A nonlinear model predictive controller has been developed to maintain normoglycemia in subjects with type 1 diabetes during fasting conditions such as during overnight fast. The controller employs a compartment model, which represents the glucoregulatory system and includes submodels representing absorption of subcutaneously administered short-acting insulin Lispro and gut absorption. The controller uses Bayesian parameter estimation to determine time-varying model parameters. Moving target trajectory facilitates slow, controlled normalization of elevated glucose levels and faster normalization of low glucose values. The predictive capabilities of the model have been evaluated using data from 15 clinical experiments in subjects with type 1 diabetes. The experiments employed intravenous glucose sampling (every 15 min) and subcutaneous infusion of insulin Lispro by insulin pump (modified also every 15 min). The model gave glucose predictions with a mean square error proportionally related to the prediction horizon with the value of 0.2 mmol L(-1) per 15 min. The assessment of clinical utility of model-based glucose predictions using Clarke error grid analysis gave 95% of values in zone A and the remaining 5% of values in zone B for glucose predictions up to 60 min (n = 1674). In conclusion, adaptive nonlinear model predictive control is promising for the control of glucose concentration during fasting conditions in subjects with type 1 diabetes.

/pdf/nonlinear-model-predictive-control-of-glucose-concentration-2l5wkss7wi.pdf

Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes

A simulation model of the glucose-insulin system in the postprandial state can be useful in several circumstances, including testing of glucose sensors, insulin infusion algorithms and decision support systems for diabetes. Here, we present a new simulation model in normal humans that describes the physiological events that occur after a meal, by employing the quantitative knowledge that has become available in recent years. Model parameters were set to fit the mean data of a large normal subject database that underwent a triple tracer meal protocol which provided quasi-model-independent estimates of major glucose and insulin fluxes, e.g., meal rate of appearance, endogenous glucose production, utilization of glucose, insulin secretion. By decomposing the system into subsystems, we have developed parametric models of each subsystem by using a forcing function strategy. Model results are shown in describing both a single meal and normal daily life (breakfast, lunch, dinner) in normal. The same strategy is also applied on a smaller database for extending the model to type 2 diabetes.

Meal Simulation Model of the Glucose-Insulin System

Arguably, a minimally invasive system using subcutaneous (s.c.) continuous glucose monitoring (CGM) and s.c. insulin delivery via insulin pump would be a most feasible step to closed-loop control in type 1 diabetes mellitus (T1DM). Consequently, diabetes technology is focusing on developing an artificial pancreas using control algorithms to link CGM with s.c. insulin delivery. The future development of the artificial pancreas will be greatly accelerated by employing mathematical modeling and computer simulation. Realistic computer simulation is capable of providing invaluable information about the safety and the limitations of closed-loop control algorithms, guiding clinical studies, and out-ruling ineffective control scenarios in a cost-effective manner. Thus computer simulation testing of closed-loop control algorithms is regarded as a prerequisite to clinical trials of the artificial pancreas. In this paper, we present a system for in silico testing of control algorithms that has three principal components: (1) a large cohort of n = 300 simulated “subjects” (n = 100 adults, 100 adolescents, and 100 children) based on real individuals’ data and spanning the observed variability of key metabolic parameters in the general population of people with T1DM; (2) a simulator of CGM sensor errors representative of Freestyle Navigator™, Guardian RT, or Dexcom™ STS™, 7-day sensor; and (3) a simulator of discrete s.c. insulin delivery via OmniPod Insulin Management System or Deltec Cozmo ® insulin pump. The system has been shown to represent adequate glucose fluctuations in T1DM observed during meal challenges, and has been accepted by the Food and Drug Administration as a substitute to animal trials in the preclinical testing of closed-loop control strategies.

/pdf/in-silico-preclinical-trials-a-proof-of-concept-in-closed-3llbpfenm5.pdf

In Silico Preclinical Trials: A Proof of Concept in Closed-Loop Control of Type 1 Diabetes

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 …

https://diabetes.diabetesjournals.org/content/diabetes/60/11/2672.full.pdf

Artificial Pancreas: Past, Present, Future

A model-based-predictive control algorithm is developed to maintain normoglycemia in the Type I diabetic patient using a closed-loop insulin infusion pump. Utilizing compartmental modeling techniques, a fundamental model of the diabetic patient is constructed. The resulting nineteenth-order nonlinear pharmacokinetic-pharmacodynamic representation is used in controller synthesis. Linear identification of an input-output model from noisy patient data is performed by filtering the impulse-response coefficients via projection onto the Laguerre basis. A linear model predictive controller is developed using the identified step response model. Controller performance for unmeasured disturbance rejection (50 g oral glucose tolerance test) is examined. Glucose setpoint tracking performance is improved by designing a second controller which substitutes a more detailed internal model including state-estimation and a Kalman filter for the input-output representation The state-estimating controller maintains glucose within 15 mg/dl of the setpoint in the presence of measurement noise. Under noise-free conditions, the model based predictive controller using state estimation outperforms an internal model controller from literature (49.4% reduction in undershoot and 45.7% reduction in settling time). These results demonstrate the potential use of predictive algorithms for blood glucose control in an insulin infusion pump.

A model-based algorithm for blood glucose control in Type I diabetic patients

For simulating glucose-insulin control systems with respect to application in an optimized therapy of insulin-dependent diabetes, a global transfer model was generated and supplemented with a structural model of the opened control circuit. The transfer characteristics within the established linear range of the intact system, which is identical with the range of euglycaemia, can be described by a 4th-order differential equation. A test strategy was developed to identify the state variables of the opened, i. e., of the diabetic, system and to determine by pole assignment those control constants of glucose-controlled insulin provision that are optimally adapted to a given set of state variables. The model system was verified by the prediction of plasma insulin and blood glucose reponses to various loads of glucose and/or insulin, by isotopic studies (U-14C-glucose) of glucose turnover, and by predicting the rates of absorption (i. e., of appearance within the distribution space) of orally administered glucose. The latter situations provide fields of application for this model strategy in addition to the main goal, namely, the individual optimization of control parameters for open-loop or closed-loop insulin therapy.

Kinetic Modeling of the Glucoregulatory System to Improve Insulin Therapy

To test the hypothesis that only an adaptive algorithm would guarantee optimal feedback control of glycemia in insulin-dependent diabetes, fasting chronically diabetic dogs at rest were subjected to short-term artificial beta cell treatment. Insulin was applied intravenously and an oral glucose load was given during the experiment. Employing the same dosing algorithm, three different control strategies were employed in a random order on different days: adaptive control (minimum variance controller, Test A), fixed command control using on-line parameter estimates (Test B), and fixed command control using off-line individually optimized dosage constants (Test C). Comparison was made to nondiabetic control animals. The glycemic profiles were entirely normal in Test A and C, but were distinctly elevated in Test B. The peripheral hyperinsulinaemia could, however, not be avoided by adaptive control. It is concluded that the restoration of physiological blood glucose control in insulin-dependent diabetes requires dosage parameters which are either continually adapted to the actual situation (adaptive control) or are optimized to meet the individual's needs. In the latter case, fixed command control may be employed. Peripheral hyperinsulinaemia cannot be avoided as long as insulin is administered by a posthepatic route.

Does Physiological Blood Glucose Control Require an Adaptive Control Strategy

The circadian periods of plasma glucose, insulin and alpha-amino nitrogen (alpha-AN) were studied in fed and fasting normal and diabetic dogs which were fed either beef or beef supplemented with carbohydrates (CH). The diabetics were either withdrawn from insulin supply or treated with an artificial beta cell (ABC) or infused a constant insulin dose (CI).--There was a significant daily glucose rhythm in normal fasting animals and in fasting diabetics on CI or on insulin withdrawal. In the fed controls, the phase of the rhythms depends on carbohydrate content of food. In CH-free fed controls the insulin maxima were related to alpha-AN but in CH-fed controls they were related to glycemia. Due to the mechanism of ABC-provided insulin dosage, the phases of glucose and of insulin oscillations were correlated in all diabetics on ABC. Thus even if the mean glucose level is normalized by ABC the intrinsic phase relations remain altered.--It is concluded that the daily glucose periodicity is based on endogenous rhythms in glucose production and utilization and is essentially independent of current insulin provision. But it is governed by the meals as main "Zeitgebers" and modified by the actual insulin supply.

Daily glucose and insulin rhythms in diabetic dogs on the artificial beta cell.

The control constants for glucose-dependent insulin dosage in diabetic dogs were determined from test results in the opened system on the basis of a global blood glucose plasma-insulin control model. The controlled plant of the model consisted of the glucose and insulin subsystems; the entire insulin providing process was considered to be the controlling element, and the glucose-dependent insulin dose estimation, the controller. The constants obtained were employed in the extracorporeal artificial beta cell. The structure of the model and the numerical values of its state variables were verified by the prediction of blood glucose responses to intravenous glucose loads and by the correspondence between glucose balances and insulin doses as calculates and those as observed in diabetic animals. The application of the optimum control constant estimates in feedback-controlled insulin infusions provides improved blood glucose patterns but unchanged needs for insulin in comparison to the application of standard control parameters.

Modelling the glucose-insulin system as a basis for the artificial beta cell.

The blood glucose responses of diabetic dogs on the ABC are nearly identical if different algorithms, but equivalent sets of parameters are used to control the glucose-dependent insulin infusion. There are however some differences in the insulin doses applied, which obviously result from different response kinetics of the particular formula to the minor BG oscillations that always occur. In the practical application of closed-loop systems the control constants should be individually estimated on the basis of certain controlled plant characteristics. For use in patients the checking and modeling systems still have to be simplified. The limits of the study, i.e. the fact that normoglycemia was restored for a short time only using the IV instead of the physiological portal route, remain the subject of further investigation.

Freyse Ej

Papers

Kinetic Modeling of the Glucoregulatory System to Improve Insulin Therapy

Does Physiological Blood Glucose Control Require an Adaptive Control Strategy

Daily glucose and insulin rhythms in diabetic dogs on the artificial beta cell.

Modelling the glucose-insulin system as a basis for the artificial beta cell.

Not the artificial beta cell algorithms but their parameter values are important in automated glucose control of insulin-dependent diabetes.