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

Blood Glucose Prediction from Nutrition Analytics in Type 1 Diabetes: A Review

INTRODUCTION

Type 1 Diabetes (T1D) affects over 9 million worldwide and necessitates meticulous self-management for blood glucose (BG) control. Utilizing BG prediction technology allows for increased BG control and a reduction in the diabetes burden caused by self-management requirements. This paper reviews BG prediction models in T1D, which include nutritional components.

METHOD

A systematic search, utilizing the PRISMA guidelines, identified articles focusing on BG prediction algorithms for T1D that incorporate nutritional variables. Eligible studies were screened and analyzed for model type, inclusion of additional aspects in the model, prediction horizon, patient population, inputs, and accuracy.

RESULTS

The study categorizes 138 blood glucose prediction models into data-driven (54%), physiological (14%), and hybrid (33%) types. Prediction horizons of ≤30 min are used in 36% of models, 31-60 min in 34%, 61-90 min in 11%, 91-120 min in 10%, and >120 min in 9%. Neural networks are the most used data-driven technique (47%), and simple carbohydrate intake is commonly included in models (data-driven: 72%, physiological: 52%, hybrid: 67%). Real or free-living data are predominantly used (83%).

CONCLUSION

The primary goal of blood glucose prediction in T1D is to enable informed decisions and maintain safe BG levels, considering the impact of all nutrients for meal planning and clinical relevance.

Multivariable identification based MPC for closed-loop glucose regulation subject to individual variability

The controller is important for the artificial pancreas to guide insulin infusion in diabetic therapy. However, the inter- and intra-individual variability and time delay of glucose metabolism bring challenges to control glucose within a normal range. In this study, a multivariable identification based model predictive control (mi-MPC) is developed to overcome the above challenges. Firstly, an integrated glucose-insulin model is established to describe insulin absorption, glucose-insulin interaction under meal disturbance, and glucose transport. On this basis, an observable glucose-insulin dynamic model is formed, in which the individual parameters and disturbances can be identified by designing a particle filtering estimator. Next, embedded with the identified glucose-insulin dynamic model, a mi-MPC method is proposed. In this controller, plasma glucose concentration (PGC), an important variable and indicator of glucose regulation, is estimated and controlled directly. Finally, the method was tested on 30 in-silico subjects produced by the UVa/Padova simulator. The results show that the mi-MPC method including the model, individual identification, and the controller can regulate glucose with the mean value of 7.45 mmol/L without meal announcement.

A metamodel-based flexible insulin therapy for type 1 diabetes patients subjected to aerobic physical activity

Patients with type 1 diabetes are subject to exogenous insulin injections, whether manually or through (semi)automated insulin pumps. Basic knowledge of the patient's characteristics and flexible insulin therapy (FIT) parameters are then needed. Specifically, artificial pancreas-like closed-loop insulin delivery systems are some of the most promising devices for substituting for endogenous insulin secretion in type 1 diabetes patients. However, these devices require self-reported information such as carbohydrates or physical activity from the patient, introducing potential miscalculations and delays that can have life-threatening consequences. Here, we display a metamodel for glucose-insulin dynamics that is subject to carbohydrate ingestion and aerobic physical activity. This metamodel incorporates major existing knowledge-based models. We derive comprehensive and universal definitions of the underlying FIT parameters to form an insulin sensitivity factor (ISF). In addition, the relevance of physical activity modelling is assessed, and the FIT is updated to take physical exercise into account. Specifically, we cope with physical activity by using heart rate sensors (watches) with a fully automated closed insulin loop, aiming to maximize the time spent in the glycaemic range (75.5% in the range and 1.3% below the range for hypoglycaemia on a virtual patient simulator).These mathematical parameter definitions are interesting on their own, may be new tools for assessing mathematical models and can ultimately be used in closed-loop artificial pancreas algorithms or to extend distinguished FIT.

Examining Type 1 Diabetes Mathematical Models Using Experimental Data

Type 1 diabetes requires treatment with insulin injections and monitoring glucose levels in affected individuals. We explored the utility of two mathematical models in predicting glucose concentration levels in type 1 diabetic mice and determined disease pathways. We adapted two mathematical models, one with β-cells and the other with no β-cell component to determine their capability in predicting glucose concentration and determine type 1 diabetes pathways using published glucose concentration data for four groups of experimental mice. The groups of mice were numbered Mice Group 1–4, depending on the diabetes severity of each group, with severity increasing from group 1–4. A Markov Chain Monte Carlo method based on a Bayesian framework was used to fit the model to determine the best model structure. Akaike information criteria (AIC) and Bayesian information criteria (BIC) approaches were used to assess the best model structure for type 1 diabetes. In fitting the model with no β-cells to glucose level data, we varied insulin absorption rate and insulin clearance rate. However, the model with β-cells required more parameters to match the data and we fitted the β-cell glucose tolerance factor, whole body insulin clearance rate, glucose production rate, and glucose clearance rate. Fitting the models to the blood glucose concentration level gave the least difference in AIC of 1.2, and a difference in BIC of 0.12 for Mice Group 4. The estimated AIC and BIC values were highest for Mice Group 1 than all other mice groups. The models gave substantial differences in AIC and BIC values for Mice Groups 1–3 ranging from 2.10 to 4.05. Our results suggest that the model without β-cells provides a more suitable structure for modelling type 1 diabetes and predicting blood glucose concentration for hypoglycaemic episodes.

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.

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.

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.

Fully Automated Artificial Pancreas for Adults With Type 1 Diabetes Using Multiple Hormones: Exploratory Experiments

OBJECTIVES

A fully automated insulin-pramlintide-glucagon artificial pancreas that alleviates the burden of carbohydrate counting without degrading glycemic control was iteratively enhanced until convergence through pilot experiments on adults with type 1 diabetes.

METHODS

Nine participants (age, 37±13 years; glycated hemoglobin, 7.7±0.7%) completed two 27-hour interventions: a fully automated multihormone artificial pancreas and a comparator insulin-alone artificial pancreas with carbohydrate counting. The baseline algorithm was a model-predictive controller that administered insulin and pramlintide in a fixed ratio, with boluses triggered by a glucose threshold, and administered glucagon in response to low glucose levels.

RESULTS

The baseline multihormone dosing algorithm resulted in noninferior time in target range (3.9 to 10.0 mmol/L) (71%) compared with the insulin-alone arm (70%) in 2 participants, with minimal glucagon delivery. The algorithm was modified to deliver insulin and pramlintide more aggressively to increase time in range and maximize the benefits of glucagon. The modified algorithm displayed a similar time in range for the multihormone arm (79%) compared with the insulin-alone arm (83%) in 2 participants, but with undesired glycemic fluctuations. Subsequently, we reduced the glucose threshold that triggers glucagon boluses. This resulted in inferior glycemic control for the multihormone arm (81% vs 91%) in 2 participants. Thereafter, a model-based meal-detection algorithm to deliver insulin and pramlintide boluses closer to mealtimes was added and glucagon was removed. The final dual-hormone system had comparable time in range (81% vs 83%) in the last 3 participants.

CONCLUSION

The final version of the fully automated system that delivered insulin and pramlintide warrants a randomized controlled trial.

A Model-Based Insulin Dose Optimization Algorithm for People With Type 1 Diabetes on Multiple Daily Injections Therapy

OBJECTIVE

Multiple daily injections (MDI) therapy is the most common treatment for type 1 diabetes (T1D) including basal insulin doses to keep glucose levels constant during fasting conditions and bolus insulin doses with meals. Optimal insulin dosing is critical to achieving satisfactory glycemia but is challenging due to inter- and intra-individual variability. Here, we present a novel model-based iterative algorithm that optimizes insulin doses using previous-day glucose, insulin, and meal data.

METHODS

Our algorithm employs a maximum-a-posteriori method to estimate parameters of a model describing the effects of changes in basal-bolus insulin doses. Then, parameter estimates, their confidence intervals, and the goodness of fit, are combined to generate new recommendations. We assessed our algorithm in three ways. First, a clinical data set of 150 days (15 participants) were used to evaluate the proposed model and the estimation method. Second, 60-day simulations were performed to demonstrate the efficacy of the algorithm. Third, a sample 6-day clinical experiment is presented and discussed.

RESULTS

The model fitted the clinical data well with a root-mean-square-error of 1.75 mmol/L. Simulation results showed an improvement in the time in target (3.9-10 mmol/L) from 64% to 77% and a decrease in the time in hypoglycemia (< 3.9 mmol/L) from 8.1% to 3.8%. The clinical experiment demonstrated the feasibility of the algorithm.

CONCLUSION

Our algorithm has the potential to improve glycemic control in people with T1D using MDI.

SIGNIFICANCE

This work is a step forward towards a decision support system that improves their quality of life.

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.

Offset-free MPC strategy for nonzero regulation of linear impulsive systems

In various biomedical applications, drug administration treatment can be modeled as an impulsive control system. Despite the development of different control strategies for impulsive systems, the elimination of the offset generated by a plant-model mismatch has not yet been researched. In biomedical systems, this mismatch is a consequence of physiological changes and can result in inaccurate treatment of patients. Therefore, control techniques that accomplish the objectives by compensating the effect of variations are required. The present paper proposes and substantiates a novel offset-free model predictive control (MPC) strategy for impulsive systems. To that aim, an impulsive disturbance model is introduced, and an observer design is developed that includes new observability criteria for estimating the disturbance and the state. Further, it is demonstrated that the proposed control strategy achieves zero offset tracking from an analysis of the observer and the controller at steady state. Additionally, the controller incorporates a recent MPC formulation to steer the state to an equilibrium set using artificial/intermediary variables to achieve nonzero regulation. Finally, these results are evaluated and illustrated using a dynamical model for type 1 diabetic patients.

Nonlinear Analysis for a Type-1 Diabetes Model with Focus on T-Cells and Pancreatic β-Cells Behavior

Type-1 diabetes mellitus (T1DM) is an autoimmune disease that has an impact on mortality due to the destruction of insulin-producing pancreatic β -cells in the islets of Langerhans. Over the past few years, the interest in analyzing this type of disease, either in a biological or mathematical sense, has relied on the search for a treatment that guarantees full control of glucose levels. Mathematical models inspired by natural phenomena, are proposed under the prey–predator scheme. T1DM fits in this scheme due to the complicated relationship between pancreatic β -cell population growth and leukocyte population growth via the immune response. In this scenario, β -cells represent the prey, and leukocytes the predator. This paper studies the global dynamics of T1DM reported by Magombedze et al. in 2010. This model describes the interaction of resting macrophages, activated macrophages, antigen cells, autolytic T-cells, and β -cells. Therefore, the localization of compact invariant sets is applied to provide a bounded positive invariant domain in which one can ensure that once the dynamics of the T1DM enter into this domain, they will remain bounded with a maximum and minimum value. Furthermore, we analyzed this model in a closed-loop scenario based on nonlinear control theory, and proposed bases for possible control inputs, complementing the model with them. These entries are based on the existing relationship between cell–cell interaction and the role that they play in the unchaining of a diabetic condition. The closed-loop analysis aims to give a deeper understanding of the impact of autolytic T-cells and the nature of the β -cell population interaction with the innate immune system response. This analysis strengthens the proposal, providing a system free of this illness—that is, a condition wherein the pancreatic β -cell population holds and there are no antigen cells labeled by the activated macrophages.

Hypoglycaemia-free artificial pancreas project

Driving blood glycaemia from hyperglycaemia to euglycaemia as fast as possible while avoiding hypoglycaemia is a major problem for decades for type-1 diabetes and is solved in this study. A control algorithm is designed that guaranties hypoglycaemia avoidance for the first time both from the theory of positive systems point of view and from the most pragmatic clinical practice. The solution consists of a state feedback control law that computes the required hyperglycaemia correction bolus in real-time to safely steer glycaemia to the target. A rigorous proof is given that shows that the control-law respects the positivity of the control and of the glucose concentration error: as a result, no hypoglycaemic episode occurs. The so-called hypo-free strategy control is tested with all the UVA/Padova T1DM simulator patients (i.e. ten adults, ten adolescents, and ten children) during a fasting-night scenario and in a hybrid closed-loop scenario including three meals. The theoretical results are assessed by the simulations on a large cohort of virtual patients and encourage clinical trials.

Modeling the variability of insulin sensitivity for people with Type 1 Diabetes based on clinical data from an artificial pancreas study

Type 1 Diabetes is an autoimmune disease that eliminates endogenous insulin production. Without the crucial hormone insulin, which is necessary to equilibrate the blood glucose level, the patient must inject insulin subcutaneously. Treatment must be personalized (timing and size of insulin delivery) to achieve glycaemic equilibrium and avoid long-term comorbidities. Patients are educated on Functional Insulin Therapy (FIT) in order to independently adjust insulin delivery several times a day (at least prior to each meal and physical activity). Among personalized parameters, the Correction Factor is used to occasionally correct hyperglycemia via the injection of an insulin dose (bolus) and its value determines the bolus size. Although well-known in common diabetes practice for chronically poorly controlled patients, the phenomenon of "hyperglycemia induces insulin resistance" on a short term basis in patients with rather well controlled diabetes is presented here. Using a new database of evidence, we show that the insulin sensitivity factor, depends on the current level of glycaemia. This opens the door to refining dosing rules for patients and insulin delivery devices in artificial pancreas systems.

Adaptive fuzzy integral sliding mode control of blood glucose level in patients with type 1 diabetes: In silico studies

Currently, artificial pancreas is an alternative treatment instead of insulin therapy for patients with type 1 diabetes mellitus. Closed-loop control of blood glucose level (BGL) is one of the difficult tasks in biomedical engineering field due to nonlinear time-varying dynamics of insulin-glucose relation that is combined with time delays and model uncertainties. In this paper, we propose a novel adaptive fuzzy integral sliding mode control scheme for BGL regulation. System dynamics is identified online using fuzzy logic systems. The presented method is evaluated in silico studies by nine different virtual patients in three different groups for two continuous days. Simulation results demonstrate effective performance of the proposed control scheme of BGL regulation in presence of simultaneous meal and physical exercise disturbances. Comparison of the proposed control method with proportional-integral-derivative (PID) control and model predictive control (MPC) shows a superiority of the adaptive fuzzy integral sliding mode control with regard to two conventional methods of BGL regulation (PID and MPC) and sliding mode control.

Identifiability Analysis of Three Control-Oriented Models for Use in Artificial Pancreas Systems

OBJECTIVE

Our aim is to analyze the identifiability of three commonly used control-oriented models for glucose control in patients with type 1 diabetes (T1D).

METHODS

Structural and practical identifiability analysis were performed on three published control-oriented models for glucose control in patients with type 1 diabetes (T1D): the subcutaneous oral glucose minimal model (SOGMM), the intensive control insulin-nutrition-glucose (ICING) model, and the minimal model control-oriented (MMC). Structural identifiability was addressed with a combination of the generating series (GS) approach and identifiability tableaus whereas practical identifiability was studied by means of (1) global ranking of parameters via sensitivity analysis together with the Latin hypercube sampling method (LHS) and (2) collinearity analysis among parameters. For practical identifiability and model identification, continuous glucose monitor (CGM), insulin pump, and meal records were selected from a set of patients (n = 5) on continuous subcutaneous insulin infusion (CSII) that underwent a clinical trial in an outpatient setting. The performance of the identified models was analyzed by means of the root mean square (RMS) criterion.

RESULTS

A reliable set of identifiable parameters was found for every studied model after analyzing the possible identifiability issues of the original parameter sets. According to an importance factor ([Formula: see text]), it was shown that insulin sensitivity is not the most influential parameter from the dynamical point of view, that is, is not the parameter impacting the outputs the most of the three models, contrary to what is assumed in the literature. For the test data, the models demonstrated similar performance with most RMS values around 20 mg/dl (min: 15.64 mg/dl, max: 51.32 mg/dl). However, MMC failed to identify the model for patient 4. Also, considering the three models, the MMC model showed the higher parameter variability when reidentified every 6 hours.

CONCLUSION

This study shows that both structural and practical identifiability analysis need to be considered prior to the model identification/individualization in patients with T1D. It was shown that all the studied models are able to represent the CGM data, yet their usefulness in a hypothetical artificial pancreas could be a matter of debate. In spite that the three models do not capture all the dynamics and metabolic effects as a maximal model (ie, our FDA-accepted UVa/Padova simulator), SOGMM and ICING appear to be more appealing than MMC regarding both the performance and parameter variability after reidentification. Although the model predictions of ICING are comparable to the ones of the SOGMM model, the large parameter set makes the model prone to overfitting if all parameters are identified. Moreover, the existence of a high nonlinear function like [Formula: see text] prevents the use of tools from the linear systems theory.

A robust fixed point transformation-based approach for type 1 diabetes control

Modeling and control of diabetes mellitus (DM) are difficult due to the highly nonlinear attitude, time-delay effects, the impulse kind input signals and the lack of continuously available blood glucose (BG) level to be regulated. Regarding the mentioned problems, identification of DM model is crucial. Furthermore, due to the lack of information about the internal states (which cannot be measured in everyday life) and because the BG level is not available in every moment over time, adaptive robust control design method regardless exact model dependency would successfully handle these unfavorable effects without simplifications. The recently developed nonlinear robust fixed point transformation (RFPT)-based controller design method requires only a roughly approximate model in order to realize the controller structure. Moreover, parallel simulated approximate models-in order to provide additional internal information-can be used with the method. In this paper, the usability of the novel RFPT-based technique is demonstrated on the physiological problem of diabetes.

Model Free iPID Control for Glycemia Regulation of Type-1 Diabetes

OBJECTIVE

The objective is to design a fully automated glycemia controller of Type-1 Diabetes (T1D) in both fasting and postprandial phases on a large number of virtual patients.

METHODS

A model-free intelligent proportional-integral-derivative (iPID) is used to infuse insulin. The feasibility of iPID is tested in silico on two simulators with and without measurement noise. The first simulator is derived from a long-term linear time-invariant model. The controller is also validated on the UVa/Padova metabolic simulator on 10 adults under 25 runs/subject for noise robustness test.

RESULTS

It was shown that without measurement noise, iPID mimicked the normal pancreatic secretion with a relatively fast reaction to meals as compared to a standard PID. With the UVa/Padova simulator, the robustness against CGM noise was tested. A higher percentage of time in target was obtained with iPID as compared to standard PID with reduced time spent in hyperglycemia.

CONCLUSION

Two different T1D simulators tests showed that iPID detects meals and reacts faster to meal perturbations as compared to a classic PID. The intelligent part turns the controller to be more aggressive immediately after meals without neglecting safety. Further research is suggested to improve the computation of the intelligent part of iPID for such systems under actuator constraints. Any improvement can impact the overall performance of the model-free controller.

SIGNIFICANCE

The simple structure iPID is a step for PID-like controllers since it combines the classic PID nice properties with new adaptive features.

Modeling Day-to-Day Variability of Glucose-Insulin Regulation Over 12-Week Home Use of Closed-Loop Insulin Delivery

Parameters of physiological models of glucose-insulin regulation in type 1 diabetes have previously been estimated using data collected over short periods of time and lack the quantification of day-to-day variability. We developed a new hierarchical model to relate subcutaneous insulin delivery and carbohydrate intake to continuous glucose monitoring over 12 weeks while describing day-to-day variability. Sensor glucose data sampled every 10-min, insulin aspart delivery and meal intake were analyzed from eight adults with type 1 diabetes (male/female 5/3, age 39.9 ± 9.5 years, BMI 25.4 ± 4.4kg/m², HbA1c 8.4 ± 0.6% ) who underwent a 12-week home study of closed-loop insulin delivery. A compartment model comprised of five linear differential equations; model parameters were estimated using the Markov chain Monte Carlo approach within a hierarchical Bayesian model framework. Physiologically, plausible a posteriori distributions of model parameters including insulin sensitivity, time-to-peak insulin action, time-to-peak gut absorption, and carbohydrate bioavailability, and good model fit were observed. Day-to-day variability of model parameters was estimated in the range of 38-79% for insulin sensitivity and 27-48% for time-to-peak of insulin action. In conclusion, a linear Bayesian hierarchical approach is feasible to describe a 12-week glucose-insulin relationship using conventional clinical data. The model may facilitate in silico testing to aid the development of closed-loop insulin delivery systems.