Linear quadratic gaussian-based closed-loop control of type 1 diabetes

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.

Positive input observer-based controller design for blood glucose regulation for type 1 diabetic patients: A backstepping approach

In practice, there are many physical systems that can have only positive inputs, such as physiological systems. Most conventional control methods cannot ensure that the main system input is positive. A positive input observer-based controller is designed for an intravenous glucose tolerance test model of type 1 diabetes mellitus (T1DM). The backstepping (BS) approach is employed to design the feedback controller for artificial pancreas (AP) systems, based on the Extended Bergman's Minimal Model (EBMM). The EBMM represents the T1DM in terms of the blood glucose concentration (BGC), insulin concentration, and plasma level and the disturbance of insulin during medication due to either meal intake or burning sugar by doing some physical exercise. The insulin concentration and plasma level are estimated using observers, and these estimations are applied as feedback to the controller. The asymptotic stability of the observer-based controller is proved using the Lyapunov theorem. Moreover, it is proved that the system is bounded input-bounded output (BIBO) stable in the presence of uncertainties generated by uncertain parameters and external disturbance. For realistic situations, we consider only the BGC to be available for measurement and additionally inter-and intra-patient variability of system parameters is considered.

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.

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.

Blood glucose regulation in type 1 diabetic patients: an adaptive parametric compensation control-based approach

Here, a direct adaptive control strategy with parametric compensation is adopted for an uncertain non‐linear model representing blood glucose regulation in type 1 diabetes mellitus patients. The uncertain parameters of the model are updated by appropriate design of adaptation laws using the Lyapunov method. The closed‐loop response of the plasma glucose concentration as well as external insulin infusion rate is analysed for a wide range of variation of the model parameters through extensive simulation studies. The result indicates that the proposed adaptive control scheme avoids severe hypoglycaemia and gives satisfactory performance under parametric uncertainty highlighting its ability to address the issue of inter‐patient variability.

Robust multi-objective blood glucose control in Type-1 diabetic patient

In this study, an automatic robust multi‐objective controller has been proposed for blood glucose (BG) regulation in Type‐1 Diabetic Mellitus (T1DM) patient through subcutaneous route. The main objective of this work is to control the BG level in T1DM patient in the presence of unannounced meal disturbances and other external noises with a minimum amount of insulin infusion rate. The multi‐objective output‐feedback controller with H_∞, H₂ and pole‐placement constraints has been designed using linear matrix inequality technique. The designed controller for subcutaneous insulin delivery was tested on in silico adult and adolescent subjects of UVa/Padova T1DM metabolic simulator. The experimental results show that the closed‐loop system tracks the reference BG level very well and does not show any hypoglycaemia effect even during the long gap of a meal at night both for in silico adults and adolescent. In the presence of 50 gm meal disturbance, average adult experience normoglycaemia 92% of the total simulation time and hypoglycaemia 0% of total simulation time. The robustness of the controller has been tested in the presence of irregular meals and insulin pump noise and error. The controller yielded robust performance with a lesser amount of insulin infusion rate than the other designed controllers reported earlier.

Design of an online-tuned model based compound controller for a fully automated artificial pancreas

This paper deals with the development of a control algorithm that can predict optimal insulin doses without patients' intervention in fully automated artificial pancreas system. An online-tuned model based compound controller comprising an online-tuned internal model control (IMC) algorithm and an enhanced IMC (eIMC) algorithm along with a meal detection module is proposed. Volterra models, used to develop IMC and eIMC algorithms, are developed online using recursive least squares (RLS) filter. The time domain kernels, computed online using RLS filter, are converted into frequency domain to obtain Volterra transfer function (VTF). VTFs are used to develop both IMC and eIMC algorithms. The compound controller is designed in such a way that eIMC predicts insulin doses when the glucose rate increase detector of meal detection module is positive, otherwise conventional IMC takes the control action. Experimental results show that the compound controller performs robustly in the presence of higher and irregular amounts of meal disturbances at random times, very high actuator and sensor noises and also with the variation in insulin sensitivity. The combination of compound control strategy and meal detection module compensates the shortcomings of both slow subcutaneous insulin action that causes postprandial hyperglycemia, and delayed peak of action that causes hypoglycaemia. Graphical Abstract A fully-automated artificial pancreas system containing glucose sensor, insulin pump and control algorithm. Block diagram showing the control algorithm i.e., online-tuned compound IMC comprising enhanced IMC, conventional IMC and meal detection module, developed in the present work.

Fractional calculus in pharmacokinetics

We are witnessing the birth of a new variety of pharmacokinetics where non-integer-order differential equations are employed to study the time course of drugs in the body: this is dubbed "fractional pharmacokinetics". The presence of fractional kinetics has important clinical implications such as the lack of a half-life, observed, for example with the drug amiodarone and the associated irregular accumulation patterns following constant and multiple-dose administration. Building models that accurately reflect this behaviour is essential for the design of less toxic and more effective drug administration protocols and devices. This article introduces the readers to the theory of fractional pharmacokinetics and the research challenges that arise. After a short introduction to the concepts of fractional calculus, and the main applications that have appeared in literature up to date, we address two important aspects. First, numerical methods that allow us to simulate fractional order systems accurately and second, optimal control methodologies that can be used to design dosing regimens to individuals and populations.

Advanced Insulin Bolus Advisor Based on Run-To-Run Control and Case-Based Reasoning

This paper presents an advanced insulin bolus advisor for people with diabetes on multiple daily injections or insulin pump therapy. The proposed system, which runs on a smartphone, keeps the simplicity of a standard bolus calculator while enhancing its performance by providing more adaptability and flexibility. This is achieved by means of applying a retrospective optimization of the insulin bolus therapy using a novel combination of run-to-run (R2R) that uses intermittent continuous glucose monitoring data, and case-based reasoning (CBR). The validity of the proposed approach has been proven by in-silico studies using the FDA-accepted UVa-Padova type 1 diabetes simulator. Tests under more realistic in-silico scenarios are achieved by updating the simulator to emulate intrasubject insulin sensitivity variations and uncertainty in the capillarity measurements and carbohydrate intake. The CBR(R2R) algorithm performed well in simulations by significantly reducing the mean blood glucose, increasing the time in euglycemia and completely eliminating hypoglycaemia. Finally, compared to an R2R stand-alone version of the algorithm, the CBR(R2R) algorithm performed better in both adults and adolescent populations, proving the benefit of the utilization of CBR. In particular, the mean blood glucose improved from 166 ± 39 to 150 ± 16 in the adult populations (p = 0.03) and from 167 ± 25 to 162 ± 23 in the adolescent population (p = 0.06). In addition, CBR(R2R) was able to completely eliminate hypoglycaemia, while the R2R alone was not able to do it in the adolescent population.

Adaptive control of artificial pancreas systems - a review

Artificial pancreas (AP) systems offer an important improvement in regulating blood glucose concentration for patients with type 1 diabetes, compared to current approaches. AP consists of sensors, control algorithms and an insulin pump. Different AP control algorithms such as proportional-integral-derivative, model-predictive control, adaptive control, and fuzzy logic control have been investigated in simulation and clinical studies in the past three decades. The variability over time and complexity of the dynamics of blood glucose concentration, unsteady disturbances such as meals, time-varying delays on measurements and insulin infusion, and noisy data from sensors create a challenging system to AP. Adaptive control is a powerful control technique that can deal with such challenges. In this paper, a review of adaptive control techniques for blood glucose regulation with an AP system is presented. The investigations and advances in technology produced impressive results, but there is still a need for a reliable AP system that is both commercially viable and appealing to patients with type 1 diabetes.

Algorithms for a closed-loop artificial pancreas: the case for proportional-integral-derivative control

Closed-loop insulin delivery continues to be one of most promising strategies for achieving near-normal control of blood glucose levels in individuals with diabetes. Of the many components that need to work well for the artificial pancreas to be advanced into routine use, the algorithm used to calculate insulin delivery has received a substantial amount of attention. Most of that attention has focused on the relative merits of proportional-integral-derivative versus model-predictive control. A meta-analysis of the clinical data obtained in studies performed to date with these approaches is conducted here, with the objective of determining if there is a trend for one approach to be performing better than the other approach. Challenges associated with implementing each approach are reviewed with the objective of determining how these approaches might be improved. Results of the meta-analysis, which focused predominantly on the breakfast meal response, suggest that to date, the two approaches have performed similarly. However, uncontrolled variables among the various studies, and the possibility that future improvements could still be effected in either approach, limit the validity of this conclusion. It is suggested that a more detailed examination of the challenges associated with implementing each approach be conducted.

Real-time state estimation and long-term model adaptation: a two-sided approach toward personalized diagnosis of glucose and insulin levels

BACKGROUND

With continuous glucose sensors (CGSs), it is possible to obtain a dynamical signal of the patient's subcutaneous glucose concentration in real time. How could that information be exploited? We suggest a model-based diagnosis system with a twofold objective: real-time state estimation and long-term model parameter identification.

METHODS

To obtain a dynamical model, Bergman's nonlinear minimal model (considering plasma glucose G, insulin I, and interstitial insulin X) is extended by two states describing first and second insulin response. Furthermore, compartments for oral glucose and subcutaneous insulin inputs as well as for subcutaneous glucose measurement are added. The observability of states and external inputs as well as the identifiability of model parameters are assessed using the empirical observability Gramian. Signals are estimated for different nondiabetic and diabetic scenarios by unscented Kalman filter.

RESULTS

(1) Observability of different state subsets is evaluated, e.g., from CGSs, {G, I} or {G, X} can be observed and the set {G, I, X} cannot. (2) Model parameters are included, e.g., it is possible to estimate the second-phase insulin response gain k(G2) additionally. This can be used for model adaptation and as a diagnostic parameter that is almost zero for diabetes patients. (3) External inputs are considered, e.g., oral glucose is theoretically observable for nondiabetic patients, but estimation scenarios show that the time delay of 1 h limits application.

CONCLUSIONS

A real-time estimation of states (such as plasma insulin I) and parameters (such as k(G2)) is possible, which allows an improved real-time state prediction and a personalized model.

A genetic algorithm tuned optimal controller for glucose regulation in type 1 diabetic subjects

An optimal state feedback controller is designed with the objective of minimizing the elevated glucose levels caused by meal intake in Type 1 diabetic subjects, by the minimal infusion of insulin. The states for the controller based on linear quadratic regulator theory are estimated from noisy data using Kalman filter. The controller designed for a physiological relevant mathematical model is coupled with another model for simulating meal dynamics, which converts meal intake into glucose appearance rate in the plasma. The tuning parameters (weighting matrices) of the controller and the design parameters (noise covariance matrices) of the Kalman filter are optimized using genetic algorithm. The controller based on the combined framework of evolutionary computing and state estimated linear quadratic regulator is found to maintain normoglycemia for meal intakes of varying carbohydrate content. The proposed approach addresses noisy output measurement, modeling error and delay in sensor measurement.

Insulin patch pumps: their development and future in closed-loop systems

Steady progress is being made toward the development of a so-called "artificial pancreas," which may ultimately be a fully automated, closed-loop, glucose control system comprising a continuous glucose monitor, an insulin pump, and a controller. The controller will use individualized algorithms to direct delivery of insulin without user input. A major factor propelling artificial pancreas development is the substantial incidence of-and attendant patient, parental, and physician concerns about-hypoglycemia and extreme hyperglycemia associated with current means of insulin delivery for type 1 diabetes mellitus (T1DM). A successful fully automated artificial pancreas would likely reduce the frequency of and anxiety about hypoglycemia and marked hyperglycemia. Patch-pump systems ("patch pumps") are likely to be used increasingly in the control of T1DM and may be incorporated into the artificial pancreas systems of tomorrow. Patch pumps are free of tubing, small, lightweight, and unobtrusive. This article describes features of patch pumps that have been approved for U.S. marketing or are under development. Included in the review is an introduction to control algorithms driving insulin delivery, particularly the two major types: proportional integrative derivative and model predictive control. The use of advanced algorithms in the clinical development of closed-loop systems is reviewed along with projected next steps in artificial pancreas development.

Impact of blood glucose self-monitoring errors on glucose variability, risk for hypoglycemia, and average glucose control in type 1 diabetes: an in silico study

BACKGROUND

Clinical trials assessing the impact of errors in self-monitoring of blood glucose (SMBG) on the quality of glycemic control in diabetes are inherently difficult to execute. Consequently, the objectives of this study were to employ realistic computer simulation based on a validated model of the human metabolic system and to provide potentially valuable information about the relationships among SMBG errors, risk for hypoglycemia, glucose variability, and long-term glycemic control.

METHODS

Sixteen thousand computer simulation trials were conducted using 100 simulated adults with type 1 diabetes. Each simulated subject was used in four simulation experiments aiming to assess the impact of SMBG errors on detection of hypoglycemia (experiment 1), risk for hypoglycemia (experiment 2), glucose variability (experiment 3), and long-term average glucose control, i.e., estimated hemoglobin A1c (HbA1c)(experiment 4). Each experiment was repeated 10 times at each of four increasing levels of SMBG errors: 5, 10, 15, and 20% deviation from the true blood glucose value.

RESULTS

When the permitted SMBG error increased from 0 to 5-10% to 15-20%-the current level allowed by International Organization for Standardization 15197-(1) the probability for missing blood glucose readings of 60 mg/dl increased from 0 to 0-1% to 3.5-10%; (2) the incidence of hypoglycemia, defined as reference blood glucose <or=70 mg/dl, changed from 0 to 0-0% to 0.1-5.5%; (3) glucose variability increased as well, as indicated by control variability grid analysis; and (4) the incidence of hypoglycemia increased from 15.0 to 15.2-18.8% to 22-25.6%. When compensating for this increase, glycemic control deteriorated with HbA1c increasing gradually from 7.00 to 7.01-7.12% to 7.26-7.40%.

CONCLUSIONS

A number of parameters of glycemic control deteriorated substantially with the increase of permitted SMBG errors, as revealed by a series of computer simulations (e.g., in silico) experiments. A threshold effect apparent between 10 and 15% permitted SMBG error for most parameters, except for HbA1c, which appeared to be increasing relatively linearly with increasing SMBG error above 10%.

Closed-loop artificial pancreas using subcutaneous glucose sensing and insulin delivery and a model predictive control algorithm: the Virginia experience

BACKGROUND

Recent progress in the development of clinically accurate continuous glucose monitors (CGMs), automated continuous insulin infusion pumps, and control algorithms for calculating insulin doses from CGM data have enabled the development of prototypes of subcutaneous closed-loop systems for controlling blood glucose (BG) levels in type 1 diabetes. The use of a new personalized model predictive control (MPC) algorithm to determine insulin doses to achieve and maintain BG levels between 70 and 140 mg/dl overnight and to control postprandial BG levels is presented.

METHODS

Eight adults with type 1 diabetes were studied twice, once using their personal open-loop systems to control BG overnight and for 4 h following a standardized meal and once using a closed-loop system that utilizes the MPC algorithm to control BG overnight and for 4 h following a standardized meal. Average BG levels, percentage of time within BG target of 70-140 mg/dl, number of hypoglycemia episodes, and postprandial BG excursions during both study periods were compared.

RESULTS

With closed-loop control, once BG levels achieved the target range (70-140 mg/dl), they remained within that range throughout the night in seven of the eight subjects. One subject developed a BG level of 65 mg/dl, which was signaled by the CGM trend analysis, and the MPC algorithm directed the discontinuance of the insulin infusion. The number of overnight hypoglycemic events was significantly reduced (p = .011) with closed-loop control. Postprandial BG excursions were similar during closed-loop and open-loop control.

CONCLUSION

Model predictive closed-loop control of BG levels can be achieved overnight and following a standardized breakfast meal. This "artificial pancreas" controls BG levels as effectively as patient-directed open-loop control following a morning meal but is significantly superior to open-loop control in preventing overnight hypoglycemia.

Progress in development of an artificial pancreas

This issue of Journal of Diabetes Science and Technology contains a collection of 12 original articles describing the latest advances in the development of algorithms for controlling insulin delivery in an artificial pancreas. Algorithms presented in this issue are affected by numerous quantifiable factors, including insulin pharmaco-kinetics, timing of meal carbohydrate appearance, meal size, amount of exercise, presence of stress, day-to-day variations in insulin sensitivity, insulin time-activity profiles, accuracy of glucose monitor calibration, metabolic profiles of both adults and neonates, and risks of hypoglycemia/hyperglycemia. These articles present theoretical advances in insulin delivery algorithms from modeled in silico patients, as well as clinical data from actual patients who have used closed loop systems. The novel approaches described in these articles are expected to bring us much closer to realization of a commercially available closed loop system for controlling glucose levels in patients with diabetes.

In silico preclinical trials: methodology and engineering guide to closed-loop control in type 1 diabetes mellitus

This article sets forth guidelines for in silico (simulation-based) proof-of-concept testing of artificial pancreas control algorithms. The goal was to design a test procedure that can facilitate regulatory approval [e.g., Food and Drug Administration Investigational Device Exemption] for General Clinical Research Center experiments without preliminary testing on animals. The methodology is designed around a software package, based on a recent meal simulation model of the glucose-insulin system. Putting a premium on generality, this document starts by specifying a generic, rather abstract, meta-algorithm for control. The meta-algorithm has two main components: (1) patient assessment and tuning of control parameters, i.e., algorithmic processes for collection and processing patient data prior to closed-loop operation, and (2) controller warm-up and run-time operation, i.e., algorithmic processes for initializing controller states and managing blood glucose. The simulation-based testing methodology is designed to reveal the conceptual/mathematical operation of both main components, as applied to a large population of in silico patients with type 1 diabetes mellitus.

Diabetes: Models, Signals, and Control

The control of diabetes is an interdisciplinary endeavor, which includes a significant biomedical engineering component, with traditions of success beginning in the early 1960s. It began with modeling of the insulin-glucose system, and progressed to large-scale in silico experiments, and automated closed-loop control (artificial pancreas). Here, we follow these engineering efforts through the last, almost 50 years. We begin with the now classic minimal modeling approach and discuss a number of subsequent models, which have recently resulted in the first in silico simulation model accepted as substitute to animal trials in the quest for optimal diabetes control. We then review metabolic monitoring, with a particular emphasis on the new continuous glucose sensors, on the analyses of their time-series signals, and on the opportunities that they present for automation of diabetes control. Finally, we review control strategies that have been successfully employed in vivo or in silico, presenting a promise for the development of a future artificial pancreas and, in particular, discuss a modular architecture for building closed-loop control systems, including insulin delivery and patient safety supervision layers. We conclude with a brief discussion of the unique interactions between human physiology, behavioral events, engineering modeling and control relevant to diabetes.