycemia behavior for type 1 diabetes. This is in contrast to traditional glucose-insulin models. Prior models fit with clinical data for a few hours only or display some nonnatural equilibria. The parameters of this new model are identifiable from standard clinical data as continuous glucose monitoring, insulin injection, and carbohydrate estimate. Moreover, it is shown that the parameters from the model allow the computation of the standard tools used in functional insulin therapy as the basal rate of insulin and the insulin sensitivity factor. This is a major outcome as they are required in therapeutic education of type 1 diabetic patients.

Circadian variability of insulin sensitivity: physiological input for in silico artificial pancreas

BACKGROUND

Closed-loop control clinical research trials have been considerably accelerated by in silico trials using the Food and Drug Administration-accepted type 1 diabetes mellitus (T1DM) simulator. We have recently demonstrated that postprandial insulin sensitivity (SI) in T1DM subjects was lower at breakfast (B) than lunch (L) and dinner (D), but not significantly, because of the small population size. The goal of this study was therefore to incorporate this novel information into the University of Virginia/Padova T1DM simulator and to reproduce in silico the observed circadian variability.

SUBJECTS AND METHODS

Twenty T1DM subjects received an identical mixed meal at B, L, and D. SI was calculated for each meal using the oral glucose minimal model. Seven SI daily patterns were identified, and their probabilities were estimated. Each in silico subject was linked to a time-varying SI profile, while random deviations of up to 40% were allowed.

RESULTS

Simulations were compared with experimental data. The integrated area above the basal glucose curve values were 2.60 ± 0.91 (B), 1.38 ± 0.91 (L), and 1.44 ± 1.07 (D) 10(4) min · mg/dL in silico versus 2.87 ± 1.65 (B), 1.98 ± 1.56 (L), and 2.16 ± 2.00 (D) 10(4) min · mg/dL in vivo. Incremental peak glucose values were 109 ± 33 (B), 80 ± 29 (L), and 81 ± 30 (D) mg/dL in silico versus 136 ± 39 (B), 126 ± 37 (L), and 125 ± 48 (D) mg/dL in vivo.

CONCLUSIONS

The incorporation of a time-varying SI into the simulator makes this technology suitable for running multiple-meal scenarios, thus enabling a more robust design of artificial pancreas algorithms.

Designing an artificial pancreas architecture: the AP@home experience

The latest achievements in sensor technologies for blood glucose level monitoring, pump miniaturization for insulin delivery, and the availability of portable computing devices are paving the way toward the artificial pancreas as a treatment for diabetes patients. This device encompasses a controller unit that oversees the administration of insulin micro-boluses and continuously drives the pump based on blood glucose readings acquired in real time. In order to foster the research on the artificial pancreas and prepare for its adoption as a therapy, the European Union in 2010 funded the AP@home project, following a series of efforts already ongoing in the USA. This paper, authored by members of the AP@home consortium, reports on the technical issues concerning the design and implementation of an architecture supporting the exploitation of an artificial pancreas platform. First a PC-based platform was developed by the authors to prove the effectiveness and reliability of the algorithms responsible for insulin administration. A mobile-based one was then adopted to improve the comfort for the patients. Both platforms were tested on real patients, and a description of the goals, the achievements, and the major shortcomings that emerged during those trials is also reported in the paper.

Quantification of the glycemic response to microdoses of subcutaneous glucagon at varying insulin levels

OBJECTIVE

Glucagon delivery in closed-loop control of type 1 diabetes is effective in minimizing hypoglycemia. However, high insulin concentration lowers the hyperglycemic effect of glucagon, and small doses of glucagon in this setting are ineffective. There are no studies clearly defining the relationship between insulin levels, subcutaneous glucagon, and blood glucose.

RESEARCH DESIGN AND METHODS

Using a euglycemic clamp technique in 11 subjects with type 1 diabetes, we examined endogenous glucose production (EGP) of glucagon (25, 75, 125, and 175 μg) at three insulin infusion rates (0.016, 0.032, and 0.05 units/kg/h) in a randomized, crossover study. Infused 6,6-dideuterated glucose was measured every 10 min, and EGP was determined using a validated glucoregulatory model. Area under the curve (AUC) for glucose production was the primary outcome, estimated over 60 min.

RESULTS

At low insulin levels, EGP rose proportionately with glucagon dose, from 5 ± 68 to 112 ± 152 mg/kg (P = 0.038 linear trend), whereas at high levels, there was no increase in glucose output (19 ± 53 to 26 ± 38 mg/kg, P = NS). Peak glucagon serum levels and AUC correlated well with dose (r2 = 0.63, P < 0.001), as did insulin levels with insulin infusion rates (r2 = 0.59, P < 0.001).

CONCLUSIONS

EGP increases steeply with glucagon doses between 25 and 175 μg at lower insulin infusion rates. However, high insulin infusion rates prevent these doses of glucagon from significantly increasing glucose output and may reduce glucagon effectiveness in preventing hypoglycemia when used in the artificial pancreas.

An iterative learning strategy for the auto-tuning of the feedforward and feedback controller in type-1 diabetes

This paper proposes a scheme for the control of the blood glucose in subjects with type-1 diabetes mellitus based on the subcutaneous (s.c.) glucose measurement and s.c. insulin administration. The tuning of the controller is based on an iterative learning strategy that exploits the repetitiveness of the daily feeding habit of a patient. The control consists of a mixed feedback and feedforward contribution whose parameters are tuned through an iterative learning process that is based on the day-by-day automated analysis of the glucose response to the infusion of exogenous insulin. The scheme does not require any a priori information on the patient insulin/glucose response, on the meal times and on the amount of ingested carbohydrates (CHOs). Thanks to the learning mechanism the scheme is able to improve its performance over time. A specific logic is also introduced for the detection and prevention of possible hypoglycaemia events. The effectiveness of the methodology has been validated using long-term simulation studies applied to a set of nine in silico patients considering realistic uncertainties on the meal times and on the quantities of ingested CHOs.

State Estimation with Sensor Recalibrations and Asynchronous Measurements for MPC of an Artificial Pancreas to Treat T1DM

A novel state estimation scheme is proposed for use in Model Predictive Control (MPC) of an artificial pancreas based on Continuous Glucose Monitor (CGM) feedback, for treating type 1 diabetes mellitus. The performance of MPC strategies heavily depends on the initial condition of the predictions, typically characterized by a state estimator. Commonly employed Luenberger-observers and Kalman-filters are effective much of the time, but suffer limitations. Three particular limitations are tackled by the proposed approach. First, CGM recalibrations, step changes that cause highly dynamic responses in recursive state estimators, are accommodated in a graceful manner. Second, the proposed strategy is not affected by CGM measurements that are asynchronous, i.e., neither of fixed sample-period, nor of a sample-period that is equal to the controller's. Third, the proposal suffers no offsets due to plant-model mismatches. The proposed approach is based on moving-horizon optimization.

LMI-Based Approaches for the Calibration of Continuous Glucose Measurement Sensors

The problem of online calibration and recalibration of continuous glucose monitoring (CGM) devices is considered. Two different parametric relations between interstitial and blood glucose are investigated and constructive algorithms to adaptively estimate the parameters within those relations are proposed. One characteristic is the explicit consideration of measurement uncertainty of the device used to collect the calibration measurements. Another feature is the automatic detection of fingerstick measurements that are not suitable to be used for calibration. Since the methods rely on the solution of linear matrix inequalities resulting in convex optimization problems, the algorithms are of moderate computational complexity and could be implemented on a CGM device. The methods were assessed on clinical data from 17 diabetic patients and the improvements with respect to the current state of the art is shown.

Reducing risks in type 1 diabetes using H∞ control

A control scheme was designed in order to reduce the risks of hyperglycemia and hypoglycemia in type 1 diabetes mellitus (T1DM). This structure is composed of three main components: an H∞ robust controller, an insulin feedback loop (IFL), and a safety mechanism (SM). A control-relevant model that is employed to design the robust controller is identified. The identification procedure is based on the distribution version of the UVA/Padova metabolic simulator using the simulation adult cohort. The SM prevents dangerous scenarios by acting upon a prediction of future glucose levels, and the IFL modifies the loop gain in order to reduce postprandial hypoglycemia risks. The procedure is tested on the complete alic>in silico adult cohort of the UVA/Padova metabolic simulator, which has been accepted by the Food and Drug Administration (FDA) in lieu of animal trials.

Novel individual metabolic profile characterizes the protein kinase B-alpha (pkbα-/-) in vivo model

CONTEXT

Type 2 diabetes and associated co-morbidities run epidemic waves worldwide. Since pathophysiological constellations are individual and display a wide spread of dysmetabolic profiles personalized health care assessments start to emerge. Therefore, we established a specific in silico assessment tool targeting metabolic characterizations individually.

MATERIALS AND METHODS

Values obtained from oral glucose and intraperitoneal insulin tolerance tests performed on pkbα(-/-) mice (KO) as well as age- and gender-matched controls (WT) were analysed using our established in silico model.

RESULTS

Generally, male pkbα(-/-) mice (KO) presented significantly increased insulin sensitivity at an age of 6 months compared with age-matched WTs (p = 0.036). Female KO and WT groups displayed improved glucose sensitivities compared with age-matched males (for WT p ≤ 0.011).

DISCUSSION AND CONCLUSION

Specific metabolic characterization should be assessed individually. Therefore, our in silico model enables novel insights inaugurating specific primary preventive strategies targeting individual metabolic profiling precisely.

The artificial pancreas: current status and future prospects in the management of diabetes

Recent advances in insulins, insulin pumps, continuous glucose-monitoring systems, and control algorithms have resulted in an acceleration of progress in the development of artificial pancreas devices. This review discusses progress in the development of external systems that are based on subcutaneous drug delivery and subcutaneous continuous glucose monitoring. There are two major system-level approaches to achieving closed-loop control of blood glucose in diabetic individuals. The unihormonal approach uses insulin to reduce blood glucose and relies on complex safety mitigation algorithms to reduce the risk of hypoglycemia. The bihormonal approach uses both insulin to lower blood glucose and glucagon to raise blood glucose, and also relies on complex algorithms to provide for safety of the user. There are several major strategies for the design of control algorithms and supervision control for application to the artificial pancreas: proportional-integral-derivative, model predictive control, fuzzy logic, and safety supervision designs. Advances in artificial pancreas research in the first decade of this century were based on the ongoing computer revolution and miniaturization of electronic technology. The advent of modern smartphones has created the ability to utilize smartphone technology as the engineering centerpiece of an artificial pancreas. With these advances, an artificial or bionic pancreas is within reach.