Diabetes: Models, Signals, and Control

Calibration algorithms for continuous glucose monitoring systems based on interstitial fluid sensing

Continuous glucose monitoring (CGM) is of great importance to the treatment and prevention of diabetes. As a proven commercial technology, electrochemical glucose sensor based on interstitial fluid (ISF) sensing has high sensitivity and wide detection range. Therefore, it has good promotion prospects in noninvasive or minimally-invasive CGM system. However, since there are concentration differences and time lag between glucose in plasma and ISF, the accuracy of this type of sensors are still limited. Typical calibration algorithms rely on simple linear regression which do not account for the variability of the sensitivity of sensors. To enhance the accuracy and stability of CGM based on ISF, optimization of calibration algorithm for sensors is indispensable. While there have been considerable researches on improving calibration algorithms for CGM, they have still received less attention. This article reviews the problem of typical calibration and presents the outstanding calibration algorithms in recent years. Finally, combined with existing research and emerging sensing technologies, this paper makes an outlook on the future calibration algorithms for CGM sensors.

Diabetes-associated Genetic Variation in MTNR1B and Its Effect on Islet Function

Context

Multiple common genetic variants have been associated with type 2 diabetes, but the mechanism by which they predispose to diabetes is incompletely understood. One such example is variation in MTNR1B, which implicates melatonin and its receptor in the pathogenesis of type 2 diabetes.

Objective

To characterize the effect of diabetes-associated genetic variation at rs10830963 in the MTNR1B locus on islet function in people without type 2 diabetes.

Design

The association of genetic variation at rs10830963 with glucose, insulin, C-peptide, glucagon, and indices of insulin secretion and action were tested in a cohort of 294 individuals who had previously undergone an oral glucose tolerance test (OGTT). Insulin sensitivity, β-cell responsivity to glucose, and Disposition Indices were measured using the oral minimal model.

Setting

The Clinical Research and Translation Unit at Mayo Clinic, Rochester, MN.

Participants

Two cohorts were utilized for this analysis: 1 cohort was recruited on the basis of prior participation in a population-based study in Olmsted County. The other cohort was recruited on the basis of TCF7L2 genotype at rs7903146 from the Mayo Biobank.

Intervention

Two-hour, 7-sample OGTT.

Main Outcome Measures

Fasting, nadir, and integrated glucagon concentrations.

Results

One or 2 copies of the G-allele at rs10830963 were associated with increased postchallenge glucose and glucagon concentrations compared to subjects with the CC genotype.

Conclusion

The effects of rs10830963 on glucose homeostasis and predisposition to type 2 diabetes are likely to be partially mediated through changes in α-cell function.

Predicting Blood Glucose Levels with Organic Neuromorphic Micro-Networks

Accurate glucose prediction is vital for diabetes management. Artificial intelligence and artificial neural networks (ANNs) are showing promising results for reliable glucose predictions, offering timely warnings for glucose fluctuations. The translation of these software-based ANNs into dedicated computing hardware opens a route toward automated insulin delivery systems ultimately enhancing the quality of life for diabetic patients. ANNs are transforming this field, potentially leading to implantable smart prediction devices and ultimately to a fully artificial pancreas. However, this transition presents several challenges, including the need for specialized, compact, lightweight, and low-power hardware. Organic polymer-based electronics are a promising solution as they have the ability to implement the behavior of neural networks, operate at low voltage, and possess key attributes like flexibility, stretchability, and biocompatibility. Here, the study focuses on implementing software-based neural networks for glucose prediction into hardware systems. How to minimize network requirements, downscale the architecture, and integrate the neural network with electrochemical neuromorphic organic devices, meeting the strict demands of smart implants for in-body computation of glucose prediction is investigated.

Validation of the UVA Simulation Replay Methodology Using Clinical Data: Reproducing a Randomized Clinical Trial

Background: Computer simulators of human metabolism are powerful tools to design and validate new diabetes treatments. However, these platforms are often limited in the diversity of behaviors and glycemic conditions they can reproduce. Replay methodologies leverage field-collected data to create ad hoc simulation environments representative of real-life conditions. After formal validations of our method in prior publications, we demonstrate its capacity to reproduce a recent clinical trial. Methods: Using the replay methodology, an ensemble of replay simulators was generated using data from a randomized crossover clinical trial comparing the hybrid closed loop (HCL) and fully closed loop (FCL) control modalities in automated insulin delivery (AID), creating 64 subject/modality pairs. Each virtual subject was exposed to the alternate AID modality to compare the simulated versus observed glycemic outcomes. Equivalence tests were performed for time in, below, and above range (TIR, TBR, and TAR) and high and low blood glucose indices (HBGI and LBGI) considering equivalence margins corresponding to clinical significance. Results: TIR, TAR, LBGI, and HBGI showed statistical and clinical equivalence between the original and the simulated data; TBR failed the equivalence test. For example, in the HCL mode, simulated TIR was 84.89% versus an observed 84.31% (P = 0.0170, confidence interval [CI] [-3.96, 2.79]), and for FCL mode, TIR was 76.58% versus 77.41% (P = 0.0222, CI [-2.54, 4.20]). Conclusion: Clinical trial data confirm the prior in silico validation of the UVA replay method in predicting the glycemic impact of modified insulin treatments. This in vivo demonstration justifies the application of the replay method to the personalization and adaptation of treatment strategies in people with type 1 diabetes.

Glucagon-like peptide-1 receptor blockade impairs islet secretion and glucose metabolism in humans

BACKGROUNDProglucagon can be processed to glucagon-like peptide1 (GLP-1) within the islet, but its contribution to islet function in humans remains unknown. We sought to understand whether pancreatic GLP-1 alters islet function in humans and whether this is affected by type 2 diabetes.METHODSWe therefore studied individuals with and without type 2 diabetes on two occasions in random order. On one occasion, exendin 9-39, a competitive antagonist of the GLP-1 Receptor (GLP1R), was infused, while on the other, saline was infused. The tracer dilution technique ([3-3H] glucose) was used to measure glucose turnover during fasting and during a hyperglycemic clamp.RESULTSExendin 9-39 increased fasting glucose concentrations; fasting islet hormone concentrations were unchanged, but inappropriate for the higher fasting glucose observed. In people with type 2 diabetes, fasting glucagon concentrations were markedly elevated and persisted despite hyperglycemia. This impaired suppression of endogenous glucose production by hyperglycemia.CONCLUSIONThese data show that GLP1R blockade impairs islet function, implying that intra-islet GLP1R activation alters islet responses to glucose and does so to a greater degree in people with type 2 diabetes.TRIAL REGISTRATIONThis study was registered at ClinicalTrials.gov NCT04466618.FUNDINGThe study was primarily funded by NIH NIDDK DK126206. AV is supported by DK78646, DK116231 and DK126206. CDM was supported by MIUR (Italian Minister for Education) under the initiative "Departments of Excellence" (Law 232/2016).

Developing the UVA/Padova Type 1 Diabetes Simulator: Modeling, Validation, Refinements, and Utility

Arguably, diabetes mellitus is one of the best quantified human conditions. In the past 50 years, the metabolic monitoring technologies progressed from occasional assessment of average glycemia via HbA1c, through episodic blood glucose readings, to continuous glucose monitoring (CGM) producing data points every few minutes. The high-temporal resolution of CGM data enabled increasingly intensive treatments, from decision support assisting insulin injection or oral medication, to automated closed-loop control, known as the "artificial pancreas." Throughout this progress, mathematical models and computer simulation of the human metabolic system became indispensable for the technological progress of diabetes treatment, enabling every step, from assessment of insulin sensitivity via the now classic Minimal Model of Glucose Kinetics, to in silico trials replacing animal experiments, to automated insulin delivery algorithms. In this review, we follow these developments, beginning with the Minimal Model, which evolved through the years to become large and comprehensive and trigger a paradigm change in the design of diabetes optimization strategies: in 2007, we introduced a sophisticated model of glucose-insulin dynamics and a computer simulator equipped with a "population" of N = 300 in silico "subjects" with type 1 diabetes. In January 2008, in an unprecedented decision, the Food and Drug Administration (FDA) accepted this simulator as a substitute to animal trials for the pre-clinical testing of insulin treatment strategies. This opened the field for rapid and cost-effective development and pre-clinical testing of new treatment approaches, which continues today. Meanwhile, animal experiments for the purpose of designing new insulin treatment algorithms have been abandoned.

Performance Effect of Adjusting Insulin Sensitivity for Model-Based Automated Insulin Delivery Systems

BACKGROUND

Model predictive control (MPC) has become one of the most popular control strategies for automated insulin delivery (AID) in type 1 diabetes (T1D). These algorithms rely on a prediction model to determine the best insulin dosing every sampling time. Although these algorithms have been shown to be safe and effective for glucose management through clinical trials, managing the ever-fluctuating relationship between insulin delivery and resulting glucose uptake (aka insulin sensitivity, IS) remains a challenge. We aim to evaluate the effect of informing an AID system with IS on the performance of the system.

METHOD

The University of Virginia (UVA) MPC control-based hybrid closed-loop (HCL) and fully closed-loop (FCL) system was used. One-day simulations at varying levels of IS were run with the UVA/Padova T1D Simulator. The AID system was informed with an estimated value of IS obtained through a mixed meal glucose tolerance test. Relevant controller parameters are updated to inform insulin dosing of IS. Performance of the HCL/FCL system with and without information of the changing IS was assessed using a novel performance metric penalizing the time outside the target glucose range.

RESULTS

Feedback in AID systems provides a certain degree tolerance to changes in IS. However, IS-informed bolus and basal dosing improve glycemic outcomes, providing increased protection against hyperglycemia and hypoglycemia according to the individual's physiological state.

CONCLUSIONS

The proof-of-concept analysis presented here shows the potentially beneficial effects on system performance of informing the AID system with accurate estimates of IS. In particular, when considering reduced IS, the informed controller provides increased protection against hyperglycemia compared with the naïve controller. Similarly, reduced hypoglycemia is obtained for situations with increased IS. Further tailoring of the adaptation schemes proposed in this work is needed to overcome the increased hypoglycemia observed in the more resistant cases and to optimize the performance of the adaptation method.

Differential Responders to a Mixed Meal Tolerance Test Associated with Type 2 Diabetes Risk Factors and Gut Microbiota-Data from the MEDGI-Carb Randomized Controlled Trial

The global prevalence of type 2 diabetes mellitus (T2DM) has surged in recent decades, and the identification of differential glycemic responders can aid tailored treatment for the prevention of prediabetes and T2DM. A mixed meal tolerance test (MMTT) based on regular foods offers the potential to uncover differential responders in dynamical postprandial events. We aimed to fit a simple mathematical model on dynamic postprandial glucose data from repeated MMTTs among participants with elevated T2DM risk to identify response clusters and investigate their association with T2DM risk factors and gut microbiota. Data were used from a 12-week multi-center dietary intervention trial involving high-risk T2DM adults, comparing high- versus low-glycemic index foods within a Mediterranean diet context (MEDGICarb). Model-based analysis of MMTTs from 155 participants (81 females and 74 males) revealed two distinct plasma glucose response clusters that were associated with baseline gut microbiota. Cluster A, inversely associated with HbA1c and waist circumference and directly with insulin sensitivity, exhibited a contrasting profile to cluster B. Findings imply that a standardized breakfast MMTT using regular foods could effectively distinguish non-diabetic individuals at varying risk levels for T2DM using a simple mechanistic model.

The importance of interpreting machine learning models for blood glucose prediction in diabetes: an analysis using SHAP

Machine learning has become a popular tool for learning models of complex dynamics from biomedical data. In Type 1 Diabetes (T1D) management, these models are increasingly been integrated in decision support systems (DSS) to forecast glucose levels and provide preventive therapeutic suggestions, like corrective insulin boluses (CIB), accordingly. Typically, models are chosen based on their prediction accuracy. However, since patient safety is a concern in this application, the algorithm should also be physiologically sound and its outcome should be explainable. This paper aims to discuss the importance of using tools to interpret the output of black-box models in T1D management by presenting a case-of-study on the selection of the best prediction algorithm to integrate in a DSS for CIB suggestion. By retrospectively "replaying" real patient data, we show that two long-short term memory neural networks (LSTM) (named p-LSTM and np-LSTM) with similar prediction accuracy could lead to different therapeutic decisions. An analysis with SHAP-a tool for explaining black-box models' output-unambiguously shows that only p-LSTM learnt the physiological relationship between inputs and glucose prediction, and should therefore be preferred. This is verified by showing that, when embedded in the DSS, only p-LSTM can improve patients' glycemic control.

Interpretable physiological forecasting in the ICU using constrained data assimilation and electronic health record data

OBJECTIVE

Prediction of physiological mechanics are important in medical practice because interventions are guided by predicted impacts of interventions. But prediction is difficult in medicine because medicine is complex and difficult to understand from data alone, and the data are sparse relative to the complexity of the generating processes. Computational methods can increase prediction accuracy, but prediction with clinical data is difficult because the data are sparse, noisy and nonstationary. This paper focuses on predicting physiological processes given sparse, non-stationary, electronic health record data in the intensive care unit using data assimilation (DA), a broad collection of methods that pair mechanistic models with inference methods.

METHODS

A methodological pipeline embedding a glucose-insulin model into a new DA framework, the constrained ensemble Kalman filter (CEnKF) to forecast blood glucose was developed. The data include tube-fed patients whose nutrition, blood glucose, administered insulins and medications were extracted by hand due to their complexity and to ensure accuracy. The model was estimated using an individual's data as if they arrived in real-time, and the estimated model was run forward producing a forecast. Both constrained and unconstrained ensemble Kalman filters were estimated to compare the impact of constraints. Constraint boundaries, model parameter sets estimated, and data used to estimate the models were varied to investigate their influence on forecasting accuracy. Forecasting accuracy was evaluated according to mean squared error between the model-forecasted glucose and the measurements and by comparing distributions of measured glucose and forecast ensemble means.

RESULTS

The novel CEnKF produced substantial gains in robustness and accuracy while minimizing the data requirements compared to the unconstrained ensemble Kalman filters. Administered insulin and tube-nutrition were important for accurate forecasting, but including glucose in IV medication delivery did not increase forecast accuracy. Model flexibility, controlled by constraint boundaries and estimated parameters, did influence forecasting accuracy.

CONCLUSION

Accurate and robust physiological forecasting with sparse clinical data is possible with DA. Introducing constrained inference, particularly on unmeasured states and parameters, reduced forecast error and data requirements. The results are not particularly sensitive to model flexibility such as constraint boundaries, but over or under constraining increased forecasting errors.

Uncovering personalized glucose responses and circadian rhythms from multiple wearable biosensors with Bayesian dynamical modeling

Wearable biosensors and smartphone applications can measure physiological variables over multiple days in free-living conditions. We measure food and drink ingestion, glucose dynamics, physical activity, heart rate (HR), and heart rate variability (HRV) in 25 healthy participants over 14 days. We develop a Bayesian inference framework to learn personal parameters that quantify circadian rhythms and physiological responses to external stressors. Modeling the effects of ingestion events on glucose levels reveals that slower glucose decay kinetics elicit larger postprandial glucose spikes, and we uncover a circadian baseline rhythm for glucose with high amplitudes in some individuals. Physical activity and circadian rhythms explain as much as 40%-65% of the HR variance, whereas the variance explained for HRV is more heterogeneous across individuals. A more complex model incorporating activity, HR, and HRV explains up to 15% of additional glucose variability, highlighting the relevance of integrating multiple biosensors to better predict glucose dynamics.

Effects of acute changes in fasting glucose and free fatty acid concentrations on indices of β-cell function and glucose metabolism in subjects without diabetes

Elevated fasting free fatty acids (FFAs) and fasting glucose are additively associated with impaired glucose tolerance (IGT) and decreased β-cell function [quantified as disposition index (DI)]. We sought to examine how changes in fasting FFA and glucose alter islet function. We studied 10 subjects with normal fasting glucose (NFG) and normal glucose tolerance (NGT) on two occasions. On one occasion, Intralipid and glucose were infused overnight to mimic conditions present in IFG/IGT. In addition, we studied seven subjects with IFG/IGT on two occasions. On one occasion, insulin was infused to lower overnight FFA and glucose concentrations to those observed in people with NFG/NGT. The following morning, a labeled mixed meal was used to measure postprandial glucose metabolism and β-cell function. Elevation of overnight fasting FFA and glucose in NFG/NGT did not alter peak or integrated glucose concentrations (2.0 ± 0.1 vs. 2.0 ± 0.1 Mol per 5 h, Saline vs. Intralipid/glucose, P = 0.55). Although overall β-cell function quantified by the Disposition Index was unchanged, the dynamic component of β-cell responsivity (ϕd) was decreased by Intralipid and glucose infusion (9 ± 1 vs. 16 ± 3 10-9, P = 0.02). In people with IFG/IGT, insulin did not alter postprandial glucose concentrations or indices of β-cell function. Endogenous glucose production and glucose disappearance were also unchanged in both groups. We conclude that acute, overnight changes in FFA, and glucose concentrations do not alter islet function or glucose metabolism in prediabetes.NEW & NOTEWORTHY This experiment studied the effect of changes in overnight concentrations of free fatty acids (FFAs) and glucose on β-cell function and glucose metabolism. In response to elevation of these metabolites, the dynamic component of the β-cell response to glucose was impaired. This suggests that in health overnight hyperglycemia and FFA elevation can deplete preformed insulin granules in the β-cell.

Clinically-Similar Clusters of Daily CGM Profiles: Tracking the Progression of Glycemic Control Over Time

BACKGROUND

The adoption of CGM results in vast amounts of data, but their interpretation is still more art than exact science. The International Consensus on Time in Range (TIR) proposed the widely accepted TIR system of metrics, which we now take forward by introducing a finite and fixed set of clinically-similar clusters (CSCs), such that the TIR metrics of the daily CGM profiles within a cluster are homogeneous.

METHODS

CSC definition and validation used 204,710 daily CGM profiles in health, type 1 and type 2 diabetes (T1D, T2D), on different treatments. The CSCs were defined using 23,916 daily CGM profiles (Training set), and the final fixed set of CSCs was obtained using another 37,758 profiles (Validation set). The Testing set (143,036 profiles) was used to establish the robustness and generalizability of the CSCs.

RESULTS

The final set of CSCs contains 32 clusters. Any daily CGM profile was classifiable to a single CSC which approximated common glycemic metrics of the daily CGM profile, as evidenced by regression analyses with 0 intercept (R-squares≥0.83, e.g., correlation≥0.91), for all TIR and several other metrics. The CSCs distinguished CGM profiles in health, T2D, and T1D on different treatments, and allowed tracking of the daily changes in a person's glycemic control over time.

CONCLUSION

Daily CGM profiles can be classified into one of 32 prefixed CSCs, which enables a host of applications, e.g. tabulated data interpretation and algorithmic approaches to treatment, database indexing, pattern recognition, and tracking disease progression.

Prediction of Blood Risk Score in Diabetes Using Deep Neural Networks

Improving the prediction of blood glucose concentration may improve the quality of life of people living with type 1 diabetes by enabling them to better manage their care. Given the anticipated benefits of such a prediction, numerous methods have been proposed. Rather than attempting to predict glucose concentration, a deep learning framework for prediction is proposed in which prediction is performed using a scale for hypo- and hyper-glycemia risk. Using the blood glucose risk score formula proposed by Kovatchev et al., models with different architectures were trained, including, a recurrent neural network (RNN), a gated recurrent unit (GRU), a long short-term memory (LSTM) network, and an encoder-like convolutional neural network (CNN). The models were trained using the OpenAPS Data Commons data set, comprising 139 individuals, each with tens of thousands of continuous glucose monitor (CGM) data points. The training set was composed of 7% of the data set, while the remaining was used for testing. Performance comparisons between the different architectures are presented and discussed. To evaluate these predictions, performance results are compared with the last measurement (LM) prediction, through a sample-and-hold approach continuing the last known measurement forward. The results obtained are competitive when compared to other deep learning methods. A root mean squared error (RMSE) of 16 mg/dL, 24 mg/dL, and 37 mg/dL were obtained for CNN prediction horizons of 15, 30, and 60 min, respectively. However, no significant improvements were found for the deep learning models compared to LM prediction. Performance was found to be highly dependent on architecture and the prediction horizon. Lastly, a metric to assess model performance by weighing each prediction point error with the corresponding blood glucose risk score is proposed. Two main conclusions are drawn. Firstly, going forward, there is a need to benchmark model performance using LM prediction to enable the comparison between results obtained from different data sets. Secondly, model-agnostic data-driven deep learning models may only be meaningful when combined with mechanistic physiological models; here, it is argued that neural ordinary differential equations may combine the best of both approaches. These findings are based on the OpenAPS Data Commons data set and are to be validated in other independent data sets.

In Silico Evaluation of the Medtronic 780G System While Using the GS3 and Its Calibration-Free Successor, the G4S Sensor

In silico simulation studies using 5807 virtual patients with insulin dependent diabetes have been conducted to estimate the risk and efficacy with the closed-loop 780G pump when switching between Medtronic Guardian Sensor 3 (GS3) and Medtronic Guardian 4 Sensor (G4S), next generation calibration free glucose sensor. To demonstrate by utilizing a case study that captures the merits of in silico studies with single hormone insulin dependent virtual patients that include variability in pharmacokinetics/pharmacodynamics, age, gender, insulin sensitivity and BMIs. Also, to show that in silico studies can uniquely isolate the effect of a single variable on clinical outcomes. Simulation studies results were compared to clinical and commercial data and were separated by age groups and pump settings. The commercial data, the clinical study data and the simulation studies predicted that switching between GS3 to G4S will introduce a change in glucose average, percentage time between 70 and 180 mg/dL, and percentage time below 70 mg/dL of: 5.2, 3.4, and 3.1 mg/dL, - 1.1, 0.2, and - 1.1%, and - 0.6, - 1.0, and - 0.3%, respectively. We demonstrated that our simulation studies were able to predict the difference in glycemic outcomes when switching between different sensors in real world setting, better than a small clinical controlled study. As predicted, switching between GS3 and G4S sensors with the 780G system does not introduce clinical risk and maintain the clinical outcomes of the sensor. We demonstrated the ability of insulin dependent diabetes virtual patients to predict clinical outcomes and to augment or even replace some small clinical studies.

SPINA Carb: a simple mathematical model supporting fast in-vivo estimation of insulin sensitivity and beta cell function

Modelling insulin-glucose homeostasis may provide novel functional insights. In particular, simple models are clinically useful if they yield diagnostic methods. Examples include the homeostasis model assessment (HOMA) and the quantitative insulin sensitivity check index (QUICKI). However, limitations of these approaches have been criticised. Moreover, recent advances in physiological and biochemical research prompt further refinement in this area. We have developed a nonlinear model based on fundamental physiological motifs, including saturation kinetics, non-competitive inhibition, and pharmacokinetics. This model explains the evolution of insulin and glucose concentrations from perturbation to steady-state. Additionally, it lays the foundation of a structure parameter inference approach (SPINA), providing novel biomarkers of carbohydrate homeostasis, namely the secretory capacity of beta-cells (SPINA-GBeta) and insulin receptor gain (SPINA-GR). These markers correlate with central parameters of glucose metabolism, including average glucose infusion rate in hyperinsulinemic glucose clamp studies, response to oral glucose tolerance testing and HbA1c. Moreover, they mirror multiple measures of body composition. Compared to normal controls, SPINA-GR is significantly reduced in subjects with diabetes and prediabetes. The new model explains important physiological phenomena of insulin-glucose homeostasis. Clinical validation suggests that it may provide an efficient biomarker panel for screening purposes and clinical research.

Universal Minimal Model for Glucose-Insulin Relationship with the Influence of Food Dynamic

We propose a minimal model defining the relationship between glucose and insulin with the added influence of food intakes. The constructed model consists of a system of 3 nonlinear ordinary differential equations (ODEs). The solutions of our model for both normal and diabetic subjects are compared with a minimal model and a maximal model representing the same relationship. We found that the outputs of our model are similar to those from the minimal and maximal models for both normal and diabetic subjects; the R² are 0.9997 and 0.9922, respectively, when compared with the minimal model, and are 0.9995 and 0.9940, respectively, when compared with the maximal model. Moreover, the relative errors between solutions are at most 0.9035% and as low as 1.488 × 10⁻²% on average when compared with the minimal model for normal subjects and at most 1.331% and as low as 0.1159% on average for diabetic subjects. The discrepancy between our model and the maximal model are at most 1.590% and 5.453% for normal and diabetic subjects, respectively, with a relative error averaging 0.2138% and 0.9002% for normal and diabetic subjects, respectively.

A glucose-insulin-glucagon coupled model of the isoglycemic intravenous glucose infusion experiment

Type 2 diabetes (T2D) is a pathophysiology that is characterized by insulin resistance, beta- and alpha-cell dysfunction. Mathematical models of various glucose challenge experiments have been developed to quantify the contribution of insulin and beta-cell dysfunction to the pathophysiology of T2D. There is a need for effective extended models that also capture the impact of alpha-cell dysregulation on T2D. In this paper a delay differential equation-based model is developed to describe the coupled glucose-insulin-glucagon dynamics in the isoglycemic intravenous glucose infusion (IIGI) experiment. As the glucose profile in IIGI is tailored to match that of a corresponding oral glucose tolerance test (OGTT), it provides a perfect method for studying hormone responses that are in the normal physiological domain and without the confounding effect of incretins and other gut mediated factors. The model was fit to IIGI data from individuals with and without T2D. Parameters related to glucagon action, suppression, and secretion as well as measures of insulin sensitivity, and glucose stimulated response were determined simultaneously. Significant impairment in glucose dependent glucagon suppression was observed in patients with T2D (duration of T2D: 8 (6–36) months) relative to weight matched control subjects (CS) without diabetes (k1 (mM)−1: 0.16 ± 0.015 (T2D, n = 7); 0.26 ± 0.047 (CS, n = 7)). Insulin action was significantly lower in patients with T2D (a1 (10 pM min)−1: 0.000084 ± 0.0000075 (T2D); 0.00052 ± 0.00015 (CS)) and the Hill coefficient in the equation for glucose dependent insulin response was found to be significantly different in T2D patients relative to CS (h: 1.4 ± 0.15; 1.9 ± 0.14). Trends in parameters with respect to fasting plasma glucose, HbA1c and 2-h glucose values are also presented. Significantly, a negative linear relationship is observed between the glucagon suppression parameter, k1, and the three markers for diabetes and is thus indicative of the role of glucagon in exacerbating the pathophysiology of diabetes (Spearman Rank Correlation: (n = 12; (−0.79, 0.002), (−0.73,.007), (−0.86,.0003)) respectively).

Minimal and Maximal Models to Quantitate Glucose Metabolism: Tools to Measure, to Simulate and to Run in Silico Clinical Trials

Several models have been proposed to describe the glucose system at whole-body, organ/tissue and cellular level, designed to measure non-accessible parameters (minimal models), to simulate system behavior and run in silico clinical trials (maximal models). Here, we will review the authors' work, by putting it into a concise historical background. We will discuss first the parametric portrait provided by the oral minimal models-building on the classical intravenous glucose tolerance test minimal models-to measure otherwise non-accessible key parameters like insulin sensitivity and beta-cell responsivity from a physiological oral test, the mixed meal or the oral glucose tolerance tests, and what can be gained by adding a tracer to the oral glucose dose. These models were used in various pathophysiological studies, which we will briefly review. A deeper understanding of insulin sensitivity can be gained by measuring insulin action in the skeletal muscle. This requires the use of isotopic tracers: both the classical multiple-tracer dilution and the positron emission tomography techniques are discussed, which quantitate the effect of insulin on the individual steps of glucose metabolism, that is, bidirectional transport plasma-interstitium, and phosphorylation. Finally, we will present a cellular model of insulin secretion that, using a multiscale modeling approach, highlights the relations between minimal model indices and subcellular secretory events. In terms of maximal models, we will move from a parametric to a flux portrait of the system by discussing the triple tracer meal protocol implemented with the tracer-to-tracee clamp technique. This allows to arrive at quasi-model independent measurement of glucose rate of appearance (Ra), endogenous glucose production (EGP), and glucose rate of disappearance (Rd). Both the fast absorbing simple carbs and the slow absorbing complex carbs are discussed. This rich data base has allowed us to build the UVA/Padova Type 1 diabetes and the Padova Type 2 diabetes large scale simulators. In particular, the UVA/Padova Type 1 simulator proved to be a very useful tool to safely and effectively test in silico closed-loop control algorithms for an artificial pancreas (AP). This was the first and unique simulator of the glucose system accepted by the U.S. Food and Drug Administration as a substitute to animal trials for in silico testing AP algorithms. Recent uses of the simulator have looked at glucose sensors for non-adjunctive use and new insulin molecules.

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

BACKGROUND AND OBJECTIVE

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

METHOD

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

RESULTS

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

CONCLUSIONS

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

Computational-Model-Based Biopharmaceutics for p53 Pathway Using Modern Control Techniques for Cancer Treatment

The p53 pathway has been the focus of many researchers in the last few decades owing to its pivotal role as a frontline cancer suppressant protein. It plays a vital role in maintaining cell cycle checkpoints and cell apoptosis in response to a broken DNA strand. This is why it is found in the mutated form in more than 50% of malignant tumors. To overcome this, various drugs have been proposed to revive the p53 pathway in cancer patients. Small-molecule-based drugs, such as Nutlin 3a, which are capable of performing this stimulation, are at the fore of advanced clinical trials. However, the calculation of their dosage is a challenge. In this work, a method to determine the dosage of Nutlin 3a is investigated. A control-systems-based model is developed to study the response of the wild-type p53 protein to this drug. The proposed strategy regulates the p53 protein along with negative and positive feedback loops mediated by the MDM2 and MDM2 mRNA, respectively, along with the reversible repression of MDM2 caused by Nutlin 3a. For a broader perspective, the reported PBK dynamics of Nutlin 3a are also incorporated. It has been reported that p53 responds to stresses in two ways in terms of concentration to this drug: either it is a sustained (constant) or an oscillatory response. The claimed dosage strategy turned out to be appropriate for sustained p53 response. However, for the induction of oscillations, inhibition of MDM2 is not enough; rather, anti-repression of the p53–MDM2 complex is also needed, which opens new horizons for a new drug design paradigm.

Multi-task disentangled autoencoder for time-series data in glucose dynamics

The objective of this study is to propose MD-VAE: a multi-task disentangled variational autoencoders (VAE) for exploring characteristics of latent representations (LR) and exploiting LR for diverse tasks including glucose forecasting, event detection, and temporal clustering.

A methodical survey of mathematical model-based control techniques based on open and closed loop control approach for diabetes management

Disturbance of blood sugar level is controlled through well-known biomechanical feedback loops: high levels of glucose in blood facilitate to release insulin from the pancreas which accelerates the absorption rate of cellular glucose. Low glucose levels encourage to release pancreatic glucagon which induces glycogen breakdown to glucose in the liver. These bio-control systems do not function properly in diabetic patients. Though the control of disease seems intuitively easy, in real life, due to many differences in structure by diet and fasting, exercise, medications, patient’s profile and other stressors, it is not that easy. The mathematical models of the glucose-insulin regulatory system follow the patient’s physiological conditions which make it difficult to identify and estimate all the model parameters. In this paper, we have given a systematic literature review on mathematical models of the diabetic patients, and various kinds of disease control techniques through the development of open and closed loop insulin deliver command system and optimization of exogenous insulin rate. It demonstrates the open and closed loop type model-based control strategies underlying the assumptions of the concerned models. The combination of mathematical model with control strategies such as genetic algorithm (GA), neural network (NN), sliding mode controller (SMC), model predictive controller (MPC), and fuzzy logic control (FLC) has been considered, which provides an overview of this area, highlighting the control profile over the diabetic model with promising clinical results, outlining key challenges, and identifying needs for the future research. Also, the significance of these control algorithms has been discussed in the presence of the noises, the controller’s robustness and various other disturbances. It provides substantial information on diabetes management through various control techniques.

Modeling the Effect of Subcutaneous Lixisenatide on Glucoregulatory Endocrine Secretions and Gastric Emptying in Type 2 Diabetes to Simulate the Effect of iGlarLixi Administration Timing on Blood Sugar Profiles

BACKGROUND

As type 2 diabetes (T2D) progresses, intensification to combination therapies, such as iGlarLixi (a fixed-ratio GLP-1 RA and basal insulin combination), may be required. Here a simulation study was used to assess the effect of iGlarLixi administration timing (am vs pm) on blood sugar profiles.

METHODS

Models of lixisenatide were built with a selection procedure, optimizing measurement fits and model complexity, and were included in a pre-existing T2D simulation platform containing glargine models. With the resulting tool, a simulated trial was conducted with 100 in-silico participants with T2D. Individuals were given iGLarLixi either before breakfast or before an evening meal for 2 weeks and daily glycemic profiles were analyzed. In the model, breakfast was considered the largest meal of the day.

RESULTS

A similar percentage of time within 24 hours was spent with blood sugar levels between 70 to 180 mg/dL when iGlarLixi was administered pre-breakfast or pre-evening meal (73% vs 71%, respectively). Overall percent of time with blood glucose levels above 180 mg/dL within a 24-hour period was similar when iGlarLixi was administered pre-breakfast or pre-evening meal (26% vs 28%, respectively). Rates of hypoglycemia were low in both regimens, with a blood glucose concentration of below 70 mg/dL only observed for 1% of the 24-hour time period for either timing of administration.

CONCLUSIONS

Good efficacy was observed when iGlarlixi was administered pre-breakfast; however, administration of iGlarlixi pre-evening meal was also deemed to be effective, even though in the model the size of the evening meal was smaller than that of the breakfast.

Controlled bio-inspired self-organised criticality

Complex biological systems are considered to be controlled using feedback mechanisms. Reduced systems modelling has been effective to describe these mechanisms, but this approach does not sufficiently encompass the required complexity that is needed to understand how localised control in a biological system can provide global stable states. Self-Organised Criticality (SOC) is a characteristic property of locally interacting physical systems, which readily emerges from changes to its dynamic state due to small nonlinear perturbations. These small changes in the local states, or in local interactions, can greatly affect the total system state of critical systems. It has long been conjectured that SOC is cardinal to biological systems, that show similar critical dynamics, and also may exhibit near power-law relations. Rate Control of Chaos (RCC) provides a suitable robust mechanism to generate SOC systems, which operates at the edge of chaos. The bio-inspired RCC method requires only local instantaneous knowledge of some of the variables of the system, and is capable of adapting to local perturbations. Importantly, connected RCC controlled oscillators can maintain global multi-stable states, and domains where power-law relations may emerge. The network of oscillators deterministically stabilises into different orbits for different perturbations, and the relation between the perturbation and amplitude can show exponential and power-law correlations. This can be considered to be representative of a basic mechanism of protein production and control, that underlies complex processes such as homeostasis. Providing feedback from the global state, the total system dynamic behaviour can be boosted or reduced. Controlled SOC can provide much greater understanding of biological control mechanisms, that are based on distributed local producers, with remote consumers of biological resources, and globally defined control.

Low-Order Nonlinear Animal Model of Glucose Dynamics for a Bihormonal Intraperitoneal Artificial Pancreas

OBJECTIVE

The design of an Artificial Pancreas to regulate blood glucose levels requires reliable control methods. Model Predictive Control has emerged as a promising approach for glycemia control. However, model-based control methods require computationally simple and identifiable mathematical models that represent glucose dynamics accurately, which is challenging due to the complexity of glucose homeostasis.

METHODS

In this work, a simple model is deduced to estimate blood glucose concentration in subjects with Type 1 Diabetes Mellitus. Novel features in the model are power-law kinetics for intraperitoneal insulin absorption and a separate glucagon sensitivity state. Profile likelihood and a method based on singular value decomposition of the sensitivity matrix are carried out to assess parameter identifiability and guide a model reduction for improving the identification of parameters.

RESULTS

A reduced model with 10 parameters is obtained and calibrated, showing good fit to experimental data from pigs where insulin and glucagon boluses were delivered in the intraperitoneal cavity.

CONCLUSION

A simple model with power-law kinetics can accurately represent glucose dynamics submitted to intraperitoneal insulin and glucagon injections.

IMPORTANCE

The parameters of the reduced model were not found to lack of local practical or structural identifiability.

A Novel Method for Generation of In Silico Subjects with Type 2 Diabetes

A type 2 diabetes (T2D) simulator has been recently proposed for supporting drug development and treatment optimization. This tool consists of a physiological model of glucose/insulin/C-peptide dynamics and a virtual cohort of T2D subjects (i.e., random extractions of model parameterizations from a joint parameter distribution) well describing both average and variability realistic T2D dynamics . However, the state-of-art procedure to get a reliable virtual population requires some post-processing after subject extraction, in order to discard implausible behaviors. We propose an improved method for virtual subjects' generation to overcome this burdensome task. To do so, we first assessed a refined joint parameter distribution, from which extracting a number of subjects, greater than the target population size. Then, target-size subsets are undersampled from the large cohort. The final virtual population is selected among the subsets as the one maximizing the similarity with T2D data and model parameter distribution, by means of measurement' outcome metrics and Euclidian distance (Δ), respectively. In the final population, almost all the outcome metrics are statistically identical to the clinical counterparts (p-value>0.05) and model parameters' distribution differs by ~5-10% from that derived from data. The methodology described here is flexible, thus resulting suitable for different T2D stages and type 1 diabetes, as well.Clinical Relevance- A straightforward subjects' generation would ease the availability of tailored in silico trials for testing diabetes treatment in a specific population.

Replay Simulations with Personalized Metabolic Model for Treatment Design and Evaluation in Type 1 Diabetes

BACKGROUND

The capacity to replay data collected in real life by people with type 1 diabetes mellitus (T1DM) would lead to individualized (vs population) assessment of treatment strategies to control blood glucose and possibly true personalization. Patek et al introduced such a technique, relying on regularized deconvolution of a population glucose homeostasis model to estimate a residual additive signal and reproduce the experimental data; therefore, allowing the subject-specific replay of what-if scenarios by altering the model inputs (eg, insulin). This early method was shown to have a limited domain of validity. We propose and test in silico a similar approach and extend the method applicability.

METHODS

A subject-specific model personalization of insulin sensitivity and meal-absorption parameters is performed. The University of Virginia (UVa)/Padova T1DM simulator is used to generate experimental scenarios and test the ability of the methodology to accurately reproduce changes in glucose concentration to alteration in meal and insulin inputs. Method performance is assessed by comparing true (UVa/Padova simulator) and replayed glucose traces, using the mean absolute relative difference (MARD) and the Clarke error grid analysis (CEGA).

RESULTS

Model personalization led to a 9.08 and 6.07 decrease in MARD over a prior published method of replaying altered insulin scenarios for basal and bolus changes, respectively. Replay simulations achieved high accuracy, with MARD <10% and more than 95% of readings falling in the CEGA A-B zones for a wide range of interventions.

CONCLUSIONS

In silico studies demonstrate that the proposed method for replay simulation is numerically and clinically valid over broad changes in scenario inputs, indicating possible use in treatment optimization.

Automatic Artificial Pancreas Systems Using an Intelligent Multiple-Model PID Strategy

In this paper, an individualized intelligent multiple-model technique is proposed to design automatic artificial pancreas (AP) systems for the glycemic regulation of type 1 diabetic patients. At first, using the multiple-model concept, the insulin-glucose regulatory system is mathematically identified by constructing some local models. In this step, trade-offs between the number of local models and the complexity of the overall closed-loop system are made by defining and solving a bi-objective optimization problem. Then, optimal AP systems are designed by tuning a bank of proportionalintegralderivative (PID) controllers via the genetic algorithm (GA). A fuzzy gain scheduling strategy is employed to determine the participation percentages of the PID controllers in the control action. Finally, two safety mechanisms, called insulin on board (IOB) constraint and pump shut-off, are installed in the AP systems to enhance their performance. To assess the proposed AP systems, in silico experiments are performed on virtual patients of the UVA/Padova metabolic simulator. The obtained results reveal that the proposed intelligent multiple-model methodology leads to AP systems with limited hyperglycemia and no severe hypoglycemia.

An OGI model for personalized estimation of glucose and insulin concentration in plasma

Plasma glucose concentration (PGC) and plasma insulin concentration (PIC) are two essential metrics for diabetic regulation, but difficult to be measured directly. Often, PGC and PIC are estimated from continuous glucose monitoring and insulin delivery data. Nevertheless, the inter-individual variability and external disturbance (e.g. carbohydrate intake) bring challenges for accurate estimations. This study is to estimate PGC and PIC adaptively by identifying personalized parameters and external disturbances. An observable glucose-insulin (OGI) dynamic model is established to describe insulin absorption, glucose regulation, and glucose transport. The model parameters and disturbances can be extended to observable state variables and be identified dynamically by Bayesian filtering estimators. Two basic Gaussian noise based Bayesian filtering estimators, extended Kalman filtering (EKF) and unscented Kalman filtering (UKF), are implemented. Recognizing the prevalence of non-Gaussian noise, in this study, two new filtering estimators: particle filtering with Gaussian noise (PFG), and particle filtering with mixed non-Gaussian noise (PFM) are designed and implemented. The proposed OGI model in conjunction with the estimators is evaluated using the data from 30 in-silico subjects and 10 human participants. For in-silico subjects, the OGI with PFM estimator has the ability to estimate PIC and PGC adaptively, achieving RMSE of PIC 9.49±3.81 mU/L, and PGC 0.89±0.19 mmol/L. For human, the OGI with PFM has the promise to identify disturbances (95.46%±0.65% accurate rate of meal identification). OGI model provides a way to fully personalize the parameters and external disturbances in real time, and has potential clinical utility for artificial pancreas.

Linear Model Identification for Personalized Prediction and Control in Diabetes

OBJECTIVE

Type-1 diabetes (T1D) is a metabolic disease, characterized by impaired blood glucose (BG) regulation, which forces patients to multiple daily therapeutic actions, the most critical of which is exogenous insulin administration. T1D management can considerably benefit of mathematical models enabling accurate BG predictions and effective/safe automated insulin delivery. In building these models, dealing with large inter- and intra-patient variability in glucose-insulin dynamics represents a major challenge. The aim of the present work is to assess linear black-box methods, including a novel non-parametric methodology, for learning individualized models of glucose response to insulin and meal, suitable for model-based prediction and control.

METHODS

We focus on data-driven techniques for linear model-learning and compare the state-of-art parametric pipeline, exploring all its degrees of freedom (including population vs. individualized parameter identification, model class chosen among ARX/ARMAX/ARIMAX/Box-Jenkins, model order selection criteria, etc.), with a novel non-parametric approach based on Gaussian regression and stable spline kernel. By using data collected in 11 T1D individuals, we evaluate effectiveness of the different models by measuring root mean squared error (RMSE), coefficient of determination (COD), and time gain of the associated BG predictors.

RESULTS

Among the tested approaches, the non-parametric technique results in the best prediction performance: median RMSE=29.8mg/dL, and median COD=57.4%, for a prediction horizon (PH) of 60 min. With respect to the state-of-the-art parametric techniques, the non-parametric approach grants a COD improvement of about 2%, 7%, 21%, and 41% for PH = 30, 60, 90, and 120 min (paired-sample t-test p 0.001, p=0.003, p=0.03, and p=0.07 respectively).

CONCLUSION

Non-parametric linear model-learning grants statistically significant improvement with respect to the state-of-art parametric approach. The higher PH, the more pronounced the improvement.

SIGNIFICANCE

The use of a linear non-parametric model-learning approach for model-based prediction and control could bring to a more prompt, safe and effective T1D management.

Variable structure robust controller design for blood glucose regulation for type 1 diabetic patients: A backstepping approach

Diabetes mellitus type 1 occurs when β - cells in the pancreas are destroyed by the immune system. As a result, the pancreas cannot produce adequate insulin, and the glucose enters the cells to produce energy. To elevate the glycaemic concentration, sufficient amount of insulin should be taken orally or injected into the human body. Artificial pancreas is a device that automatically regulates the level of body insulin by injecting the requisite amount of insulin into the human body. A finite-time robust feedback controller based on the Extended Bergman Minimal Model is designed here. The controller is designed utilizing the backstepping approach and is robust against the unknown external disturbance and parametric uncertainties. The stability of the system is proved using the Lyapunov theorem. The controller is exponentially stable and hence provides the finite-time convergence of the blood glucose concentration to its desired magnitude. The effectiveness of the proposed control method is shown through simulation in MATLAB/Simulink environment via comparisons with previous studies.

A combined in vivo and in silico model shows specific predictors of individual trans-generational diabetic programming

Diabetic pregnancies are cleary associated with maternal type 2 diabetes and metabolic syndrome as well as atherosclerotic diseases in the offspring. The global prevalence of hyperglycemia in pregnancy was estimated as 15.8% of live births to women in 2019, with an upward trend. Numerous parental risk factors as well as trans-generational mechanisms targeting the utero-placental system, leading to diabetes, dysmetabolic and atherosclerotic conditions in the next generation, seem to be involved within this pathophysiological context. To focus on the predictable impact of trans-generational diabetic programming, we studied age- and gender-matched offspring of diabetic and nondiabetic mothers. The offspring generation consists of three groups: C57BL/6-J-Ins2Akita (positive control group), wild-type C57BL/6-J-Ins2Akita (experimental group), and C57BL/6-J mice (negative control group). We undertook intraperitoneal glucose tolerance tests at 3 and 11 weeks of age. Moreover, this in vivo model was complemented by a corresponding in silico model. Although at 3 weeks of age, no significant effects could be observed, we could demonstrate at 11 weeks of age characteristic and significant differences in relation to maternal diabetic imprinting based on the in silico model-based predictors. These predictors allow the generation of a concise classification tree assigning maternal diabetic imprinting correctly in 91% of study cases. Our data show that hyperglycemic in utero milieu contributes to trans-generational diabetic programming leading to impaired glucose tolerance in the offspring of diabetic mothers early on. These observations can be clearly and early distinguished from genetically determined diabetes, for example, type 1 diabetes, in which basal glucose values are significantly raised.

Fast-acting insulin aspart (Fiasp®) improves glycemic outcomes when used with MiniMedTM 670G hybrid closed-loop system in simulated trials compared to NovoLog®

INTRODUCTION

Medtronic has developed a virtual patient simulator for modeling and predicting insulin therapy outcomes for people with type 1 diabetes (T1D). An enhanced simulator was created to estimate outcomes when using the MiniMed^TM 670G system with standard NovoLog® (EU: NovoRapid, US: NovoLog) versus Fiasp ® by using clinical data.

METHODS

Sixty-seven participants' PK profiles were generated per type of insulin (Total of 134 PK profiles). 7,485 virtual patients' PK measurements was matched with one of the 67 NovoLog® PK Tmax values. These 7,485 virtual patients were then simulated using the Medtronic MiniMed™ 670G algorithm following an in-silico protocol of 90 days: 14 days in open loop (Manual Mode) followed by 76 days in closed loop (Auto Mode). Simulation study was repeated with each NovoLog® PK profile being replaced by its corresponding Fiasp® PK profile in the same virtual patient. To validate our in-silico analysis, we compared the results of "actual" 19 "real life" patients from a clinical study RESULTS: Simulated overall and postprandial glycemic outcomes improved in all age groups with Fiasp®. The percentage of time in the euglycemic range increased by about ~2.2% with Fiasp®, in all age groups (p < 0.01). The percentage of time spent at <70 mg/dL was reduced by about ~0.6% with insulin Fiasp® (p < 0.01) and the mean glucose was reduced by about 1.3 mg/dL (p < 0.01), excluding those age <7 years. The simulated mean postprandial SG was reduced by ~5 mg/dL, a significant difference for all age groups. A clinical study results showed similar improvements with MiniMed^TM 670G system when switching from NovoLog® to Fiasp®.

CONCLUSIONS

The simulation studies indicate that using Fiasp® in place of NovoLog® with the MiniMed^TM 670G system will significantly improve the time spent in the healthy, euglycemic range and reduce exposure to hyperglycemia and hypoglycemia in most patients.

Probabilistic Model of Transition between Categories of Glucose Profiles in Patients with Type 1 Diabetes Using a Compositional Data Analysis Approach

The time spent in glucose ranges is a common metric in type 1 diabetes (T1D). As the time in one day is finite and limited, Compositional Data (CoDa) analysis is appropriate to deal with times spent in different glucose ranges in one day. This work proposes a CoDa approach applied to glucose profiles obtained from six T1D patients using continuous glucose monitor (CGM). Glucose profiles of 24-h and 6-h duration were categorized according to the relative interpretation of time spent in different glucose ranges, with the objective of presenting a probabilistic model of prediction of category of the next 6-h period based on the category of the previous 24-h period. A discriminant model for determining the category of the 24-h periods was obtained, achieving an average above 94% of correct classification. A probabilistic model of transition between the category of the past 24-h of glucose to the category of the future 6-h period was obtained. Results show that the approach based on CoDa is suitable for the categorization of glucose profiles giving rise to a new analysis tool. This tool could be very helpful for patients, to anticipate the occurrence of potential adverse events or undesirable variability and for physicians to assess patients' outcomes and then tailor their therapies.

Sliding-mode-based controllers for automation of blood glucose concentration for type 1 diabetes

Destruction of β-cells in pancreas causes deficiency in insulin production that leads to diabetes in the human body. To cope with this problem, insulin is either taken orally during the day or injected into the patient's body using artificial pancreas (AP) during sleeping hours. Some mathematical models indicate that AP uses control algorithms to regulate blood glucose concentration (BGC). The extended Bergman minimal model (EBMM) incorporates, as a state variable, the disturbance in insulin level during medication due to either meal intake or burning sugar by engaging in physical exercise. In this research work, EBMM and proposed finite time robust controllers are used, including the sliding mode controller (SMC), backstepping SMC (BSMC) and supertwisting SMC (second-order SMC or SOSMC) for automatic stabilisation of BGC in type 1 diabetic patients. The proposed SOSMC diminishes the chattering phenomenon which appears in the conventional SMC. The proposed BSMC is a recursive technique which becomes robust by the addition of the SMC. Lyapunov theory has been used to prove the asymptotic stability of the proposed controllers. Simulations have been carried out in MATLAB/Simulink for the comparative study of the proposed controllers under varying data of six different type 1 diabetic patients available in the literature.

GLU: a software package for analysing continuously measured glucose levels in epidemiology

Continuous glucose monitors (CGM) record interstitial glucose levels 'continuously', producing a sequence of measurements for each participant (e.g. the average glucose level every 5 min over several days, both day and night). To analyse these data, researchers tend to derive summary variables such as the area under the curve (AUC), to then use in subsequent analyses. To date, a lack of consistency and transparency of precise definitions used for these summary variables has hindered interpretation, replication and comparison of results across studies. We present GLU, an open-source software package for deriving a consistent set of summary variables from CGM data. GLU performs quality control of each CGM sample (e.g. addressing missing data), derives a diverse set of summary variables (e.g. AUC and proportion of time spent in hypo-, normo- and hyper- glycaemic levels) covering six broad domains, and outputs these (with quality control information) to the user. GLU is implemented in R and is available on GitHub at https://github.com/MRCIEU/GLU. Git tag v0.2 corresponds to the version presented here.

Pregnancy Outcomes and Maternal Insulin Sensitivity: Design and Rationale of a Multi-Center Longitudinal Study in Mother and Offspring (PROMIS)

The worldwide prevalence of overweight and obesity in women of reproductive age is rapidly increasing and a risk factor for the development of gestational diabetes (GDM). Excess adipose tissue reduces insulin sensitivity and may underlie adverse outcomes in both mother and child. The present paper describes the rationale and design of the PRegnancy Outcomes and Maternal Insulin Sensitivity (PROMIS) study, an exploratory cohort study to obtain detailed insights in insulin sensitivity and glucose metabolism during pregnancy and its relation to pregnancy outcomes including early infancy growth. We aim to recruit healthy pregnant women with a body mass index (BMI) ≥ 25 kg/m² before 12 weeks of gestation in Northern Netherlands. A total of 130 woman will be checked on fasted (≤7.0 mmol/L) or random (≤11.0 mmol/L) blood glucose to exclude pregestational diabetes at inclusion. Subjects will be followed up to six months after giving birth, with a total of nine contact moments for data collection. Maternal data include postprandial measures following an oral meal tolerance test (MTT), conducted before 16 weeks and repeated around 24 weeks of gestation, followed by a standard oral glucose tolerance test before 28 weeks of gestation. The MTT is again performed around three months postpartum. Blood analysis is done for baseline and postprandial glucose and insulin, baseline lipid profile and several biomarkers of placental function. In addition, specific body circumferences, skinfold measures, and questionnaires about food intake, eating behavior, physical activity, meal test preference, mental health, and pregnancy complications will be obtained. Fetal data include assessment of growth, examined by sonography at week 28 and 32 of gestation. Neonatal and infant data consist of specific body circumferences, skinfolds, and body composition measurements, as well as questionnaires about eating behavior and complications up to 6 months after birth. The design of the PROMIS study will allow for detailed insights in the metabolic changes in the mother and their possible association with fetal and postnatal infant growth and body composition. We anticipate that the data from this cohort women with an elevated risk for the development of GDM may provide new insights to detect metabolic deviations already in early pregnancy. These data could inspire the development of new interventions that may improve the management of maternal, as well as offsrping complications from already early on in pregnancy with the aim to prevent adverse outcomes for mother and child.

Modeling Ketogenesis for Use in Pediatric Diabetes Simulation

BACKGROUND

Simulation is being increasingly integrated into medical education. Diabetes simulation is well-received by trainees and has demonstrated improved clinical results, including reduced adult inpatient hyperglycemia. However, no pediatric-specific diabetes simulation programs exist for use in medical education. None of the existing diabetes models incorporate ketones as an input or an output, which is essential for use in teaching pediatric diabetes management.

METHODS

We created a pediatric diabetes simulation incorporating both blood sugar and urine ketones as output. Ketone output is implemented as a state variable but is obfuscated to simulate hospital experience. Blood sugar output is similar to other models and incorporates the current blood sugar, insulin on board (IOB) and carbohydrates on board (COB), and insulin and carbohydrate sensitivities. The program calculates all IOB and COB every 15 minutes based on user input and provides written summary feedback at the end of the simulation about inaccurate dosing and timing.

RESULTS

The simulation realistically incorporated both blood glucose and urine ketones in clinically valid and actionable formats. After completing this simulation, 16/17 pediatric residents indicated that they wanted more simulated diabetes cases integrated into their curriculum.

CONCLUSION

Implementing simulation into pediatric diabetes education was feasible and well-received. More work is needed to further study the role of simulation in pediatric diabetes education when used adjunctively or in lieu of lectures when time or resources are limited.

Development platform for artificial pancreas algorithms

BACKGROUND AND AIMS

Assessing algorithms of artificial pancreas systems is critical in developing automated and fault-tolerant solutions that work outside clinical settings. The development and evaluation of algorithms can be facilitated with a platform that conducts virtual clinical trials. We present in this paper a clinically validated cloud-based distributed platform that supports the development and comprehensive testing of single and dual-hormone algorithms for type 1 diabetes mellitus (T1DM).

METHODS

The platform is built on principles of object-oriented design and runs user algorithms in real-time virtual clinical trials utilizing a multi-threaded environment enabled by concurrent execution over a cloud infrastructure. The platform architecture isolates user algorithms located on personal machines from proprietary patient data running on the cloud. Users import a plugin into their algorithms (Matlab, Python, or Java) to connect to the platform. Once connected, users interact with a graphical interface to design experimental protocols for their trials. Protocols include trial duration in days, mealtimes and amounts, variability in mealtimes and amounts, carbohydrate counting errors, snacks, and onboard insulin levels.

RESULTS

The platform facilitates development by solving the ODE model in the cloud on large CPU-optimized machines, providing a 62% improvement in memory, speed and CPU utilization. Users can easily debug & modify code, test multiple strategies, and generate detailed clinical performance reports. We validated and integrated into the platform a glucoregulatory system of ordinary differential equations (ODEs) parameterized with clinical data to mimic the inter and intra-day variability of glucose responses of 15 T1DM patients.

CONCLUSION

The platform utilizes the validated patient model to conduct virtual clinical trials for the rapid development and testing of closed-loop algorithms for T1DM.

Arbitrary-order sliding mode-based robust control algorithm for the developing artificial pancreas mechanism

In Diabetes Mellitus, the pancreas remains incapable of insulin administration that leads to hyperglycaemia, an escalated glycaemic concentration, which may stimulate many complications. To circumvent this situation, a closed-loop control strategy is much needed for the exogenous insulin infusion in diabetic patients. This closed-loop structure is often termed as an artificial pancreas that is generally established by the employment of different feedback control strategies. In this work, the authors have proposed an arbitrary-order sliding mode control approach for development of the said mechanism. The term, arbitrary, is exercised in the sense of its applicability to any n-order controllable canonical system. The proposed control algorithm affirms the finite-time effective stabilisation of the glucose-insulin regulatory system, at the desired level, with the alleviation of sharp fluctuations. The novelty of this work lies in the sliding manifold that incorporates indirect non-linear terms. In addition, the necessary discontinuous terms are filtered-out once before its employment to the plant, i.e. diabetic patient. The robustness, in the presence of external disturbances, i.e. meal intake is confirmed via rigorous mathematical stability analysis. In addition, the effectiveness of the proposed control strategy is ascertained by comparing the results with the standard literature.

Blood glucose concentration control for type 1 diabetic patients: a multiple-model strategy

In this study, a multiple-model strategy is evaluated as an alternative closed-loop method for subcutaneous insulin delivery in type 1 diabetes. Non-linearities of the glucose-insulin regulatory system are considered by modelling the system around five different operating points. After conducting some identification experiments in the UVA/Padova metabolic simulator (accepted simulator by the US Food and Drug Administration (FDA)), five transfer functions are obtained for these operating points. Paying attention to some physiological facts, the control objectives such as the required settling time and permissible bounds of overshoots and undershoots are determined for any transfer functions. Then, five PID controllers are tuned to achieve these objectives and a bank of controllers is constructed. To cope with difficulties of the presence of delays in subcutaneous blood glucose (BG) measuring and in administration of insulin, a glucose-dependent setpoint is considered as the desired trajectory for the BG concentration. The performance of the obtained closed-loop glucose-insulin regulatory system is investigated on the in silico adult cohort of the UVA/Padova metabolic simulator. The obtained results show that the proposed multiple-model strategy leads to a closed-loop mechanism with limited hyperglycemia and no severe hypoglycemia.

Improving blood glucose level predictability using machine learning

This study was designed to improve blood glucose level predictability and future hypoglycemic and hyperglycemic event alerts through a novel patient-specific supervised-machine-learning (SML) analysis of glucose level based on a continuous-glucose-monitoring system (CGM) that needs no human intervention, and minimises false-positive alerts. The CGM data over 7 to 50 non-consecutive days from 11 type-1 diabetic patients aged 18 to 39 with a mean HbA1C of 7.5% ± 1.2% were analysed using four SML models. The algorithm was constructed to choose the best-fit model for each patient. Several statistical parameters were calculated to aggregate the magnitudes of the prediction errors. The personalised solutions provided by the algorithm were effective in predicting glucose levels 30 minutes after the last measurement. The average root-mean-square-error was 20.48 mg/dL and the average absolute-mean-error was 15.36 mg/dL when the best-fit model was selected for each patient. Using the best-fit-model, the true-positive-hypoglycemia-prediction-rate was 64%, whereas the false-positive- rate was 4.0%, and the false-negative-rate was 0.015%. Similar results were found even when only CGM samples below 70 were considered. The true-positive-hyperglycemia-prediction-rate was 61%. State-of-the-art SML tools are effective in predicting the glucose level values of patients with type-1diabetes and notifying these patients of future hypoglycemic and hyperglycemic events, thus improving glycemic control. The algorithm can be used to improve the calculation of the basal insulin rate and bolus insulin, and suitable for a closed loop "artificial pancreas" system. The algorithm provides a personalised medical solution that can successfully identify the best-fit method for each patient.

Method to generate a large cohort in-silico for type 1 diabetes

BACKGROUND AND OBJECTIVE

In the last decade, several technological solutions have been proposed as artificial pancreas systems able to treat type 1 diabetes; most often they are built based on a control algorithm that needs to be validated before it is used with real patients. Control algorithms are usually tested with simulation tools that integrate mathematical models related mainly to the glucose-insulin dynamics, but other variables can be considered as well. In general, the simulators have a limited set of subjects. The main goal of this paper is to propose a new computational method to increase the number of virtual subjects, with physiological characteristics, included in the original mathematical models.

METHODS

A subject is defined by a set of parameters given by a mathematical model. From the available reduced number of subjects in the model, the covariance of each parameter of every subject is obtained to establish a mathematical relationship. Then, new sets of parameters are calculated using linear regression methods; this generates larger cohorts, which allows for testing insulin therapies in open-loop or closed-loop scenarios. The new method proposed here increases the number of subjects in a virtual cohort using two versions of Hovorka's mathematical model.

RESULTS

Two covariant cohorts are obtained with linear regression. Both cohorts are clustered to avoid overlapping in the glucose-insulin dynamics and are compared in terms of their qualitative and quantitative behaviours in the normoglycemic range. As a result, there have been generated two larger cohorts (256 subjects) than the original population, which contributes to improving the variability in in-silico tests. In addition, for analysing the characteristics of the covariant generation method, two random cohorts have been generated, where the parameters are obtained individually and independently from each other, exhibiting only distribution limitations so that these cohorts do not have physiological subjects.

CONCLUSIONS

The proposed methodology has enabled the generation of a large cohort of 256 subjects, with different characteristics that are plausible in the T1DM population, significantly increasing the number of available subjects in existing mathematical models. The proposed methodology does not limit the number of subjects that can be generated and thus, it can be used to increase the number of cohorts provided by other mathematical models in diabetes, or even other scientific problems.

A Glucose-Insulin Mixture Model and Application to Short-Term Hypoglycemia Prediction in the Night Time

OBJECTIVE

Insulin-induced hypoglycemia is recognized as a critical problem for diabetic patients, especially at night. To give glucose prediction and advance warning of hypoglycemia of at least 30 minutes, various glucose-insulin models have been proposed. Recognizing the complementary nature of the models, this research proposes a Glucose-Insulin Mixture (GIM) model to predict the glucose values for hypoglycemia detection, by optimally fusing different models with its adjusted parameters to address the inter- and intra-individual variability.

METHODS

Two types of classic glucose-insulin models, the Ruan model, with single-compartment glucose kinetics, and the Hovorka model, with two-compartment glucose kinetics, are selected as two candidate models. Based on Bayesian inference, GIM is introduced with quantified contributions from the models with the associated parameters. GIM is then applied to predict the glucose values and hypoglycemia events.

RESULTS

The proposed model is validated by the nocturnal glucose data collected from 12 participants with type 1 diabetes. The GIM model has promising fitting of RMSE within 0.3465 mmol/L and predicting of RMSE within 0.5571 mmol/L. According to the literature, the hypoglycemia is defined as 3.9 mmol/L, and the GIM model shows good short-term hypoglycemia prediction performance with the data collected within the last hour (accuracy: 95.97%, precision: 91.77%, recall: 95.60%). In addition, the probability of hypoglycemia event in 30 minutes is inferred.

CONCLUSION

GIM, by fusing various glucose-insulin models via Bayesian inference, has the promise to capture glucose dynamics and predict hypoglycemia.

SIGNIFICANCE

GIM based short-term hypoglycemia prediction has potential clinical utility for timely intervention.