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

Robust nonlinear control of blood glucose in diabetic patients subject to model uncertainties

Recent advances in the artificial pancreas system provide an emerging treatment option for type 1 diabetes. The performance of the blood glucose regulation directly relies on the accuracy of the glucose-insulin modeling. Sorenson model involves the behavior of different organs and offers precise representation. However, the high complexity of such a model makes the controller design procedure a hard task. Therefore, the high-order nonlinear Sorensen model as a popular high-fidelity physiological model is opted in this paper to analyze the glucose-insulin interactions in great detail, and a new robust nonlinear approach to regulate the blood glucose concentration (BGC) in Type-I diabetic patients is proposed. Inspiring the backstepping technique, for designing an acceptable controller, the model is divided into three main subsystems such that in each subsystem, the virtual control input laws are obtained using both Lyapunov stability and input-to-state theorems. Since the measurement of the parameters in the glucose-insulin system is not accurate, parametric uncertainties are defined in the investigated model. Furthermore, owing to the fact that the only measurable state variable is blood glucose, the estimation of inaccessible state variables is an important issue that is properly considered by the unscented Kalman filter (UKF) estimator. The suggested approach is compared to H_∞, robust H_∞, and linear parameter-varying control approaches. The comparison results on 500 simulated patients imply a remarkable superiority of the proposed controller approach to the compared methods in terms of the BGC tracking and the algorithm robustness in the presence of food intake disturbance patterns.

Two compartmental fractional derivative model with general fractional derivative

This study presents a new two compartmental model with, recently defined General fractional derivative. We review that concept of General fractional derivative and use the kernel function that generalizes the classical Caputo derivative in a mathematically consistent way. Next we use this model to study the release of antibiotic gentamicin in poly (vinyl alcohol)/gentamicin(PVA/Gent) hydrogel aimed for wound dressing in medical treatment of deep chronical wounds. The PVA/Gent hydrogel was prepared by physical cross linking of poly (vinyl alcohol) dispersion using freezing-thawing method, and then was swollen in gentamicin solution at 37 °C during 48 h. The concentration of released gentamicin was determined using a high-performance liquid chromatography coupled with mass spectrometer. The advantage of this model is the existence of new parameters in the definition of fractional derivative, as compared with classical fractional compartmental models. The model proposed here in the special case reduces to the classical (integer order) linear two compartmental model as well as classical fractional order two compartmental model since it has more parameters that are determined from the experimental results.

A comparison among three maximal mathematical models of the glucose-insulin system

The most well-known and widely used mathematical representations of the physiology of a diabetic individual are the Sorensen and Hovorka models as well as the UVAPadova Simulator. While the Hovorka model and the UVAPadova Simulator only describe the glucose metabolism of a subject with type 1 diabetes, the Sorensen model was formulated to simulate the behaviour of both normal and diabetic individuals. The UVAPadova model is the most known model, accepted by the FDA, with a high level of complexity. The Hovorka model is the simplest of the three models, well documented and used primarily for the development of control algorithms. The Sorensen model is the most complete, even though some modifications were required both to the model equations (adding useful compartments for modelling subcutaneous insulin delivery) and to the parameter values. In the present work several simulated experiments, such as IVGTTs and OGTTs, were used as tools to compare the three formulations in order to establish to what extent increasing complexity translates into richer and more correct physiological behaviour. All the equations and parameters used for carrying out the simulations are provided.

A revised Sorensen model: Simulating glycemic and insulinemic response to oral and intra-venous glucose load

In 1978, Thomas J. Sorensen defended a thesis in chemical engineering at the University of California, Berkeley, where he proposed an extensive model of glucose-insulin control, model which was thereafter widely employed for virtual patient simulation. The original model, and even more so its subsequent implementations by other Authors, presented however a few imprecisions in reporting the correct model equations and parameter values. The goal of the present work is to revise the original Sorensen's model, to clearly summarize its defining equations, to supplement it with a missing gastrio-intestinal glucose absorption and to make an implementation of the revised model available on-line to the scientific community.

Chatteringfree hybrid adaptive neuro-fuzzy inference system-particle swarm optimisation data fusion-based BG-level control

In this study, a closed-loop control scheme is proposed for the glucose-insulin regulatory system in type-1 diabetic mellitus (T1DM) patients. Some innovative hybrid glucose-insulin regulators have combined artificial intelligence such as fuzzy logic and genetic algorithm with well known Palumbo model to regulate the blood glucose (BG) level in T1DM patients. However, most of these approaches have focused on the glucose reference tracking, and the qualitative of this tracking such as chattering reduction of insulin injection has not been well-studied. Higher-order sliding mode (HoSM) controllers have been employed to attenuate the effect of chattering. Owing to the delayed nature and non-linear property of glucose-insulin mechanism as well as various unmeasurable disturbances, even the HoSM methods are partly successful. In this study, data fusion of adaptive neuro-fuzzy inference systems optimised by particle swarm optimisation has been presented. The excellent performance of the proposed hybrid controller, i.e. desired BG-level tracking and chattering reduction in the presence of daily glucose-level disturbances is verified.

Artificial Pancreas: Clinical Study in Latin America Without Premeal Insulin Boluses

BACKGROUND

Emerging therapies such as closed-loop (CL) glucose control, also known as artificial pancreas (AP) systems, have shown significant improvement in type 1 diabetes mellitus (T1DM) management. However, demanding patient intervention is still required, particularly at meal times. To reduce treatment burden, the automatic regulation of glucose (ARG) algorithm mitigates postprandial glucose excursions without feedforward insulin boluses. This work assesses feasibility of this new strategy in a clinical trial.

METHODS

A 36-hour pilot study was performed on five T1DM subjects to validate the ARG algorithm. Subjects wore a subcutaneous continuous glucose monitor (CGM) and an insulin pump. Insulin delivery was solely commanded by the ARG algorithm, without premeal insulin boluses. This was the first clinical trial in Latin America to validate an AP controller.

RESULTS

For the total 36-hour period, results were as follows: average time of CGM readings in range 70-250 mg/dl: 88.6%, in range 70-180 mg/dl: 74.7%, <70 mg/dl: 5.8%, and <50 mg/dl: 0.8%. Results improved analyzing the final 15-hour period of this trial. In that case, the time spent in range was 70-250 mg/dl: 94.7%, in range 70-180 mg/dl: 82.6%, <70 mg/dl: 4.1%, and <50 mg/dl: 0.2%. During the last night the time spent in range was 70-250 mg/dl: 95%, in range 70-180 mg/dl: 87.7%, <70 mg/dl: 5.0%, and <50 mg/dl: 0.0%. No severe hypoglycemia occurred. No serious adverse events were reported.

CONCLUSIONS

The ARG algorithm was successfully validated in a pilot clinical trial, encouraging further tests with a larger number of patients and in outpatient settings.

Tumor Volume Estimation and Quasi-Continuous Administration for Most Effective Bevacizumab Therapy

Background

Bevacizumab is an exogenous inhibitor which inhibits the biological activity of human VEGF. Several studies have investigated the effectiveness of bevacizumab therapy according to different cancer types but these days there is an intense debate on its utility. We have investigated different methods to find the best tumor volume estimation since it creates the possibility for precise and effective drug administration with a much lower dose than in the protocol.

Materials and Methods

We have examined C38 mouse colon adenocarcinoma and HT-29 human colorectal adenocarcinoma. In both cases, three groups were compared in the experiments. The first group did not receive therapy, the second group received one 200 μg bevacizumab dose for a treatment period (protocol-based therapy), and the third group received 1.1 μg bevacizumab every day (quasi-continuous therapy). Tumor volume measurement was performed by digital caliper and small animal MRI. The mathematical relationship between MRI-measured tumor volume and mass was investigated to estimate accurate tumor volume using caliper-measured data. A two-dimensional mathematical model was applied for tumor volume evaluation, and tumor- and therapy-specific constants were calculated for the three different groups. The effectiveness of bevacizumab administration was examined by statistical analysis.

Results

In the case of C38 adenocarcinoma, protocol-based treatment did not result in significantly smaller tumor volume compared to the no treatment group; however, there was a significant difference between untreated mice and mice who received quasi-continuous therapy (p = 0.002). In the case of HT-29 adenocarcinoma, the daily treatment with one-twelfth total dose resulted in significantly smaller tumors than the protocol-based treatment (p = 0.038). When the tumor has a symmetrical, solid closed shape (typically without treatment), volume can be evaluated accurately from caliper-measured data with the applied two-dimensional mathematical model.

Conclusion

Our results provide a theoretical background for a much more effective bevacizumab treatment using optimized administration.

Switched LPV Glucose Control in Type 1 Diabetes

OBJECTIVE

The purpose of this paper is to regulate the blood glucose level in Type 1 Diabetes Mellitus patients with a practical and flexible procedure that can switch among a finite number of distinct controllers, depending on the user's choice.

METHODS

A switched linear parameter-varying controller with multiple switching regions, related to hypo-, hyper-, and euglycemia situations, is designed. The key feature is to arrange the controller into a framework that provides stability and performance guaranty.

RESULTS

The closed-loop performance is tested on the complete in silico adult cohort of the UVA/Padova metabolic simulator, which has been accepted by the U.S. Food and Drug Administration in lieu of animal trials. The outcome produces comparable or improved results with respect to previous works.

CONCLUSION

The strategy is practical because it is based on a model tuned only with a priori patient information in order to cover the interpatient uncertainty. Results confirm that this control structure yields tangible improvements in minimizing risks of hyper- and hypoglycemia in scenarios with unannounced meals.

SIGNIFICANCE

This flexible procedure opens the possibility of taking into account, at the design stage, unannounced meals and/or patients' physical exercise.

The significance of LPV modeling of a widely used T1DM model

The paper investigates the specificity of Linear Parameter Varying (LPV) modeling and robust controller design on a widely used Type 1 Diabetes Mellitus model. LPV systems can be seen as an extension of linear time invariant systems, which allows us to extend some powerful control methodologies to the highly nonlinear and uncertain models of the human metabolism. Different LPV models are proposed with their own advantages and disadvantages. The possible choices are separately analyzed for both controller and observer design perspective.

A therapy parameter-based model for predicting blood glucose concentrations in patients with type 1 diabetes

In this paper, the problem of predicting blood glucose concentrations (BG) for the treatment of patients with type 1 diabetes, is addressed. Predicting BG is of very high importance as most treatments, which consist in exogenous insulin injections, rely on the availability of BG predictions. Many models that can be used for predicting BG are available in the literature. However, it is widely admitted that it is almost impossible to perfectly model blood glucose dynamics while still being able to identify model parameters using only blood glucose measurements. The main contribution of this work is to propose a simple and identifiable linear dynamical model, which is based on the static prediction model of standard therapy. It is shown that the model parameters are intrinsically correlated with physician-set therapy parameters and that the reduction of the number of model parameters to identify leads to inferior data fits but to equivalent or slightly improved prediction capabilities compared to state-of-the-art models: a sign of an appropriate model structure and superior reliability. The validation of the proposed dynamic model is performed using data from the UVa simulator and real clinical data, and potential uses of the proposed model for state estimation and BG control are discussed.

Model-based control of plasma glycemia: Tests on populations of virtual patients

Closed-loop devices delivering medical treatments in an automatic fashion clearly require a thorough preliminary phase according to which the proposed control law is tested and validated as realistically as possible, before arranging in vivo experiments in a clinical setting. The present note develops a virtual environment aiming to validate a recently proposed model-based glucose control law on a solid simulation framework. From a theoretical viewpoint, the artificial pancreas has been designed by suitably exploiting a minimal set of delay differential equations modeling the glucose-insulin regulatory system; on the other hand, the validation platform makes use of a different, multi-compartmental model to build up a population of virtual patients. Simulations are carried out by properly addressing the available technological limits and the unavoidable uncertainties in real-time continuous glucose sensors as well as possible malfunctioning on the insulin delivery devices. The results show the robustness of the proposed control law that turns out to be efficient and extremely safe on a heterogenous population of virtual patients.

Analysis of three T1DM simulation models for evaluating robust closed-loop controllers

This work compares three well-known models and simulators in terms of their use in the analysis and design of glucose controllers for patients with Type 1 Diabetes Mellitus (T1DM). The objective is to compare them in practical scenarios which include: model uncertainty, time variance, nonlinearities, glucose measurement noise, delays between subcutaneous and plasma levels, pump saturation, and real-time controller implementation. The pros and cons of all models/simulators are presented. Finally, the simulators are tested with different robust controllers in order to identify the difficulties in the design and implementation phases. To this end, three sources of uncertainty are considered: nonlinearities, time-varying behavior (intra-patient) and inter-patient differences.

Applicability results of a nonlinear model-based robust blood glucose control algorithm

INTRODUCTION

Generating optimal control algorithms for an artificial pancreas is an intensively researched problem. The available models are all nonlinear and rather complex. Model predictive control or run-to-run-based methodologies have proven to be efficient solutions for individualized treatment of type 1 diabetes mellitus (T1DM). However, the controller has to ensure safety and stability under all circumstances. Robust control methods seek to provide this safety and guarantee to handle even the worst-case situations and, hence, to generalize and complement results obtained by individualized control algorithms.

METHODS

Modern robust (e.g., Hinf) control is a linear model-based methodology that we have combined with the nonlinear model-based linear parameter varying technique. The control algorithm was designed on the high-complexity modified nonlinear glucose-insulin model of Sorensen, and it was compared step-by-step with linear model-based Hinf control results published in the literature. The applicability of the developed algorithm was tested first on a control cohort of 10 healthy persons' oral glucose tolerance test results and then on a large meal absorption profile adapted from the literature. In the latter case, two preliminary virtual patients were generated based on 1-1 week real continuous glucose monitor measurements.

RESULTS

We have found that the algorithm avoids hypoglycemia (not caused by physical activity or stress) independently from the considered absorption profiles.

CONCLUSION

Use of hard constraints proved their efficiency in fitting blood glucose level within a defined interval. However, in the future, more data of different T1DM patients will be collected and tested, including dynamic absorption model and in silico tests on validated simulators.

A closed-loop artificial pancreas using a proportional integral derivative with double phase lead controller based on a new nonlinear model of glucose metabolism

BACKGROUND

Most closed-loop insulin delivery systems rely on model-based controllers to control the blood glucose (BG) level. Simple models of glucose metabolism, which allow easy design of the control law, are limited in their parametric identification from raw data. New control models and controllers issued from them are needed.

METHODS

A proportional integral derivative with double phase lead controller was proposed. Its design was based on a linearization of a new nonlinear control model of the glucose-insulin system in type 1 diabetes mellitus (T1DM) patients validated with the University of Virginia/Padova T1DM metabolic simulator. A 36 h scenario, including six unannounced meals, was tested in nine virtual adults. A previous trial database has been used to compare the performance of our controller with their previous results. The scenario was repeated 25 times for each adult in order to take continuous glucose monitoring noise into account. The primary outcome was the time BG levels were in target (70-180 mg/dl).

RESULTS

Blood glucose values were in the target range for 77% of the time and below 50 mg/dl and above 250 mg/dl for 0.8% and 0.3% of the time, respectively. The low blood glucose index and high blood glucose index were 1.65 and 3.33, respectively.

CONCLUSION

The linear controller presented, based on the linearization of a new easily identifiable nonlinear model, achieves good glucose control with low exposure to hypoglycemia and hyperglycemia.

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.