Model-based blood glucose control for Type 1 diabetes via parametric programming

Universal glucose models for predicting subcutaneous glucose concentration in humans

This paper tests the hypothesis that a "universal," data-driven model can be developed based on glucose data from one diabetic subject, and subsequently applied to predict subcutaneous glucose concentrations of other subjects, even of those with different types of diabetes. We employed three separate studies, each utilizing a different continuous glucose monitoring (CGM) device, to verify the model's universality. Two out of the three studies involved subjects with type 1 diabetes and the other one with type 2 diabetes. We first filtered the subcutaneous glucose concentration data by imposing constraints on their rate of change. Then, using the filtered data, we developed data-driven autoregressive models of order 30, and used them to make short-term, 30-min-ahead glucose-concentration predictions. We used same-subject model predictions as a reference for comparisons against cross-subject and cross-study model predictions, which were evaluated using the root-mean-squared error (RMSE) and Clarke error grid analysis (EGA). We found that, for each studied subject, the average cross-subject and cross-study RMSEs of the predictions were small and indistinguishable from those obtained with the same-subject models. These observations were corroborated by EGA, where better than 99.0% of the paired sensor-predicted glucose concentrations lay in the clinically acceptable zone A. In addition, the predictive capability of the models was found not to be affected by diabetes type, subject age, CGM device, and interindividual differences. We conclude that it is feasible to develop universal glucose models that allow for clinical use of predictive algorithms and CGM devices for proactive therapy of diabetic patients.

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.

Control to range for diabetes: functionality and modular architecture

BACKGROUND

Closed-loop control of type 1 diabetes is receiving increasing attention due to advancement in glucose sensor and insulin pump technology. Here the function and structure of a class of control algorithms designed to exert control to range, defined as insulin treatment optimizing glycemia within a predefined target range by preventing extreme glucose fluctuations, are studied.

METHODS

The main contribution of the article is definition of a modular architecture for control to range. Emphasis is on system specifications rather than algorithmic realization. The key system architecture elements are two interacting modules: range correction module, which assesses the risk for incipient hyper- or hypoglycemia and adjusts insulin rate accordingly, and safety supervision module, which assesses the risk for hypoglycemia and attenuates or discontinues insulin delivery when necessary. The novel engineering concept of range correction module is that algorithm action is relative to a nominal open-loop strategy-a predefined combination of basal rate and boluses believed to be optimal under nominal conditions.

RESULTS

A proof of concept of the feasibility of our control-to-range strategy is illustrated by using a prototypal implementation tested in silico on patient use cases. These functional and architectural distinctions provide several advantages, including (i) significant insulin delivery corrections are only made if relevant risks are detected; (ii) drawbacks of integral action are avoided, e.g., undershoots with consequent hypoglycemic risks; (iii) a simple linear model is sufficient and complex algorithmic constraints are replaced by safety supervision; and (iv) the nominal profile provides straightforward individualization for each patient.

CONCLUSIONS

We believe that the modular control-to-range system is the best approach to incremental development, regulatory approval, industrial deployment, and clinical acceptance of closed-loop control for diabetes.

Closed-loop artificial pancreas using subcutaneous glucose sensing and insulin delivery and a model predictive control algorithm: preliminary studies in Padova and Montpellier

New effort has been made to develop closed-loop glucose control, using subcutaneous (SC) glucose sensing and continuous subcutaneous insulin infusion (CSII) from a pump, and a control algorithm. An approach based on a model predictive control (MPC) algorithm has been utilized during closed-loop control in type 1 diabetes patients. Here we describe the preliminary clinical experience with this approach. Six type 1 diabetes patients (three in each of two clinical investigation centers in Padova and Montpellier), using CSII, aged 36 +/- 8 and 48 +/- 6 years, duration of diabetes 12 +/- 8 and 29 +/- 4 years, hemoglobin A1c 7.4% +/- 0.1% and 7.3% +/- 0.3%, body mass index 23.2 +/- 0.3 and 28.4 +/- 2.2 kg/m(2), respectively, were studied on two occasions during 22 h overnight hospital admissions 2-4 weeks apart. A Freestyle Navigator(R) continuous glucose monitor and an OmniPod insulin pump were applied in each trial. Admission 1 used open-loop control, while admission 2 employed closed-loop control using our MPC algorithm. In Padova, two out of three subjects showed better performance with the closed-loop system compared to open loop. Altogether, mean overnight plasma glucose (PG) levels were 134 versus 111 mg/dl during open loop versus closed loop, respectively. The percentage of time spent at PG > 140 mg/dl was 45% versus 12%, while postbreakfast mean PG was 165 versus 156 mg/dl during open loop versus closed loop, respectively. Also, in Montpellier, two patients out of three showed a better glucose control during closed-loop trials. Avoidance of nocturnal hypoglycemic excursions was a clear benefit during algorithm-guided insulin delivery in all cases. This preliminary set of studies demonstrates that closed-loop control based entirely on SC glucose sensing and insulin delivery is feasible and can be applied to improve glucose control in patients with type 1 diabetes, although the algorithm needs to be further improved to achieve better glycemic control.

Run-to-run tuning of model predictive control for type 1 diabetes subjects: in silico trial

BACKGROUND

The technological advancements in subcutaneous continuous glucose monitoring and insulin pump delivery systems have paved the way to clinical testing of artificial pancreas devices. The experience derived by clinical trials poses technological challenges to the automatic control expert, the most notable being the large interpatient and intrapatient variability and the inherent uncertainty of patient information.

METHODS

A new model predictive control (MPC) glucose control system is proposed. The starting point is an MPC algorithm applied in 20 type 1 diabetes mellitus (T1DM) subjects. Three main changes are introduced: individualization of the ARX model used for prediction; synthesis of the MPC law on top of the open-loop basal/bolus therapy; and a run-to-run approach for implementing day-by-day tuning of the algorithm. In order to individualize the ARX model, a sufficiently exciting insulin profile is imposed by splitting the premeal bolus into two smaller boluses (40% and 60%) injected 30 min before and 30 min after the meal.

RESULTS

The proposed algorithm was tested on 100 virtual subjects extracted from an in silico T1DM population. The trial simulates 44 consecutive days, during which the patient receives breakfast, lunch, and dinner each day. For 10 days, meals are multiplied by a random variable uniformly distributed in [0.5, 1.5], while insulin delivery is based on nominal meals. Moreover, for 10 days, either a linear increase or decrease of insulin sensitivity (+/-25% of nominal value) is introduced.

CONCLUSIONS

The ARX model identification procedure offers an automatic tool for patient model individualization. The run-to-run approach is an effective way to auto-tune the aggressiveness of the closed-loop control law, is robust to meal variation, and is also capable of adapting the regulator to slow parameter variations, e.g., on insulin sensitivity.

Closed-loop control of artificial pancreatic Beta -cell in type 1 diabetes mellitus using model predictive iterative learning control

A novel combination of iterative learning control (ILC) and model predictive control (MPC), referred to here as model predictive iterative learning control (MPILC), is proposed for glycemic control in type 1 diabetes mellitus. MPILC exploits two key factors: frequent glucose readings made possible by continuous glucose monitoring technology; and the repetitive nature of glucose-meal-insulin dynamics with a 24-h cycle. The proposed algorithm can learn from an individual's lifestyle, allowing the control performance to be improved from day to day. After less than 10 days, the blood glucose concentrations can be kept within a range of 90-170 mg/dL. Generally, control performance under MPILC is better than that under MPC. The proposed methodology is robust to random variations in meal timings within +/-60 min or meal amounts within +/-75% of the nominal value, which validates MPILC's superior robustness compared to run-to-run control. Moreover, to further improve the algorithm's robustness, an automatic scheme for setpoint update that ensures safe convergence is proposed. Furthermore, the proposed method does not require user intervention; hence, the algorithm should be of particular interest for glycemic control in children and adolescents.

Short-term diabetes blood glucose prediction based on blood glucose measurements

Insulin Dependent Diabetes Mellitus (IDDM) is a chronic disease characterized by the inability of the pancreas to produce sufficient amounts of insulin. Daily compensation of the deficiency requires 4-6 insulin injections to be taken daily, the aim of this insulin therapy being to maintain normoglycemia--i.e., a blood glucose level between 4-7 mmol/L. To determine the quantity and timing of these injections, various different approaches are used. Currently, mostly qualitative and semi-quantitative models and reasoning are used to design such a therapy. Here, an attempt is made to show how system identification and control may be used to estimate predictive quantitative models to be used in design of optimal insulin regimens. The system was divided into three subsystems, the insulin subsystem, the glucose subsystem and the insulin-glucose interaction. The insulin subsystem aims to describe the absorbtion of injected insulin from the subcutaneous depots and the glucose subsystem the absorbtion of glucose from the gut following a meal. These subsystems were modeled using compartment models and proposed models found in the literature. Several black-box models and grey-box models describing the insulin/glucose interaction were developed and analysed. These models were fitted to real data monitored by a IDDM patient. Many difficulties were encountered, typical of biomedical systems: Non-uniform and scarce sampling, time-varying dynamics and severe nonlinearities were some of the difficulties encountered during the modeling. None of the proposed models were able to describe the system accurately in all aspects during all conditions. However, all the linear models shared some dynamics. Based on the estimated models, short-term blood glucose predictors for up to two-hour-ahead blood glucose prediction were investigated.

Multi-objective blood glucose control for type 1 diabetes

For people with type 1 diabetes, automatic controllers aim to maintain the blood glucose concentration within the desired range of 60-120 mg/dL by infusing the appropriate amount of insulin in the presence of meal and exercise disturbances. Blood glucose concentration outside the desired range can be harmful to an individual's health but concentration below 60 mg/dL, a state known as hypoglycemia, is considered to be more harmful than the concentration above 120 mg/dL, a state known as hyperglycemia. In this paper, two techniques to address this issue within a multi-parametric model based control framework are presented. The first technique introduces asymmetry into the objective function to penalize the deviation towards hypoglycemia more than the deviation towards hyperglycemia. The second technique is based upon placing higher priority on satisfaction of constraints on hypoglycemia than on satisfaction of constraints on hyperglycemia. The performance of both the control techniques is analyzed and compared in the presence of disturbances.

Model Predictive Control of blood glucose in Type 1 diabetes: the Principal Dynamic Modes approach

This computational study demonstrates the efficacy of regulating blood glucose in Type 1 diabetics with a Model Predictive Control strategy, utilizing a nonparametric / Principal Dynamic Modes model. For this purpose, a stochastic glucose disturbance signal is introduced and a simple methodology for predicting its future values is developed. The results of our simulations confirm that the proposed algorithm achieves very good performance, is computationally efficient and avoids hypoglycaemic events.

Architecture of a wireless Personal Assistant for telemedical diabetes care

PURPOSE

Advanced information technologies joined to the increasing use of continuous medical devices for monitoring and treatment, have made possible the definition of a new telemedical diabetes care scenario based on a hand-held Personal Assistant (PA). This paper describes the architecture, functionality and implementation of the PA, which communicates different medical devices in a personal wireless network.

DESCRIPTION OF THE SYSTEM

The PA is a mobile system for patients with diabetes connected to a telemedical center. The software design follows a modular approach to make the integration of medical devices or new functionalities independent from the rest of its components. Physicians can remotely control medical devices from the telemedicine server through the integration of the Common Object Request Broker Architecture (CORBA) and mobile GPRS communications. Data about PA modules' usage and patients' behavior evaluation come from a pervasive tracing system implemented into the PA.

RESULTS AND DISCUSSION

The PA architecture has been technically validated with commercially available medical devices during a clinical experiment for ambulatory monitoring and expert feedback through telemedicine. The clinical experiment has allowed defining patients' patterns of usage and preferred scenarios and it has proved the Personal Assistant's feasibility. The patients showed high acceptability and interest in the system as recorded in the usability and utility questionnaires. Future work will be devoted to the validation of the system with automatic control strategies from the telemedical center as well as with closed-loop control algorithms.

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.

Diabetes mellitus modeling and short-term prediction based on blood glucose measurements

Insulin-Dependent Diabetes Mellitus (IDDM) is a chronic disease characterized by the inability of the pancreas to produce sufficient amounts of insulin. Daily compensation of the deficiency requires 4-6 insulin injections to be taken daily, the aim of this insulin therapy being to maintain normoglycemia - i.e., a blood glucose level between 4 and 7mmol/l. To determine the quantity and timing of these injections, various different approaches are used. Currently, mostly qualitative and semi-quantitative models and reasoning are used to design such a therapy. Here, an attempt is made to show how system identification and control may be used to estimate predictive quantitative models to be used in design of optimal insulin regimens. The system was divided into three subsystems, the insulin subsystem, the glucose subsystem and the insulin-glucose interaction. The insulin subsystem aims to describe the absorption of injected insulin from the subcutaneous depots and the glucose subsystem the absorption of glucose from the gut following a meal. These subsystems were modeled using compartment models and proposed models found in the literature. Several black-box models and grey-box models describing the insulin/glucose interaction were developed and analyzed. These models were fitted to real data monitored by an IDDM patient. Many difficulties were encountered, typical of biomedical systems: Non-uniform and scarce sampling, time-varying dynamics and severe nonlinearities were some of the difficulties encountered during the modeling. None of the proposed models were able to describe the system accurately in all aspects during all conditions. However, all the linear models shared some dynamics. Based on the estimated models, short-term blood glucose predictors for up to two-hour-ahead blood glucose prediction were designed. Furthermore, we explored the issues that arise when applying prediction theory and control to short-term blood glucose prediction.

Model predictive control of type 1 diabetes: an in silico trial

BACKGROUND

The development of artificial pancreas has received a new impulse from recent technological advancements in subcutaneous continuous glucose monitoring and subcutaneous insulin pump delivery systems. However, the availability of innovative sensors and actuators, although essential, does not guarantee optimal glycemic regulation. Closed-loop control of blood glucose levels still poses technological challenges to the automatic control expert, most notable of which are the inevitable time delays between glucose sensing and insulin actuation.

METHODS

A new in silico model is exploited for both design and validation of a linear model predictive control (MPC) glucose control system. The starting point is a recently developed meal glucose-insulin model in health, which is modified to describe the metabolic dynamics of a person with type 1 diabetes mellitus. The population distribution of the model parameters originally obtained in healthy 204 patients is modified to describe diabetic patients. Individual models of virtual patients are extracted from this distribution. A discrete-time MPC is designed for all the virtual patients from a unique input-output-linearized approximation of the full model based on the average population values of the parameters. The in silico trial simulates 4 consecutive days, during which the patient receives breakfast, lunch, and dinner each day.

RESULTS

Provided that the regulator undergoes some individual tuning, satisfactory results are obtained even if the control design relies solely on the average patient model. Only the weight on the glucose concentration error needs to be tuned in a quite straightforward and intuitive way. The ability of the MPC to take advantage of meal announcement information is demonstrated. Imperfect knowledge of the amount of ingested glucose causes only marginal deterioration of performance. In general, MPC results in better regulation than proportional integral derivative, limiting significantly the oscillation of glucose levels.

CONCLUSIONS

The proposed in silico trial shows the potential of MPC for artificial pancreas design. The main features are a capability to consider meal announcement information, delay compensation, and simplicity of tuning and implementation.

Prandial insulin dosing using run-to-run control: application of clinical data and medical expertise to define a suitable performance metric

OBJECTIVE

We propose a novel algorithm to adjust prandial insulin dose using sparse blood glucose measurements. The dose is adjusted on the basis of a performance measure for the same meal on the previous day. We determine the best performance measure and tune the algorithm to match the recommendations of experienced physicians.

RESEARCH DESIGN AND METHODS

Eleven subjects with type 1 diabetes, using continuous subcutaneous insulin infusion, were recruited (seven women and four men, aged 21-65 years with A1C of 7.1 +/- 1.3%). Basal insulin infusion rates were optimized. Target carbohydrate content for the lunch meal was calculated on the basis of a weight-maintenance diet. Over a period of 2-4 days, subjects were asked to measure their blood glucose according to the algorithm's protocol. Starting with their usual insulin-to-carbohydrate ratio, the insulin bolus dose was titrated downward until postprandial glucose levels were high (180-250 mg/dl [10-14 mmol/l]). Subsequently, physicians made insulin bolus recommendations to normalize postprandial glucose concentrations. Graphical methods were then used to determine the most appropriate performance measure for the algorithm to match the physician's decisions. For the best performance measure, the gain of the controller was determined to be the best match to the dose recommendations of the physicians.

RESULTS

The correlation between the clinically determined dose adjustments and those of the algorithm is R2 = 0.95, P < 1e - 18.

CONCLUSIONS

We have shown how engineering methods can be melded with medical expertise to develop and refine a dosing algorithm. This algorithm has the potential of drastically simplifying the determination of correct insulin-to-carbohydrate ratios.