Modeling the physiological glucose-insulin system on normal and diabetic subjects

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.

Socioeconomic Level and the Relationship in Glycemic Behavior in the Mexican Population. A Nutritional Alternative Focused on Vulnerable Populations

In this study, numerical approximations were generated to analyze the behavior of glycemic variations in the non-diabetic population of the Mexican republic. The main objective of this work is to obtain an overview of the glycemic variations in the non-diabetic population from different socioeconomic statuses in Mexico (Medium-high, medium, and low). Thus, evaluating the effect on the glucose level under a healthy diet considering the socioeconomic capabilities of the population. Through the national health and nutrition survey of Mexico 2020 and the Mexican food base, 1420 virtual patients were proposed (522 low status, 485 medium status and 413 Medium-High status) focused on simulating the glycemic behavior in each of the survey participants. Considering that the average food expenditure of the Mexican population is $107.00 MXN, and the cost of a healthy diet is $66.50 MXN, the economic sustainability of the Mexican population to adopt a healthy diet is revealed. The particularity of this work is focused on obtaining diverse data that are difficult to access in the development of population analyses. Such is the case of the approach proposed for different socioeconomic statuses. In this way, the proposed methodology provides a framework for complementary research contributions to the subject.

A Glucose-Only Model to Extract Physiological Information from Postprandial Glucose Profiles in Subjects with Normal Glucose Tolerance

BACKGROUND

Current mathematical models of postprandial glucose metabolism in people with normal and impaired glucose tolerance rely on insulin measurements and are therefore not applicable in clinical practice. This research aims to develop a model that only requires glucose data for parameter estimation while also providing useful information on insulin sensitivity, insulin dynamics and the meal-related glucose appearance (GA).

METHODS

The proposed glucose-only model (GOM) is based on the oral minimal model (OMM) of glucose dynamics and substitutes the insulin dynamics with a novel function dependant on glucose levels and GA. A Bayesian method and glucose data from 22 subjects with normal glucose tolerance are utilised for parameter estimation. To validate the results of the GOM, a comparison to the results of the OMM, obtained by using glucose and insulin data from the same subjects is carried out.

RESULTS

The proposed GOM describes the glucose dynamics with comparable precision to the OMM with an RMSE of 5.1 ± 2.3 mg/dL and 5.3 ± 2.4 mg/dL, respectively and contains a parameter that is significantly correlated to the insulin sensitivity estimated by the OMM (r = 0.7) Furthermore, the dynamic properties of the time profiles of GA and insulin dynamics inferred by the GOM show high similarity to the corresponding results of the OMM.

CONCLUSIONS

The proposed GOM can be used to extract useful physiological information on glucose metabolism in subjects with normal glucose tolerance. The model can be further developed for clinical applications to patients with impaired glucose tolerance under the use of continuous glucose monitoring data.

H∞ controller and observer synthesis with delay and nonlinear perturbation of double diabetes systems

Patient having type 1 diabetes mellitus (having insulin resistance experience) cannot be treated solely by treatment procedure of type 1 patient nor does treatment employed for type 2 diabetes work for such patient. This type of diabetes patient needs a specific insulin injection procedure. For continuous insulin injection, the patient has to be classified as a different group from type 1 and type 2 patient. The patients experiencing both type 1 and 2 are called double diabetes mellitus (DDM) patient. Dynamic behavior of the patient was presented in delay differential equation (DDE). Based on the developed DDE of DDM model, controllers and observers fulfilling H_∞ norm bound are designed for this specific group of diabetes mellitus patient. Also, a nominal controller and a nominal observer are synthesized to check the proposed controller's ability for disturbance rejection, which is the glucose intake. The performance of the designed controller and observer is evaluated for a population of simulated patients. It shows that controller and observer are able to regulate and estimate, respectively, glycaemic for population of double diabetes patients.

A mathematical model of food intake

The metabolic, hormonal and psychological determinants of the feeding behavior in humans are numerous and complex. A plausible model of the initiation, continuation and cessation of meals taking into account the most relevant such determinants would be very useful in simulating food intake over hours to days, thus providing input into existing models of nutrient absorption and metabolism. In the present work, a meal model is proposed, incorporating stomach distension, glycemic variations, ghrelin dynamics, cultural habits and influences on the initiation and continuation of meals, reflecting a combination of hedonic and appetite components. Given a set of parameter values (portraying a single subject), the timing and size of meals are stochastic. The model parameters are calibrated so as to reflect established medical knowledge on data of food intake from the National Health and Nutrition Examination Survey (NHANES) database during years 2015 and 2016.

NUMERICAL SIMULATION OF AN ELECTRODYNAMIC TRANSDUCER CONTROL OF INSULIN PROVISION IN THE BERGMAN’S AND THE CHENG’S MODELS FOR THE DYNAMICS OF THE COUPLE GLUCOSE-INSULIN IN DIABETICS

This paper deals with the numerical simulation of a model of blood glucose level control of a diabetic person using an electrodynamic transducer. Two mathematical models describing the dynamics of the couple glucose–insulin are used: the Bergman’s and the Cheng’s models. First, the adaptive control is applied on the dynamics of a reservoir opener by an electrodynamic transducer. Then it is applied on the two models of the glucose–insulin dynamics. It is found that the control of the reservoir opener and that of the glycemia of a diabetic patient are efficient for some values of the control parameters.

An adaptive technique based blood glucose control in type-1 diabetes mellitus patients

This study proposes Grasshopper Optimization Algorithm (GOA) based type 1 diabetes mellitus system utilizing the nonlinear Bergman minimal model with proportional integral derivative (PID) controller. GOA is the optimization algorithm, which is utilized for selecting the optimized tuning parameters of the PID controller also solves the nonlinear system parameter identification problem. The novelty of the proposed study is to stabilize the glucose level in blood for type 1 diabetic patients by infusion of insulin in reduced time with optimal quantity. Without any intervention to the normal activities of patients, the supply of insulin injection and glucose monitoring is performed automatically for type 1 diabetic patients using this controller. In between the measured variable and set point, the difference is calculated by the PID controller to evaluate an error values. In realistic patient oriented conditions, the control performance evaluation, control optimization, and advanced patient modelling should be highly concentrated during the research/analysis on blood glucose control. Evaluation is performed to analyze control performances and implementation is done on Simulink/MATLAB environment. The performance analysis of the type 1 diabetes mellitus system with GOA technique is also discussed and to improve the control performance, to optimize the controller parameters. The simulation results have proved the substantial improvement in the performance of proposed algorithm with the better results achieved than the other conventional controllers such as PSO-PID and EHO-PID.

The effects of time valuation in cancer optimal therapies: a study of chronic myeloid leukemia

BACKGROUND

The mathematical design of optimal therapies to fight cancer is an important research field in today's Biomathematics and Biomedicine given its relevance to formulate patient-specific treatments. Until now, however, cancer optimal therapies have considered that malignancy exclusively depends on the drug concentration and the number of cancer cells, ignoring that the faster the cancer grows the worse the cancer is, and that early drug doses are more prejudicial. Here, we analyze how optimal therapies are affected when the time evolution of treated cancer is envisaged as an additional element determining malignancy, analyzing in detail the implications for imatinib-treated Chronic Myeloid Leukemia.

METHODS

Taking as reference a mathematical model describing Chronic Myeloid Leukemia dynamics, we design an optimal therapy problem by modifying the usual malignancy objective function, unaware of any temporal dimension of cancer malignance. In particular, we introduce a time valuation factor capturing the increase of malignancy associated to the quick development of the disease and the persistent negative effects of initial drug doses. After assigning values to the parameters involved, we solve and simulate the model with and without the new time valuation factor, comparing the results for the drug doses and the evolution of the disease.

RESULTS

Our computational simulations unequivocally show that the consideration of a time valuation factor capturing the higher malignancy associated with early growth of cancer and drug administration allows more efficient therapies to be designed. More specifically, when this time valuation factor is incorporated into the objective function, the optimal drug doses are lower, and do not involve medically relevant increases in the number of cancer cells or in the disease duration.

CONCLUSIONS

In the light of our simulations and as biomedical evidence strongly suggests, the existence of a time valuation factor affecting malignancy in treated cancer cannot be ignored when designing cancer optimal therapies. Indeed, the consideration of a time valuation factor modulating malignancy results in significant gains of efficiency in the optimal therapy with relevant implications from the biomedical perspective, specially when designing patient-specific treatments.

Neural network-based model predictive control for type 1 diabetic rats on artificial pancreas system

Artificial pancreas system (APS) is a viable option to treat diabetic patients. Researchers, however, have not conclusively determined the best control method for APS. Due to intra-/inter-variability of insulin absorption and action, an individualized algorithm is required to control blood glucose level (BGL) for each patient. To this end, we developed model predictive control (MPC) based on artificial neural networks (ANNs), which combines ANN for BGL prediction based on inputs and MPC for BGL control based on the ANN (NN-MPC). First, we developed a mathematical model for diabetic rats, which was used to identify individual virtual subjects by fitting to empirical data collected through an APS, including BGL data, insulin injection, and food intake. Then, the virtual subjects were used to generate datasets for training ANNs. The NN-MPC determines control actions (insulin injection) based on BGL predicted by the ANN. To evaluate the NN-MPC, we conducted experiments using four virtual subjects under three different scenarios. Overall, the NN-MPC maintained BGL within the normal range about 90% of the time with a mean absolute deviation of 4.7 mg/dl from a desired BGL. Our findings suggest that the NN-MPC can provide subject-specific BGL control in conjunction with a closed-loop APS. Graphical abstract ᅟ.

Correlation of Electrophotonic Imaging Parameters With Fasting Blood Sugar in Normal, Prediabetic, and Diabetic Study Participants

INTRODUCTION

Electrophotonic imaging (EPI), also known as gas discharge visualization, is a technique of capturing images of phenomena not quantifiable by the naked eye. Different sectors at the tip of fingers represent various organs and systems as per the Chinese system of acupuncture. The images from these fingertips can be used to determine the state of health. This is done with the help of a CCD camera fitted in the EPI equipment and the specific software relevant for analysis.

AIM

To observe the correlation between EPI parameters and fasting blood sugar (FBS) levels in normal, prediabetic, and diabetic study participants.

MATERIALS AND METHODS

A total of 102 participants were selected for this study from various yoga camps and Arogyadham at Swami Vivekananda Yoga Anusandhana Samsthana Yoga University, Bengaluru, India. The selected participants belonged to 3groups-normal, prediabetic, and diabetic-depending on the FBS levels. The distribution of participants was 29 normal, 13 prediabetic, and 60 diabetic.

RESULTS

Regression analysis in the case of prediabetics showed a significant relationship of FBS with pancreas and right kidney. In the case of normal participants, a significant relationship of FBS was found with area and form coefficient of the EPI gram. For diabetics, regression analysis showed significant relationship of FBS with immune organs, left kidney, area, intensity, and entropy of EPI grams.

CONCLUSION

FBS correlates differently in the normal, prediabetic, and diabetic groups. In the prediabetic group, correlation of FBS with EPI parameters pancreas and right kidney is noteworthy and in line with latest findings in medical research.

A review of personalized blood glucose prediction strategies for T1DM patients

This paper presents a methodological review of models for predicting blood glucose (BG) concentration, risks and BG events. The surveyed models are classified into three categories, and they are presented in summary tables containing the most relevant data regarding the experimental setup for fitting and testing each model as well as the input signals and the performance metrics. Each category exhibits trends that are presented and discussed. This document aims to be a compact guide to determine the modeling options that are currently being exploited for personalized BG prediction.

Performance Analysis of Fuzzy-PID Controller for Blood Glucose Regulation in Type-1 Diabetic Patients

This paper presents Fuzzy-PID (FPID) control scheme for a blood glucose control of type 1 diabetic subjects. A new metaheuristic Cuckoo Search Algorithm (CSA) is utilized to optimize the gains of FPID controller. CSA provides fast convergence and is capable of handling global optimization of continuous nonlinear systems. The proposed controller is an amalgamation of fuzzy logic and optimization which may provide an efficient solution for complex problems like blood glucose control. The task is to maintain normal glucose levels in the shortest possible time with minimum insulin dose. The glucose control is achieved by tuning the PID (Proportional Integral Derivative) and FPID controller with the help of Genetic Algorithm and CSA for comparative analysis. The designed controllers are tested on Bergman minimal model to control the blood glucose level in the facets of parameter uncertainties, meal disturbances and sensor noise. The results reveal that the performance of CSA-FPID controller is superior as compared to other designed controllers.

Simulation and qualitative analysis of glucose variability, mean glucose, and hypoglycemia after subcutaneous insulin therapy for stress hyperglycemia

Background

The critically ill can have persistent dysglycemia during the “subacute” recovery phase of their illness because of altered gene expression; it is also not uncommon for these patients to receive continuous enteral nutrition during this time. The optimal short-acting subcutaneous insulin therapy that should be used in this clinical scenario, however, is unknown. Our aim was to conduct a qualitative numerical study of the glucose-insulin dynamics within this patient population to answer the above question. This analysis may help clinicians design a relevant clinical trial.

Methods

Eight virtual patients with stress hyperglycemia were simulated by means of a mathematical model. Each virtual patient had a different combination of insulin resistance and insulin deficiency that defined their unique stress hyperglycemia state; the rate of gluconeogenesis was also doubled. The patients received 25 injections of subcutaneous regular or Lispro insulin (0-6 U) with 3 rates of continuous nutrition. The main outcome measurements were the change in mean glucose concentration, the change in glucose variability, and hypoglycemic episodes. These end points were interpreted by how the ultradian oscillations of glucose concentration were affected by each insulin preparation.

Results

Subcutaneous regular insulin lowered both mean glucose concentrations and glucose variability in a linear fashion. No hypoglycemic episodes were noted. Although subcutaneous Lispro insulin lowered mean glucose concentrations, glucose variability increased in a nonlinear fashion. In patients with high insulin resistance and nutrition at goal, “rebound hyperglycemia” was noted after the insulin analog was rapidly metabolized. When the nutritional source was removed, hypoglycemia tended to occur at higher Lispro insulin doses. Finally, patients with severe insulin resistance seemed the most sensitive to insulin concentration changes.

Conclusions

Subcutaneous regular insulin consistently lowered mean glucose concentrations and glucose variability; its linear dose-response curve rendered the preparation better suited for a sliding-scale protocol. The longer duration of action of subcutaneous regular insulin resulted in better glycemic-control metrics for patients who were continuously postprandial. Clinical trials are needed to examine whether these numerical results represent the glucose-insulin dynamics that occur in intensive care units; if present, their clinical effects should be evaluated.

Comparison of Subcutaneous Regular Insulin and Lispro Insulin in Diabetics Receiving Continuous Nutrition: A Numerical Study

BACKGROUND

Optimal management of non-critically ill patients with diabetes maintained on continuous enteral feeding (CEN) is poorly defined. Subcutaneous (SQ) lispro and SQ regular insulin were compared in a simulated type 1 and type 2 diabetic patient receiving CEN.

METHOD

A glucose-insulin feedback mathematical model was employed to simulate type 1 and type 2 diabetic patients on CEN. Each patient received 25 SQ injections of regular insulin or insulin lispro, ranging from 0-6 U. Primary endpoints were the change in mean glucose concentration (MGC) and change in glucose variability (GV); hypoglycemic episodes were also reported. The model was first validated against patient data.

RESULTS

Both SQ insulin preparations linearly decreased MGC, however, SQ regular insulin decreased GV whereas SQ lispro tended to increase GV. Hourly glucose concentration measurements were needed to capture the increase in GV. In the type 2 diabetic patient, "rebound hyperglycemia" occurred after SQ lispro was rapidly metabolized. Although neither SQ insulin preparation caused hypoglycemia, SQ lispro significantly lowered MGC compared to SQ regular insulin. Thus, it may be more likely to cause hypoglycemia. Analyses of the detailed glucose concentration versus time data suggest that the inferior performance of lispro resulted from its shorter duration of action. Finally, the effects of both insulin preparations persisted beyond their duration of actions in the type 2 diabetic patient.

CONCLUSIONS

Subcutaneous regular insulin may be the short-acting insulin preparation of choice for this subset of diabetic patients. Clinical trial is required before a definitive recommendation can be made.

Prediction model for glucose metabolism based on lipid metabolism

OBJECTIVES

We developed a robust, long-term clinical prediction model to predict conditions leading to early diabetes using laboratory values other than blood glucose and insulin levels. Our model protects against missing data and noise that occur during long-term analysis.

METHODS

RESULTS of a 75-g oral glucose tolerance test (OGTT) were divided into three groups: diabetes, impaired glucose tolerance (IGT), and normal (n = 114, 235, and 325, respectively). For glucose metabolic and lipid metabolic parameters, near 30-day mean values and 10-year integrated values were compared. The relation between high-density lipoprotein cholesterol (HDL-C) and variations in HbA1c was analyzed in 158 patients. We also constructed a state space model consisting of an observation model (HDL-C and HbA1c) and an internal model (disorders of lipid metabolism and glucose metabolism) and applied this model to 116 cases.

RESULTS

The root mean square error between the observed HbA1c and predicted HbA1c was 0.25.

CONCLUSIONS

In the observation model, HDL-C levels were useful for prediction of increases in HbA1c. Even with numerous missing values over time, as occurs in clinical practice, clinically valid predictions can be made using this state space model.

Qualitative analysis of subcutaneous Lispro and regular insulin injections for stress hyperglycemia: a pilot numerical study

Increased glucose variability (GV) is an independent risk factor for mortality in the critically ill; unfortunately, the optimal insulin therapy that minimizes GV is not known. We simulate the glucose-insulin feedback system to study how stress hyperglycemia (SH) states, taken to be a non-uniform group of physiologic disorders with varying insulin resistance (IR) and similar levels of hyperglycemia, respond to the type and dose of subcutaneous (SQ) insulin. Two groups of 100 virtual patients are studied: those receiving and those not receiving continuous enteral feeds. Stress hyperglycemia was facilitated by doubling the gluconeogenesis rate and IR was stepwise varied from a borderline to a high value. Lispro and regular insulin were simulated with dosages that ranged from 0 to 6 units; the resulting GV was analyzed after each insulin injection. The numerical model used consists of a set of non-linear differential equations with two time delays and five adjustable parameters. The results show that regular insulin decreased GV in both patient groups and rarely caused hypoglycemia. With continuous enteral feeds and borderline to mild IR, Lispro showed minimal effect on GV; however, rebound hyperglycemia that increased GV occurred when the IR was moderate to high. Without a nutritional source, Lispro worsened GV through frequent hypoglycemia episodes as the injection dose increased. The inferior performance of Lispro is a result of its rapid absorption profile; half of its duration of action is similar to the glucose ultradian period. Clinical trials are needed to examine whether these numerical results represent the glucose-insulin dynamics that occur in intensive care units, and if such dynamics are present, their clinical effects should be evaluated.

Glucose-insulin regulation model with subcutaneous insulin injection and evaluation using diabetic inpatients data

Closed-loop insulin delivery systems often implement glucose measurement and insulin administration in the subcutis. However some existing models for glucose-insulin system ignored the dynamics of subcutaneous glucose and subcutaneously-injected insulin. This paper reports a two-compartment model that includes glucose and insulin dynamics in subcutis, and its evaluation using patient data. Clinical information such as glucose level, insulin dosage, insulin injection time and meals of anonymous diabetes inpatients was collected. Measured glucose level of the diabetic inpatients agrees with that of computer simulation. Due to the lack of glucose-insulin model with subcutaneously-injected insulin for type 2 diabetic patients, our model was compared with existing model for type 1 subjects. The new glucose-insulin model can mimic dynamics of glucose and insulin under the disturbance of insulin injections and meals. Model parameters were estimated using nonlinear least square method and their effect on pathology and physiology of diabetes were analyzed.