RobustH∞ glucose control in diabetes using a physiological model

Experimental glucose regulation with a high-order sliding-mode controller

Theoretically High-Order Sliding-Mode Controllers are well suited to perform closed loop glucose regulation because they are insensitive to parameter uncertainties and robust to unknown dynamics that may perturb the system. The implementation of the controller based on the concept of practical relative degree is presented. The controller was tested in Sprague-Dawley rats with steptozotocin induced diabetes. The tests demonstrated high efficacy and robustness of the controller.

A genetic algorithm tuned optimal controller for glucose regulation in type 1 diabetic subjects

An optimal state feedback controller is designed with the objective of minimizing the elevated glucose levels caused by meal intake in Type 1 diabetic subjects, by the minimal infusion of insulin. The states for the controller based on linear quadratic regulator theory are estimated from noisy data using Kalman filter. The controller designed for a physiological relevant mathematical model is coupled with another model for simulating meal dynamics, which converts meal intake into glucose appearance rate in the plasma. The tuning parameters (weighting matrices) of the controller and the design parameters (noise covariance matrices) of the Kalman filter are optimized using genetic algorithm. The controller based on the combined framework of evolutionary computing and state estimated linear quadratic regulator is found to maintain normoglycemia for meal intakes of varying carbohydrate content. The proposed approach addresses noisy output measurement, modeling error and delay in sensor measurement.

A DISCRETE-TIME RECURRENT NEUROFUZZY NETWORK FOR BLACK-BOX MODELING OF INSULIN DYNAMICS IN DIABETIC TYPE-1 PATIENTS

In this work we present a data-driven modeling of the insulin dynamics in different in silico patients using a recurrent neural network with output feedback. The inputs for the identification is the rate of insulin (μU / dl / min) applied to the patient, and blood glucose concentration. The output is insulin concentration (μU / ml) present in the blood stream. Once completed the off-line modeling, this model could be used for on-line monitoring of the insulin concentration for a better treatment. The learning law of the recurrent neural network is inspired by adaptive observer theory, and proven to be convergent in the parameters and stable in the Lyapunov sense, even with only 13 samples available. Simulation results are shown to validate the presented modeling.

Artificial neural networks for closed loop control of in silico and ad hoc type 1 diabetes

The closed loop control of blood glucose levels might help to reduce many short- and long-term complications of type 1 diabetes. Continuous glucose monitoring and insulin pump systems have facilitated the development of the artificial pancreas. In this paper, artificial neural networks are used for both the identification of patient dynamics and the glycaemic regulation. A subcutaneous glucose measuring system together with a Lispro insulin subcutaneous pump were used to gather clinical data for each patient undergoing treatment, and a corresponding in silico and ad hoc neural network model was derived for each patient to represent their particular glucose-insulin relationship. Based on this nonlinear neural network model, an ad hoc neural network controller was designed to close the feedback loop for glycaemic regulation of the in silico patient. Both the neural network model and the controller were tested for each patient under simulation, and the results obtained show a good performance during food intake and variable exercise conditions.

Induced L₂-norm minimization of glucose-insulin system for Type I diabetic patients

Using induced L₂-norm minimization, a robust controller was developed for insulin delivery in Type I diabetic patients. The high-complexity nonlinear diabetic patient Sorensen-model was considered and Linear Parameter Varying methodology was used to develop open-loop model and robust H(∞) controller. Considering the normoglycaemic set point (81.1 mg/dL), a polytopic set was created over the physiologic boundaries of the glucose-insulin interaction of the Sorensen-model. In this way, Linear Parameter Varying model formalism was defined. The robust control was developed considering input and output multiplicative uncertainties with two additional uncertainties from those used in the literature: sensor noise and worst-case design for meal disturbance (60 g carbohydrate). Simulation scenario on large meal absorption illustrates the applicability of the robust LPV control technique, while patient variability is tested with real data taken from the SPRINT clinical protocol on ICU patients.

Quasi-Model-Based Control of Type 1 Diabetes Mellitus

Glucose-insulin models appeared in the literature are varying in complexity. Hence, their use in control theory is not trivial. The paper presents an optimal controller design framework to investigate the type 1 diabetes from control theory point of view. Starting from a recently published glucose-insulin model a Quasi Model with favorable control properties is developed minimizing the physiological states to be taken into account. The purpose of the Quasi Model is not to model the glucose-glucagon-insulin interaction precisely, but only to grasp the characteristic behavior such that the designed controller can successfully regulate the unbalanced system. Different optimal control strategies (pole-placement, LQ, Minimax control) are designed on the Quasi Model, and the obtained controllers' applicability is investigated on two more sophisticated type 1 diabetic models using two absorption scenarios. The developed framework could help researchers engaging the control problem of diabetes.

Time-Varying Procedures for Insulin-Dependent Diabetes Mellitus Control

This work considers the problem of automatically controlling the glucose level in insulin dependent diabetes mellitus (IDDM) patients. The objective is to include several important and practical issues in the design: model uncertainty, time variations, nonlinearities, measurement noise, actuator delay and saturation, and real time implementation. These are fundamental issues to be solved in a device implementing this control. Two time-varying control procedures have been proposed which take into consideration all of them: linear parameter varying (LPV) and unfalsified control (UC). The controllers are implemented with low-order dynamics that adapt continuously according to the glucose levels measured in real time in one case (LPV) and by controller switching based on the actual performance in the other case (UC). Both controllers have performed adequately under all these practical restrictions, and a discussion on pros and cons of each method is presented at the end.

LPV control of glucose for Diabetes type I

This paper considers the problem of automatically controlling the glucose level in a Diabetes type I patient. Three issues have been considered: model uncertainty, time-varying/nonlinear phenomena and controller implementation. To that end, the dynamical model of the insulin/glucose relation is framed as a Linear Parameter Varying system and a controller is designed based on it. In addition, this framework allows not only a better performance than other classical methods, but also provides stability and performance guarantees. Design computations are based on convex Linear Matrix Inequality (LMI) optimization. Implementation is based on a low order controller whose dynamics adapts according to the glucose levels measured in real-time.

Systems engineering medicine: engineering the inflammation response to infectious and traumatic challenges

The complexity of the systemic inflammatory response and the lack of a treatment breakthrough in the treatment of pathogenic infection demand that advanced tools be brought to bear in the treatment of severe sepsis and trauma. Systems medicine, the translational science counterpart to basic science's systems biology, is the interface at which these tools may be constructed. Rapid initial strides in improving sepsis treatment are possible through the use of phenomenological modelling and optimization tools for process understanding and device design. Higher impact, and more generalizable, treatment designs are based on mechanistic understanding developed through the use of physiologically based models, characterization of population variability, and the use of control-theoretic systems engineering concepts. In this review we introduce acute inflammation and sepsis as an example of just one area that is currently underserved by the systems medicine community, and, therefore, an area in which contributions of all types can be made.

Automatic data processing to achieve a safe telemedical artificial pancreas

BACKGROUND

The use of telemedicine for diabetes care has evolved over time, proving that it contributes to patient self-monitoring, improves glycemic control, and provides analysis tools for decision support. The timely development of a safe and robust ambulatory artificial pancreas should rely on a telemedicine architecture complemented with automatic data analysis tools able to manage all the possible high-risk situations and to guarantee the patient's safety.

METHODS

The Intelligent Control Assistant system (INCA) telemedical artificial pancreas architecture is based on a mobile personal assistant integrated into a telemedicine system. The INCA supports four control strategies and implements an automatic data processing system for risk management (ADP-RM) providing short-term and medium-term risk analyses. The system validation comprises data from 10 type 1 pump-treated diabetic patients who participated in two randomized crossover studies, and it also includes in silico simulation and retrospective data analysis.

RESULTS

The ADP-RM short-term risk analysis prevents hypoglycemic events by interrupting insulin infusion. The pump interruption has been implemented in silico and tested for a closed-loop simulation over 30 hours. For medium-term risk management, analysis of capillary blood glucose notified the physician with a total of 62 alarms during a clinical experiment (56% for hyperglycemic events). The ADP-RM system is able to filter anomalous continuous glucose records and to detect abnormal administration of insulin doses with the pump.

CONCLUSIONS

Automatic data analysis procedures have been tested as an essential tool to achieve a safe ambulatory telemedical artificial pancreas, showing their ability to manage short-term and medium-term risk situations.

Probabilistic evolving meal detection and estimation of meal total glucose appearance

BACKGROUND

Automatic compensation of meals for type 1 diabetes patients will require meal detection from continuous glucose monitor (CGM) readings. This is challenged by the uncertainty and variability inherent to the digestion process and glucose dynamics as well as the lag and noise associated with CGM sensors. Thus any estimation of meal start time, size, and shape is fundamentally uncertain. This uncertainty can be reduced, but not eliminated, by estimating total glucose appearance and using new readings as they become available.

METHOD

In this article, we propose a probabilistic, evolving method to detect the presence and estimate the shape and total glucose appearance of a meal. The method is unique in continually evolving its estimates and simultaneously providing uncertainty measures to monitor their convergence. The algorithm operates in three phases. First, it compares the CGM signal to no-meal predictions made by a simple insulin-glucose model. Second, it fits the residuals to potential, assumed meal shapes. Finally, it compares and combines these fits to detect any meals and estimate the meal total glucose appearance, shape, and total glucose appearance uncertainty.

RESULTS

We validate the performance of this meal detection and total glucose appearance estimation algorithm both separately and in cooperation with a controller on the Food and Drug Administration-approved University of Virginia/Padova Type I Diabetes Simulator. In cooperation with a controller, the algorithm reduced the mean blood glucose from 137 to 132 mg/dl over 1.5 days of control without any increased hypoglycemia.

CONCLUSION

This novel, extensible meal detection and total glucose appearance estimation method shows the feasibility, relevance, and performance of evolving estimates with explicit uncertainty measures for use in closed-loop control of type 1 diabetes.

Computational study of an augmented minimal model for glycaemia control

In this paper we introduce a new model structure for the metabolic effects of intravenous insulin on blood glucose in man and derive its parameter values from the widely used model of Sorensen. The proposed model attempts to combine the advantages of the existing comprehensive and minimal models. Validation of the new model is done through deriving equivalent nonparametric nonlinear models in the form of Principal Dynamic Modes. We show that the new structure can represent the insulin-glucose dynamics of healthy subjects as well as Type 1 and Type 2 diabetics, with appropriate adjustment in its parameters.

Effectiveness of Intravenous Infusion Algorithms for Glucose Control in Diabetic Patients Using Different Simulation Models

The effectiveness of closed-loop insulin infusion algorithms is assessed for three different mathematical models describing insulin and glucose dynamics within a Type I diabetes patient. Simulations are performed to assess the effectiveness of proportional plus integral plus derivative (PID) control, feedforward control, and a physiologically-based control system with respect to maintaining normal glucose levels during a meal and during exercise. Control effectiveness is assessed by comparing the simulated response to a simulation of a healthy patient during both a meal and exercise and establishing maximum and minimum glucose levels and insulin infusion levels, as well as maximum duration of hyperglycemia. Controller effectiveness is assessed within the minimal model, the Sorensen model, and the Hovorka model. Results showed that no type of control was able to maintain normal conditions when simulations were performed using the minimal model. For both the Sorensen model and the Hovorka model, proportional control was sufficient to maintain normal glucose levels. Given published clinical data showing the ineffectiveness of PID control in patients, the work demonstrates that controller success based on simulation results can be misleading, and that future work should focus on addressing the model discrepancies.

Multi-objective blood glucose control for type 1 diabetes

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

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

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

The future of open- and closed-loop insulin delivery systems

We have analysed several aspects of insulin-dependent diabetes mellitus, including the glucose metabolic system, diabetes complications, and previous and ongoing research aimed at controlling glucose in diabetic patients. An expert review of various models and control algorithms developed for the glucose homeostasis system is presented, along with an analysis of research towards the development of a polymeric insulin infusion system. Recommendations for future directions in creating a true closed-loop glucose control system are presented, including the development of multivariable models and control systems to more accurately describe and control the multi-metabolite, multi-hormonal system, as well as in-vivo assessments of implicit closed-loop control systems.

Design of Luenberger observer for glucose-insulin control via mathematica

Many articles dealing with insulin-glucose control have been published in the last decades, and they mostly assumed that all the system state variables are available for feedback. However, this is not usually the case, or they are not so cheap in practice as blood glucose measurements are. In this paper the use of the reduced-order estimator (also known as the Luenberger observer) is considered in symbolic form employing Polynomial Control System Application of Mathematica for the three-state minimal Bergman model, [1], as this can be used to reconstruct those state variables that are hard to be recovered directly from the system outputs: remote compartment insulin and plasma insulin. Nonlinear closed loop simulations with H(2)/H(infinity) control (disturbance rejection LQ method) showed that the observer, which is faster than the system itself, can provide a very good state recovery performance.

A minimal model for glycemia control in critically ill patients

In this paper we propose a modified minimal model to be used for glycemia control in critically ill patients. For various reasons the Bergman minimal model is widely used to describe glucose and insulin dynamics. However, since this model is mostly valid in a rather restrictive setting, it might not be suitable to be used in a model predictive controller. Simulations show that the new model exhibits a similar glycemia behaviour but clinically more realistic insulin kinetics. Therefore it is potentially more suitable for glycemia control. The designed model is also estimated on a set of critically ill patients giving promising results.

A Feedforward-Feedback Glucose Control Strategy for Type 1 Diabetes Mellitus

As the "artificial pancreas" becomes closer to reality, automated insulin delivery based on real-time glucose measurements becomes feasible for people with diabetes. This paper is concerned with the development of novel feedforward-feedback control strategies for real-time glucose control and type 1 diabetes. Improved post-meal responses can be achieved by a pre-prandial snack or bolus, or by reducing the glucose setpoint prior to the meal. Several feedforward-feedback control strategies provide attractive alternatives to the standard meal insulin bolus and are evaluated in simulations using a physiological model.

Model-based nonlinear optimal blood glucose control of type I diabetes patients

Using induced L(2)-norm minimization, a robust controller was developed for insulin delivery in Type I diabetic patients. The high-complexity nonlinear diabetic patient Sorensen-model [1] was considered. LPV (Linear Parameter Varying) methodology was used to develop open loop model and robust controller. Considering the normoglycemic set point (81.1 mg/dL), a polytopic set was created over the physiologic boundaries of the glucose-insulin interaction of the Sorensen-model. In this way, LPV model formalism was defined. The robust control was developed considering input and output multiplicative uncertainties with other weighting functions.

A Run-to-Run Control Strategy to Adjust Basal Insulin Infusion Rates in Type 1 Diabetes

Maintaining good glycemic control is a daily challenge for people with type 1 diabetes. Insulin requirements are changing constantly due to many factors, such as levels of stress and physical activity. The basal insulin requirement also has a circadian rhythm, adding another level of complexity. Automating the adjustment of insulin dosing would result in improved glycemic control, as well as an improved quality of life by significantly reducing the burden on the patient. Building on our previous success of using run-to-run control for prandial insulin dosing (a strategy adapted from the chemical process industry), we show how this same framework can be used to adjust basal infusion profiles. We present a mathematical model of insulin-glucose dynamics which we augment in order to capture the circadian variation in insulin requirements. Using this model, we show that the run-to-run framework can also be successfully applied to adjust basal insulin dosing.

On hyperglicemic glucose basal levels in Type 1 Diabetes Mellitus from dynamic analysis

Compartmental-Physiological Models (CPM's) have been used to derive feedback controllers for the glucose regulation in Diabetes Mellitus (DM). Despite these important advances, there are two criticisms about the use of the CPM's in DM: (i) Can this class of model reproduce severe basal glucose levels (e.g., larger than 300 mg/dl)? and (ii) Does a CPM reproduce a distinct glucose level as its parameters change or is it unique even if its parameters change? This contribution aims these criticisms from the study of the parametric sensitivity of a CPM. The results exploit the analysis of the dynamic properties of the chosen CPM and permit to show that such model can reproduce distinct severe basal levels by modifying the values of the metabolic parameters, which agree with expectations on a realistic model. Mainly, the chosen CPM has been selected due to the following two reasons. (i) It includes the main organs related to the glucose metabolism in Type 1 Diabetes Mellitus (T1DM); as, for example, the liver, brain and kidney. (ii) It models metabolic phenomena as, for instance, the counter-regulatory effects by glucagon and the hepatic glucose uptake/production. Additionally, the chosen model has been recently used to design feedback controllers for the glucose regulation with very promissory results.

A system model of oral glucose absorption: validation on gold standard data

A reliable model of glucose absorption after oral ingestion may facilitate simulation as well as pathophysiological studies. One of the difficulties for the development and quality assessment of such models has been the lack of gold standard data for their validation. Thus, while data on plasma concentrations of glucose are available, the rates of appearance in plasma of ingested glucose (Ra) were not available to develop such models. Here we utilize the recent availability of Ra data, estimated with a model-independent multiple tracer technique, to formulate a system model of intestinal glucose absorption. Two published and two new models are tested on this new data set. One of the two new models performed best: it is nonlinear, describes the Ra data well and its parameters are estimated with good precision. This model has important potential both in simulation contexts, e.g., it can be incorporated in whole-body models of the glucose regulatory system, as well as in physiological and clinical studies to quantitatively characterize possible impairment of glucose absorption in particular populations such as elderly and diabetic individuals.

Fuzzy-based controller for glucose regulation in type-1 diabetic patients by subcutaneous route

This paper presents an advisory/control algorithm for a type-1 diabetes mellitus (TIDM) patient under an intensive insulin treatment based on a multiple daily injections regimen (MDIR). The advisory/control algorithm incorporates expert knowledge about the treatment of this disease by using Mamdani-type fuzzy logic controllers to regulate the blood glucose level (BGL). The overall control strategy is based on a two-loop feedback strategy to overcome the variability in the glucose-insulin dynamics from patient to patient. An inner-loop provides the amount of both rapid/short and intermediate/long acting insulin (RSAI and ILAI) formulations that are programmed in a three-shots daily basis before meals. The combined preparation is then injected by the patient through a subcutaneous route. Meanwhile, an outer-loop adjusts the maximum amounts of insulin provided to the patient in a time-scale of days. The outer-loop controller aims to work as a supervisor of the inner-loop controller. Extensive closed-loop simulations are illustrated, using a detailed compartmental model of the insulin-glucose dynamics in a TIDM patient with meal intake.

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

An advanced model-based control technique for regulating the blood glucose for patients with Type 1 diabetes is presented. The optimal insulin delivery rate is obtained off-line as an explicit function of the current blood glucose concentration of the patient by using novel parametric programming algorithms, developed at Imperial College London. The implementation of the optimal insulin delivery rate, therefore, requires simple function evaluation and minimal on-line computations. The proposed framework also addresses the uncertainty in the model due to interpatient and intrapatient variability by identifying the model parameters which ensure that a feasible control law can be obtained. The developments reported in this paper are expected to simplify the insulin delivery mechanism, thereby enhancing the quality of life of the patient.

An adaptive input-output modeling approach for predicting the glycemia of critically ill patients

In this paper we apply system identification techniques in order to build a model suitable for the prediction of glycemia levels of critically ill patients admitted to the intensive care unit. These patients typically show increased glycemia levels, and it has been shown that glycemia control by means of insulin therapy significantly reduces morbidity and mortality. Based on a real-life dataset from 15 critically ill patients, an initial input-output model is estimated which captures the insulin effect on glycemia under different settings. To incorporate patient-specific features, an adaptive modeling strategy is also proposed in which the model is re-estimated at each time step (i.e., every hour). Both one-hour-ahead predictions and four-hours-ahead simulations are executed. The optimized adaptive modeling technique outperforms the general initial model. To avoid data selection bias, 500 permutations, in which the patients are randomly selected, are considered. The results are satisfactory both in terms of forecasting ability and in the clinical interpretation of the estimated coefficients.

Optimal$H^infty$Insulin Injection Control for Blood Glucose Regulation in Diabetic Patients

The theory of H infinity optimal control has the feature of minimizing the worst-case gain of an unknown disturbance input. When appropriately modified, the theory can be used to design a "switching" controller that can be applied to insulin injection for blood glucose (BG) regulation. The "switching" controller is defined by a collection of basic insulin rates and a rule that switches the insulin rates from one value to another. The rule employed an estimation of BG from noisy measurements, and the subsequent optimization of a performance index that involves the solution of a "jump" Riccati differential equation and a discrete-time dynamic programming equation. With an appropriate patient model, simulation studies have shown that the controller could correct BG deviation using clinically acceptable insulin delivery rates.

Effect of Poly (Ethylene Glycol) Molecular Weight and Microparticle Size on Oral Insulin Delivery from P(MAA‐g‐EG) Microparticles

Five years of successful work in our lab have shown that graft copolymer networks of poly(methacrylic acid-g-ethylene) [P(MAA-g-EG)], are very promising candidates for oral drug delivery. In an acidic environment, these copolymers form interpolymer complexes, protecting the active agent from the harsh environment of the gastrointestinal tract. At high pH, these complexes dissociate, causing the polymer to swell and release the drug. Films of P(MAA-g-EG) with a monomer ratio of 1:1 (MAA:EG) were prepared by free radical solution UV-polymerization, washed in order to remove the unreacted monomer, and crushed to form microparticles with different particle size distribution. Previous studies in our lab have focused on using polymer disks in their swelling studies. The swelling properties of polymer disks vs. crushed particles were investigated via equilibrium swelling experiments in this study. Another goal in this study is to compare different PEG chain length (MW-400 and MW-1000) and different particle size (150-212 microns, 90-150 microns and 25-90 microns) in their loading and release behavior. After 6 hours of exposing the polymer with the insulin solution we achieved approximately 90% of insulin loading.