Glucose-insulin Regulatory System Research Articles

Optimizing Blood Glucose Regulation in Type 1 Diabetes Patients via Genetic Algorithm-Based Fuzzy Logic Controller Considering Substantial Meal Protocol

Effective management of blood glucose levels in individuals with type 1 diabetes, especially after meals, is crucial for diabetes care. Artificial pancreas systems (APS) perform automated insulin delivery in subjects with type 1 diabetes mellitus (T1DM). In this study, an optimized fuzzy logic controller was designed to achieve a euglycemic range after a substantial meal intake. All in silico simulations were performed using the MATLAB/Simulink environment, leveraging control variability grid analysis (CVGA), and the performance of the controller was evaluated. The proposed controller is based on a fuzzy-logic control law designed in three stages. First, a nonlinear framework of the glucose-insulin regulatory system was identified based on the heavy meal protocol of three patients given as follows: for subject ID 117-1, a total of 295 gCHO; for subject ID 126-1, 236 gCHO; and subject ID 128-1, 394 gCHO over a day. Then, an iterative tree structure was employed to establish a stabilizing control rule for insulin delivery, integrating inputs from two Mamdani Fuzzy Inference System (FIS) objects. Finally, a genetic algorithm refines the control system by fine-tuning the uncertainty of the fuzzy membership functions. Two scenarios were considered for three patients to assess the performance of the proposed controller. The results indicated its effectiveness under various conditions, achieving a time in the range of 61.25%, 71% and 61.10% respectively for the three subjects. The obtained results are analyzed and compared with IMC and multi-objective output feedback controllers. The findings of the study reveal that the proposed controller shows promising advancements in tailored strategies for type 1 diabetes patients, outperforming the other controllers in terms of blood glucose regulation.

Dynamical modeling the effect of glucagon-like peptide on glucose–insulin regulatory system based on mice experimental observation

As an emerging global epidemic, type 2 diabetes mellitus (T2DM) represents one of the leading causes of morbidity and mortality worldwide. Existing evidences demonstrated that glucagon-like peptide-1 (GLP-1) modulate the glucose regulatory system by enhancing the β-cell function. However, the detailed process of GLP-1 in glycaemic regulator for T2DM remains to be clarified. Thus, in this study, we propose an Institute of Cancer Research (ICR) mice high fat and cholesterol dietary experimental data-driven mathematical model to investigate the secretory effect of GLP-1 on the dynamics of glucose–insulin regulatory system. Specifically, we develop a mathematical model of GLP-1 dynamics as part of the interaction model of β-cell, insulin, and glucose dynamics. The parameter estimation and data fitting are in agreement with the data in mice experiments In addition, uncertainty quantification is performed to explore the possible factors that influence the pathways leading to the pathological state. Model analyses reveal that the high fat or high cholesterol diet stimulated GLP-1 plays an important role in the dynamics of glucose, insulin and β cells in short-term. These results show that enhanced GLP-1 may mitigate the dysregulation of glucose–insulin regulatory system via promoting the β cells function and stimulating secretion of insulin, which offers an in-depth insights into the mechanistic of hyperglycemia from dynamical approach and provide the theoretical basis for GLP-1 served as a potential clinical targeted drug for treatment of T2DM.

Dynamical analysis of a glucose-insulin regulatory system with insulin-degrading enzyme and multiple delays.

This paper investigates the dynamics of a glucose-insulin regulatory system model that incorporates: (1) insulin-degrading enzyme in the insulin equation; and (2) discrete time delays respectively in the insulin production term, hepatic glucose production term, and the insulin-degrading enzyme. We provide rigorous results of our model including the asymptotic stability of the equilibrium solution and the existence of Hopf bifurcation. We show that analytically and numerically at a certain value the time delays driven stability or instability occurs when the corresponding model has an interior equilibrium. Moreover, we illustrate the oscillatory regulation and insulin secretion via numerical simulations, which show that the model dynamics exhibit physiological observations and more information by allowing parameters to vary. Our results may provide useful biological insights into diabetes for the glucose-insulin regulatory system model.

Nondimensional diabetes indices for accurate diagnosis of diabetic subjects

ObjectivesNondimensional indices or numbers can provide a generalized approach for integrating several biological parameters into one Nondimensional Physiological Index (NDPI) that can help characterize an abnormal state associated with a particular physiological system. In this paper, we have presented four Nondimensional Physiological Indices (NDI, DBI, DIN, CGMDI) for the accurate detection of diabetes subjects. MethodologyThe NDI, DBI, and DIN diabetes indices are based on the Glucose-Insulin Regulatory System (GIRS) Model, represented by the governing differential equation of blood glucose concentration response to the glucose input rate. The solutions of this governing differential equation are employed to simulate the clinical data of the Oral Glucose Tolerance Test (OGTT), and thereby evaluate the GIRS model-system parameters, which are distinctly different for the normal and diabetic subjects. Then these GIRS model parameters are combined to form singular nondimensional indices: NDI, DBI, and DIN. When these indices are applied to the OGTT clinical data, we get significantly different values for normal and diabetic subjects.The DIN diabetes index is a more objective index involving extensive clinical studies, incorporating the GIRS model parameters as well as some key clinical-data markers (based on the information gained from the model clinical simulation and parametric identification).We have then developed another CGMDI diabetes index based on the GIRS model, for the assessment of diabetic subjects using the glucose levels measured by wearable continuous glucose monitoring (CGM) devices. Clinical study and resultsFor the DIN diabetes index, our clinical study comprised of 47 subjects (26 normal and 21 diabetics). After applying DIN to the OGTT data, a Distribution Plot of DIN was developed, displaying the ranges of DIN for (i) normal (i.e., non-diabetic) subjects with no risk of becoming diabetic, (ii) normal subjects at risk of becoming diabetic, (iii) borderline diabetic subjects who can become normal (with diet control and treatment), and (iv) distinctly diabetic subjects. This distribution plot is shown to distinctly separate normal subjects from diabetic subjects and also from subjects at risk of becoming diabetic. ConclusionsIn this paper, we have developed several NDPIs in the form of novel nondimensional diabetes indices for the accurate detection of diabetes and diagnosis of diabetic subjects. These nondimensional diabetes indices can enable precision medical diagnostics of diabetes, and thereby also help to develop interventional guidelines for lowering glucose levels by means of insulin infusion. The novelty of our proposed CGMDI is that it utilizes the glucose value monitored by the CGM wearable device. In the future, an app can be developed to use the CGM data in the CGMDI to enable precision diabetes detection.

Section I - Pancreatic and Glucose-Insulin Regulatory System Engineering and Medical Assessment

Section I - Pancreatic and Glucose-Insulin Regulatory System Engineering and Medical Assessment

Sample-data output-feedback parameter variable control of glucose for type 1 diabetes mellitus patients

This paper presents a new approach for nonlinear sampled-data output-feedback control of blood glucose concentration (BGC) in patients with type 1 diabetes mellitus (T1DM). The Bergman minimal model (BMM) describing the glucose-insulin regulatory system is framed as a linear parameter-varying (LPV) model that the sampled glucose measurement with the quantized insulin infusion is considered as input delay. The proposed method utilizes the input-delay approach based on a parameter-dependent Lyapunov–Krasovskii functional (LKF) and provides the parameterized matrix inequality conditions for the design of the controller. Using the slack variables, the design conditions are converted to a new form that can achieve feasible solutions by solving a limited number of bilinear matrix inequality. The proposed architecture guarantees stability in a compact set of states for all the trajectories with the parametric uncertainty to address the issue of inter-patient variability. Simulation results confirm that the proposed sampled-data static output-feedback LPV controller with only glucose measurement regulates the BGC despite the parametric uncertainty and meal disturbances in T1DM patients.

Chaos and Its Control in a Fractional Order Glucose-insulin Regulatory System

Chaos and Its Control in a Fractional Order Glucose-insulin Regulatory System

Stability analysis for Nabla discrete fractional-order of Glucose–Insulin Regulatory System on diabetes mellitus with Mittag-Leffler kernel

In this paper, we study an existence theory as well as stability results to the new fractional Nabla difference biological model of glucose–insulin regulatory system (GIRS) on diabetes mellitus involving the Atangana Baleanu–Caputo (ABC) derivative. We consider the proposed model under ABC derivative, and it has the nonsingular Mittag-Leffler function as its kernel. We utilize the fixed point technique for the existence and uniqueness analysis. The stability of the concerned solution in Hyers–Ulam sense is also investigated. Further to derive the approximate solution in the form of series to the considered model, we use iterative technique method. Numerical simulations are given to support the theoretical results. The results show that order of the fractional derivative has a significant effect on the dynamic process. Many informations on the dynamics of GIRS in diabetes mellitus were obtained using this model. It is recognized as a deterministic fractional Nabla difference model for diabetes mellitus that provides a better control approach at fractional values for the development of an artificial pancreas.

A Multi-Agent Approach Used to Predict Long-Term Glucose Oscillation in Individuals with Type 1 Diabetes

The glucose–insulin regulatory system and its glucose oscillations is a recurring theme in the literature because of its impact on human lives, mostly the ones affected by diabetes mellitus. Several approaches have been proposed, from mathematical to data-based models, with the aim of modeling the glucose oscillation curve. Having such a curve, it is possible to predict when to inject insulin in type 1 diabetes (T1D) individuals. However, the literature presents prediction horizons of no longer than 6 h, which could be a problem considering their sleeping time. This work presents Tesseratus, a model that adopts a multi-agent approach used to combine machine learning and mathematical modeling to predict the glucose oscillation for up to 8 h. Tesseratus can support endocrinologists and provide personalized recommendations for T1D individuals to keep their glucose concentration in the ideal range. It brings pioneering results in an experiment with seven real T1D individuals. Using the Parkes error grid as an evaluation metric, it can be depicted that 93.7% of measurements fall in zones A and B during the night period with MAE 27.77 mg/dL. It is our claim that Tesseratus will be a reference for the classification of a glucose prediction model, supporting the mitigation of long-term complications in the T1D individuals.

Bernoulli wavelet method for non-linear fractional Glucose–Insulin regulatory dynamical system

In this paper, we propose a model that explains the glucose–insulin regulatory system (GIRS). The literature has demonstrated that fractional-order analysis can uncover new aspects of complex systems that were not previously explored. As a result of our studies, the GIRS is stable in its non-linear fractional-order form. Each numerical investigation is derived in order to demonstrate the effectiveness and applicability of fractional order analysis, including the Toufik–Atangana method and the Bernoulli wavelet operational matrix method (BWOMM). An unregulated glucose–insulin system causes a wide variety of biological disorders. These studies may permit a deeper understanding of the regulatory system.

Master–slave synchronization for glucose–insulin metabolism of type-1 diabetic Mellitus model based on new fractal–fractional order derivative

Type-1 diabetes mellitus (T1DM) is one of the most extensive diseases in the world. In this disorder, a malfunction occurs in the glucose–insulin regulatory system when one intakes food. Therefore, the synchronization of T1DM and perturbed T1DM models are necessary to transform the disturbance behavior of T1DM into a typical T1DM model. In this paper, a type-1 diabetic mellitus glucose–insulin metabolism (T1DMGIM) model is concerned with a new fractal–fractional operator β∈(0,1],η∈(0,1] by adding food intake as a disturbance to the plant system. A new generalized differentiation operator is introduced as the convolution of the power law. This new operator is based on the fractal–fractional differentiation and integration operators in the Riemann–Liouville (R-L) sense. Sufficient conditions are achieved for the existence, uniqueness, and stability of an error T1DMGIM model by employing the Mönch contraction principle. Finally, numerical simulations are provided to verify the theoretical results.

A methodical survey of mathematical model-based control techniques based on open and closed loop control approach for diabetes management

Disturbance of blood sugar level is controlled through well-known biomechanical feedback loops: high levels of glucose in blood facilitate to release insulin from the pancreas which accelerates the absorption rate of cellular glucose. Low glucose levels encourage to release pancreatic glucagon which induces glycogen breakdown to glucose in the liver. These bio-control systems do not function properly in diabetic patients. Though the control of disease seems intuitively easy, in real life, due to many differences in structure by diet and fasting, exercise, medications, patient’s profile and other stressors, it is not that easy. The mathematical models of the glucose-insulin regulatory system follow the patient’s physiological conditions which make it difficult to identify and estimate all the model parameters. In this paper, we have given a systematic literature review on mathematical models of the diabetic patients, and various kinds of disease control techniques through the development of open and closed loop insulin deliver command system and optimization of exogenous insulin rate. It demonstrates the open and closed loop type model-based control strategies underlying the assumptions of the concerned models. The combination of mathematical model with control strategies such as genetic algorithm (GA), neural network (NN), sliding mode controller (SMC), model predictive controller (MPC), and fuzzy logic control (FLC) has been considered, which provides an overview of this area, highlighting the control profile over the diabetic model with promising clinical results, outlining key challenges, and identifying needs for the future research. Also, the significance of these control algorithms has been discussed in the presence of the noises, the controller’s robustness and various other disturbances. It provides substantial information on diabetes management through various control techniques.

Automatic Artificial Pancreas Systems Using an Intelligent Multiple-Model PID Strategy.

In this paper, an individualized intelligent multiple-model technique is proposed to design automatic artificial pancreas (AP) systems for the glycemic regulation of type 1 diabetic patients. At first, using the multiple-model concept, the insulin-glucose regulatory system is mathematically identified by constructing some local models. In this step, trade-offs between the number of local models and the complexity of the overall closed-loop system are made by defining and solving a bi-objective optimization problem. Then, optimal AP systems are designed by tuning a bank of proportional-integral-derivative (PID) controllers via the genetic algorithm (GA). A fuzzy gain scheduling strategy is employed to determine the participation percentages of the PID controllers in the control action. Finally, two safety mechanisms, called insulin on board (IOB) constraint and pump shut-off, are installed in the AP systems to enhance their performance. To assess the proposed AP systems, in silico experiments are performed on virtual patients of the UVA/Padova metabolic simulator. The obtained results reveal that the proposed intelligent multiple-model methodology leads to AP systems with limited hyperglycemia and no severe hypoglycemia.

Analysis of a Fractional-order Glucose-Insulin Biological System with Time Delay

In the human glucose-insulin regulatory system, diverse metabolic issues can arise, including diabetes type I and type II, hyperinsulinemia, hypoglycemia, etc. Therefore, the analysis and characterization of such a biological system is a must. It is well known that mathematical models are an excellent option to study and predict natural phenomena to some extent. On the other hand, fractional-order calculus provides a generalization of derivatives and integrals to arbitrary orders giving us a framework to add memory properties and an extra degree of freedom to the mathematical models to approximate real-world phenomena with higher accuracy. In this work, we introduce a fractional-order version of a mathematical model of the glucose-insulin regulatory system. Using the fractional-order Caputo derivative, we can investigate different concentration rates among insulin, glucose, and healthy beta cells. Additionally, the model incorporates two time-lags to represent the elapsed time in insulin secretion in response to blood glucose level and the delay in glucose drop due to increased insulin concentration. Analytical results of the equilibrium points and their corresponding stability are given. Numerical results, including phase portraits and bifurcation diagrams, reveal that the fractional-order increases the chaotic regions, leading to potential metabolic problems. Vice versa, the system seems to work correctly when the behavior evolves to periodic windows.

A Digital Glucose Control Strategy via Subcutaneous Insulin Infusion

In this paper, the plasma glucose regulation problem for Type 2 diabetic patients by subcutaneous insulin infusion is studied. A nonlinear time-delay model of the glucose-insulin regulatory system, which takes into account the subcutaneous infusion of insulin, is exploited for the design of a quantized sampled-data static state feedback glucose controller. Quantization in both input/output channels is considered. Spline interpolation methodologies are used in order to obtain an approximation of suitable needed past values of the system state that cannot be always available from the buffer. The stabilization in the sample-and-hold sense is used in order to prove that the proposed digital glucose regulator ensures the semi-global practical stability of the related closed-loop tracking error system, with arbitrarily small final target ball. The proposed digital glucose regulator is validated through simulations.

Delay-Independent regulation of blood glucose for type-1 diabetes mellitus patients via an observer-based predictor feedback approach by considering quantization constraints

Diabetes, as a widespread chronic disease, is caused by the increase of blood glucose concentration (BGC) due to pancreatic insulin production failure and/or insulin resistance in the body. The artificial pancreas (AP) known as a closed-loop insulin delivery control system consists of a glucose sensor for BGC measurement, a control algorithm for calculation of exogenous insulin delivery rate (IDR), and an insulin infusion pump. The AP provides a closed-loop glucose-insulin regulatory system for type-1 diabetes mellitus (T1DM) patients in order to effectively reduce the high BGC level. In this paper, we aim to design a controller in order to regulate the BGC of T1DM patients at its basal value with considering meal disturbance in the system. We confront with different problems for glucose control such as sampled and quantized glucose measurement by the sensor, quantized IDR by the insulin infusion pump, and an unknown input delay of the insulin infusion pump as the actuator of the control system. The bergman minimal model (BMM) as the most famous model for describing the glucose-insulin regulatory system is reviewed and the delay-independent observer for the estimation of the system’s state vector from the sensor output (sampled and quantized BGC) is considered. Moreover, the observer works on the basis of an event-triggered strategy in order to avoid unnecessary signal updating. At the end, the IDR calculated by the proposed delay-independent truncated predictor output feedback controller (based on the observer’s output) is delivered to the T1DM patient. A sufficient condition on the insulin infusion pump delay’s upper bound value in order to guarantee the ultimate boundedness of the glucose-insulin regulatory system under the mentioned constraints is derived. Also, the nonoccurrence of Zeno behavior in the proposed control system is proved. Numerical simulation results confirm the effectiveness of the designed controller in the presence of meal disturbance, unknown input delay, and quantization errors for blood glucose regulation of the glucose-insulin regulatory system in T1DM patients. Moreover, a pre-clinical verification of the applicability of the proposed glucose controller is carried out on a large-scale and multi-compartmental model that is the base of the UVA/PADOVA Type-1 Diabetes Simulator.

Bifurcation and Stability Analysis of Glucose-Insulin Regulatory System in the Presence of β-Cells

Bifurcation and Stability Analysis of Glucose-Insulin Regulatory System in the Presence of β-Cells

Numerical Simulation of Free Convection in a Three-Dimensional Enclosure Full of Nanofluid with the Existence a Magnetic Field

Blood glucose automatic regulation achievement depends on the robustness of the used control algorithm. However, some constraints were encountered due to the human glucose-insulin regulatory system’s complexity. It is proposed to tackle such a goal through the development of a robust synergetic control algorithm. An adaptive approach is integrated into this synergetic control scheme to handle disturbances and parameters variations. Multiple meal disturbances often occur daily as well as some other stochastic noises making efficient glucose regulation a tough challenge addressed in this paper via a new synergetic scheme. Simulation results show a robust function during multiple meal disturbances with good noise rejection.

Quantized sampled-data static output feedback control of the glucose–insulin system

In this paper, the plasma glucose regulation problem for type 2 diabetic patients is studied. A nonlinear time-delay model of the glucose–insulin regulatory system is exploited to design a quantized sampled-data static output feedback control, using only glucose measurements. It is shown that the proposed control law achieves semiglobal practical stability of the related quantized sampled-data closed-loop glucose–insulin system with arbitrary small steady-state tracking error. The controller involves past values of the glucose, which may not be available in the buffer, for instance because of non-uniform sampling. Such a drawback is overcome by means of spline interpolation. Furthermore, quantization in both input and output channels are taken into account. A pre-clinical validation, concerning the performances of the proposed glucose regulator, is carried out by means of a well-known simulator of diabetic patients, broadly accepted for testing insulin infusion therapies. The simulation results pave the way for further clinical evaluation.

Close Loop Design in Glucose Insulin Model with Effect of Physical Exercise

The minimal mathematical models for exercise and its extension is included the major exercise effects on plasma glucose and insulin levels. Model expectations for glucose and insulin dynamics are steady with current literature statistics. The extended model offers innovative disruption test stage for the enlargement of closed-loop glucose control algorithms. Stability analysis as well as qualitative analysis has been made for the model. We treat the controllability and observability of the system for glucose insulin regulatory system during feedback design. Numerical simulation has been carried out to check the effectiveness and actual behavior for the proposed system.