Boris P. Kovatchev

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.

Artificial Pancreas: Past, Present, Future

The artificial pancreas (AP), known as closed-loop control of blood glucose in diabetes, is a system combining a glucose sensor, a control algorithm, and an insulin infusion device. AP developments can be traced back 50 years to when the possibility for external blood glucose regulation was established by studies in individuals with type 1 diabetes using intravenous glucose measurement and infusion of insulin and glucose. After the pioneering work by Kadish (1) in 1964, expectations for effectively closing the loop were inspired by the nearly simultaneous work of five teams reporting closed-loop control results between 1974 and 1978: Albisser et al. (2), Pfeiffer et al. (3), Mirouze et al. (4), Kraegen et al. (5), and Shichiri et al. (6). In 1977, one of these realizations (3) resulted in the first commercial device—the Biostator (7; Fig. 1), followed by another inpatient system, the Nikkiso STG-22 Blood Glucose Controller, now in use in Japan (8). FIG. 1. The Biostator (courtesy of William Clarke, University of Virginia). Although the intravenous route of glucose sensing and insulin infusion is unsuitable for outpatient use, these devices proved the feasibility of external glucose control and stimulated further technology development. Figure 2 presents key milestones in the timeline of AP progress. FIG. 2. Key milestones in the timeline of AP progress. EU, Europe; IP, intraperitoneal; NIH, National Institutes of Health; SC, subcutaneous. In 1979, landmark studies by Pickup et al. (9) and Tamborlane et al. (10) showed that the subcutaneous route was feasible for continuous insulin delivery. Three years later, Shichiri et al. (11) tested a prototype of a wearable AP, which was further developed in subsequent studies (12,13). In the late 1980s, an implantable system was introduced using intravenous glucose sensing and intraperitoneal insulin infusion (14). This technology was further developed, leading to clinical trials and …

A Behavior Change Model for Internet Interventions

BackgroundThe Internet has become a major component to health care and has important implications for the future of the health care system. One of the most notable aspects of the Web is its ability to provide efficient, interactive, and tailored content to the user. Given the wide reach and extensive capabilities of the Internet, researchers in behavioral medicine have been using it to develop and deliver interactive and comprehensive treatment programs with the ultimate goal of impacting patient behavior and reducing unwanted symptoms. To date, however, many of these interventions have not been grounded in theory or developed from behavior change models, and no overarching model to explain behavior change in Internet interventions has yet been published.PurposeThe purpose of this article is to propose a model to help guide future Internet intervention development and predict and explain behavior changes and symptom improvement produced by Internet interventions.ResultsThe model purports that effective Internet interventions produce (and maintain) behavior change and symptom improvement via nine nonlinear steps: the user, influenced by environmental factors, affects website use and adherence, which is influenced by support and website characteristics. Website use leads to behavior change and symptom improvement through various mechanisms of change. The improvements are sustained via treatment maintenance.ConclusionBy grounding Internet intervention research within a scientific framework, developers can plan feasible, informed, and testable Internet interventions, and this form of treatment will become more firmly established.

Model Predictive Control of Type 1 Diabetes: An in Silico Trial:

Background: The development of artificial pancreas has received a new impulse from recent technological advancements in subcutaneous continuous glucose monitoring and subcutaneous insulin pump delivery systems. However, the availability of innovative sensors and actuators, although essential, does not guarantee optimal glycemic regulation. Closed-loop control of blood glucose levels still poses technological challenges to the automatic control expert, most notable of which are the inevitable time delays between glucose sensing and insulin actuation. Methods: A new in silico model is exploited for both design and validation of a linear model predictive control (MPC) glucose control system. The starting point is a recently developed meal glucose-insulin model in health, which is modified to describe the metabolic dynamics of a person with type 1 diabetes mellitus. The population distribution of the model parameters originally obtained in healthy 204 patients is modified to describe diabetic patients. Individual models of virtual patients are extracted from this distribution. A discrete-time MPC is designed for all the virtual patients from a unique input-output-linearized approximation of the full model based on the average population values of the parameters. The in silico trial simulates 4 consecutive days, during which the patient receives breakfast, lunch, and dinner each day. Results: Provided that the regulator undergoes some individual tuning, satisfactory results are obtained even if the control design relies solely on the average patient model. Only the weight on the glucose concentration error needs to be tuned in a quite straightforward and intuitive way. The ability of the MPC to take advantage of meal announcement information is demonstrated. Imperfect knowledge of the amount of ingested glucose causes only marginal deterioration of performance. In general, MPC results in better regulation than proportional integral derivative, limiting significantly the oscillation of glucose levels. Conclusions: The proposed in silico trial shows the potential of MPC for artificial pancreas design. The main features are a capability to consider meal announcement information, delay compensation, and simplicity of tuning and implementation.

Fully Integrated Artificial Pancreas in Type 1 Diabetes: Modular Closed-Loop Glucose Control Maintains Near Normoglycemia

Integrated closed-loop control (CLC), combining continuous glucose monitoring (CGM) with insulin pump (continuous subcutaneous insulin infusion [CSII]), known as artificial pancreas, can help optimize glycemic control in diabetes. We present a fundamental modular concept for CLC design, illustrated by clinical studies involving 11 adolescents and 27 adults at the Universities of Virginia, Padova, and Montpellier. We tested two modular CLC constructs: standard control to range (sCTR), designed to augment pump plus CGM by preventing extreme glucose excursions; and enhanced control to range (eCTR), designed to truly optimize control within near normoglycemia of 3.9–10 mmol/L. The CLC system was fully integrated using automated data transfer CGM→algorithm→CSII. All studies used randomized crossover design comparing CSII versus CLC during identical 22-h hospitalizations including meals, overnight rest, and 30-min exercise. sCTR increased significantly the time in near normoglycemia from 61 to 74%, simultaneously reducing hypoglycemia 2.7-fold. eCTR improved mean blood glucose from 7.73 to 6.68 mmol/L without increasing hypoglycemia, achieved 97% in near normoglycemia and 77% in tight glycemic control, and reduced variability overnight. In conclusion, sCTR and eCTR represent sequential steps toward automated CLC, preventing extremes (sCTR) and further optimizing control (eCTR). This approach inspires compelling new concepts: modular assembly, sequential deployment, testing, and clinical acceptance of custom-built CLC systems tailored to individual patient needs.

Multinational Study of Subcutaneous Model-Predictive Closed-Loop Control in Type 1 Diabetes Mellitus: Summary of the Results

Background: In 2008–2009, the first multinational study was completed comparing closed-loop control (artificial pancreas) to state-of-the-art open-loop therapy in adults with type 1 diabetes mellitus (T1DM). Methods: The design of the control algorithm was done entirely in silico, i.e., using computer simulation experiments with N = 300 synthetic “subjects” with T1DM instead of traditional animal trials. The clinical experiments recruited 20 adults with T1DM at the Universities of Virginia (11); Padova, Italy (6); and Montpellier, France (3). Open-loop and closed-loop admission was scheduled 3–4 weeks apart, continued for 22 h (14.5 h of which were in closed loop), and used a continuous glucose monitor and an insulin pump. The only difference between the two sessions was that insulin dosing was performed by the patient under a physicians supervision during open loop, whereas insulin dosing was performed by a control algorithm during closed loop. Results: In silico design resulted in rapid (less than 6 months compared to years of animal trials) and cost-effective system development, testing, and regulatory approvals in the United States, Italy, and France. In the clinic, compared to open-loop, closed-loop control reduced nocturnal hypoglycemia (blood glucose below 3.9 mmol/liter) from 23 to 5 episodes (p < .01) and increased the amount of time spent overnight within the target range (3.9 to 7.8 mmol/liter) from 64% to 78% (p = .03). Conclusions: In silico experiments can be used as viable alternatives to animal trials for the preclinical testing of insulin treatment strategies. Compared to open-loop treatment under identical conditions, closed-loop control improves the overnight regulation of diabetes.

Analysis, Modeling, and Simulation of the Accuracy of Continuous Glucose Sensors

Background: Continuous glucose monitors (CGMs) collect a detailed time series of consecutive observations of the underlying process of glucose fluctuations. To some extent, however, the high temporal resolution of the data is accompanied by increased probability of error in any single data point. Due to both physiological and technical reasons, the structure of these errors is complex and their analysis is not straightforward. In this article, we describe some of the methods needed to obtain a description of the sensor error that is detailed enough for simulation. Methods: Data were provided by Abbott Diabetes Care and included two data sets collected by the FreeStyle Navigator™ CGM: The first set consisted of 1032 time series of glucose readings from 136 patients with type 1 diabetes and parallel time series of reference blood glucose (BG) collected via self-monitoring at irregular intervals. The average duration of a time series was 5 days; the total number of sensor-reference data pairs was approximately 20,600. The second data set consisted of 56 time series of glucose readings from 28 patients with type 1 diabetes and a parallel time series of reference BG measured via the YSI 2300 Stat Plus™ analyzer every 15 minutes. The average duration of a time series was 2 days; the total number of sensor-reference data pairs was approximately 7000. Results: Three sets of results are discussed: analysis of sensor errors with respect to the BG rate of change, mathematical modeling of sensor error patterns and distribution, and computer simulation of sensor errors: Sensor errors depend nonlinearly on the BG rate of change: Errors tend to be positive (high readings) when the BG rate of change is negative and negative (low readings) when the BG rate of change is positive, which is indicative of an underlying time delay. In addition, the sensor noise is non-white (non-Gaussian) and the consecutive sensor errors are highly interdependent. Thus, the modeling of sensor errors is based on a diffusion model of blood-to-interstitial glucose transport, which accounts for the time delay, and a time-series approach, which includes autoregressive moving average (ARMA) noise to account for the interdependence of consecutive sensor errors. Based on modeling, we have developed a computer simulator of sensor errors that includes both generic and sensor-specific error components. A χ2 test showed that no significant difference exists between the observed and the simulated distribution of sensor errors and the distribution of errors of the FreeStyle Navigator (p > .46). Conclusions: CGM accuracy was modeled via diffusion and additive ARMA noise, which allowed for designing a computer simulator of sensor errors. The simulator, a component of a larger simulation platform approved by the Food and Drug Administration in January 2008 for pre-clinical testing of closed-loop strategies, has been successfully applied to in silico testing of closed-loop control algorithms, resulting in an investigational device exemption for closed-loop trials at the University of Virginia.

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

Background: Recent progress in the development of clinically accurate continuous glucose monitors (CGMs), automated continuous insulin infusion pumps, and control algorithms for calculating insulin doses from CGM data have enabled the development of prototypes of subcutaneous closed-loop systems for controlling blood glucose (BG) levels in type 1 diabetes. The use of a new personalized model predictive control (MPC) algorithm to determine insulin doses to achieve and maintain BG levels between 70 and 140 mg/dl overnight and to control postprandial BG levels is presented. Methods: Eight adults with type 1 diabetes were studied twice, once using their personal open-loop systems to control BG overnight and for 4 h following a standardized meal and once using a closed-loop system that utilizes the MPC algorithm to control BG overnight and for 4 h following a standardized meal. Average BG levels, percentage of time within BG target of 70–140 mg/dl, number of hypoglycemia episodes, and postprandial BG excursions during both study periods were compared. Results: With closed-loop control, once BG levels achieved the target range (70–140 mg/dl), they remained within that range throughout the night in seven of the eight subjects. One subject developed a BG level of 65 mg/dl, which was signaled by the CGM trend analysis, and the MPC algorithm directed the discontinuance of the insulin infusion. The number of overnight hypoglycemic events was significantly reduced (p = .011) with closed-loop control. Postprandial BG excursions were similar during closed-loop and open-loop control Conclusion: Model predictive closed-loop control of BG levels can be achieved overnight and following a standardized breakfast meal. This “artificial pancreas” controls BG levels as effectively as patient-directed open-loop control following a morning meal but is significantly superior to open-loop control in preventing overnight hypoglycemia.

The UVA/PADOVA Type 1 Diabetes Simulator New Features

Objective: Recent studies have provided new insights into nonlinearities of insulin action in the hypoglycemic range and into glucagon kinetics as it relates to response to hypoglycemia. Based on these data, we developed a new version of the UVA/PADOVA Type 1 Diabetes Simulator, which was submitted to FDA in 2013 (S2013). Methods: The model of glucose kinetics in hypoglycemia has been improved, implementing the notion that insulin-dependent utilization increases nonlinearly when glucose decreases below a certain threshold. In addition, glucagon kinetics and secretion and action models have been incorporated into the simulator: glucagon kinetics is a single compartment; glucagon secretion is controlled by plasma insulin, plasma glucose below a certain threshold, and glucose rate of change; and plasma glucagon stimulates with some delay endogenous glucose production. A refined statistical strategy for virtual patient generation has been adopted as well. Finally, new rules for determining insulin to carbs ratio (CR) and correction factor (CF) of the virtual patients have been implemented to better comply with clinical definitions. Results: S2013 shows a better performance in describing hypoglycemic events. In addition, the new virtual subjects span well the real type 1 diabetes mellitus population as demonstrated by good agreement between real and simulated distribution of patient-specific parameters, such as CR and CF. Conclusions: S2013 provides a more reliable framework for in silico trials, for testing glucose sensors and insulin augmented pump prediction methods, and for closed-loop single/dual hormone controller design, testing, and validation.

Evaluating the Efficacy of Closed-Loop Glucose Regulation via Control-Variability Grid Analysis

Background: Advancements in subcutaneous continuous glucose monitoring and subcutaneous insulin delivery are stimulating the development of a minimally invasive artificial pancreas that facilitates optimal glycemic regulation in diabetes. The key component of such a system is the blood glucose controller for which different design strategies have been investigated in the literature. In order to evaluate and compare the efficacy of the various algorithms, several performance indices have been proposed. Methods: A new tool—control-variability grid analysis (CVGA)—for measuring the quality of closed-loop glucose control on a group of subjects is introduced. It is a method for visualization of the extreme glucose excursions caused by a control algorithm in a group of subjects, with each subject presented by one data point for any given observation period. A numeric assessment of the overall level of glucose regulation in the population is given by the summary outcome of the CVGA. Results: It has been shown that CVGA has multiple uses: Comparison of different patients over a given time period, of the same patient over different time periods, of different control laws, and of different tuning of the same controller on the same population. Conclusions: Control-variability grid analysis provides a summary of the quality of glycemic regulation for a population of subjects and is complementary to measures such as area under the curve or low/high blood glucose indices, which characterize a single glucose trajectory for a single subject.