Bergman's Minimal Model Research Articles

Observer-based control for plasma glucose regulation in type 1 diabetes mellitus patients with unknown input delay.

This article introduces an observer-based control strategy tailored for regulating plasma glucose in type 1 diabetes mellitus patients, addressing challenges like unknown time-varying delays and meal disturbances. This control strategy is based on an extended Bergman minimal model, a nonlinear glucose-insulin model to encompass unknown inputs, such as unplanned meals, exercise disturbances, or delays. The primary contribution lies in the design of an observer-based state feedback control in the presence of unknown long delays, which seeks to support and enhance the performance of the traditional artificial pancreas by considering realistic scenarios. The observer and control gains for the observer-based control are computed through linear matrix inequalities formulated from Lyapunov conditions that guarantee closed-loop stability. This design deploys a soft and gentle dynamic response, similar to a natural pancreas, despite meal disturbances and input delays. Numerical tests demonstrate the scheme's effectiveness in glycemic level regulation and hypoglycemic episode avoidance.

Robust adaptive observer-based control of blood glucose level for type 1 diabetic patient

In this paper, an adaptive controller is designed to regulate the blood glucose level of type 1 diabetes mellitus while not all states of the system are measurable and also its parameters are unknown. The main goal in the control of diabetes is to preserve blood glucose level within a safe rang by a suitable injecting insulin rate to the patient. Herein, it is achieved by measuring the blood glucose level and proposed an observer based adaptive control system. In the proposed method, firstly, the dynamic equations of nonlinear Bergman minimal model (BMM) are transformed into a companion form. Then an adaptive observer is presented to simultaneously estimate the state variables and the system’s parameters. Afterward, based on the designed observer and using a new meal simulation model, an adaptive control is presented to bring back the blood glucose level to its safe range. The overall stability of the developed adaptive control is established using the Lyapunov direct method. Simulation results have been performed to verify the effectiveness of the proposed approach in tracking the desired blood glucose.

Analysis of the performances of various controllers adopted in the biomedical field for blood glucose regulation: a case study of the type-1 diabetes

Diabetes remains a critical global health concern that necessitates urgent attention. The contemporary clinical approach to closed-loop care, specifically tailored for insulin-dependent patients, aims to precisely monitor blood glucose levels while mitigating the risks of hyperglycaemia and hypoglycaemia due to erroneous insulin dosing. This study seeks to address this life-threatening issue by assessing and comparing the performance of different controllers to achieve quicker settling and convergence rates with reduced steady-state errors, particularly in scenarios involving meal interruptions. The methodology involves the detection of plasma blood glucose levels, delivery of precise insulin doses to the actuator through a control architecture, and subsequent administration of the calculated insulin dosage to patients based on the control signal. Glucose-insulin dynamics were modelled using kinetics and mass balance equations from the Bergman minimal model. The simulation results revealed that the PID controller exhibited superior performance, maintaining blood glucose concentration around the preferred threshold ∼98.8% of the time, with a standard deviation of 2.50. This was followed by RST with a success rate of 98.5% and standard deviation of 5.00, SPC with a success rate of 58% and standard deviation of 2.99, SFC with a success rate of 55% and standard deviation of 10.08, and finally LCFB with a rate of 10% and significantly higher standard deviation of 64.55.

Automated blood glucose regulation for nonlinear model of type-1 diabetic patient under uncertainties: GWOCS type-2 fuzzy approach.

Regulating blood glucose level (BGL) for type-1 diabetic patient (T1DP) accurately is very important issue, an uncontrolled BGL outside the standard safe range between 70 and 180mg/dl results in dire consequences for health and can significantly increase the chance of death. So the purpose of this study is to design an optimized controller that infuses appropriate amounts of exogenous insulin into the blood stream of T1DP proportional to the amount of obtained glucose from food. The nonlinear extended Bergman minimal model is used to present glucose-insulin physiological system, an interval type-2 fuzzy logic controller (IT2FLC) is utilized to infuse the proper amount of exogenous insulin. Superiority of IT2FLC in minimizing the effect of uncertainties in the system depends primarily on the best choice of footprint of uncertainty (FOU) of IT2FLC. So a comparison includes four different optimization methods for tuning FOU including hybrid grey wolf optimizer-cuckoo search (GWOCS) and fuzzy logic controller (FLC) method is constructed to select the bestcontroller approach. The effectiveness of the proposed controller was evaluated under six different scenarios of T1DP using Matlab/Simulink platform. A 24-h scenario close to real for 100 virtual T1DPs subjected to parametric uncertainty, uncertain meal disturbance and random initial condition showed that IT2FLC accurately regulate BGL for all T1DPs within the standard safe range. The results indicated that IT2FLC using GWOCS can prevent side effect of treatment with blood-sugar-lowering medication. Also stability analysis for the system indicated that the system operates within the stability region of nonlinear system.

Optimized type-2 fuzzy controller based on IoMT for stabilizing the glucose level in type-1 diabetic patients

Due to advancements in existing Internet of Medical Things (IoMT) systems and devices, the blood glucose level (BGL) for type-1 diabetic patients (T1DPs) is effectively and continually monitored and controlled by Artificial Pancreas. Because the regulation of BGL is a very complex process, many efforts have been conducted to design a powerful and effective controller for the exogenous insulin infusion system. The main objective of this study is to propose an optimized interval type-2 fuzzy (IT2F) based controller of artificial pancreas for regulation BGL of T1DP based on IoMT. The proposed controller should avoid the risk of hyperglycemia and hypoglycemia situations that T1DP faces during the infusion of exogenous insulin. The main contribution of this work is using meta-heuristic method called grey wolf optimizer (GWO) to tune the footprint of uncertainty for IT2F’s membership functions to inject the proper dose of insulin under different conditions. The nonlinear extended Bergman minimal model (EBMM) with uncertainty is used to represent the blood glucose regulation and represent the dynamics of meal disturbance in T1DP. The effectiveness and the performance of the proposed controller are investigated using MATLAB/Simulink platform. Simulation results show that the proposed controller can avoid both severe hypoglycemia and hyperglycemia for nominal parameters of the model, in addition to model under the presence of both parametric uncertainty and uncertain meal disturbance.

ADAPTIVE FUZZY BACKSTEPPING CONTROL FOR BLOOD GLUCOSE REGULATION

In this paper, we propose an adaptive type-2 fuzzy backstepping controller for blood glucose regulation. To mimic at best the behavior of a real pancras, the nonlinear Bergman minimal model is adopted. To deal with the strict feedback form of this model, we use backstepping algorithm. To overcome the knowledge of the several parameters of model to deduce the control laws, we use adaptive type-2 fuzzy systems to obtain the control signals. The stability of the closed loop system is proven using Lypunov theory. A simulation example with a comparative study is given to schow the performances of the proposed approach.

Editorial for the special issue “Control‐theoretic approaches for systems in the life sciences”

Editorial for the special issue “Control<scp>‐theoretic</scp> approaches for systems in the life sciences”

Splanchnic Infusions of Short Chain Fatty Acids Do Not Change Insulin Sensitivity of Pigs

Long-term ingestion of high fiber diets is associated with reduced glucose concentrations during fasting and improved glucose tolerance (KG) in humans. Our objective was to determine if the beneficial effects of fiber were attributable to increased production of short-chain fatty acid (SCFA) in the large intestine. Effects of SCFA on insulin sensitivity (Si), glucose effectiveness (SG), KG and baseline concentrations of glucose, insulin, glucagon and free fatty acids were examined in unfed 20–50 kg pigs (n = 6). Animals randomly received separate portal infusions (0.32 mL·min-1) of saline, acetic, propionic, and butyric acid solutions (0.01 mmol SCFA kg body weight-1·min-1) for 7-d periods. On d 7, somatostatin and tolbutamide modified frequently sampled intravenous glucose tolerance tests were performed. Si and SG were calculated using Bergman's Minimal-Model. KG was determined by regression of log glucose curve versus time. Si, SG and KG values did not differ among the treatments (P > 0.05). Baseline concentrations of glucose, insulin, glucagon and free fatty acids were unaffected by infusion treatment (P > 0.05). Our results suggest that SCFA delivery is not directly responsible for improvements in glucose metabolism observed with long-term ingestion of high fiber diets.

Mathematical Modelling of Combined Intervention Strategies for the Management and Control of Plasma Glucose of a Diabetes Mellitus Patient: A System Dynamic Modelling Approach

With the rapid increase of diabetes mellitus cases in the world, management and control of the disease has become a complex and highly dynamic process. This challenge requires a multifaceted approach to manage and control the complications associated with the hyperglycaemia or hypoglycaemia conditions. This paper presents a mathematical model for determining the influence of combined intervention strategies in the management and control for the plasma glucose of the type II diabetes. System dynamics (SD) techniques were used in modelling the sub-compartments of biological systems of an Identifiable Patient (IP). The system dynamic model developed gave an illustration on how typical glucose-insulin dynamics occur at different intervention strategies involving varying amounts of carbohydrates taken, intensity of physical exercises, stress levels and the amount of exogenous insulin administered. The model was conceptualized within a semi-closed loop system representing the patient ecosystem by extending the Bergman Minimal Model. Stochastic differential equations (SDE) were used to capture the non-linear, continuous time varying interactions of the measurements associated with plasma glucose-insulin dynamics. The estimated results from the model showed combined intervention strategies of reduced amounts of carbohydrates intake, reduced stress levels and varying moderately high-to-low exercise intensity at a constant unit of exogenous insulin produced good plasma glucose levels control.

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.

Positive input observer‐based controller design for blood glucose regulation for type 1 diabetic patients: A backstepping approach

In practice, there are many physical systems that can have only positive inputs, such as physiological systems. Most conventional control methods cannot ensure that the main system input is positive. A positive input observer‐based controller is designed for an intravenous glucose tolerance test model of type 1 diabetes mellitus (T1DM). The backstepping (BS) approach is employed to design the feedback controller for artificial pancreas (AP) systems, based on the Extended Bergman's Minimal Model (EBMM). The EBMM represents the T1DM in terms of the blood glucose concentration (BGC), insulin concentration, and plasma level and the disturbance of insulin during medication due to either meal intake or burning sugar by doing some physical exercise. The insulin concentration and plasma level are estimated using observers, and these estimations are applied as feedback to the controller. The asymptotic stability of the observer‐based controller is proved using the Lyapunov theorem. Moreover, it is proved that the system is bounded input‐bounded output (BIBO) stable in the presence of uncertainties generated by uncertain parameters and external disturbance. For realistic situations, we consider only the BGC to be available for measurement and additionally inter‐and intra‐patient variability of system parameters is considered.

Correlation in Dose-Response to Rapid- and Long-Acting Insulin for People with Type 1 Diabetes.

In diabetes, it can become necessary to switch between pump- and pen-based insulin treatment. This switch involves a translation between rapid- and long-acting insulin analogues. In standard-of-care translation algorithms, a unit-to-unit conversion is applied. However, this simplification may not fit all individuals. In this paper, we investigate the correlation between dose-response to rapid- and long-acting insulin in the same individual, and compare the correlation across individuals. As a measure of dose-response, we estimate the insulin sensitivity in clinical data from 25 subjects with type 1 diabetes. For parameter estimation, we use maximum likelihood with a continuous-discrete extended Kalman filter and Bergman's minimal model. The results show a weak correlation between insulin sensitivity to rapid- and long-acting insulin across individuals. On this sparse data set, the analysis suggests that the standardized unit-to-unit translation between insulin analogues may not benefit all subjects.

Insulin infusion rate control in type 1 diabetes patients using information-theoretic model predictive control

The present paper examines the glucose regulation system in patients with type 1 diabetes. To this end, the nonlinear Bergman's minimal model with parametric uncertainty, which represents this system, is converted to a fractional-order model using Caputo’s definition. As the recent literature suggests, the noise in the interstitial glucose concentration continuous control sensors is considered non-Gaussian. With this in mind, first an optimal non-fragile H∞ observer is designed for a Lipschitz nonlinear fractional-order system including parametric uncertainty and input disturbance in order to estimate the unknown states. Second, feedback linearization method for nonlinear fractional-order system with parametric uncertainty is used, after which the linearized system is used to design controller for diabetes mellitus patients. Third, robust fractional model predictive control (RFMPC) with a minimax optimization approach is presented for closed-loop insulin delivery. Finally, the performance of the proposed controller under non-Gaussian measurement noise is enhanced with a suitable choice of a cost function based on generalized correntropy (GC), whereas the performance of a mean square error (MSE)-based controller is simulated. The results indicate that not only the proposed controller performs better under non-Gaussian conditions but also it effectively recovers and maintains the glucose concentration within the desired range by appropriately infusing insulin under parametric uncertainty and meal disturbances.

Minimally-Invasive and Efficient Method to Accurately Fit the Bergman Minimal Model to Diabetes Type 2.

Diabetes mellitus is a global burden that is expected to grow by 2030. This will increase the need for prevention, diagnosis and treatment of diabetes. Animal and individualized in silico models will allow understanding and compensation for inter and intra-individual differences in treatment and management strategies for diabetic patients. The method presented here can advance the concept of personalized medicine. Twenty experiments were performed with Sprague-Dawley rats with streptozotocin induced experimental diabetes in which the insulin-glucose response curve was recorded over 60-100min using only an insulin pump and a percutaneous glucose sensor. The information was used to fit the five-parameter Bergman Minimal Model to the experimental results using a genetic algorithm with a root-mean-squared optimization rule. The Bergman Minimal Model parameters were estimated with high accuracy, low prediction bias, and low average root-mean-squared error of 15.27mg/dl glucose. This study demonstrates a simple method to accurately parameterize the Bergman Minimal Model. We used Sprague-Dawley rats since their physiology is close to that of humans. The parameters can be used to objectively characterize the physiological severity of diabetes. In this way, planned treatments can compensate for natural variations of conditions both inter and intra patients. Changes in parameters indicate the patient's diabetic condition using values of glucose effectiveness ( ) and insulin sensitivity ( ). Quantifying the diabetic patient's condition is consistent with the trend toward personalized medicine. Parameter values can also be used to explain atypical research results of other studies and increase understanding of diabetes.

Parameter identification and state estimation for a diabetic glucose‐insulin model via an adaptive observer

AbstractIn this article, an adaptive observer is designed for patients with Type 1 Diabetes Mellitus. The adaptive observer, synthesized using the so‐called Bergman's Minimal Model, simultaneously estimates the states and the parameter corresponding to the insulin‐independent glucose disappearance rate. The adaptive observer deals with parameter uncertainties, whereas the food intake is regarded as an external disturbance. The adaptive observer relies on intravenous glucose measurements. The state estimation error converges to a neighborhood of the origin despite the effects of the external disturbances and uncertainties, while the parameter estimation error converges in a fixed time to a neighborhood of the origin. The adaptive observer synthesis is given by a constructive method based on linear matrix inequalities. Simulation results show the feasibility of the proposed scheme. Moreover, the approach is validated in UVA/Padova metabolic simulator for ten in silico adult patients.

Glucose-insulin dynamics: a grey-box analogy

Regulating plasma glucose levels for both type I and type II diabetic patients is a challenging task. Understanding the effects of meals taken, the physical exercises and stress levels will contribute significantly to the overall management of the plasma glucose levels. This paper provides an extension of the Bergman minimal model to represent 12-compartmental models associated with meals taken, physical exercises and stress levels interactions within a semi-closed loop system using stochastic differential equations (SDE). The mathematical modelling is constructed following the grey-box model analogy as applied on an identifiable patient. Obtained results from the study demonstrate the predictive capability of the model to be good and its sensitivity is enhanced with increased dataset.

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.

Variable structure robust controller design for blood glucose regulation for type 1 diabetic patients: A backstepping approach

Diabetes mellitus type 1 occurs when β‐cells in the pancreas are destroyed by the immune system. As a result, the pancreas cannot produce adequate insulin, and the glucose enters the cells to produce energy. To elevate the glycaemic concentration, sufficient amount of insulin should be taken orally or injected into the human body. Artificial pancreas is a device that automatically regulates the level of body insulin by injecting the requisite amount of insulin into the human body. A finite‐time robust feedback controller based on the Extended Bergman Minimal Model is designed here. The controller is designed utilizing the backstepping approach and is robust against the unknown external disturbance and parametric uncertainties. The stability of the system is proved using the Lyapunov theorem. The controller is exponentially stable and hence provides the finite‐time convergence of the blood glucose concentration to its desired magnitude. The effectiveness of the proposed control method is shown through simulation in MATLAB/Simulink environment via comparisons with previous studies.

MODIFICATION OF THE MINIMAL BERGMAN MODEL OF THE "INSULIN-GLUCOSE" SYSTEM AND ITS IMPLEMENTATION IN MATLAB/SIMULINK

The article discusses a modification of Bergman's minimal mathematical model of the "insulin-glucose" system, which allows simulating controlled exogenous sources of glucose and insulin into the patient's blood on the model and investigating the dynamics of changes in their concentrations in normal conditions, in type I DM and type II DM. A modeling scheme is presented in graphic notations of the MatLab / Simulink computer mathematics system and a number of computational experiments on it are described to determine the type of glycemic profiles of glucose and insulin concentration in the patient's blood in the noted situations. The fundamental possibility of using model mappings in the MatLab/Simulink environment for the study and tuning of the loop for automatic regulation of the "insulin-glucose" balance in the patient's blood using a controlled insulin pump is demonstrated. It was also found that the modified minimal model can be customized for a specific patient with diabetes, which makes it possible to use it to solve the problems of individual prediction of the development of a diabetic disease in a specific patient. In addition, the described model makes it possible to recreate and virtually investigate various conditions and cases on it that affect the dynamics of insulin and glucose concentrations in the patient's blood, for example, when he performs physically stressed activities, in the presence of the effects of “aging” of insulin-producing cells in the pancreas. iron, etc.

71 Distribution of carbohydrate concentrated feeds in 8 meals/24H during the first winter improves feed efficiency without affecting carbohydrate metabolism nor incidence of osteochondrosis in foals

Osteochondrosis is a multifactorial pathology that affects up to 75% of equids and impacts their sports career. Feeding excess dietary concentrates, thus inducing increased blood glucose and insulin peaks associated with meals, has been linked to an increased incidence of osteochondrosis in foals. The objective of the study was to analyze the effects of different of concentrate distribution in 2 or 8 meals throughout day and night on glucose metabolism and the incidence of osteochondrosis in foals. Anglo-Arabian foals born to the same sire and bred in the same facilities were used from 6 to 18 mo of age over a 2-year period. At weaning (6 mo), they were housed in stables. After an adaptation period, they received 2.5–3kg of cereal pellets in 2 meals (year 1, 9 females (F) and 10 males (M) and year 2, 5 F and 6 M) or in 8 meals/d (year 1, 10 F, 10 M and year 2, 5 F and 4 M) using an automatic horse feeder (AHF) until 12 mo of age, when the males were gelded and all foals sent to pasture. At 6, 12 and 18 mo, Frequent Sampling Intravenous Glucose Tolerance Tests (FSIVGTT) and joint x-rays were performed. Glucose and insulin FSIVGTT data were analyzed with Bergman minimal model (MinMod software). Data were analyzed using chi2 or linear model test with permutations according to data type. Nutritional intakes per individual were not different in overall terms between year, groups nor sex. Foals receiving 8 meals/day during their first winter had a better average daily gain (562.2 ± 55.0 g/d for 2 meals/d vs 616.1 ± 100.1g/d for 8 meals/d, P < 0.01) and were heavier (307.4 ± 23.4 kg for 2 meals/d vs 314.6 ± 23.2 kg for 8 meals/d, P < 0.05) at 12 mo of age. Withers' height, response to FSIVGTT and incidence of osteochondrosis (overall 23.7% of foals with at least one joint affected joint at 18 mo) did not differ between groups. The overall foal response to glucose challenge was higher at 18 mo of age ( P < 0.0001) and in females ( P < 0.01). In conclusion, foals' glucose metabolism evolves with age and differs between males and females, as previously described. Feeding concentrated diet 8 times/day does not modify glucose metabolism nor the prevalence of osteochondrosis but slightly increases feed efficiency. Thus, the use of a AHF could provide better foal growth but current data does not support any effect on osteochondrosis.