Effect of input excitation on the quality of empirical dynamic models for type 1 diabetes

A predictive model incorporating the change detection and Winsorization methods for alerting hypoglycemia and hyperglycemia

This paper focuses on establishing an effective predictive model to quickly and accurately alert hypoglycemia and hyperglycemia for helping control blood glucose levels of people with diabetes. In general, a good predictive model is established on the features of data. Inspired by this, we first analyze the characteristics of continuous glucose monitoring (CGM) data by the equality of variances test and outlier detection, which show time-varying fluctuations and jump points in CGM data. Therefore, we incorporate the change detection method and the Winsorization method into the predictive model based on the autoregressive moving average (ARMA) model and the recursive least squares (RLS) method to fit the above characteristics. To the best of our knowledge, the proposed method is the first attempt to give a solution for matching the time-varying fluctuations and jump points of CGM data simultaneously. A case study using CGM data is given to validate the effectiveness of the proposed method under 30-min-ahead prediction. The results show that the proposed method can improve the true alarm ratio of hypoglycemia and hyperglycemia from 0.7983 to 0.8783, and lengthen the average advance detection time of hypoglycemia and hyperglycemia from 19.77 to 22.64 min.

Linear Model Identification for Personalized Prediction and Control in Diabetes

OBJECTIVE

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

METHODS

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

RESULTS

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

CONCLUSION

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

SIGNIFICANCE

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

A Data-Driven Personalized Model of Glucose Dynamics Taking Account of the Effects of Physical Activity for Type 1 Diabetes: An In Silico Study

This paper aims to develop a data-driven model for glucose dynamics taking into account the effects of physical activity (PA) through a numerical study. It intends to investigate PA's immediate effect on insulin-independent glucose variation and PA's prolonged effect on insulin sensitivity. We proposed a nonlinear model with PA (NLPA), consisting of a linear regression of PA and a bilinear regression of insulin and PA. The model was identified and evaluated using data generated from a physiological PA-glucose model by Dalla Man et al. integrated with the uva/padova Simulator. Three metrics were computed to compare blood glucose (BG) predictions by NLPA, a linear model with PA (LPA), and a linear model with no PA (LOPA). For PA's immediate effect on glucose, NLPA and LPA showed 45-160% higher mean goodness of fit (FIT) than LOPA under 30 min-ahead glucose prediction (P < 0.05). For the prolonged PA effect on glucose, NLPA showed 87% higher FIT than LPA (P < 0.05) for simulations using no previous measurements. NLPA had 25-37% and 31-54% higher sensitivity in predicting postexercise hypoglycemia than LPA and LOPA, respectively. This study demonstrated the following qualitative trends: (1) for moderate-intensity exercise, accuracy of BG prediction was improved by explicitly accounting for PA's effect; and (2) accounting for PA's prolonged effect on insulin sensitivity can increase the chance of early prediction of postexercise hypoglycemia. Such observations will need to be further evaluated through human subjects in the future.

Black-box Model Identification of Physical Activity in Type-l Diabetes Patients

In this paper we consider the problem of predicting future values of glucose in type-1 diabetes. In particular, we investigate the benefit of including physical activity, measured by an off-the-shelf wearable device, to other physiologic signals frequently used to predict blood-glucose concentration, namely injected insulin, carbohydrates intake, and past glucose samples measured by a Continuous Glucose Monitoring (CGM) sensor. Derivation of individualized predictors is crucial to cope with the wide inter- and intra-subject variability: learning and updating patient-specific models of the glucose-insulin system and using them to design personalized control actions has the potential to improve substantially patients' quality oflife. On data collected by 6 subjects for 5 days, we identify a black-box liner model that uses insulin and meal as inputs and glucose as output. Prediction Error Method (PEM) is used for parameter estimation. The personalized model is employed to derive patient-tailored predictors. This procedure is then repeated using a further physiological input, accounting for physical activity. The prediction accuracy of the two models, including or not physical activity, was compared on the basis of two metrics commonly used in system identification, namely Coefficient of Determination (COD) and Root Mean Squared Error. The models identified with physical activity have better performance, increasing the 3-hr prediction COD by mean ± standard deviation of 18.5% ± 30.1%.

Neural network-based model predictive control for type 1 diabetic rats on artificial pancreas system

Artificial pancreas system (APS) is a viable option to treat diabetic patients. Researchers, however, have not conclusively determined the best control method for APS. Due to intra-/inter-variability of insulin absorption and action, an individualized algorithm is required to control blood glucose level (BGL) for each patient. To this end, we developed model predictive control (MPC) based on artificial neural networks (ANNs), which combines ANN for BGL prediction based on inputs and MPC for BGL control based on the ANN (NN-MPC). First, we developed a mathematical model for diabetic rats, which was used to identify individual virtual subjects by fitting to empirical data collected through an APS, including BGL data, insulin injection, and food intake. Then, the virtual subjects were used to generate datasets for training ANNs. The NN-MPC determines control actions (insulin injection) based on BGL predicted by the ANN. To evaluate the NN-MPC, we conducted experiments using four virtual subjects under three different scenarios. Overall, the NN-MPC maintained BGL within the normal range about 90% of the time with a mean absolute deviation of 4.7 mg/dl from a desired BGL. Our findings suggest that the NN-MPC can provide subject-specific BGL control in conjunction with a closed-loop APS. Graphical abstract ᅟ.

Short-term prediction of glucose in type 1 diabetes using kernel adaptive filters

This study aims at presenting a nonlinear, recursive, multivariate prediction model of the subcutaneous glucose concentration in type 1 diabetes. Nonlinear regression is performed in a reproducing kernel Hilbert space, by either the fixed budget quantized kernel least mean square (QKLMS-FB) or the approximate linear dependency kernel recursive least-squares (KRLS-ALD) algorithm, such that a sparse model structure is accomplished. A multivariate feature set (i.e., subcutaneous glucose, food carbohydrates, insulin regime and physical activity) is used and its influence on short-term glucose prediction is investigated. The method is evaluated using data from 15 patients with type 1 diabetes in free-living conditions. In the case when all the input variables are considered: (i) the average root mean squared error (RMSE) of QKLMS-FB increases from 13.1 mg dL^-1 (mean absolute percentage error (MAPE) 6.6%) for a 15-min prediction horizon (PH) to 37.7 mg dL^-1 (MAPE 20.8%) for a 60-min PH and (ii) the RMSE of KRLS-ALD, being predictably lower, increases from 10.5 mg dL^-1 (MAPE 5.2%) for a 15-min PH to 31.8 mg dL^-1 (MAPE 18.0%) for a 60-min PH. Multivariate data improve systematically both the regularity and the time lag of the predictions, reducing the errors in critical glucose value regions for a PH ≥ 30 min. Graphical abstract ᅟ.

Rapid model identification for online subcutaneous glucose concentration prediction for new subjects with type I diabetes

GOAL

For conventional modeling methods, the work of model identification has to be repeated with sufficient data for each subject because different subjects may have different response to exogenous inputs. This may cause repetitive cost and burden for patients and clinicians and require a lot of modeling efforts. Here, to overcome the aforementioned problems, a rapid model development strategy for new subjects is proposed using the idea of model migration for online glucose prediction.

METHODS

First, a base model is obtained that can be empirically identified from any subject or constructed by a priori knowledge. Then, parameters of inputs in the base model are properly revised based on a small amount of new data from new subjects so that the updated models can reflect the specific glucose dynamics excited by inputs for new subjects. These problems are investigated by developing autoregressive models with exogenous inputs (ARX) based on 30 in silico subjects using UVA/Padova metabolic simulator.

RESULTS

The prediction accuracy of the rapid modeling method is comparable to that for subject-dependent modeling method for some cases. Also, it can present better generalization ability.

CONCLUSION

The proposed method can be regarded as an effective and economic modeling method instead of repetitive subject-dependent modeling method especially for lack of modeling data.

Systematically in silico comparison of unihormonal and bihormonal artificial pancreas systems

Automated closed-loop control of blood glucose concentration is a daily challenge for type 1 diabetes mellitus, where insulin and glucagon are two critical hormones for glucose regulation. According to whether glucagon is included, all artificial pancreas (AP) systems can be divided into two types: unihormonal AP (infuse only insulin) and bihormonal AP (infuse both insulin and glucagon). Even though the bihormonal AP is widely considered a promising direction, related studies are very scarce due to this system's short research history. More importantly, there are few studies to compare these two kinds of AP systems fairly and systematically. In this paper, two switching rules, P-type and PD-type, were proposed to design the logic of orchestrates switching between insulin and glucagon subsystems, where the delivery rates of both insulin and glucagon were designed by using IMC-PID method. These proposed algorithms have been compared with an optimal unihormonal system on virtual type 1 diabetic subjects. The in silico results demonstrate that the proposed bihormonal AP systems have outstanding superiorities in reducing the risk of hypoglycemia, smoothing the glucose level, and robustness with respect to insulin/glucagon sensitivity variations, compared with the optimal unihormonal AP system.

Wiener sliding-mode control for artificial pancreas: a new nonlinear approach to glucose regulation

Type 1 diabetic patients need insulin therapy to keep their blood glucose close to normal. In this paper an attempt is made to show how nonlinear control-oriented model may be used to improve the performance of closed-loop control of blood glucose in diabetic patients. The nonlinear Wiener model is used as a novel modeling approach to be applied to the glucose control problem. The identified Wiener model is used in the design of a robust nonlinear sliding mode control strategy. Two configurations of the nonlinear controller are tested and compared to a controller designed with a linear model. The controllers are designed in a Smith predictor structure to reduce the effect of system time delay. To improve the meal compensation features, the controllers are provided with a simple feedforward controller to inject an insulin bolus at meal time. Different simulation scenarios have been used to evaluate the proposed controllers. The obtained results show that the new approach outperforms the linear control scheme, and regulates the glucose level within safe limits in the presence of measurement and modeling errors, meal uncertainty and patient variations.

Detecting failures of the glucose sensor-insulin pump system: improved overnight safety monitoring for Type-1 diabetes

New sensors for real-time continuous glucose monitoring (CGM) and pumps for continuous subcutaneous insulin infusion (CSII), possibly mounted on the same device, opened new scenarios for Type-1 diabetes treatment. However, possible failures of either CGM or CSII can expose diabetic patients to risks that can be dangerous especially overnight. In this contribution we present a proof-of-concept method, developed in a state-space context and implemented through a Kalman estimator, to detect in real time possible overnight failures of the sensor-pump system by simultaneously using CGM and CSII data. The method is tested on two simulated and one real subject. Results show that the method is able to correctly generate alerts for sensor-pump failures and stimulates further investigation on its development.

Predicting subcutaneous glucose concentration using a latent-variable-based statistical method for type 1 diabetes mellitus

BACKGROUND

Accurate prediction of future glucose concentration for type 1 diabetes mellitus (T1DM) is needed to improve glycemic control and to facilitate proactive management before glucose concentrations reach undesirable concentrations. The availability of frequent glucose measurements, insulin infusion rates, and meal carbohydrate estimates can be used to good advantage to capture important information concerning glucose dynamics.

METHODS

This article evaluates the feasibility of using a latent variable (LV)-based statistical method to model glucose dynamics and to forecast future glucose concentrations for T1DM applications. The prediction models are developed using a proposed LV-based approach and are evaluated for retrospective clinical data from seven individuals with T1DM and for In silico simulations using the Food and Drug Administration-accepted University of Virginia/University of Padova metabolic simulator. This article provides comparisons of the prediction accuracy of the LV-based method with that of a standard modeling alternative. The influence of key design parameters on the performance of the LV-based method is also illustrated.

RESULTS

In general, the LV-based method provided improved prediction accuracy in comparison with conventional autoregressive (AR) models and autoregressive with exogenous input (ARX) models. For larger prediction horizons (≥30 min), the LV-based model with exogenous inputs achieved the best prediction performance based on a paired t-test (α = 0.05).

CONCLUSIONS

The LV-based method resulted in models whose glucose prediction accuracy was as least as good as the accuracies of standard AR/ARX models and a simple model-free approach. Furthermore, the new approach is less sensitive to changing conditions and the effect of key design parameters.

Modular closed-loop control of diabetes

Modularity plays a key role in many engineering systems, allowing for plug-and-play integration of components, enhancing flexibility and adaptability, and facilitating standardization. In the control of diabetes, i.e., the so-called "artificial pancreas," modularity allows for the step-wise introduction of (and regulatory approval for) algorithmic components, starting with subsystems for assured patient safety and followed by higher layer components that serve to modify the patient's basal rate in real time. In this paper, we introduce a three-layer modular architecture for the control of diabetes, consisting in a sensor/pump interface module (IM), a continuous safety module (CSM), and a real-time control module (RTCM), which separates the functions of insulin recommendation (postmeal insulin for mitigating hyperglycemia) and safety (prevention of hypoglycemia). In addition, we provide details of instances of all three layers of the architecture: the APS© serving as the IM, the safety supervision module (SSM) serving as the CSM, and the range correction module (RCM) serving as the RTCM. We evaluate the performance of the integrated system via in silico preclinical trials, demonstrating 1) the ability of the SSM to reduce the incidence of hypoglycemia under nonideal operating conditions and 2) the ability of the RCM to reduce glycemic variability.

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.

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.

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.

Modeling the effects of subcutaneous insulin administration and carbohydrate consumption on blood glucose

BACKGROUND

Estimation of the magnitude and duration of effects of carbohydrate (CHO) and subcutaneously administered insulin on blood glucose (BG) is required for improved BG regulation in people with type 1 diabetes mellitus (T1DM). The goal of this study was to quantify these effects in people with T1DM using a novel protocol.

METHODS

The protocol duration was 8 hours: a 1-3 U subcutaneous (SC) insulin bolus was administered and a 25-g CHO meal was consumed, with these inputs separated by 3-5 hours. The DexCom SEVEN® PLUS continuous glucose monitor was used to obtain SC glucose measurements every 5 minutes and YSI 2300 Stat Plus was used to obtain intravenous glucose measurements every 15 minutes.

RESULTS

The protocol was tested on 11 subjects at Sansum Diabetes Research Institute. The intersubject parameter coefficient of variation for the best identification method was 170%. The mean percentages of output variation explained by the bolus insulin and meal models were 68 and 69%, respectively, with root mean square error of 14 and 10 mg/dl, respectively. Relationships between the model parameters and clinical parameters were observed.

CONCLUSION

Separation of insulin boluses and meals in time allowed unique identification of model parameters. The wide intersubject variation in parameters supports the notion that glucose-insulin models and thus insulin delivery algorithms for people with T1DM should be personalized. This experimental protocol could be used to refine estimates of the correction factor and the insulin-to-carbohydrate ratio used by people with T1DM.

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.

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.

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.