A critical assessment of algorithms and challenges in the development of a closed-loop artificial pancreas

Effects of everyday life events on glucose, insulin, and glucagon dynamics in continuous subcutaneous insulin infusion-treated type 1 diabetes: collection of clinical data for glucose modeling

BACKGROUND

In the development of glucose control algorithms, mathematical models of glucose metabolism are useful for conducting simulation studies and making real-time predictions upon which control calculations can be based. To obtain type 1 diabetes (T1D) data for the modeling of glucose metabolism, we designed and conducted a clinical study.

METHODS

Patients with insulin pump-treated T1D were recruited to perform everyday life events on two separate days. During the study, patients wore their insulin pumps and, in addition, a continuous glucose monitor and an activity monitor to estimate energy expenditure. The sequence of everyday life events was predetermined and included carbohydrate intake, insulin boluses, and bouts of exercise; the events were introduced, temporally separated, in different orders and in different quantities. Throughout the study day, 10-min plasma glucose measurements were taken, and samples for plasma insulin and glucagon analyses were obtained every 10 min for the first 30 min after an event and subsequently every 30 min.

RESULTS

We included 12 patients with T1D (75% female, 34.3±9.1 years old [mean±SD], hemoglobin A1c 6.7±0.4%). During the 24 study days we collected information-rich, high-quality data during fast and slow changes in plasma glucose following carbohydrate intake, exercise, and insulin boluses.

CONCLUSIONS

This study has generated T1D data suitable for glucose modeling, which will be used in the development of glucose control strategies. Furthermore, the study has given new physiologic insight into the metabolic effects of carbohydrate intake, insulin boluses, and exercise in continuous subcutaneous insulin infusion-treated patients with T1D.

Closed-loop insulin delivery in type 1 diabetes

Advances in diabetes technology have led to significant improvements in the quality of life and care received by individuals with diabetes. Despite this, achieving tight glycemic control through intensive insulin therapy and modern insulin regimens is challenging because of the barrier of hypoglycemia, the most feared complication of insulin therapy as reported by patients, caregivers, and physicians. This article outlines the individual components of the closed-loop system together with the existing clinical evidence. The artificial pancreas prototypes currently used in clinical studies are reviewed as well as obstacles and limitations facing the technology.

Control-relevant models for glucose control using a priori patient characteristics

One of the difficulties in the development of a reliable artificial pancreas for people with type 1 diabetes mellitus (T1DM) is the lack of accurate models of an individual's response to insulin. Most control algorithms proposed to control the glucose level in subjects with T1DM are model-based. Avoiding postprandial hypoglycemia ( 60 mg/dl) while minimizing prandial hyperglycemia ( > 180 mg/dl) has shown to be difficult in a closed-loop setting due to the patient-model mismatch. In this paper, control-relevant models are developed for T1DM, as opposed to models that minimize a prediction error. The parameters of these models are chosen conservatively to minimize the likelihood of hypoglycemia events. To limit the conservatism due to large intersubject variability, the models are personalized using a priori patient characteristics. The models are implemented in a zone model predictive control algorithm. The robustness of these controllers is evaluated in silico, where hypoglycemia is completely avoided even after large meal disturbances. The proposed control approach is simple and the controller can be set up by a physician without the need for control expertise.

Diabetes technology and treatments in the paediatric age group

Type 1 diabetes (T1D) is one of the most common chronic childhood diseases and its incidence has doubled during the last decade. The goals of intensive management of diabetes were established in 1993 by the Diabetes Control and Complications Trial (DCCT) (1). Children with T1D and their caregivers continue to face the challenge to maintain blood glucose levels in the near-normal range. It is important to prevent sustained hyperglycaemia which is associated with long-term microvascular and macrovascular complications and to avoid recurrent episodes of hypoglycaemia or hyperglycaemia, especially in young children, which may have adverse effects on cognitive function and impede efforts to achieve the recommended glycaemic targets. Advances in the use of technology that may help maintain the metabolic control goals for young people with T1D were centred on continuous subcutaneous insulin infusion (CSII) (2-4), continuous glucose monitoring (CGM) (5-7), and combining both technologies into a closed-loop system (8-10). The dilemma in paediatrics of patient selection for insulin pump therapy was found to be most successful in those with more frequent self-monitoring of blood glucose (SMBG) and younger age prior to pump initiation (2). Similarly, those who used a dual-wave bolus probably paid closer attention to their management and had lower HbA1c levels (3). The advantage of using a pre-meal bolus to improve postprandial glucose levels was shown to offer another potential method to improve glycaemic control (4). SMBG is an important component of therapy in patients with diabetes, especially in the paediatric age group. Standard use of glucose meters for SMBG provides only intermittent single blood glucose levels, without giving the 'whole picture' of glucose variability during the 24 h, and especially during the night, when blood glucose levels are seldom measured. Therefore, the use of a device such as real-time continuous glucose monitoring (RT-CGM) that provides continuous glucose measurements can help patients optimise glycaemic control. These devices may have the potential to increase the proportion of patients who are able to maintain target HbA1c values, to decrease glucose excursions and to decrease the risk of severe hypoglycaemia. Previous studies in paediatric T1D patients (11,12) have demonstrated that the frequency of CGM use was significantly associated with the effect of lowering HbA1c levels. The important STAR 3 study of 485 patients (156 children) with T1D showed the benefit of sensor-augmented pump therapy over remaining on multiple daily injections (MDI) (10). The Juvenile Diabetes Research Foundation Continuous Glucose Monitoring (JDRF-CGM) studies were initially described in the 2009 Yearbook (13). Further reports of youths and adults in this study found that those with initial low HbA1c levels (< 7%) show a significant benefit from the use of CGM (5). Prolonged nocturnal hypoglycaemia was shown to continue to be a common occurrence in the entire cohort using CGM (7). Thus, there is an obvious need for closing the loop. Many patients with diabetes and especially parents of diabetic children dream about the invention of an 'artificial pancreas'. CSII and RT-CGM can be combined to form closed-loop systems. Insulin is then delivered according to RT-CGM data, as directed by a control algorithm, rather than at pre-programmed rates. Few closed-loop prototypes have been developed with advanced control algorithms, such as those that are based on model predictive control (14). The group at Cambridge studied 19 young people in closed-loop systems and was able to demonstrate that exercise and diet variations could be aptly managed (9). It is expected that closed-loop studies in young people will continue to multiply in future years. T1D is characterised by immune-mediated pancreatic β-cell destruction. Thus, a major goal in the treatment of T1D in youth will be in the area of prevention. The identification of increased levels of inflammatory markers in the SEARCH study of young people with T1D may provide an important clue (15). Most of the studies countered the diabetes process by immunomodulation and/or enhancement of β-cell proliferation and regeneration (16). An initial pilot trial of a tumour necrosis factor α (TNF-α) binding agent, Entanercept, showed benefit in preserving C-peptide production in 18 young people with newly diagnosed T1D. HbA1c levels were also lower in the treatment group (5.9% ± 0.5% vs. 6.98% ± 1.2%; p < 0.05) (17). Similarly, β-cell function was shown to be preserved in children receiving the lower of two doses of ingested human recombinant interferon-α (hrINF-α) in comparison with subjects who received placebo (18). A future larger trial of both of these agents will be of interest. In this review of the literature we have tried to select recent publications that offer some insight into these issues in paediatric patients with T1D.

Closed-loop insulin delivery for treatment of type 1 diabetes

Type 1 diabetes is one of the most common endocrine problems in childhood and adolescence, and remains a serious chronic disorder with increased morbidity and mortality, and reduced quality of life. Technological innovations positively affect the management of type 1 diabetes. Closed-loop insulin delivery (artificial pancreas) is a recent medical innovation, aiming to reduce the risk of hypoglycemia while achieving tight control of glucose. Characterized by real-time glucose-responsive insulin administration, closed-loop systems combine glucose-sensing and insulin-delivery components. In the most viable and researched configuration, a disposable sensor measures interstitial glucose levels, which are fed into a control algorithm controlling delivery of a rapid-acting insulin analog into the subcutaneous tissue by an insulin pump. Research progress builds on an increasing use of insulin pumps and availability of glucose monitors. We review the current status of insulin delivery, focusing on clinical evaluations of closed-loop systems. Future goals are outlined, and benefits and limitations of closed-loop therapy contrasted. The clinical utility of these systems is constrained by inaccuracies in glucose sensing, inter- and intra-patient variability, and delays due to absorption of insulin from the subcutaneous tissue, all of which are being gradually addressed.

Continuous glucose monitoring considerations for the development of a closed-loop artificial pancreas system

BACKGROUND

Commercialization of a closed-loop artificial pancreas system that employs continuous subcutaneous insulin infusion and interstitial fluid glucose sensing has been encumbered by state-of-the-art technology. Continuous glucose monitoring (CGM) devices with improved accuracy could significantly advance development efforts. However, the current accuracy of CGM devices might be adequate for closed-loop control.

METHODS

The influence that known CGM limitations have on closed-loop control was investigated by integrating sources of sensor inaccuracy with the University of Virginia Padova Diabetes simulator. Non-glucose interference, physiological time lag and sensor error measurements, selected from 83 Enlite™ glucose sensor recordings with the Guardian® REAL-Time system, were used to modulate simulated plasma glucose signals. The effect of sensor accuracy on closed-loop controller performance was evaluated in silico, and contrasted with closed-loop clinical studies during the nocturnal control period.

RESULTS

Based on n = 2472 reference points, a mean sensor error of 14% with physiological time lags of 3.28 ± 4.62 min (max 13.2 min) was calculated for simulation. Sensor bias reduced time in target for both simulation and clinical experiments. In simulation, additive error increased time <70 mg/dl and >180 mg/dl by 0.2% and 5.6%, respectively. In-clinic, the greatest low blood glucose index values (max = 5.9) corresponded to sensor performance.

CONCLUSION

Sensors have sufficient accuracy for closed-loop control, however, algorithms are necessary to effectively calibrate and detect erroneous calibrations and failing sensors. Clinical closed-loop data suggest that control with a higher target of 140 mg/dl during the nocturnal period could significantly reduce the risk for hypoglycemia.

Closed-loop insulin delivery utilizing pole placement to compensate for delays in subcutaneous insulin delivery

BACKGROUND

We have previously used insulin feedback (IFB) as a component of a closed-loop algorithm emulating the β cell. This was based on the observation that insulin secretion is inhibited by insulin concentration. We show here that the effect of IFB is to make a closed-loop system behave as if delays in the insulin pharmacokinetic (PK)/pharmacodynamic (PD) response are reduced. We examine whether the mechanism can be used to compensate for delays in the subcutaneous PK/PD insulin response.

METHOD

Closed-loop insulin delivery was performed in seven diabetic dogs using a proportional-integral-derivative model of the β cell modified by model-predicted IFB. The level of IFB was set using pole placement. Meal responses were obtained on three occasions: without IFB (NONE), reference IFB (REF), and 2xREF, with experiments performed in random order. The ability of the insulin model to predict insulin concentration was evaluated by correlation with the measured profile and results reported as R(2). The ability of IFB to improve the meal response was evaluated by comparing peak and nadir postprandial glucose and area under the curve (AUC; repeated measures analysis of variance with post hoc test for linear trend).

RESULTS

Insulin concentration was well predicted by the model (median R(2) = 0.87, 0.79, and 0.90 for NONE, REF, and 2xREF, respectively). Peak postprandial glucose (294 ± 15, 243 ± 21, and 247 ± 16 mg/dl) and AUC (518.2 ± 36.13, 353.5 ± 45.04, and 280.3 ± 39.37 mg/dl · min) decreased with increasing IFB (p < .05, linear trend). Nadir glucose was not affected by IFB (76 ± 5.4, 68 ± 7.3, and 72 ± 4.3 mg/dl; p = .63).

CONCLUSIONS

Insulin feedback provides an effective mechanism to compensate for delay in the insulin PK/PD profile.

Fitting dynamic models with forcing functions: application to continuous glucose monitoring in insulin therapy

The artificial pancreas is an emerging technology to treat type 1 diabetes (T1D). It has the potential to revolutionize diabetes care and improve quality of life. The system requires extensive testing, however, to ensure that it is both effective and safe. Clinical studies are resource demanding and so a principle aim is to develop an in silico population of subjects with T1D on which to conduct pre-clinical testing. This paper aims to reliably characterize the relationship between blood glucose and glucose measured by subcutaneous sensor as a major step towards this goal. Blood-and sensor-glucose are related through a dynamic model, specified in terms of differential equations. Such models can present special challenges for statistical inference, however. In this paper we make use of the BUGS software, which can accommodate a limited class of dynamic models, and it is in this context that we discuss such challenges. For example, we show how dynamic models involving forcing functions can be accommodated. To account for fluctuations away from the dynamic model that are apparent in the observed data, we assume an autoregressive structure for the residual error model. This leads to some identifiability issues but gives very good predictions of virtual data. Our approach is pragmatic and we propose a method to mitigate the consequences of such identifiability issues.

A stepwise approach toward closed-loop blood glucose control for intensive care unit patients: results from a feasibility study in type 1 diabetic subjects using vascular microdialysis with infrared spectrometry and a model predictive control algorithm

BACKGROUND

Glycemic control can reduce the mortality and morbidity of intensive care patients. The CLINICIP (closed-loop insulin infusion for critically ill patients) project aimed to develop a closed-loop control system for this patient group. Following a stepwise approach, we combined three independently tested subparts to form a semiautomatic closed-loop system and evaluated it with respect to safety and performance aspects by testing it in subjects with type 1 diabetes mellitus (T1DM) in a first feasibility trial.

METHODS

Vascular microdialysis, a multianalyte infrared spectroscopic glucose sensor, and a standard insulin infusion pump controlled by an adaptive model predictive control (MPC) algorithm were combined to form a closed-loop device, which was evaluated in four T1DM subjects during 30-hour feasibility studies. The aim was to maintain blood glucose concentration in the target range between 80 and 110 mg/dl.

RESULTS

Mean plasma glucose concentration was 110.5 ± 29.7 mg/dl. The MPC managed to establish normoglycemia within 105 ± 78 minutes after trial start and managed to maintain glucose concentration within the target range for 47% of the time. The hyperglycemic index averaged to 11.9 ± 5.3 mg/dl.

CONCLUSION

Data of the feasibility trial illustrate the device being effective in controlling glycemia in T1DM subjects. However, the monitoring part of the loop must be improved with respect to accuracy and precision before testing the system in the target population.

Physiologic insulin delivery with insulin feedback: a control systems perspective

Individuals with type 1 diabetes mellitus must effectively manage glycemia to avoid acute and chronic complications related to aberrations of glucose levels. Because optimal diabetes management can be difficult to achieve and burdensome, research into a closed-loop insulin delivery system has been of interest for several decades. This paper provides an overview, from a control systems perspective, of the research and development effort of a particular algorithm--the external physiologic insulin delivery system. In particular the introduction of insulin feedback, based on β-cell physiology, is covered in detail. A summary of human clinical trials is provided in the context of the evolution of this algorithm, and this paper outlines some of the research avenues that show particular promise.

Anticipating the next meal using meal behavioral profiles: a hybrid model-based stochastic predictive control algorithm for T1DM

Automatic control of Type 1 Diabetes Mellitus (T1DM) with subcutaneous (SC) measurement of glucose concentration and subcutaneous (SC) insulin infusion is of great interest within the diabetes technology research community. The main challenge with the so-called "SC-SC" route to control is sensing and actuation delay, which tends to either destabilize the system or inhibit the aggressiveness of the controller in responding to meals and exercise. Model predictive control (MPC) is one strategy for mitigating delay, where optimal insulin infusions can be given in anticipation of future meal disturbances. Unfortunately, exact prior knowledge of meals can only be assured in a clinical environment and uncertainty about when and if meals will arrive could lead to catastrophic outcomes. As a follow-on to our recent paper in the IFAC symposium on Biological and Medical Systems (MCBMS 2009), we develop a control law that can anticipate meals given a probabilistic description of the patient's eating behavior in the form of a random meal (behavioral) profile. Preclinical in silico trials using the oral glucose meal model of Dalla Man et al. show that the control strategy provides a convenient means of accounting for uncertain prior knowledge of meals without compromising patient safety, even in the event that anticipated meals are skipped.

Overnight closed loop insulin delivery (artificial pancreas) in adults with type 1 diabetes: crossover randomised controlled studies

OBJECTIVE

To compare the safety and efficacy of overnight closed loop delivery of insulin (artificial pancreas) with conventional insulin pump therapy in adults with type 1 diabetes.

DESIGN

Two sequential, open label, randomised controlled crossover, single centre studies.

SETTING

Clinical research facility.

PARTICIPANTS

24 adults (10 men, 14 women) with type 1 diabetes, aged 18-65, who had used insulin pump therapy for at least three months: 12 were tested after consuming a medium sized meal and the other 12 after consuming a larger meal accompanied by alcohol.

INTERVENTION

During overnight closed loop delivery, sensor measurements of glucose were fed into a computer algorithm, which advised on insulin pump infusion rates at 15 minute intervals. During control nights, conventional insulin pump settings were applied. One study compared closed loop delivery of insulin with conventional pump therapy after a medium sized evening meal (60 g of carbohydrates) at 1900, depicting the scenario of "eating in." The other study was carried out after a later large evening meal (100 g of carbohydrates) at 2030, accompanied by white wine (0.75 g/kg ethanol) and depicted the scenario of "eating out."

MAIN OUTCOME MEASURES

The primary outcome was the time plasma glucose levels were in target (3.91-8.0 mmol/L) during closed loop delivery and a comparable control period. Secondary outcomes included pooled data analysis and time plasma glucose levels were below target (≤ 3.9 mmol/L).

RESULTS

For the eating in scenario, overnight closed loop delivery of insulin increased the time plasma glucose levels were in target by a median 15% (interquartile range 3-35%), P = 0.002. For the eating out scenario, closed loop delivery increased the time plasma glucose levels were in target by a median 28% (2-39%), P = 0.01. Analysis of pooled data showed that the overall time plasma glucose was in target increased by a median 22% (3-37%) with closed loop delivery (P < 0.001). Closed loop delivery reduced overnight time spent hypoglycaemic (plasma glucose ≤ 3.9 mmol/L) by a median 3% (0-20%), P=0.04, and eliminated plasma glucose concentrations below 3.0 mmol/L after midnight.

CONCLUSION

These two small crossover trials suggest that closed loop delivery of insulin may improve overnight control of glucose levels and reduce the risk of nocturnal hypoglycaemia in adults with type 1 diabetes. Trial registration ClinicalTrials.gov NCT00910767 and NCT00944619.

Automated overnight closed-loop glucose control in young children with type 1 diabetes

BACKGROUND

We evaluated the effectiveness of automated overnight closed-loop (AOCL) insulin delivery and the influence of timing of initiation on glucose control overnight in young children with type 1 diabetes (T1D).

METHODS

Eight children with T1D (four boys, four girls) (mean ± SD: 9.4 ± 2.7 years old; body mass index, 18.3 ± 2.3 kg/m(2); duration of diabetes, 3.9 ± 2.5 years; total daily insulin dose, 0.7 ± 0.1 U/kg/day; glycosylated hemoglobin, 7.9 ± 0.9%) were studied in a clinical research facility on two separate occasions. Subjects had a meal at 18:00 (77 ± 8 g of carbohydrate [CHO]) and snack at 21:00 (21 ± 6 g of CHO), both accompanied by a prandial insulin bolus. In random order, AOCL was started at 18:00 or 21:00 h and ran until 08:00 h the next day. Subcutaneous continuous glucose monitoring data were fed automatically into the model predictive control algorithm. Calculated subcutaneous insulin infusion rates were sent wirelessly to an insulin pump. Plasma glucose was measured to assess closed-loop performance.

RESULTS

No rescue CHOs were administered. Time spent with plasma glucose in the target range from 3.9 to 8.0 mmol/L was 50.7% (29.0%, 72.2%), and it did not differ on the two occasions: median (interquartile range), 42% (18%, 64%) versus 58% (32%, 79%) (P = 0.161). Time when plasma glucose was above 8.0 mmol/L (42% [25%, 82%] vs. 29% [14%, 64%], P = 0.093), time below 3.9 mmol/L (0% [0%, 11%] vs. 8% [0%, 17%], P = 0.500), low blood glucose index (0.1 [0.0, 2.5] vs. 1.7 [0.4, 3.3], P = 0.380), plasma glucose at the start of AOCL (12.5 ± 2.7 vs. 11.6 ± 4.2 mmol/L, P = 0.562), and mean overnight plasma glucose (8.3 ± 2.1 vs. 7.5 ± 2.2 mmol/L, P = 0.246) were also similar.

CONCLUSIONS

AOCL is feasible in young children with T1D. Comparable results were obtained when closed-loop was initiated at 18:00 or 21:00 h.

Development of a multi-parametric model predictive control algorithm for insulin delivery in type 1 diabetes mellitus using clinical parameters

A multi-parametric model predictive control (mpMPC) algorithm for subcutaneous insulin delivery for individuals with type 1 diabetes mellitus (T1DM) that is computationally efficient, robust to variations in insulin sensitivity, and involves minimal burden for the user is proposed. System identification was achieved through impulse response tests feasible for ambulatory conditions on the UVa/Padova simulator adult subjects with T1DM. An alternative means of system identification using readily available clinical parameters was also investigated. A safety constraint was included explicitly in the algorithm formulation using clinical parameters typical of those available to an attending physician. Closed-loop simulations were carried out with daily consumption of 200 g carbohydrate. Controller robustness was assessed by subject/model mismatch scenarios addressing daily, simultaneous variation in insulin sensitivity and meal size with the addition of Gaussian white noise with a standard deviation of 10%. A second-order-plus-time-delay transfer function model fit the validation data with a mean (coefficient of variation) root-mean-square-error (RMSE) of 26 mg/dL (19%) for a 3 h prediction horizon. The resulting control law maintained a low risk Low Blood Glucose Index without any information about carbohydrate consumption for 90% of the subjects. Low-order linear models with clinically meaningful parameters thus provided sufficient information for a model predictive control algorithm to control glycemia. The use of clinical knowledge as a safety constraint can reduce hypoglycemic events, and this same knowledge can further improve glycemic control when used explicitly as the controller model. The resulting mpMPC algorithm was sufficiently compact to be implemented on a simple electronic device.

A closed-loop artificial pancreas based on risk management

BACKGROUND

Control algorithms that regulate blood glucose (BG) levels in individuals with type 1 diabetes mellitus face several fundamental challenges. Two of these are the asymmetric risk of clinical complications associated with low and high glucose levels and the irreversibility of insulin action when using only insulin. Both of these nonlinearities force a controller to be more conservative when uncertainties are high. We developed a novel extended model predictive controller (EMPC) that explicitly addresses these two challenges.

METHOD

Our extensions to model predictive control (MPC) operate in three ways. First, they explicitly minimize the combined risk of hypoglycemia and hyperglycemia. Second, they integrate the effect of prediction uncertainties into the risk. Third, they understand that future control actions will vary if measurements fall above or below predictions. Using the University of Virginia/Padova Simulator, we compared our novel controller (EMPC) against optimized versions of a proportional-integral-derivative (PID) controller, a traditional MPC, and a basal/bolus (BB) controller, as well as against published results of an independent MPC (IMPC). The BB controller was optimized retrospectively to serve as a bound on the possible performance.

RESULTS

We tuned each controller, where possible, to minimize a published blood glucose risk index (BGRI). The simulated controllers (PID/MPC/EMPC/BB) provided BGRI values of 2.99/3.05/2.51/1.27 as compared to the published IMPC BGRI value of 4.10. These correspond to 73/79/84/92% of BG values lying in the euglycemic range (70-180 mg/dl), respectively, with mean BG levels of 151/156/147/140 mg/dl.

CONCLUSION

The EMPC strategy extends MPC to explicitly address the issues of asymmetric glycemic risk and irreversible insulin action using estimated prediction uncertainties and an explicit risk function. This controller reduces the avoidable BGRI by 56% (p < .05) relative to a published MPC algorithm studied on a similar population.

Closed-loop insulin delivery: from bench to clinical practice

Automated closed-loop insulin delivery, also referred to as the 'artificial pancreas', has been an important but elusive goal of diabetes treatment for many decades. Research milestones include the conception of continuous glucose monitoring in the early 1960s, followed by the production of the first commercial hospital-based artificial pancreas in the late 1970s that combined intravenous glucose sensing and insulin delivery. In the past 10 years, research into the artificial pancreas has gained substantial momentum and focused on the subcutaneous route for glucose measurement and insulin delivery, which reflects technological advances in interstitial glucose monitoring and the increasing use of the continuous subcutaneous insulin infusion. This Review discusses the design of an artificial pancreas, its components and clinical results, as well as the advantages and disadvantages of different types of automated closed-loop systems and potential future advances. The introduction of the artificial pancreas into clinical practice will probably occur gradually, starting with simpler approaches, such as overnight control of blood glucose concentration and temporary pump shut-off, that are adapted to more complex situations, such as glycemic control during meals and exercise.

Can technological solutions for diabetes replace islet cell function?

The central objective of diabetes research and management is to restore the deficient secretion of insulin, thereby restoring a state of euglycemia and minimizing short- and long-term risks associated with poor glucose control. The development of the artificial pancreas seeks to imitate the action of the pancreatic beta cell by employing closed-loop control to respond to glycemic excursions by appropriately infusing appropriate amounts of insulin. This article examines progress towards implementing an artificial pancreas in the context of the pancreatic islet as the ideal model for controlling blood glucose. Physiologic insulin secretion will form our foundation for considering the technical design elements relevant to electromechanically imitating the beta cell. The most recent clinical trials using closed-loop control are reviewed and this modality is compared to other curative approaches including islet cell transplantation and preservation. Finally, the potential of the artificial pancreas as a method to adequately reestablish euglycemia is considered.

International recommendations for glucose control in adult non diabetic critically ill patients

INTRODUCTION

The purpose of this research is to provide recommendations for the management of glycemic control in critically ill patients.

METHODS

Twenty-one experts issued recommendations related to one of the five pre-defined categories (glucose target, hypoglycemia, carbohydrate intake, monitoring of glycemia, algorithms and protocols), that were scored on a scale to obtain a strong or weak agreement. The GRADE (Grade of Recommendation, Assessment, Development and Evaluation) system was used, with a strong recommendation indicating a clear advantage for an intervention and a weak recommendation indicating that the balance between desirable and undesirable effects of an intervention is not clearly defined.

RESULTS

A glucose target of less than 10 mmol/L is strongly suggested, using intravenous insulin following a standard protocol, when spontaneous food intake is not possible. Definition of the severe hypoglycemia threshold of 2.2 mmol/L is recommended, regardless of the clinical signs. A general, unique amount of glucose (enteral/parenteral) to administer for any patient cannot be suggested. Glucose measurements should be performed on arterial rather than venous or capillary samples, using central lab or blood gas analysers rather than point-of-care glucose readers.

CONCLUSIONS

Thirty recommendations were obtained with a strong (21) and a weak (9) agreement. Among them, only 15 were graded with a high level of quality of evidence, underlying the necessity to continue clinical studies in order to improve the risk-to-benefit ratio of glucose control.

A robust sliding mode controller with internal model for closed-loop artificial pancreas

The study presents a robust closed-loop sliding mode controller with internal model for blood glucose control in type-1 diabetes. Type-1 diabetic patients depend on external insulin delivery to keep their blood glucose within near-normal ranges. Closed-loop artificial pancreas is developed to help avoid dangerous, potentially life-threatening hypoglycemia, as well as to prevent complication-inducing hyperglycemia. The proposed controller is designed using a combination of sliding mode and internal model control techniques. To enhance postprandial performance, a feedforward controller is added to inject insulin bolus. Simulation studies have been performed to test the controller, which revealed that the proposed control strategy is able to control the blood glucose well within the safe limits in the presence of meals and measurements errors. The controller shows acceptable robustness against changes in insulin sensitivity, model-patient mismatch, and errors in estimating meal's contents.

Feedforward-feedback multiple predictive controllers for glucose regulation in type 1 diabetes

Type 1 diabetic patients depend on insulin therapy to maintain blood glucose levels within safe range. The idea behind the "Artificial Pancreas" is to mimic, as close as possible, the functions of the natural pancreas in glucose sensing and insulin delivery, by using closed-loop control techniques. This work presents a model-based predictive control strategy for blood glucose regulation in diabetic patients. The controller is provided with a feedforward loop to improve meal compensation, a gain scheduling scheme to improve the controller performance in controlling the nonlinear glucose-insulin system, and an asymmetric cost function to reduce the hypoglycemic risk. Simulation scenarios with virtual patients are used to test the designed controller. The obtained results show a good controller performance in fasting conditions and meal disturbance rejection, and robustness against measurements errors, meal estimation errors, and changes in insulin sensitivity.

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.

Therapeutics of diabetes mellitus: focus on insulin analogues and insulin pumps

Aim. Inadequately controlled diabetes accounts for chronic complications and increases mortality. Its therapeutic management aims in normal HbA1C, prandial and postprandial glucose levels. This review discusses diabetes management focusing on the latest insulin analogues, alternative insulin delivery systems and the artificial pancreas. Results. Intensive insulin therapy with multiple daily injections (MDI) allows better imitation of the physiological rhythm of insulin secretion. Longer-acting, basal insulin analogues provide concomitant improvements in safety, efficacy and variability of glycaemic control, followed by low risks of hypoglycaemia. Continuous subcutaneous insulin infusion (CSII) provides long-term glycaemic control especially in type 1 diabetic patients, while reducing hypoglycaemic episodes and glycaemic variability. Continuous subcutaneous glucose monitoring (CGM) systems provide information on postprandial glucose excursions and nocturnal hypo- and/or hyperglycemias. This information enhances treatment options, provides a useful tool for self-monitoring and allows safer achievement of treatment targets. In the absence of a cure-like pancreas or islets transplants, artificial “closed-loop” systems mimicking the pancreatic activity have been also developed. Conclusions. Individualized treatment plans for insulin initiation and administration mode are critical in achieving target glycaemic levels. Progress in these fields is expected to facilitate and improve the quality of life of diabetic patients.

Automatic Detection of Stress States in Type 1 Diabetes Subjects in Ambulatory Conditions

Two levels of control are crucial to the robustness of an artificial β-cell, a medical device that would automatically regulate blood glucose levels in patients with type 1 diabetes. A low-level component would attempt to regulate blood glucose continuously, while a supervisory-level, or monitoring, component would detect underlying changes in the subject's glucose-insulin dynamics and take corrective actions accordingly. These underlying changes, or "faults," can include changes in insulin sensitivity, sensor problems, and insulin delivery problems, to name a few. A multivariate statistical monitoring technique, principal component analysis (PCA), has been applied to both simulated and experimental type 1 diabetes data. The objective of this study was to determine if PCA could be used to distinguish between normal patient data, and data for abnormal conditions that included a variety of "faults." The PCA results showed a high degree of accuracy; for data from nine type 1 diabetes subjects in ambulatory conditions, 33 of 37 total test days (89%), including fault days and normal days, were classified correctly. Thus, the proposed monitoring technique shows considerable promise for incorporation into an artificial β-cell.

Suspended insulin infusion during overnight closed-loop glucose control in children and adolescents with Type 1 diabetes

AIMS

We assessed an extended interruption of subcutaneous insulin delivery during overnight closed-loop glucose control in children and adolescents with Type 1 diabetes (T1D).

METHODS

In seven young subjects with T1D [age 14.2+/-2.1 years, diabetes duration 6.9+/-4.0 years, glycated haemoglobin (HbA1c) 8.0+/-1.5%, body mass index (BMI) 21.4+/-4.0 kg/m2, total daily insulin dose 0.9+/-0.2 units/kg/day; mean+/-sd) participating in overnight closed-loop glucose control studies, insulin delivery was interrupted for at least 90 min on the basis of predicted hypoglycaemia, low prevailing glucose levels or a too-steep decline in glucose levels.

RESULTS

Insulin delivery was interrupted for 165 (105, 210) min [median, interquartile range (IQR)]. Plasma glucose was 6.2+/-3.2 mmol/l at the time of interruption and 5.5+/-2.0 mmol/l 105 min later (P=0.15, paired t-test). Plasma glucose declined during the first hour of the interruption at a rate of 0.02+/-0.03 mmol/l per min and reached a nadir of 5.2+/-2.7 mmol/l; 105 min after the interruption, plasma glucose was increasing at a rate of 0.01+/-0.03 mmol/l per min. When insulin delivery restarted, plasma glucose was 6.4+/-2.2 mmol/l and peaked at 7.9+/-2.1 mmol/l in 60 min (P=0.01). Physiological levels of plasma insulin were measured throughout with a nadir of 119+/-78 pmol/l.

CONCLUSIONS

A prolonged interruption of insulin delivery during overnight closed-loop glucose control to prevent hypoglycaemia was not associated with an increased risk of hyperglycaemia in young people with T1D.

PSECMAC intelligent insulin schedule for diabetic blood glucose management under nonmeal announcement

Therapeutically, the closed-loop blood glucose-insulin regulation paradigm via a controllable insulin pump offers a potential solution to the management of diabetes. However, the development of such a closed-loop regulatory system to date has been hampered by two main issues: 1) the limited knowledge on the complex human physiological process of glucose-insulin metabolism that prevents a precise modeling of the biological blood glucose control loop; and 2) the vast metabolic biodiversity of the diabetic population due to varying exogneous and endogenous disturbances such as food intake, exercise, stress, and hormonal factors, etc. In addition, current attempts of closed-loop glucose regulatory techniques generally require some form of prior meal announcement and this constitutes a severe limitation to the applicability of such systems. In this paper, we present a novel intelligent insulin schedule based on the pseudo self-evolving cerebellar model articulation controller (PSECMAC) associative learning memory model that emulates the healthy human insulin response to food ingestion. The proposed PSECMAC intelligent insulin schedule requires no prior meal announcement and delivers the necessary insulin dosage based only on the observed blood glucose fluctuations. Using a simulated healthy subject, the proposed PSECMAC insulin schedule is demonstrated to be able to accurately capture the complex human glucose-insulin dynamics and robustly addresses the intraperson metabolic variability. Subsequently, the PSECMAC intelligent insulin schedule is employed on a group of type-1 diabetic patients to regulate their impaired blood glucose levels. Preliminary simulation results are highly encouraging. The work reported in this paper represents a major paradigm shift in the management of diabetes where patient compliance is poor and the need for prior meal announcement under current treatment regimes poses a significant challenge to an active lifestyle.

Continuous glucose monitoring: real-time algorithms for calibration, filtering, and alarms

Algorithms for real-time use in continuous glucose monitors are reviewed, including calibration, filtering of noisy signals, glucose predictions for hypoglycemic and hyperglycemic alarms, compensation for capillary blood glucose to sensor time lags, and fault detection for sensor degradation and dropouts. A tutorial on Kalman filtering for real-time estimation, prediction, and lag compensation is presented and demonstrated via simulation examples. A limited number of fault detection methods for signal degradation and dropout have been published, making that an important area for future work.

Manual closed-loop insulin delivery in children and adolescents with type 1 diabetes: a phase 2 randomised crossover trial

BACKGROUND

Closed-loop systems link continuous glucose measurements to insulin delivery. We aimed to establish whether closed-loop insulin delivery could control overnight blood glucose in young people.

METHODS

We undertook three randomised crossover studies in 19 patients aged 5-18 years with type 1 diabetes of duration 6.4 years (SD 4.0). We compared standard continuous subcutaneous insulin infusion and closed-loop delivery (n=13; APCam01); closed-loop delivery after rapidly and slowly absorbed meals (n=7; APCam02); and closed-loop delivery and standard treatment after exercise (n=10; APCam03). Allocation was by computer-generated random code. Participants were masked to plasma and sensor glucose. In APCam01, investigators were masked to plasma glucose. During closed-loop nights, glucose measurements were fed every 15 min into a control algorithm calculating rate of insulin infusion, and a nurse adjusted the insulin pump. During control nights, patients' standard pump settings were applied. Primary outcomes were time for which plasma glucose concentration was 3.91-8.00 mmol/L or 3.90 mmol/L or lower. Analysis was per protocol. This trial is registered, number ISRCTN18155883.

FINDINGS

17 patients were studied for 33 closed-loop and 21 continuous infusion nights. Primary outcomes did not differ significantly between treatment groups in APCam01 (12 analysed; target range, median 52% [IQR 43-83] closed loop vs 39% [15-51] standard treatment, p=0.06;

INTERPRETATION

Closed-loop systems could reduce risk of nocturnal hypoglycaemia in children and adolescents with type 1 diabetes.

FUNDING

Juvenile Diabetes Research Foundation; European Foundation for Study of Diabetes; Medical Research Council Centre for Obesity and Related Metabolic Diseases; National Institute for Health Research Cambridge Biomedical Research Centre.

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Key Words Collapse

MESH Headings

• Adolescent
• Algorithms
• Biosensing Techniques
• Blood Glucose/metabolism
• Child
• Child, Preschool
• Cross-Over Studies
• Diabetes Mellitus, Type 1/blood
• Diabetes Mellitus, Type 1/drug therapy
• Female
• Humans
• Hypoglycemic Agents/administration & dosage
• Infusions, Subcutaneous
• Insulin/administration & dosage
• Insulin/blood
• Insulin Infusion Systems
• Male
• Treatment Outcome

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Grants

• G0600717 Medical Research Council

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Affiliation(s)

Roman Hovorka Department of Paediatrics, University of Cambridge, Cambridge, UK.
Janet M Allen
Daniela Elleri
Ludovic J Chassin
Julie Harris
Dongyuan Xing
Craig Kollman
Tomas Hovorka
Anne Mette F Larsen
Marianna Nodale
Alessandra De Palma
Malgorzata E Wilinska
Carlo L Acerini
David B Dunger

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SMARTDIAB: a communication and information technology approach for the intelligent monitoring, management and follow-up of type 1 diabetes patients

SMARTDIAB is a platform designed to support the monitoring, management, and treatment of patients with type 1 diabetes mellitus (T1DM), by combining state-of-the-art approaches in the fields of database (DB) technologies, communications, simulation algorithms, and data mining. SMARTDIAB consists mainly of two units: 1) the patient unit (PU); and 2) the patient management unit (PMU), which communicate with each other for data exchange. The PMU can be accessed by the PU through the internet using devices, such as PCs/laptops with direct internet access or mobile phones via a Wi-Fi/General Packet Radio Service access network. The PU consists of an insulin pump for subcutaneous insulin infusion to the patient and a continuous glucose measurement system. The aforementioned devices running a user-friendly application gather patient's related information and transmit it to the PMU. The PMU consists of a diabetes data management system (DDMS), a decision support system (DSS) that provides risk assessment for long-term diabetes complications, and an insulin infusion advisory system (IIAS), which reside on a Web server. The DDMS can be accessed from both medical personnel and patients, with appropriate security access rights and front-end interfaces. The DDMS, apart from being used for data storage/retrieval, provides also advanced tools for the intelligent processing of the patient's data, supporting the physician in decision making, regarding the patient's treatment. The IIAS is used to close the loop between the insulin pump and the continuous glucose monitoring system, by providing the pump with the appropriate insulin infusion rate in order to keep the patient's glucose levels within predefined limits. The pilot version of the SMARTDIAB has already been implemented, while the platform's evaluation in clinical environment is being in progress.

Glycemic control in the burn intensive care unit: focus on the role of anemia in glucose measurement

Glycemic control with intensive insulin therapy (IIT) has received widespread adoption secondary to findings of improved clinical outcomes and survival in the burn population. Severe burn as a model for trauma is characterized by a hypermetabolic state, hyperglycemia, and insulin resistance. In this article, we review the findings of a burn center research facility in terms of understanding glucose management. The conferred benefits from IIT, our findings of poor outcomes associated with glycemic variability, advantages from preserved diurnal variation of glucose and insulin, and impacts of glucometer error and hematocrit correction factor are discussed. We conclude with direction for further study and the need for a reliable continuous glucose monitoring system. Such efforts will further the endeavor for achieving adequate glycemic control in order to assess the efficacy of target ranges and use of IIT.

A gain-scheduling model predictive controller for blood glucose control in type 1 diabetes

This paper presents a control strategy for blood glucose (BG) level regulation in type 1 diabetic patients. To design the controller, model-based predictive control scheme has been applied to a newly developed diabetic patient model. The controller is provided with a feedforward loop to improve meal compensation, a gain-scheduling scheme to account for different BG levels, and an asymmetric cost function to reduce hypoglycemic risk. A simulation environment that has been approved for testing of artificial pancreas control algorithms has been used to test the controller. The simulation results show a good controller performance in fasting conditions and meal disturbance rejection, and robustness against model-patient mismatch and errors in meal estimation.

Health technology assessment review: Computerized glucose regulation in the intensive care unit--how to create artificial control

Current care guidelines recommend glucose control (GC) in critically ill patients. To achieve GC, many ICUs have implemented a (nurse-based) protocol on paper. However, such protocols are often complex, time-consuming, and can cause iatrogenic hypoglycemia. Computerized glucose regulation protocols may improve patient safety, efficiency, and nurse compliance. Such computerized clinical decision support systems (Cuss) use more complex logic to provide an insulin infusion rate based on previous blood glucose levels and other parameters. A computerized CDSS for glucose control has the potential to reduce overall workload, reduce the chance of human cognitive failure, and improve glucose control. Several computer-assisted glucose regulation programs have been published recently. In order of increasing complexity, the three main types of algorithms used are computerized flowcharts, Proportional-Integral-Derivative (PID), and Model Predictive Control (MPC). PID is essentially a closed-loop feedback system, whereas MPC models the behavior of glucose and insulin in ICU patients. Although the best approach has not yet been determined, it should be noted that PID controllers are generally thought to be more robust than MPC systems. The computerized Cuss that are most likely to emerge are those that are fully a part of the routine workflow, use patient-specific characteristics and apply variable sampling intervals.

A closed-loop artificial pancreas using model predictive control and a sliding meal size estimator

The objective of this article is to present a comprehensive strategy for a closed-loop artificial pancreas. A meal detection and meal size estimation algorithm is developed for situations in which the subject forgets to provide a meal insulin bolus. A pharmacodynamic model of insulin action is used to provide insulin-on-board constraints to explicitly include the future effect of past and currently delivered insulin boluses. In addition, a supervisory pump shut-off feature is presented to avoid hypoglycemia. All of these components are used in conjunction with a feedback control algorithm using model predictive control (MPC). A model for MPC is developed based on a study of 20 subjects and is tested in a hypothetical clinical trial of 100 adolescent and 100 adult subjects using a Food and Drug Administration-approved diabetic subject simulator. In addition, a performance comparison of previously and newly proposed meal size estimation algorithms using 200 in silico subjects is presented. Using the new meal size estimation algorithm, the integrated artificial pancreas system yielded a daily mean glucose of 138 and 132 mg/dl for adolescents and adults, respectively, which is a substantial improvement over the MPC-only case, which yielded 159 and 145 mg/dl.

Overnight closed-loop insulin delivery with model predictive control: assessment of hypoglycemia and hyperglycemia risk using simulation studies

BACKGROUND

Hypoglycemia and hyperglycemia during closed-loop insulin delivery based on subcutaneous (SC) glucose sensing may arise due to (1) overdosing and underdosing of insulin by control algorithm and (2) difference between plasma glucose (PG) and sensor glucose, which may be transient (kinetics origin and sensor artifacts) or persistent (calibration error [CE]). Using in silico testing, we assessed hypoglycemia and hyperglycemia incidence during over-night closed loop. Additionally, a comparison was made against incidence observed experimentally during open-loop single-night in-clinic studies in young people with type 1 diabetes mellitus (T1DM) treated by continuous SC insulin infusion.

METHODS

Simulation environment comprising 18 virtual subjects with T1DM was used to simulate overnight closed-loop study with a model predictive control (MPC) algorithm. A 15 h experiment started at 17:00 and ended at 08:00 the next day. Closed loop commenced at 21:00 and continued for 11 h. At 18:00, protocol included meal (50 g carbohydrates) accompanied by prandial insulin. The MPC algorithm advised on insulin infusion every 15 min. Sensor glucose was obtained by combining model-calculated noise-free interstitial glucose with experimentally derived transient and persistent sensor artifacts associated with FreeStyle Navigator (FSN). Transient artifacts were obtained from FSN sensor pairs worn by 58 subjects with T1DM over 194 nighttime periods. Persistent difference due to FSN CE was quantified from 585 FSN sensor insertions, yielding 1421 calibration sessions from 248 subjects with diabetes.

RESULTS

Episodes of severe (PG < or = 36 mg/dl) and significant (PG < or = 45 mg/dl) hypoglycemia and significant hyperglycemia (PG > or = 300 mg/dl) were extracted from 18,000 simulated closed-loop nights. Severe hypoglycemia was not observed when FSN CE was less than 45%. Hypoglycemia and hyperglycemia incidence during open loop was assessed from 21 overnight studies in 17 young subjects with T1DM (8 males; 13.5 +/- 3.6 years of age; body mass index 21.0 +/- 4.0 kg/m2; duration diabetes 6.4 +/- 4.1 years; hemoglobin A1c 8.5% +/- 1.8%; mean +/- standard deviation) participating in the Artificial Pancreas Project at Cambridge. Severe and significant hypoglycemia during simulated closed loop occurred 0.75 and 17.11 times per 100 person years compared to 1739 and 3479 times per 100 person years during experimental open loop, respectively. Significant hyperglycemia during closed loop and open loop occurred 75 and 15,654 times per 100 person years, respectively.

CONCLUSIONS

The incidence of severe and significant hypoglycemia reduced 2300- and 200-fold, respectively, during stimulated overnight closed loop with MPC compared to that observed during open-loop overnight clinical studies in young subjects with T1DM. Hyperglycemia was 200 times less likely. Overnight closed loop with the FSN and the MPC algorithm is expected to reduce substantially the risk of hypoglycemia and hyperglycemia.

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.

Experimental evaluation of a recursive model identification technique for type 1 diabetes

BACKGROUND

A model-based controller for an artificial beta cell requires an accurate model of the glucose-insulin dynamics in type 1 diabetes subjects. To ensure the robustness of the controller for changing conditions (e.g., changes in insulin sensitivity due to illnesses, changes in exercise habits, or changes in stress levels), the model should be able to adapt to the new conditions by means of a recursive parameter estimation technique. Such an adaptive strategy will ensure that the most accurate model is used for the current conditions, and thus the most accurate model predictions are used in model-based control calculations.

METHODS

In a retrospective analysis, empirical dynamic autoregressive exogenous input (ARX) models were identified from glucose-insulin data for nine type 1 diabetes subjects in ambulatory conditions. Data sets consisted of continuous (5-minute) glucose concentration measurements obtained from a continuous glucose monitor, basal insulin infusion rates and times and amounts of insulin boluses obtained from the subjects' insulin pumps, and subject-reported estimates of the times and carbohydrate content of meals. Two identification techniques were investigated: nonrecursive, or batch methods, and recursive methods. Batch models were identified from a set of training data, whereas recursively identified models were updated at each sampling instant. Both types of models were used to make predictions of new test data. For the purpose of comparison, model predictions were compared to zero-order hold (ZOH) predictions, which were made by simply holding the current glucose value constant for p steps into the future, where p is the prediction horizon. Thus, the ZOH predictions are model free and provide a base case for the prediction metrics used to quantify the accuracy of the model predictions. In theory, recursive identification techniques are needed only when there are changing conditions in the subject that require model adaptation. Thus, the identification and validation techniques were performed with both "normal" data and data collected during conditions of reduced insulin sensitivity. The latter were achieved by having the subjects self-administer a medication, prednisone, for 3 consecutive days. The recursive models were allowed to adapt to this condition of reduced insulin sensitivity, while the batch models were only identified from normal data.

RESULTS

Data from nine type 1 diabetes subjects in ambulatory conditions were analyzed; six of these subjects also participated in the prednisone portion of the study. For normal test data, the batch ARX models produced 30-, 45-, and 60-minute-ahead predictions that had average root mean square error (RMSE) values of 26, 34, and 40 mg/dl, respectively. For test data characterized by reduced insulin sensitivity, the batch ARX models produced 30-, 60-, and 90-minute-ahead predictions with average RMSE values of 27, 46, and 59 mg/dl, respectively; the recursive ARX models demonstrated similar performance with corresponding values of 27, 45, and 61 mg/dl, respectively. The identified ARX models (batch and recursive) produced more accurate predictions than the model-free ZOH predictions, but only marginally. For test data characterized by reduced insulin sensitivity, RMSE values for the predictions of the batch ARX models were 9, 5, and 5% more accurate than the ZOH predictions for prediction horizons of 30, 60, and 90 minutes, respectively. In terms of RMSE values, the 30-, 60-, and 90-minute predictions of the recursive models were more accurate than the ZOH predictions, by 10, 5, and 2%, respectively.

CONCLUSION

In this experimental study, the recursively identified ARX models resulted in predictions of test data that were similar, but not superior, to the batch models. Even for the test data characteristic of reduced insulin sensitivity, the batch and recursive models demonstrated similar prediction accuracy. The predictions of the identified ARX models were only marginally more accurate than the model-free ZOH predictions. Given the simplicity of the ARX models and the computational ease with which they are identified, however, even modest improvements may justify the use of these models in a model-based controller for an artificial beta cell.